URL
stringlengths 15
1.68k
| text_list
listlengths 1
199
| image_list
listlengths 1
199
| metadata
stringlengths 1.19k
3.08k
|
|---|---|---|---|
https://shortlearner.com/convert-1000-to-1k-php/
|
[
"# How to Convert 1000 to 1k |using PHP\n\n0\n677",
null,
"Welcome back to shorltearner.com, in our previous post we learn how to Convert words to numbers with the help of PHP. so in this post today we will learn how to convert number into sort number format in PHP.\nso before start this tutorial we take an overview on number_format which is also a predefined PHP function that are used to The number_format() function formats a number with grouped thousands.\n\nfor example if i take the below code as an example\n\n``<?php echo number_format(\"1000000\"); ?>``\n\nthan the number_format function returns an output like\n\n``outout : 1,000,000``\n\nso If we want to convert number into sort form in thousand, million, billion then we used another predefined PHP function number_format_short that will help to convert any number to it’s sort form like (Eg: 1.4K, 14.32M, 40B ) etc.\nso in the below code we take an example which converts a number 1,43,20000 into 14.32M.\n\n``````<?php\nfunction number_format_short(\\$n) {\n// first strip any formatting;\n\\$n = (0+str_replace(\",\", \"\", \\$n));\n// is this a number?\nif (!is_numeric(\\$n)) return false;\n// now filter it;\nif (\\$n > 1000000000000) return round((\\$n/1000000000000), 2).'T';\nelseif (\\$n > 1000000000) return round((\\$n/1000000000), 2).'B';\nelseif (\\$n > 1000000) return round((\\$n/1000000), 2).'M';\nelseif (\\$n > 1000) return round((\\$n/1000), 2).'K';\n\nreturn number_format(\\$n);\n}\necho number_format_short('14320000'); //14.32M\n\n?>``````"
] |
[
null,
"https://shortlearner.com/wp-content/uploads/2020/06/post11.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5868573,"math_prob":0.99094105,"size":1701,"snap":"2023-14-2023-23","text_gpt3_token_len":441,"char_repetition_ratio":0.152033,"word_repetition_ratio":0.007662835,"special_character_ratio":0.32333922,"punctuation_ratio":0.16816817,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99656105,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-29T02:42:25Z\",\"WARC-Record-ID\":\"<urn:uuid:5e31d440-f2c8-43ca-82b1-2437a7a202d5>\",\"Content-Length\":\"121850\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c54ac59a-6637-4495-b1c1-ccf06ea027be>\",\"WARC-Concurrent-To\":\"<urn:uuid:f10c1341-be82-40d8-8038-0cc311db1b3b>\",\"WARC-IP-Address\":\"156.67.222.157\",\"WARC-Target-URI\":\"https://shortlearner.com/convert-1000-to-1k-php/\",\"WARC-Payload-Digest\":\"sha1:TGM7CJ7NOC5YLEXZP5FSRHBN4SPRZU5A\",\"WARC-Block-Digest\":\"sha1:52MGLX5SUT5AD5NNBX4FVHVKLMORGW5N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224644574.15_warc_CC-MAIN-20230529010218-20230529040218-00245.warc.gz\"}"}
|
https://www.tutorialspoint.com/class-and-static-variables-in-chash
|
[
"# Class and Static Variables in C#\n\nStatic variables are used for defining constants because their values can be retrieved by invoking the class without creating an instance of it. Static variables can be initialized outside the member function or class definition. You can also initialize static variables inside the class definition.\n\n## Example\n\nLive Demo\n\nusing System;\n\nnamespace StaticVarApplication {\nclass StaticVar {\npublic static int num;\n\npublic void count() {\nnum++;\n}\npublic int getNum() {\nreturn num;\n}\n}\nclass StaticTester {\nstatic void Main(string[] args) {\nStaticVar s1 = new StaticVar();\nStaticVar s2 = new StaticVar();\n\ns1.count();\ns1.count();\ns1.count();\n\ns2.count();\ns2.count();\ns2.count();\n\nConsole.WriteLine(\"Variable num for s1: {0}\", s1.getNum());\nConsole.WriteLine(\"Variable num for s2: {0}\", s2.getNum());\n}\n}\n}\n\n## Output\n\nVariable num for s1: 6\nVariable num for s2: 6\n\nClass variables are the attributes of an object (from design perspective) and they are kept private to implement encapsulation. These variables can only be accessed using the public member functions.\n\nLet us see an example −\n\n## Example\n\nLive Demo\n\nusing System;\n\nnamespace BoxApplication {\nclass Box {\nprivate double length; // Length of a box\nprivate double height; // Height of a box\n\npublic void setLength( double len ) {\nlength = len;\n}\npublic void setBreadth( double bre ) {\n}\npublic void setHeight( double hei ) {\nheight = hei;\n}\npublic double getVolume() {\nreturn length * breadth * height;\n}\n}\nclass Boxtester {\nstatic void Main(string[] args) {\nBox Box1 = new Box(); // Declare Box1 of type Box\nBox Box2 = new Box();\ndouble volume;\n\n// Declare Box2 of type Box\n// box 1 specification\nBox1.setLength(6.0);\nBox1.setHeight(5.0);\n\n// box 2 specification\nBox2.setLength(12.0);\nBox2.setHeight(10.0);\n\n// volume of box 1\nvolume = Box1.getVolume();\nConsole.WriteLine(\"Volume of Box1 : {0}\" ,volume);\n\n// volume of box 2\nvolume = Box2.getVolume();\nConsole.WriteLine(\"Volume of Box2 : {0}\", volume);\n}\nVolume of Box1 : 210\nVolume of Box2 : 1560"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5553564,"math_prob":0.94604856,"size":3296,"snap":"2022-40-2023-06","text_gpt3_token_len":803,"char_repetition_ratio":0.15704739,"word_repetition_ratio":0.031657357,"special_character_ratio":0.27396846,"punctuation_ratio":0.15053764,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9576954,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-31T16:10:53Z\",\"WARC-Record-ID\":\"<urn:uuid:404ab157-0d17-447a-8703-c6391b1fa049>\",\"Content-Length\":\"44484\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d4491007-9d56-4b18-8a85-247b515060b4>\",\"WARC-Concurrent-To\":\"<urn:uuid:c27609ad-bf3f-4020-9feb-98239a5d7a6c>\",\"WARC-IP-Address\":\"192.229.210.176\",\"WARC-Target-URI\":\"https://www.tutorialspoint.com/class-and-static-variables-in-chash\",\"WARC-Payload-Digest\":\"sha1:XHQXV3FYUK4KILJP7DMMWMBX4E5WL73F\",\"WARC-Block-Digest\":\"sha1:M72Y7WFBD5T6SZMYCUEPLTHYLXUVGAFV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499888.62_warc_CC-MAIN-20230131154832-20230131184832-00329.warc.gz\"}"}
|
https://www.geeksforgeeks.org/program-to-print-the-initials-of-a-name-with-the-surname/
|
[
"# Program to print the initials of a name with the surname\n\n• Last Updated : 28 Jan, 2020\n\nGiven a full name in the form of a string, the task is to print the initials of a name, in short, and surname in full.\n\nExamples:\n\nHey! Looking for some great resources suitable for young ones? You've come to the right place. Check out our self-paced courses designed for students of grades I-XII\n\nStart with topics like Python, HTML, ML, and learn to make some games and apps all with the help of our expertly designed content! So students worry no more, because GeeksforGeeks School is now here!\n\n```Input: Devashish Kumar Gupta\nOutput: D. K. Gupta\n\nInput: Ishita Bhuiya\nOutput: I. Bhuiya\n```\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nApproach: The basic approach is to extract words one by one and then print the first letter of the word, followed by a dot(.). For the surname, extract and print the whole word.\n\nBelow is the implementation of the above approach:\n\n## C++\n\n `// C++ program to print the initials``// of a name with the surname``#include ``using` `namespace` `std;`` ` `void` `printInitials(string str) ``{`` ``int` `len = str.length();`` ` ` ``// to remove any leading or trailing spaces`` ``str.erase(0, str.find_first_not_of(``' '``));`` ``str.erase(str.find_last_not_of(``' '``) + 1);`` ` ` ``// to store extracted words`` ``string t = ``\"\"``;`` ``for` `(``int` `i = 0; i < len; i++) `` ``{`` ``char` `ch = str[i];`` ` ` ``if` `(ch != ``' '``)`` ` ` ``// forming the word`` ``t = t + ch;`` ` ` ``// when space is encountered`` ``// it means the name is completed`` ``// and thereby extracted`` ``else`` ``{`` ``// printing the first letter`` ``// of the name in capital letters`` ``cout << (``char``)``toupper``(t) << ``\". \"``;`` ``t = ``\"\"``;`` ``}`` ``}`` ` ` ``string temp = ``\"\"``;`` ` ` ``// for the surname, we have to print the entire`` ``// surname and not just the initial`` ``// string \"t\" has the surname now`` ``for` `(``int` `j = 0; j < t.length(); j++) `` ``{`` ``// first letter of surname in capital letter`` ``if` `(j == 0) temp = temp + (``char``)``toupper``(t);`` ` ` ``// rest of the letters in small`` ``else`` ``temp = temp + (``char``)``tolower``(t[j]);`` ``}`` ` ` ``// printing surname`` ``cout << temp << endl;``}`` ` `// Driver Code``int` `main() ``{`` ``string str = ``\"ishita bhuiya\"``;`` ``printInitials(str);``}`` ` `// This code is contributed by``// sanjeev2552`\n\n## Java\n\n `// Java program to print the initials``// of a name with the surname``import` `java.util.*;`` ` `class` `Initials {`` ``public` `static` `void` `printInitials(String str)`` ``{`` ``int` `len = str.length();`` ` ` ``// to remove any leading or trailing spaces`` ``str = str.trim();`` ` ` ``// to store extracted words`` ``String t = ``\"\"``;`` ``for` `(``int` `i = ``0``; i < len; i++) {`` ``char` `ch = str.charAt(i);`` ` ` ``if` `(ch != ``' '``) {`` ` ` ``// forming the word`` ``t = t + ch;`` ``}`` ` ` ``// when space is encountered`` ``// it means the name is completed`` ``// and thereby extracted`` ``else` `{`` ``// printing the first letter`` ``// of the name in capital letters`` ``System.out.print(Character.toUpperCase(t.charAt(``0``))`` ``+ ``\". \"``);`` ``t = ``\"\"``;`` ``}`` ``}`` ` ` ``String temp = ``\"\"``;`` ` ` ``// for the surname, we have to print the entire`` ``// surname and not just the initial`` ``// string \"t\" has the surname now`` ``for` `(``int` `j = ``0``; j < t.length(); j++) {`` ` ` ``// first letter of surname in capital letter`` ``if` `(j == ``0``)`` ``temp = temp + Character.toUpperCase(t.charAt(``0``));`` ` ` ``// rest of the letters in small`` ``else`` ``temp = temp + Character.toLowerCase(t.charAt(j));`` ``}`` ` ` ``// printing surname`` ``System.out.println(temp);`` ``}`` ` ` ``public` `static` `void` `main(String[] args)`` ``{`` ``String str = ``\"ishita bhuiya\"``;`` ``printInitials(str);`` ``}``}`\n\n## Python3\n\n `# Python program to print the initials``# of a name with the surname``def` `printInitials(string: ``str``):`` ``length ``=` `len``(string)`` ` ` ``# to remove any leading or trailing spaces`` ``string.strip()`` ` ` ``# to store extracted words`` ``t ``=` `\"\"`` ``for` `i ``in` `range``(length):`` ``ch ``=` `string[i]`` ``if` `ch !``=` `' '``:`` ` ` ``# forming the word`` ``t ``+``=` `ch`` ` ` ``# when space is encountered`` ``# it means the name is completed`` ``# and thereby extracted`` ``else``:`` ` ` ``# printing the first letter`` ``# of the name in capital letters`` ``print``(t[``0``].upper() ``+` `\". \"``, end``=``\"\")`` ``t ``=` `\"\"`` ` ` ``temp ``=` `\"\"`` ` ` ``# for the surname, we have to print the entire`` ``# surname and not just the initial`` ``# string \"t\" has the surname now`` ``for` `j ``in` `range``(``len``(t)):`` ` ` ``# first letter of surname in capital letter`` ``if` `j ``=``=` `0``:`` ``temp ``+``=` `t[``0``].upper()`` ` ` ``# rest of the letters in small`` ``else``:`` ``temp ``+``=` `t[j].lower()`` ` ` ``# printing surname`` ``print``(temp)`` ` `# Driver Code``if` `__name__ ``=``=` `\"__main__\"``:`` ` ` ``string ``=` `\"ishita bhuiya\"`` ``printInitials(string)`` ` `# This code is contributed by``# sanjeev2552`\n\n## C#\n\n `// C# program to print the initials ``// of a name with the surname ``using` `System;`` ` `class` `Initials { `` ` ` ``public` `static` `void` `printInitials(``string` `str) `` ``{ `` ``int` `len = str.Length ;`` ` ` ``// to remove any leading or trailing spaces `` ``str = str.Trim(); `` ` ` ``// to store extracted words `` ``String t = ``\"\"``; `` ``for` `(``int` `i = 0; i < len; i++) { `` ``char` `ch = str[i]; `` ` ` ``if` `(ch != ``' '``) { `` ` ` ``// forming the word `` ``t = t + ch; `` ``} `` ` ` ``// when space is encountered `` ``// it means the name is completed `` ``// and thereby extracted `` ``else` `{ `` ``// printing the first letter `` ``// of the name in capital letters `` ``Console.Write(Char.ToUpper(t) `` ``+ ``\". \"``); `` ``t = ``\"\"``; `` ``} `` ``} `` ` ` ``string` `temp = ``\"\"``; `` ` ` ``// for the surname, we have to print the entire `` ``// surname and not just the initial `` ``// string \"t\" has the surname now `` ``for` `(``int` `j = 0; j < t.Length; j++) { `` ` ` ``// first letter of surname in capital letter `` ``if` `(j == 0) `` ``temp = temp + Char.ToUpper(t); `` ` ` ``// rest of the letters in small `` ``else`` ``temp = temp + Char.ToLower(t[j]); `` ``} `` ` ` ``// printing surname `` ``Console.WriteLine(temp); `` ``} `` ` ` ``public` `static` `void` `Main() `` ``{ `` ``string` `str = ``\"ishita bhuiya\"``; `` ``printInitials(str); `` ``} `` ``// This code is contributed by Ryuga``} `\nOutput:\n```I. Bhuiya\n```\n\nMy Personal Notes arrow_drop_up"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.6748107,"math_prob":0.8582546,"size":5284,"snap":"2021-43-2021-49","text_gpt3_token_len":1500,"char_repetition_ratio":0.14469697,"word_repetition_ratio":0.4650048,"special_character_ratio":0.32702497,"punctuation_ratio":0.14328657,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99590695,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-09T00:35:12Z\",\"WARC-Record-ID\":\"<urn:uuid:7b6a7052-83f8-4cba-a10c-d262334d0ca8>\",\"Content-Length\":\"158088\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:697b63e0-7d12-4638-a56e-5ac1512b0f93>\",\"WARC-Concurrent-To\":\"<urn:uuid:a0622863-93f6-45f7-bd7a-51be044ac030>\",\"WARC-IP-Address\":\"23.205.105.172\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/program-to-print-the-initials-of-a-name-with-the-surname/\",\"WARC-Payload-Digest\":\"sha1:G53QUZLHE7G7HO5G6UPXHPKEZAFDVJPS\",\"WARC-Block-Digest\":\"sha1:G7OIJKEBGQ7O74OOTLLAMA3O6FXR4QTV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363641.20_warc_CC-MAIN-20211209000407-20211209030407-00499.warc.gz\"}"}
|
https://animalbiotelemetry.biomedcentral.com/articles/10.1186/s40317-022-00273-3/tables/2
|
[
"Time stamp $${\\delta }^{2}L$$ PDH $$\\mathrm{HR}$$ $$\\mathrm{CRL}$$ $$\\mathrm{RSS}$$ $$\\mathrm{NR}$$",
null,
""
] |
[
null,
"https://animalbiotelemetry.biomedcentral.com/track/article/10.1186/s40317-022-00273-3",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.55045366,"math_prob":1.00001,"size":350,"snap":"2022-27-2022-33","text_gpt3_token_len":159,"char_repetition_ratio":0.1618497,"word_repetition_ratio":0.0,"special_character_ratio":0.56,"punctuation_ratio":0.15714286,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9996698,"pos_list":[0,1,2],"im_url_duplicate_count":[null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-06T00:24:15Z\",\"WARC-Record-ID\":\"<urn:uuid:dec75416-2978-406a-ae4d-9ddd1de9ce8f>\",\"Content-Length\":\"158915\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:36ee7e03-0a7a-4f1d-a738-2ee912b2fcee>\",\"WARC-Concurrent-To\":\"<urn:uuid:b18e5b68-4e03-4693-ba5d-1da76fe5b0b8>\",\"WARC-IP-Address\":\"146.75.36.95\",\"WARC-Target-URI\":\"https://animalbiotelemetry.biomedcentral.com/articles/10.1186/s40317-022-00273-3/tables/2\",\"WARC-Payload-Digest\":\"sha1:TVK3WE76D4BR2LD7CCSHBPU6Q2GVVNFT\",\"WARC-Block-Digest\":\"sha1:HNXLUROLBX6H2G5TTLEVMEVOQ2ZTQR4G\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104655865.86_warc_CC-MAIN-20220705235755-20220706025755-00779.warc.gz\"}"}
|
https://it.mathworks.com/help/dsp/ref/dsp.channelizer-system-object.html
|
[
"# dsp.Channelizer\n\nPolyphase FFT analysis filter bank\n\n## Description\n\nThe `dsp.Channelizer` System object™ separates a broadband input signal into multiple narrow subbands using a fast Fourier transform (FFT)-based analysis filter bank. The filter bank uses a prototype lowpass filter and is implemented using a polyphase structure. You can specify the filter coefficients directly or through design parameters.\n\nTo separate a broadband signal into multiple narrow subbands:\n\n1. Create the `dsp.Channelizer` object and set its properties.\n\n2. Call the object with arguments, as if it were a function.\n\n## Creation\n\n### Syntax\n\n``channelizer = dsp.Channelizer``\n``channelizer = dsp.Channelizer(M)``\n``channelizer = dsp.Channelizer(Name,Value)``\n\n### Description\n\nexample\n\n````channelizer = dsp.Channelizer` creates a polyphase FFT analysis filter bank System object that separates a broadband input signal into multiple narrowband output signals. This object implements the inverse operation of the `dsp.ChannelSynthesizer` System object.```\n\nexample\n\n````channelizer = dsp.Channelizer(M)` creates an M-band polyphase FFT analysis filter bank, with the NumFrequencyBands property set to M. Example: channelizer = dsp.Channelizer(16);```\n\nexample\n\n````channelizer = dsp.Channelizer(Name,Value)` creates a polyphase FFT analysis filter bank with each specified property set to the specified value. Enclose each property name in single quotes.Example: channelizer = dsp.Channelizer('NumTapsPerBand',20,'StopbandAttenuation',140);```\n\n## Properties\n\nexpand all\n\nUnless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the `release` function unlocks them.\n\nIf a property is tunable, you can change its value at any time.\n\nNumber of frequency bands into which the object separates the input broadband signal, specified as a positive integer greater than 1. This property corresponds to the number of polyphase branches and the FFT length used in the filter bank.\n\nExample: 16\n\nExample: 64\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`\n\nOversampling ratio, specified as a positive scalar divisor of the number of frequency bands.\n\nIf the value is greater than `1`, the output sample rate is different from the channel spacing. The channelizer is then known as the non-maximally decimated channelizer or oversampled channelizer. For more details, see Algorithm.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`\n\nFilter design parameters or filter coefficients, specified as one of these options:\n\n• `'Number of taps per band and stopband attenuation'` — Specify the filter design parameters through the `NumTapsPerBand` and Stopband attenuation (dB) properties.\n\n• `'Coefficients'` — Specify the filter coefficients directly using the LowpassCoefficients property.\n\nNumber of filter coefficients each polyphase branch uses, specified as a positive integer. The number of polyphase branches matches the number of frequency bands. The total number of filter coefficients for the prototype lowpass filter is given by `NumFrequencyBands` × `NumTapsPerBand`. For a given stopband attenuation, increasing the number of taps per band narrows the transition width of the filter. As a result, there is more usable bandwidth for each frequency band at the expense of increased computation.\n\nExample: 8\n\nExample: 16\n\n#### Dependencies\n\nThis property applies when you set `Specification` to `'Number of taps per band and stopband attenuation'`.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`\n\nStopband attenuation of the lowpass filter, specified as a positive real scalar in dB. This value controls the maximum amount of aliasing from one frequency band to the next. When the stopband attenuation increases, the passband ripple decreases. For a given stopband attenuation, increasing the number of taps per band narrows the transition width of the filter. As a result, there is more usable bandwidth for each frequency band at the expense of increased computation.\n\nExample: 80\n\n#### Dependencies\n\nThis property applies when you set `Specification` to `'Number of taps per band and stopband attenuation'`.\n\nData Types: `single` | `double`\n\nCoefficients of the prototype lowpass filter, specified as a row vector. The default vector of coefficients is obtained using `rcosdesign(0.25,6,8,'sqrt')`. There must be at least one coefficient per frequency band. If the length of the lowpass filter is less than the number of frequency bands, the object zero-pads the coefficients.\n\nIf you specify complex coefficients, the object designs a prototype filter that is centered at a nonzero frequency, also known as a bandpass filter. The modulated versions of the prototype bandpass filter appear with respect to the prototype filter and are wrapped around the frequency range [−Fs Fs]. For an example, see Channelizer with Complex Coefficients.\n\nTunable: Yes\n\n#### Dependencies\n\nThis property applies when you set `Specification` to `'Coefficients'`.\n\nData Types: `single` | `double`\nComplex Number Support: Yes\n\n## Usage\n\n### Syntax\n\n``channOut = channelizer(input)``\n\n### Description\n\nexample\n\n````channOut = channelizer(input)` separates the broadband input signal into a number of narrow band signals contained in the columns of the channelizer output. ```\n\n### Input Arguments\n\nexpand all\n\nData input, specified as a vector or a matrix. The number of rows in the input signal must be a multiple of the number of frequency bands of the filter bank. Each column of the input corresponds to a separate channel. If M is the number of frequency bands, and the input is an L-by-1 matrix, then the output signal has dimensions L/M-by-M. Each narrowband signal forms a column in the output. If the input has more than one channel, that is, it has dimensions L-by-N with N > 1, then the output has dimensions L/M-by-M-by-N.\n\nThis object supports variable-size input signals. You can change the input frame size (number of rows) even after calling the algorithm. However, the number of channels (number of columns) must remain constant.\n\nExample: randn(64,4)\n\nData Types: `single` | `double`\nComplex Number Support: Yes\n\n### Output Arguments\n\nexpand all\n\nChannelizer output, returned as a matrix or a 3-D array. If the input is an L-by-1 matrix, then the output signal has dimensions L/M-by-M, where M is the number of frequency bands. Each narrowband signal forms a column in the output. If the input has more than one channel, that is, it has dimensions L-by-N with N > 1, then the output has dimensions L/M-by-M-by-N.\n\nData Types: `single` | `double`\nComplex Number Support: Yes\n\n## Object Functions\n\nTo use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named `obj`, use this syntax:\n\n`release(obj)`\n\nexpand all\n\n `coeffs` Coefficients of prototype lowpass filter `tf` Return transfer function of overall prototype lowpass filter `polyphase` Return polyphase matrix `freqz` Frequency response of filters in channelizer `fvtool` Visualize the filters in the channelizer `bandedgeFrequencies` Compute the bandedge frequencies `centerFrequencies` Compute center frequencies `getFilters` Return matrix of channelizer FIR filters\n `step` Run System object algorithm `release` Release resources and allow changes to System object property values and input characteristics `reset` Reset internal states of System object\n\n## Examples\n\ncollapse all\n\nThe quadrature mirror filter bank (QMF) contains an analysis filter bank section and a synthesis filter bank section. `dsp.Channelizer` implements the analysis filter bank. `dsp.ChannelSynthesizer` implements the synthesis filter bank using the efficient polyphase implementation based on a prototype lowpass filter.\n\nInitialization\n\nInitialize the `dsp.Channelizer` and `dsp.ChannelSynthesizer` System objects. Each object is set up with 8 frequency bands, 8 polyphase branches in each filter, 12 coefficients per polyphase branch, and a stopband attenuation of 140 dB. Use a sine wave with multiple frequencies as the input signal. View the input spectrum and the output spectrum using a spectrum analyzer.\n\n```offsets = [-40,-30,-20,10,15,25,35,-15]; sinewave = dsp.SineWave('ComplexOutput',true,'Frequency',... offsets+(-375:125:500),'SamplesPerFrame',800); channelizer = dsp.Channelizer('StopbandAttenuation',140); synthesizer = dsp.ChannelSynthesizer('StopbandAttenuation',140); spectrumAnalyzer = dsp.SpectrumAnalyzer('ShowLegend',true,'NumInputPorts',... 2,'ChannelNames',{'Input','Output'},'Title','Input and Output of QMF'); ```\n\nStreaming\n\nUse the channelizer to split the broadband input signal into multiple narrow bands. Then pass the multiple narrowband signals into the synthesizer, which merges these signals to form the broadband signal. Compare the spectra of the input and output signals. The input and output spectra match very closely.\n\n```for i = 1:5000 x = sum(sinewave(),2); y = channelizer(x); v = synthesizer(y); spectrumAnalyzer(x,v) end ```",
null,
"Create a `dsp.Channelizer` object and set the `LowpassCoefficients `property to a vector of complex coefficients.\n\nComplex Coefficients\n\nUsing `firpm`, determine the coefficients of a Park-McClellan's optimal equiripple FIR filter of order 30, and frequency and amplitude characteristics described by F = [0 0.2 0.4 1.0] and A = [1 1 0 0] vectors, respectively.\n\nCreate a complex version of these coefficients by multiplying with a complex exponential. The resultant frequency response is that of a bandpass filter at the specified frequency, in this case 0.4.\n\n```blowpass = firpm(30,[0 .2 .4 1],[1 1 0 0]); N = length(blowpass)-1; Fc = 0.4; j = complex(0,1); bbandpass = blowpass.*exp(j*Fc*pi*(0:N));```\n\nChannelizer\n\nCreate a `dsp.Channelizer` object with 4 frequency bands and set the `Specification` property to `'Coefficients'`.\n\n`chann = dsp.Channelizer('NumFrequencyBands',4,'Specification',\"Coefficients\");`\n\nPass the complex coefficients to the channelizer. The prototype filter is a bandpass filter with a center frequency of 0.4. The modulated versions of this filter appear with respect to the prototype filter and are wrapped around the frequency range [$-$Fs Fs].\n\n`chann.LowpassCoefficients = bbandpass`\n```chann = dsp.Channelizer with properties: NumFrequencyBands: 4 OversamplingRatio: 1 Specification: 'Coefficients' LowpassCoefficients: [1x31 double] ```\n\nVisualize the frequency response of the channelizer.\n\n`fvtool(chann)`",
null,
"expand all\n\n## Algorithms\n\nexpand all\n\n Harris, Fredric J, Multirate Signal Processing for Communication Systems, Prentice Hall PTR, 2004.\n\n Harris, F.J., Chris Dick, and Michael Rice. \"Digital Receivers and Transmitters Using Polyphase Filter Banks for Wireless Communications.\" IEEE® Transactions on Microwave Theory and Techniques. 51, no. 4 (2003).\n\nWatch now"
] |
[
null,
"https://it.mathworks.com/help/examples/dsp/win64/QuadratureMirrorFilterBankExample_01.png",
null,
"https://it.mathworks.com/help/examples/dsp/win64/DesignAChannelizerWithComplexCoefficientsExample_01.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.86557543,"math_prob":0.9354596,"size":4859,"snap":"2020-45-2020-50","text_gpt3_token_len":1141,"char_repetition_ratio":0.15653965,"word_repetition_ratio":0.108641975,"special_character_ratio":0.21156617,"punctuation_ratio":0.12486883,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96962863,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-28T12:02:24Z\",\"WARC-Record-ID\":\"<urn:uuid:f69ee0be-4f15-4b12-a8e4-ba0ad59c0c57>\",\"Content-Length\":\"150385\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9d8f2516-0671-4684-9d33-e55925c26e26>\",\"WARC-Concurrent-To\":\"<urn:uuid:72950fff-0f9a-4a81-b3cb-200208ceebeb>\",\"WARC-IP-Address\":\"184.24.72.83\",\"WARC-Target-URI\":\"https://it.mathworks.com/help/dsp/ref/dsp.channelizer-system-object.html\",\"WARC-Payload-Digest\":\"sha1:FSCAZWQAVTIKSR4CJOFDPPNBF3HWIIYL\",\"WARC-Block-Digest\":\"sha1:JVGG5TFRJECITHL4NWT6K2DZ3K534KB5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141195417.37_warc_CC-MAIN-20201128095617-20201128125617-00536.warc.gz\"}"}
|
https://snapey.our.dmu.ac.uk/page/2/
|
[
"## Green Dealers\n\n### Lies, damn lies and statistics… or the story of how 10 households using the Green Deal financing option is inspirational\n\nYesterday, DECC issued a press release announcing in triumphal tones that “New research shows the Government’s Green Deal is inspiring people across the UK to install energy saving home improvements.” The release stated that 47% of those households which had received a Green Deal assessment report had installed or were in the process of installing an energy saving measure and that a further 31% said they were likely to. This, of course, gives the impression that 78% of those having an assessment were on the cusp of installing energy saving measures. A more careful reading of the press release reveals that percentage to be taken from those that have received a report following the assessment – on which more below. The undoubted tone of the statement is that the Green Deal is working as an incentive to encourage the installation of energy efficiency measures. Whether the fact that less than half those having an assessment have actually acted on the advice is a success is debatable but not the main point of this post. My issue is with the way that the statistics have been presented to give a rather biased spin on the success of the Green Deal to date.\n\nThe press release was based upon this report. Admirably, this research (and a second study tracking progress) have been commissioned by DECC in order to provide useful information with which to evaluate the Green Deal. The raw data on which the report is based is available here.\n\nHaving read the methodology and downloaded the data, my rather quick and dirty analysis tells a rather different story to that told in the press release.\n\nThe report reveals that up to March 31st 2013, a grand total of 9000 Green Deal Assessments had been undertaken. The “official launch date” of the Green Deal is given as 28th January 2013 – this is in itself interesting, as the launch date has been somewhat difficult to pin down as shown by Guertler et al. (2013) (hat-tip to their excellent paper for the information behind the following sentence). As recently as September 2012, Energy Minister Ed Davey said “Most aspects […] will start on 1 October […] finance plans only from January 2013.” – although this was qualified by his colleague Greg Barker in October 2012 – “ [that] was not, in fact, a launch.”. One wonders whether the 9000 assessments were undertaken in the period 1 October 2012 – 31 March 2013, or between 28 January 2013 and 31 March 2013…\n\nOf these 9000 or so, 900 were selected to be surveyed for the report – with 507 eventually responding to the survey. This seems a reasonable sample. Of these, the data sheet (Q10) shows that 64% had received their report following the assessment – with a further 13% unsure whether they had received it or had it sent to their landlord. Interestingly, though – the data sheet shows the base sample for those who had received a Green Deal Assessment Report (GDAR) to be 285 respondents (Q17 of data sheet) – which appears to include those whose assessment was arranged by a landlord. Which would be 56% of 507. The source of this discrepancy is unclear from the data sheet and worthy of further investigation.\n\nWorking with that sample of 285 – the data sheet then goes on to show which measures had been recommended to various householders, and for each of the improvements whether the respondents2:\n\n2. In the process of doing this\n3. Definitely will do this\n4. Probably will do this\n5. Might or might not do this\n6. Probably won’t do this\n7. Definitely won’t do this\n\nQuestions 19-32 in the survey relate to subgroups of the respondents who have installed (A), are about to install (B), are likely to install (C&D), Might or might not (E) or won’t install (F&G) measures. The motivation for their decision and choice of financing option are reported. These are examined below, however a caveat is needed at this point. The percentages presented in Qs 19-30 are rather difficult to interpret. They appear to be related to questions asked per measure, but presented as a single percentage figure for each category. Thus, the percentages do not sum to 100% – often summing to, for instance, 150% or more. This may be due to two factors – one respondent may respond twice if they have acted on two measures from their report. In addition some of the categories are not mutually exclusive – for instance a respondent who paid for a measure from their savings may also take advantage of the Green Deal cashback scheme – both of which are options on the financing questions (Qs 19, 25 and 29).\n\nFrom the base sizes given for questions 19-21 (those who have already installed a recommended key measure 1) and questions 22-25 (those who are in the process of installation) we can determine the number of households in each of those categories. These are 91 and 43 respectively. So, in all – 134 households have installed or are in the process of installing a measure recommended following a Green Deal Assessment. And 134 of 285 is indeed 47%. However – this figure makes no mention of the 222 respondents who have had an assessment but no report. This leaves almost half those who have had an assessment out of the calculation – given considerable uncertainty to the 47% figure – although as mentioned previously the press release is carefully worded to state that the 47% is of those who have received a report\n\nNext, I looked at the methods by which those installing measures had financed them. This, surely, is an important consideration as the Green Deal is designed as a financing scheme to encourage investments and, as former Energy Minister Chris Huhne put it, “The Green Deal is about putting energy consumers back in control of their bills and banishing Britain’s draughty homes to the history books” DECC (2011), quoted in Guertler et al (2013).\n\nOn face value (taking account of the caveats above regarding presented percentages), I conclude that only 7 households have taken advantage of the Green Deal Financing scheme and got to the point where an energy efficiency measure has been installed. A further 3 households intend to use Green Deal financing to finance measures being installed currently. So, in total, it appears that 10 households are using the Green Deal financing option of the 507 who have had the initial assessment. Those who have not started any work, but are “definitely” or “probably” going to install measures are more positive about the financing option – with 31% of the 86 involved stating that they intend to use Green Deal financing – some 27 respondents. This is not quite the message that would be gleaned from the press release.\n\nUnderstandably, the Green Deal Cashback scheme (which is effectively a capital subsidy for works undertaken) is more popular. It appears that ~15 respondents that have had work completed have used the cashback voucher scheme – with a further 9 of those currently having work carried out intending to use the cashback.\n\nTellingly – when asked why they did not or will not use Green Deal financing 18% of the 150 in this category said they “were not aware of it”, with a further 23% saying that they “Don’t like borrowing/taking out finance/prefer to pay up-front”. These seem like major issues for a government “flagship policy”. This should all be set against a backdrop where orders for energy efficiency measures have fallen through the floor (non-paywalled summary here), whilst the Energy Minister Ed Davey announces in this press release that ““This is great news for the energy efficiency industry as well, because this shows a genuine appetite among householders for more energy efficient homes.”\n\nThe government should be lauded for making data available to those who want to delve behind the headlines. However, the presentation of those data in a way that rather over-eggs the success of policies, whilst unsurprising, is less laudable.\n\nThe first official statistics on the Green Deal are due tomorrow. I await them, and how they are reported, with bated breath.\n\nAs always – comments are welcome.\n\nReferences:\n\nPedro Guertler, David Robson and Sarah Royston (2013) Somewhere between a ‘Comedy of errors’ and ‘As you like it’? A brief history of Britain’s ‘Green Deal’ so far in proceeding of ECEEE Summer Study 2013 – available from http://www.ukace.org/wp-content/uploads/2013/06/1-306-13_Guertler.pdf\nDECC 2011 “Homes and economy to benefit from energy and climate policies – Huhne” Department of Energy & Climate Change – available from https://www.gov.uk/government/news/homes-and-economy-to-benefit-from-energy-and-climate-policies-huhne\n\nFootnotes:\n\n1. Note that this does not mean that the respondent has installed everything that was recommended on the GDAR, but that at least one measure was installed.\n2. It should be noted here that this information is recorded per measure recommended to the respondent. It is to be expected that some households had few (if any) measures recommended, whilst others had multiple measures recommended.\n\nPosted in Uncategorized | 26 Comments\n\n## Heronian triangles\n\nDespite the picture, Heronian triangles are not named for the Heron, but actually for Hero of Alexandria (c. 10–70 AD), an ancient Greek mathematician and engineer (links are to Wikipedia).\n\nSuch triangles are interesting in that both their side lengths and areas are integer. It should be fairly easy to see that all pythagorean triangles fulfil this property (which, by the way, shows that my heron picture is in fact not made of heronian triangles at all – as all the right angle triangles are isoceles which means they cannot have all integer sides…)\n\nI’ve been having a little look at a problem asking for all triangles with integer sides which have an integer ratio of area to perimeter. The problem is delimited by giving a maximum value of that ratio – for the original see Problem 283 at projecteuler.net. A little thought shows that to have an integral ratio, the ratio must first be rational. For a triangle to have integer sides and a rational area:perimeter ratio, the area must be integral – therefore the triangles in question must be Heronian.\n\nWhat makes the puzzle a bit tricky is that not all Heronian triangles are right angled (pythagorean). If they were – it is relatively easy to generate all pythagorean triples with the required property. However, the non-pythagorean Heronian triangles are harder to generate and it is rather harder to convert the limit on the ratio to the largest Heronian triangle which might fall within the constraint.\n\nThis post simply records my line of thinking on a first inspection of the problem:\n\nConsider pythagorean triples (3,4,5) and (5,12,13). The triangle with sides 3,4,5 has area 6 (=(3*4)/2) and perimeter 12. Thus, it has an area:perimeter ratio 0.5. For ease of notation – let’s call the area:perimeter ratio r. If we double the side lengths (i.e. triangle with sides 6,8,10) the triangle has area 24 and perimeter 24 => r=1. So, we have a triangle fulfilling our criterion. Similarly with 5,12,13: area=30, perimeter=30 => r=1.\n\nNow consider right angled triangles 12,16,20 (3,4,5 * 4) and 5,12,13. The former has r=2 and the latter r=1 – both within the set we are looking for. If we then sit them together with the edges of length 12 touching (adjoin them), we form another triangle with side lengths 13,20 and 21. As the right angled triangles have integral ares, the triangle formed by their adjunction must also have integral area and therefore this must be Heronian. In this case, the triangle so formed has area = 126 and perimeter = 54. r = 7/3. It doesn’t fit our criterion, but all is not lost. If we multiply the whole thing by 3, it does! Thus – triangle with sides 39,60,63 is a Heronian triangle with r=1 again. This is the adjunction of right angled triangles 36,48,60 and 15,36,39 with r=6 and r=3 respectively (non-primitive pythagorean triangles = (3,4,5)*12 and (5,12,13)*3) to give a Heronian with r=1.\n\nSo, we can see that adjoining two right angled triangles with (relatively) large r gives a Heronian with fairly large side lengths and a perimeter larger than either right angled triangle, but with a much smaller r (=1 in the example case). This means we might have to find some very large Heronian triangles to ensure I’ve caught all of them with ratio <= 1000. So, thoughts continue. Parameterisations should help with both generation of the triangles and turning the limits on r into limits on the size of the triangle (either in terms of perimeter or longest side). In fact turning the limit on r into a limit on size of right-angled triangles is fairly easy – we need to find triangles with a maximum non-hypotenuse side length of 2*maximum_r + 1. I’ll sign off now – proof of that in a future post, maybe.\n\n## In which I think about relative importance\n\nI have been thinking a lot recently about the relative importance, or weighting, that people give to various activities in their own lives and the lives of others. It’s an area in which I am not particularly well versed and would welcome comments from philosophers, psychologists, sociologists or, in fact, anyone with an opinion to share. This post represents little more than a documentation of musings so far. It is not a researched piece, but is recorded here to be picked up later – by me and (hopefully) others.\n\nMy thinking in this direction started to form from a combination of observations in my own life, bolstered by some reading I did as part of my ‘real’ research (about which more in a future post) and some vicarious observations I made. It struck me that people find certain activities in their lives in some way non-negotiable, unquestionable, imperative or, maybe, essential. I’m aware that all those words are somewhat loaded and part of the reason for writing this post is to tease out some language to describe what I’m getting at. I’ll start from a few examples and work out from there – one from my research and an observation of behaviour to illustrate.\n\n1. Personal – my partner and I requested some assistance from a relative. The help would have allowed us to conduct leisure activities separately on the same evening. Unfortunately the relative couldn’t help. Later, my work required that I take a trip away which encompassed the same evening. The relative then revised the decision and helped my partner to attend another event. It is clear that the relative viewed my work commitment as imperative, whereas my social commitment was not.\n2. Research – my research focuses on people’s willingness to alter (in quantity or time) their use of electricity. In a large number of papers, presentations and other material on this subject, a number of aspects of electricity use are taken as ‘givens’. For example, “People will watch television when they want to watch television” could be quoted as a premise in a number of papers I read, even without the usual standards of academic evidence, without much question. It is taken as unquestionable that people will watch television whenever they like – irrespective of (reasonable) influence.\n3. Observed – an acquaintance from one city took a job in another city. She felt that she could not move her family as they had many ties in their original city. However, the job was a career progression. Rather than not take the job, she commutes each week, spending a number of days each week away from home. She is not unique in my peer group – it appears that a number of people find career progression an imperative and continue with an arrangement that is likely to be inconvenient at least.\n\nHaving considered a number of such examples for a while, it seemed to me that there is possibly interest beyond anecdote if we can draw out some general principles. Analysing a number of situations from this point of view has given me some interesting insight into what is happening. My thoughts have begun to crystallise into something more general. If there is a discrepancy between what people involved in a negotiation (or conversation) view as imperative, common understanding becomes very difficult. In turn, debate and resolution become virtually unattainable. This appears to be observable in situations from the minutiae of a single point in a business meeting to stand-offs between large institutions. It seems also that non-negotiables, or even perception thereof, may ‘lock-in’ a particular behaviour or norm in a situation – either for an individual or group.\n\nI think this mode of understanding can be powerful at a number of scales. In daily conversations, say between cohabiting partners, a difference in opinion on what is imperative can lead to oft repeated arguments, whereas as collective imperatives reinforced by repeated discussion will determine the lifestyle of that partnership. On a much larger scale, collective acceptance of the non-negotiable primacy of rational economic evaluation of any action determines not only what institutions do, but also how actions are described and debated (in this instance, in terms of investment, payback period). Where people or institutions having different ideas on the non-negotiables in such evaluation engage, the result is often incomprehension between debating parties – quite often descending into mud-slinging. An example of this is often seen when environmentalists engage with rational economists with regard to climate change. They fundamentally find different elements of the debate important and therefore, usually, each fails to even see the others’ position as other than ill thought out.\n\nMy point here is not, I think, one of platonic idealism or some form of essentialism. I am not arguing that there are some objective characteristics which define a group or are in some way virtuous. Nor am I arguing that the importance of certain actions is an entirely individual matter – rather that the importance or non-negotiability is determined as a product of individual experience, social consensus (or influence) and vicarious observation. What I am trying to argue is that these perceptions of what form the essential elements of a persons life have a very deep influence on the path that they choose and, by implication, the paths followed by groups of various sizes.\n\nI’m trying to place this idea within what I know of theories of structure and agency. In some ways, carried to its conclusion the idea would tend toward an ontology which minimises the effect of cognition on individual agency. Actions would be pre-determined if they were to be seen as purely due to satisfying a number of imperatives. However, that would be to neglect both the possibility of the imperatives changing over time and the possibility that imperatives may contradict each other in some situations.\n\nThe above is rather a stream of conciousness on an idea that has been intriguing me. I think this idea bears some more thought and maybe generalises to a scale of relative importance rather than the simple binary treatment implied by ‘non-negotiable’ or ‘imperative’ and their opposites. I am absolutely sure that there is a lot of thought out there about this very subject – probably hiding in the literature of disciplines with which I am not so familiar having originally trained as an engineer. I shall no doubt return to this theme as I think more about it and try to develop it into something more coherent. As I said at the top, comments most welcome.\n\n## Identifying a polynomial\n\nA tweet has got me musing again. @ColinTheMathmo sent out a tweet making a seemingly audacious claim that from just two data points he could deduce all the coefficients and powers in a polynomial that you had defined as long as the coefficients and powers were zero or positive integers\n\ni.e. you pick a polynomial of the form:\n\n\\begin{equation} y = \\sum {a_i \\cdot x^i} \\qquad for \\qquad i \\in Z^*, a_i \\in Z^* \\qquad (1)\\end{equation}\n\nHe then supplies an $$x$$ value, you return the corresponding $$y$$ value, this procedure is repeated once only and then he can tell you all the $$a_i$$ values in your polynomial.\n\nI looked at this tweet on the way to work one day and starting thinking about it. I wondered whether you cleverly supplied some complex numbers for the $$x$$ values which could indicate the powers of x in use, but Colin assured me that the $$x$$ values could be in $$Z$$ too. In my head, I started drawing graphs. Let’s call the first number asked for $$x_1$$. I could see that, given $$y_1$$ for that value, there are a finite number of graphs for polynomials satisfying $$(1)$$ that go through that point and that for the constraints given, these graphs were all monotonically increasing in $$x$$.\n\nI could see all this in my mind’s eye, but couldn’t quite work out how that would let me uniquely identify each one – i.e. at what point all those lines no longer cross. So, when I had a minute, I wrote a little python program to spit some graphs out. Below is one graph for a particular sample pair ($$x_1=2$$,$$y_1=41$$) showing all the possible polynomials satisfying $$(1)$$ that go through that point. For those who would like to look at the graphs in a bit more detail – there’s a gallery at the end of the post with various $$x,y$$ pairs and zoom levels. Scrappy Python code to generate these is also available on request.\n\nClick the graph to see a full size, better resolution, image",
null,
"From the picture above and a bit of reasoning that any higher powers of $$x$$ will cross all curves at lower values of $$x$$, I’m pretty convinced that for any point you ask for, if you work out the shallowest polynomial of order 2 through the point and the steepest straight line and then find their intersection, all the graphs beyond that point are distinct, will never cross and are monotonically increasing in $$x$$.\n\nWith this insight, if I define\n\\begin{aligned}\nb & ={\\lfloor}{\\frac{y_1}{x_1}}{\\rfloor} \\\\\nc & = y_1-{x_1}^2 – (y_1 mod x_1)\n\\end{aligned}\nThe intersection is at\n\\begin{equation}x = \\frac{b + \\sqrt{b^2 – 4c}}{2} \\end{equation}\nSo, we ask for $$x_2$$ greater than that value and the polynomial is uniquely identified. For instance, in the example above, this works out to $$x_2 \\geq 18$$ How to then get back to each co-efficient is interesting, but basically a search problem.\n\nNow, Colin has reliably informed me that this is way too complicated and also challenged me as to whether I can prove it will always work – which I’m not sure I can, but I think the above sort of shows it.\n\nI’m going to have a think about a few of my other ideas, which are (in no particular order)\n\n• ask for 1 as the first x ($$x_1 = 1$$), thus giving you at least the sum of all co-efficients. I have a feeling this might be useful\n• put in the value that you get back from the first answer as the second value you ask for (not sure why I think that might be good – I doubt it really)\n• find a value of $$x_2$$ which is $$f(x_1)$$ but lower than the value outlined above which can similarly always have the graphs distinct. I’m not hopeful.\nGallery of graphs\nClick on any of the images below for the full size picture\nPosted in Maths, Puzzles | 2 Comments\n\n## Sums of consecutive integers\n\nThis post is inspired by a tweet from @standupmaths who sends out puzzles tagged #mathspuzzle irregularly but fairly frequently. I won’t put out any spoilers on the blog, but once the solution is out on twitter, I may occasionally muse on these here. It’s my first go at both maths blogging and embedding equations into a webpage, so any comments welcome. I’m pretty sure I’ve gone round the houses on this one, so shortened method / notation welcome (as well as pointing out any errors that I’ve made, obviously).\n\nThe problem was stated thus: “#MathsPuzzle: What is the only number 10 →20 that is not a sum of consecutive numbers? (eg. Not 12 because 3 + 4 + 5 = 12)”. Tweeters fairly quickly answered 16 and the follow up question (abbreviated) was – how does this generalise? To which the answer is the only positive integers that cannot be represented as the sum of consecutive integers are the set $$x \\in \\{2^n\\}$$ where n is an integer.\n\nAfter finding this result, I tried to express why $$\\{2^n\\}$$ and only $$\\{2^n\\}$$ exhibit this property in 140 characters and failed miserably. So, I decided to blog about it and write the method I followed in my head down – if only to clarify to myself how I came to the result (and whether it was valid).\n\nI began by using the result:\n\\begin{aligned} \\sum_{i=1}^{i=j}{i} = \\frac {j \\cdot (j+1)}{2} \\end{aligned}\n\ntherefore, the sum of integers between j and k is:\n\\begin{aligned} \\sum_{i=1}^{i=k}{i} \\quad – \\quad \\sum_{i=1}^{i=j}{i} \\qquad & = \\qquad \\frac {k \\cdot (k+1)}{2} – \\frac {j \\cdot (j+1)}{2} \\\\ & = \\qquad \\frac {k^2 – j^2 + k – j}{2} \\\\ & = \\qquad \\frac {(k+j) \\cdot (k – j) + (k – j)}{2} \\\\ & = \\qquad \\frac {(k+j+1) \\cdot (k-j)}{2} \\end{aligned}\n\ntherefore, if x is to be expressed as the sum of some set of consecutive integers, the following must hold:\n\n\\begin{aligned} x \\qquad &= \\qquad \\frac {(k+j+1) \\cdot (k-j)}{2} \\\\ 2x \\qquad &= \\qquad{(k+j+1) \\cdot (k-j)} \\qquad (1)\\end{aligned}\n\nWe notice that if both $$k$$ and $$j$$ are odd, or both $$k$$ and $$j$$ are even, then both $$k + j$$ and $$k – j$$ are even, therefore $$(k+j+1)$$ is odd and $$(k-j)$$ is even. Conversely, if one of $$k$$ or $$j$$ is even and the other odd, both $$(k + j)$$ and $$(k – j)$$ are odd $$(k+j+1)$$ is even and $$(k-j)$$ is odd.\n\nSo we may state that if $$x$$ is the sum of consecutive integers then we must be able to express $$2x$$ as the product of one even and one odd integer\n\nIf we next consider any integer as a product of primes, we can say that for any integer\n\\begin{equation}\\label{primefactors} i = 2^a \\cdot 3^b \\cdot 5^c \\cdot 7^d \\cdots \\qquad (2)\\end{equation} and so on for all primes.\n\nIf we set $$i = 2x$$ then we can combine (1) and (2) to see that for x to be the sum of consecutive integers,\n\n\\begin{aligned} 2x \\qquad &= \\qquad {(k+j+1) \\cdot (k-j)} \\\\&= \\qquad 2^a \\cdot 3^b \\cdot 5^c \\cdot 7^d \\cdots \\\\ \\\\ \\text{therefore} \\\\ \\\\{(k+j+1) \\cdot (k-j)}&= \\qquad 2^a \\cdot 3^b \\cdot 5^c \\cdot 7^d \\cdots \\qquad \\qquad (3) \\end{aligned}\n\nAs all primes are odd except 2, and $$(\\text{odd}\\times\\text{odd})$$ is always odd, we can say that the right hand side of (3) will always be $$(\\text{even}\\times\\text{odd})$$ except in the case where $$b = c = d = \\cdots = 0$$ where it will be $$2^a$$. However, for $$x$$ to be the sum of consecutive digits, this expression is required to be $$(\\text{even}\\times\\text{odd})$$, which holds in all cases except where $$2x = 2^a \\rightarrow x = 2^{a-1} \\rightarrow x \\in \\{2^n\\}$$"
] |
[
null,
"https://snapey.our.dmu.ac.uk/files/2012/11/Polys_through_2_41.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9746123,"math_prob":0.9629978,"size":9059,"snap":"2023-40-2023-50","text_gpt3_token_len":1944,"char_repetition_ratio":0.13031474,"word_repetition_ratio":0.013166557,"special_character_ratio":0.22320345,"punctuation_ratio":0.07090909,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.952227,"pos_list":[0,1,2],"im_url_duplicate_count":[null,9,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-03T11:00:03Z\",\"WARC-Record-ID\":\"<urn:uuid:be3e0f8d-a9df-4b80-af93-1a6a5a78fd9e>\",\"Content-Length\":\"80800\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6dd74d47-d377-4e78-82f2-da1c6ca8dc9a>\",\"WARC-Concurrent-To\":\"<urn:uuid:58d61c9f-382d-44fe-b0ac-41a413dbcab4>\",\"WARC-IP-Address\":\"146.227.216.157\",\"WARC-Target-URI\":\"https://snapey.our.dmu.ac.uk/page/2/\",\"WARC-Payload-Digest\":\"sha1:XDIF6AQJLCB4JITHPKLXDUEGVJ3MQCFH\",\"WARC-Block-Digest\":\"sha1:6FYD6R7VJASWI52CNQCLI3B7ALLF7G3C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511075.63_warc_CC-MAIN-20231003092549-20231003122549-00440.warc.gz\"}"}
|
https://physicsoverflow.org/30194/anderson-mechanism-relativistic-theory-under-unitarity-gauge
|
[
"#",
null,
"Anderson-Higgs mechanism for the (non-relativistic) $U(1)$ gauge theory under the unitarity gauge\n\n+ 2 like - 0 dislike\n102 views\n\nOn Page 138, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons by Xiaogang Wen, when he demonstrates the Anderson-Higgs mechanism for the $U(1)$ gauge theory, he starts with the general (real time) Lagrangian\n\n$${\\cal{L}} ~=~ \\frac{i}{2}\\left(\\varphi^*(\\partial_t + iA_0)\\varphi -\\varphi(\\partial_t - iA_0)\\varphi^*\\right) - \\frac{1}{2m} |(\\partial_i +i A_i) \\varphi|^2$$ $$+ \\mu |\\varphi|^2 -\\frac{V_0}{2}|\\varphi|^4 + \\frac{1}{8\\pi e^2}(\\mathbf{E}^2 -\\mathbf{B}^2), \\tag{3.7.5}$$ with $c=1$. (I wonder why this is the correct non-relativistic form because in my derivation I always have a term $A_0^2|\\phi|^2/2m$.)\n\nThen he chooses the gauge such that $\\varphi$ is real (unitarity gauge according to Peskin and Schroeder) and obtains\n\n$${\\cal{L}} ~=~ -A_0 \\phi^2 - \\frac{1}{2m} (\\partial_i \\phi)^2 -\\frac{\\phi^2}{2m}A_i^2 + \\mu \\phi^2 -\\frac{V_0}{2}\\phi^4$$ $$+ \\frac{1}{8\\pi e^2}(\\mathbf{E}^2 -\\mathbf{B}^2).\\tag{3.7.16b}$$\n\nHe claims that if we have $\\phi = \\phi_0 +\\delta \\phi$ and integrate the small fluctuation $\\delta \\phi$, we can get\n\n$${\\cal{L}} ~=~ \\frac{A_0^2}{2V_0} -\\frac{\\rho A_i^2}{2m} + \\frac{1}{8\\pi e^2}(\\mathbf{E}^2 -\\mathbf{B}^2).\\tag{3.7.17}$$\n\nI am curious what approximations he has done to get here.\n\nAny help is appreciated.\n\nThis post imported from StackExchange Physics at 2015-04-15 10:43 (UTC), posted by SE-user L. Su\n Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the \"link\" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor) Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\\varnothing$ in the following word:p$\\hbar$ysicsO$\\varnothing$erflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register."
] |
[
null,
"https://physicsoverflow.org/qa-plugin/po-printer-friendly/print_on.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.69206756,"math_prob":0.98624325,"size":1399,"snap":"2020-24-2020-29","text_gpt3_token_len":548,"char_repetition_ratio":0.12258065,"word_repetition_ratio":0.0,"special_character_ratio":0.39814153,"punctuation_ratio":0.07446808,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9970707,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-06T04:36:54Z\",\"WARC-Record-ID\":\"<urn:uuid:51a34ffa-8ae3-469b-86b7-65b83c7880cb>\",\"Content-Length\":\"99280\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:72fbcfc7-3e07-473e-a18a-895374a0815d>\",\"WARC-Concurrent-To\":\"<urn:uuid:08fed2cd-449d-43b7-a74d-2b607987cc83>\",\"WARC-IP-Address\":\"129.70.43.86\",\"WARC-Target-URI\":\"https://physicsoverflow.org/30194/anderson-mechanism-relativistic-theory-under-unitarity-gauge\",\"WARC-Payload-Digest\":\"sha1:UIRFUPFNWBGH3C3E6X62IRBFMBJKVFU2\",\"WARC-Block-Digest\":\"sha1:SUVYL55C5V2JWB5YDTZHTZ6BLY43HOZO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590348509972.80_warc_CC-MAIN-20200606031557-20200606061557-00591.warc.gz\"}"}
|
https://www.geeksforgeeks.org/gate-gate-cs-2015-set-3-question-65/
|
[
"Open In App\n\n# GATE | GATE-CS-2015 (Set 3) | Question 65\n\nConsider three software items: Program-X, Control Flow Diagram of Program-Y and Control Flow Diagram of Program-Z as shown below",
null,
"The values of McCabe’s Cyclomatic complexity of Program-X, Program-Y and Program-Z respectively are\n(A) 4, 4, 7\n(B) 3, 4, 7\n(C) 4, 4, 8\n(D) 4, 3, 8\n\nExplanation:\n\n```The cyclomatic complexity of a structured program[a] is defined\nwith reference to the control flow graph of the program, a directed\ngraph containing the basic blocks of the program, with an edge\nbetween two basic blocks if control may pass from the first to the\nsecond. The complexity M is then defined as.\n\nM = E − N + 2P,\n\nwhere\n\nE = the number of edges of the graph.\nN = the number of nodes of the graph.\nP = the number of connected components.\n\nSource: http://en.wikipedia.org/wiki/Cyclomatic_complexity\n\nFor first program X, E = 11, N = 9, P = 1, So M = 11-9+2*1 = 4\nFor second program Y, E = 10, N = 8, p = 1, So M = 10-8+2*1 = 4\nFor Third program X, E = 22, N = 17, p = 1, So M = 22-17+2*1 = 7```"
] |
[
null,
"https://media.geeksforgeeks.org/wp-content/cdn-uploads/gq/2015/02/Q651.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8348116,"math_prob":0.9969698,"size":1115,"snap":"2023-40-2023-50","text_gpt3_token_len":358,"char_repetition_ratio":0.12871288,"word_repetition_ratio":0.023364486,"special_character_ratio":0.335426,"punctuation_ratio":0.15175097,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9989885,"pos_list":[0,1,2],"im_url_duplicate_count":[null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-03T15:12:03Z\",\"WARC-Record-ID\":\"<urn:uuid:1ac593ae-124f-4a80-ab88-b64a3e43056d>\",\"Content-Length\":\"227475\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:013d8a4c-9230-405d-9b54-28a259a0a38e>\",\"WARC-Concurrent-To\":\"<urn:uuid:f8137fc7-2045-4835-9931-3b668dc969b5>\",\"WARC-IP-Address\":\"23.222.5.204\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/gate-gate-cs-2015-set-3-question-65/\",\"WARC-Payload-Digest\":\"sha1:2XEJ2YHD7H2OIUSM4RSSZQW7LIV7DTKG\",\"WARC-Block-Digest\":\"sha1:XVI3XN75A3ZLIGVRNA7RZ7SRR5J2N7IY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511106.1_warc_CC-MAIN-20231003124522-20231003154522-00771.warc.gz\"}"}
|
http://victorbalaguer.es/a-guide-to-definition-of-discrete-mathematics/
|
[
"Seleccionar página\n\nBe aware that the totality of a type is dependent on the chosen semantics. It follows that subsets can be produced from any defined universal set. https://rankmywriter.com/ This will give us an opportunity to show extra notation employed in sets. But the integers aren’t dense. There are just a limited number of combinations you are able to choose from.\n\n## What Is So Fascinating About Definition of Discrete Mathematics?\n\nData are the end result of sampling from a population. The aim of statistics isn’t to carry out quite a few calculations utilizing the formulas, yet to get a comprehension of your data. Trees are wonderful methods to inspect the outcomes of discrete sequential decisions. On the other hand, the most innovative maturation of discrete analysis is a result of the visual appeal of cybernetics and its theoretical part mathematical cybernetics. Estimating abundance and the impact of heterogeneity.\n\nThe exact same model applies to Medium, too, which enables you to follow and unfollow authors! This usually means that to be able to learn the fundamental algorithms utilized by computer programmers, students will require a good background in these subjects. Information theory requires the quantification of information.\n\n## The Awful Side of Definition of Discrete Mathematics\n\nAlso within this section you make your own cheat sheet by utilizing these formulas. To put it differently, a graph that maynot be drawn without a minumum of one pair of its edges crossing. The following are a few of the more basic methods of defining graphs and related mathematical structures. The several types of edges are pretty important if it has to do with recognizing and defining graphs.\n\nThe variety of kids in your class is likewise a case of discrete data. https://www.weber.edu/ You’ve induced from specific scenario information regarding the overall population of the lake. This kind of tree is known as a decision tree. This part illustrates the method through an assortment of examples. Let’s return to the set of pure numbers. Well lets draw an image.\n\nThis is going to be the notation used within this lesson. Variables could be numerical or categorical. Example Solution We choose to use digraphs to produce the explanations within this situation. An empty set has no elements.\n\n## The One Thing to Do for Definition of Discrete Mathematics\n\nThis lets you know that it’s not so possible you will win. We’ll also observe some former GATE issues. Let’s visit the Monoid and Semigroup. I don’t look at this necessary.\n\nThis has caused several mistranslations. It’s strongly advised that you practice them. Let’s visit the Monoid and Semigroup. I’m not really certain where to start here.\n\nThe chapter begins the procedure for accomplishing that goal, and also demonstrates how to use induction to demonstrate that algorithms correctly address the problems they are made to fix. Numerical analysis offers an important example. Mathematical discoveries continue to get made today. Students in mathematics courses are often given the impression it to fix an issue, an individual must imitate the remedy to a similar problem that has been solved.\n\nPapers describing the undertaking has to be turned into the concentration for evaluation by the conclusion of the semester where the AM 91r is completed. You might purchase at least one of these online or at your community college bookstore. Accordingly, in instances where the calculations are comparatively easy, working throughout with BCD can result in a simpler overall system than converting to and from binary. Students will be asked to contribute as individuals and as an element of cooperative groups.\n\nA vertex-induced subgraph is one which is made up of a number of the vertices of the original graph and all the edges that connect them in the original. Inside this activity students are going to be in pairs and has to finish a worksheet that list various types of the equation sine and cosine that illustrate a number of the transformations for sine and cosine. In other words, it’s a directed graph that may be formed as an orientation of an undirected graph. This type of graph could possibly be called vertex-labeled. Otherwise, it’s called an infinite graph. A graph with a single node is usually called a singleton graph, though we won’t really be dealing with those."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.94072485,"math_prob":0.8689173,"size":4325,"snap":"2022-40-2023-06","text_gpt3_token_len":836,"char_repetition_ratio":0.10229114,"word_repetition_ratio":0.0056980057,"special_character_ratio":0.18427746,"punctuation_ratio":0.08553459,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95687884,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-05T16:34:05Z\",\"WARC-Record-ID\":\"<urn:uuid:644646d2-f12b-4b89-bd98-4b22634cad07>\",\"Content-Length\":\"39525\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f73d997c-a1eb-439e-9b3b-e0c231f68dd6>\",\"WARC-Concurrent-To\":\"<urn:uuid:444e0117-e86d-47e1-932b-bd9a0f4a5eb8>\",\"WARC-IP-Address\":\"86.109.170.4\",\"WARC-Target-URI\":\"http://victorbalaguer.es/a-guide-to-definition-of-discrete-mathematics/\",\"WARC-Payload-Digest\":\"sha1:6MMJZPCE3HJO44EVHEVNXHMBIN5RN342\",\"WARC-Block-Digest\":\"sha1:ATNQH3HNX7W37JMCTMTMTGL2HY7Z3MFF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337631.84_warc_CC-MAIN-20221005140739-20221005170739-00278.warc.gz\"}"}
|
https://www.teachexcel.com/excel-tutorials/n-1454,Excel-Finance-Trick-14--NPV-function-Capital-Invest-Decision.html
|
[
"Similar Content\nReference Other Excel Files with Formulas and Functions\nTutorial: In Excel you can use formulas and functions to reference data that is stored in another Ex...\nCapitalize First Letter of Every Word in a Cell - PROPER Function\nTutorial: In Excel you can use a function to capitalize the first letter of every word in a cell. ...\nNest IF Statements in Excel\nTutorial: How to nest IF statements inside of each other in Excel so that you can make more complex...\n\n# Excel Finance Trick 14: NPV function Capital Invest Decision\n\nYou can use the NPV function when the cash flows are of different amounts but the time periods between cash flows is the same.\n\nWhen an asset DOES NOT have an annuity cash flow pattern, you can use the NPV function for Capital Investment Decision.\n\nAsset Valuation with Discounting Cash Flow Analysis.\n\nIn This Series learn 17 amazing Finance Tricks. Learn about the PMT, PV, FV, NPER, RATE, SLN, DB, EFFECT, NOMINAL, NPV, XNPV, and the CUMIPMT functions that can make your financing tasks much easier in Excel. See how to use the PMT function in the standard way, but also see how to use it while incorporating a Balloon payment or a delayed payment. Lean how to translate a Nominal interest rate into an Effective Interest rate. Learn how to calculate how long it takes to pay off a credit card balance. Lean how to calculate the Effect Rate on a Payday loan. And many more financing Tricks!!\n\nThe Excel Finance Tricks 1-17 will show an assortment of Excel Financing Tricks!\n\nExcel Formula\n\nGot a Question? Ask it Here in the Forum."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.86166626,"math_prob":0.8400226,"size":1942,"snap":"2019-13-2019-22","text_gpt3_token_len":439,"char_repetition_ratio":0.11971104,"word_repetition_ratio":0.8772455,"special_character_ratio":0.20700309,"punctuation_ratio":0.1285347,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97439885,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-25T10:58:16Z\",\"WARC-Record-ID\":\"<urn:uuid:fb0541ed-7222-45ab-9c67-8df0231f956a>\",\"Content-Length\":\"35169\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eebb73b4-7fe9-40c7-9bbf-ae55ecb20dcd>\",\"WARC-Concurrent-To\":\"<urn:uuid:bc5e4e8e-c07e-47f6-9b21-6e6a2486b6a7>\",\"WARC-IP-Address\":\"216.92.234.45\",\"WARC-Target-URI\":\"https://www.teachexcel.com/excel-tutorials/n-1454,Excel-Finance-Trick-14--NPV-function-Capital-Invest-Decision.html\",\"WARC-Payload-Digest\":\"sha1:CG3PZC5B4NGYW2XOWIA7NDM4QWGLUBVW\",\"WARC-Block-Digest\":\"sha1:H6MC6FIYXRCGP2NC5ZJWZJIP3C63JLOU\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912203865.15_warc_CC-MAIN-20190325092147-20190325114147-00152.warc.gz\"}"}
|
http://ixtrieve.fh-koeln.de/birds/litie/document/28646
|
[
"# Document (#28646)\n\nAuthor\nMooers, C.N.\nTitle\n¬The indexing language of an information retrieval system\nSource\nTheory of subject analysis: a sourcebook. Ed.: L.M. Chan, et al\nImprint\nLittleton, CO : Libraries Unlimited\nYear\n1985\nPages\nS.247-261\nAbstract\nCalvin Mooers' work toward the resolution of the problem of ambiguity in indexing went unrecognized for years. At the time he introduced the \"descriptor\" - a term with a very distinct meaning-indexers were, for the most part, taking index terms directly from the document, without either rationalizing them with context or normalizing them with some kind of classification. It is ironic that Mooers' term came to be attached to the popular but unsophisticated indexing methods which he was trying to root out. Simply expressed, what Mooers did was to take the dictionary definitions of terms and redefine them so clearly that they could not be used in any context except that provided by the new definition. He did, at great pains, construct such meanings for over four hundred words; disambiguation and specificity were sought after and found for these words. He proposed that all indexers adopt this method so that when the index supplied a term, it also supplied the exact meaning for that term as used in the indexed document. The same term used differently in another document would be defined differently and possibly renamed to avoid ambiguity. The disambiguation was achieved by using unabridged dictionaries and other sources of defining terminology. In practice, this tends to produce circularity in definition, that is, word A refers to word B which refers to word C which refers to word A. It was necessary, therefore, to break this chain by creating a new, definitive meaning for each word. Eventually, means such as those used by Austin (q.v.) for PRECIS achieved the same purpose, but by much more complex means than just creating a unique definition of each term. Mooers, however, was probably the first to realize how confusing undefined terminology could be. Early automatic indexers dealt with distinct disciplines and, as long as they did not stray beyond disciplinary boundaries, a quick and dirty keyword approach was satisfactory. The trouble came when attempts were made to make a combined index for two or more distinct disciplines. A number of processes have since been developed, mostly involving tagging of some kind or use of strings. Mooers' solution has rarely been considered seriously and probably would be extremely difficult to apply now because of so much interdisciplinarity. But for a specific, weIl defined field, it is still weIl worth considering. Mooers received training in mathematics and physics from the University of Minnesota and the Massachusetts Institute of Technology. He was the founder of Zator Company, which developed and marketed a coded card information retrieval system, and of Rockford Research, Inc., which engages in research in information science. He is the inventor of the TRAC computer language.\nFootnote\nNachdruck des Originalartikels mit Kommentierung durch die Herausgeber\nOriginal in: Information retrieval today: papers presented at an Institute conducted by the Library School and the Center for Continuation Study, University of Minnesota, Sept. 19-22, 1962. Ed. by Wesley Simonton. Minneapolis, Minn.: The Center, 1963. S.21-36.\nTheme\nTheorie verbaler Dokumentationssprachen\nKonzeption und Anwendung des Prinzips Thesaurus\n\n## Similar documents (content)\n\n1. Austin, D.; Digger, J.A.: PRECIS: The Preserved Context Index System (1985) 0.44\n```0.43601626 = sum of:\n0.43601626 = product of:\n0.72669375 = sum of:\n0.044100896 = weight(abstract_txt:terminology in 4653) [ClassicSimilarity], result of:\n0.044100896 = score(doc=4653,freq=2.0), product of:\n0.13904688 = queryWeight, product of:\n1.0321327 = boost\n5.741312 = idf(docFreq=372, maxDocs=42740)\n0.023464676 = queryNorm\n0.31716567 = fieldWeight in 4653, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n5.741312 = idf(docFreq=372, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.03435295 = weight(abstract_txt:kind in 4653) [ClassicSimilarity], result of:\n0.03435295 = score(doc=4653,freq=1.0), product of:\n0.14831406 = queryWeight, product of:\n1.0659727 = boost\n5.929549 = idf(docFreq=308, maxDocs=42740)\n0.023464676 = queryNorm\n0.23162302 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.929549 = idf(docFreq=308, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.06342366 = weight(abstract_txt:weil in 4653) [ClassicSimilarity], result of:\n0.06342366 = score(doc=4653,freq=3.0), product of:\n0.15476286 = queryWeight, product of:\n1.0889008 = boost\n6.0570884 = idf(docFreq=271, maxDocs=42740)\n0.023464676 = queryNorm\n0.40981188 = fieldWeight in 4653, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n6.0570884 = idf(docFreq=271, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.01938897 = weight(abstract_txt:document in 4653) [ClassicSimilarity], result of:\n0.01938897 = score(doc=4653,freq=1.0), product of:\n0.11595066 = queryWeight, product of:\n1.1543491 = boost\n4.280766 = idf(docFreq=1606, maxDocs=42740)\n0.023464676 = queryNorm\n0.16721742 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.280766 = idf(docFreq=1606, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.049505018 = weight(abstract_txt:indexing in 4653) [ClassicSimilarity], result of:\n0.049505018 = score(doc=4653,freq=6.0), product of:\n0.119202614 = queryWeight, product of:\n1.1704246 = boost\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.023464676 = queryNorm\n0.41530144 = fieldWeight in 4653, product of:\n2.4494898 = tf(freq=6.0), with freq of:\n6.0 = termFreq=6.0\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.028325712 = weight(abstract_txt:used in 4653) [ClassicSimilarity], result of:\n0.028325712 = score(doc=4653,freq=5.0), product of:\n0.096090436 = queryWeight, product of:\n1.2134168 = boost\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.023464676 = queryNorm\n0.2947818 = fieldWeight in 4653, product of:\n2.236068 = tf(freq=5.0), with freq of:\n5.0 = termFreq=5.0\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.06428613 = weight(abstract_txt:index in 4653) [ClassicSimilarity], result of:\n0.06428613 = score(doc=4653,freq=6.0), product of:\n0.14188325 = queryWeight, product of:\n1.2769271 = boost\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.023464676 = queryNorm\n0.45309174 = fieldWeight in 4653, product of:\n2.4494898 = tf(freq=6.0), with freq of:\n6.0 = termFreq=6.0\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.06172221 = weight(abstract_txt:ambiguity in 4653) [ClassicSimilarity], result of:\n0.06172221 = score(doc=4653,freq=1.0), product of:\n0.21919666 = queryWeight, product of:\n1.2959012 = boost\n7.2085433 = idf(docFreq=85, maxDocs=42740)\n0.023464676 = queryNorm\n0.28158373 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.2085433 = idf(docFreq=85, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.025472408 = weight(abstract_txt:which in 4653) [ClassicSimilarity], result of:\n0.025472408 = score(doc=4653,freq=6.0), product of:\n0.09075054 = queryWeight, product of:\n1.318407 = boost\n2.9334934 = idf(docFreq=6181, maxDocs=42740)\n0.023464676 = queryNorm\n0.28068602 = fieldWeight in 4653, product of:\n2.4494898 = tf(freq=6.0), with freq of:\n6.0 = termFreq=6.0\n2.9334934 = idf(docFreq=6181, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.065663554 = weight(abstract_txt:probably in 4653) [ClassicSimilarity], result of:\n0.065663554 = score(doc=4653,freq=1.0), product of:\n0.22843145 = queryWeight, product of:\n1.3229178 = boost\n7.358825 = idf(docFreq=73, maxDocs=42740)\n0.023464676 = queryNorm\n0.2874541 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.358825 = idf(docFreq=73, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.06677767 = weight(abstract_txt:came in 4653) [ClassicSimilarity], result of:\n0.06677767 = score(doc=4653,freq=1.0), product of:\n0.23100807 = queryWeight, product of:\n1.3303579 = boost\n7.400211 = idf(docFreq=70, maxDocs=42740)\n0.023464676 = queryNorm\n0.28907073 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.400211 = idf(docFreq=70, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.022399731 = weight(abstract_txt:that in 4653) [ClassicSimilarity], result of:\n0.022399731 = score(doc=4653,freq=8.0), product of:\n0.0846631 = queryWeight, product of:\n1.506732 = boost\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.023464676 = queryNorm\n0.2645749 = fieldWeight in 4653, product of:\n2.828427 = tf(freq=8.0), with freq of:\n8.0 = termFreq=8.0\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.043768317 = weight(abstract_txt:meaning in 4653) [ClassicSimilarity], result of:\n0.043768317 = score(doc=4653,freq=1.0), product of:\n0.1995308 = queryWeight, product of:\n1.5142777 = boost\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.023464676 = queryNorm\n0.2193562 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.07066347 = weight(abstract_txt:indexers in 4653) [ClassicSimilarity], result of:\n0.07066347 = score(doc=4653,freq=1.0), product of:\n0.27459967 = queryWeight, product of:\n1.77644 = boost\n6.5877166 = idf(docFreq=159, maxDocs=42740)\n0.023464676 = queryNorm\n0.25733268 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.5877166 = idf(docFreq=159, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.06684303 = weight(abstract_txt:word in 4653) [ClassicSimilarity], result of:\n0.06684303 = score(doc=4653,freq=1.0), product of:\n0.31373075 = queryWeight, product of:\n2.4513395 = boost\n5.4543004 = idf(docFreq=496, maxDocs=42740)\n0.023464676 = queryNorm\n0.2130586 = fieldWeight in 4653, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.4543004 = idf(docFreq=496, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4653)\n0.6 = coord(15/25)\n```\n2. Besler, G.; Szulc, J.: Gottlob Frege's theory of definition as useful tool for knowledge organization : definition of 'context' - case study (2014) 0.23\n```0.22538532 = sum of:\n0.22538532 = product of:\n0.70432913 = sum of:\n0.057143908 = weight(abstract_txt:achieved in 3441) [ClassicSimilarity], result of:\n0.057143908 = score(doc=3441,freq=1.0), product of:\n0.15220875 = queryWeight, product of:\n1.0798781 = boost\n6.006899 = idf(docFreq=285, maxDocs=42740)\n0.023464676 = queryNorm\n0.37543118 = fieldWeight in 3441, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n6.006899 = idf(docFreq=285, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.028663602 = weight(abstract_txt:used in 3441) [ClassicSimilarity], result of:\n0.028663602 = score(doc=3441,freq=2.0), product of:\n0.096090436 = queryWeight, product of:\n1.2134168 = boost\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.023464676 = queryNorm\n0.29829818 = fieldWeight in 3441, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.016638506 = weight(abstract_txt:which in 3441) [ClassicSimilarity], result of:\n0.016638506 = score(doc=3441,freq=1.0), product of:\n0.09075054 = queryWeight, product of:\n1.318407 = boost\n2.9334934 = idf(docFreq=6181, maxDocs=42740)\n0.023464676 = queryNorm\n0.18334334 = fieldWeight in 3441, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n2.9334934 = idf(docFreq=6181, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.24987307 = weight(abstract_txt:definition in 3441) [ClassicSimilarity], result of:\n0.24987307 = score(doc=3441,freq=14.0), product of:\n0.19331267 = queryWeight, product of:\n1.4904957 = boost\n5.5273256 = idf(docFreq=461, maxDocs=42740)\n0.023464676 = queryNorm\n1.292585 = fieldWeight in 3441, product of:\n3.7416575 = tf(freq=14.0), with freq of:\n14.0 = termFreq=14.0\n5.5273256 = idf(docFreq=461, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.0126712015 = weight(abstract_txt:that in 3441) [ClassicSimilarity], result of:\n0.0126712015 = score(doc=3441,freq=1.0), product of:\n0.0846631 = queryWeight, product of:\n1.506732 = boost\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.023464676 = queryNorm\n0.14966616 = fieldWeight in 3441, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.09903639 = weight(abstract_txt:meaning in 3441) [ClassicSimilarity], result of:\n0.09903639 = score(doc=3441,freq=2.0), product of:\n0.1995308 = queryWeight, product of:\n1.5142777 = boost\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.023464676 = queryNorm\n0.49634638 = fieldWeight in 3441, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.15124851 = weight(abstract_txt:word in 3441) [ClassicSimilarity], result of:\n0.15124851 = score(doc=3441,freq=2.0), product of:\n0.31373075 = queryWeight, product of:\n2.4513395 = boost\n5.4543004 = idf(docFreq=496, maxDocs=42740)\n0.023464676 = queryNorm\n0.48209658 = fieldWeight in 3441, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n5.4543004 = idf(docFreq=496, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.0890539 = weight(abstract_txt:term in 3441) [ClassicSimilarity], result of:\n0.0890539 = score(doc=3441,freq=1.0), product of:\n0.295077 = queryWeight, product of:\n2.6042533 = boost\n4.8287816 = idf(docFreq=928, maxDocs=42740)\n0.023464676 = queryNorm\n0.30179885 = fieldWeight in 3441, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.8287816 = idf(docFreq=928, maxDocs=42740)\n0.0625 = fieldNorm(doc=3441)\n0.32 = coord(8/25)\n```\n3. Hudon, M.: ¬A preliminary investigation of the usefulness of semantic relations and of standardized definitions for the purpose of specifying meaning in a thesaurus (1998) 0.20\n```0.19683099 = sum of:\n0.19683099 = product of:\n0.7029678 = sum of:\n0.06859616 = weight(abstract_txt:indexing in 1056) [ClassicSimilarity], result of:\n0.06859616 = score(doc=1056,freq=2.0), product of:\n0.119202614 = queryWeight, product of:\n1.1704246 = boost\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.023464676 = queryNorm\n0.5754585 = fieldWeight in 1056, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.09375 = fieldNorm(doc=1056)\n0.030402344 = weight(abstract_txt:used in 1056) [ClassicSimilarity], result of:\n0.030402344 = score(doc=1056,freq=1.0), product of:\n0.096090436 = queryWeight, product of:\n1.2134168 = boost\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.023464676 = queryNorm\n0.31639302 = fieldWeight in 1056, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.09375 = fieldNorm(doc=1056)\n0.06298728 = weight(abstract_txt:index in 1056) [ClassicSimilarity], result of:\n0.06298728 = score(doc=1056,freq=1.0), product of:\n0.14188325 = queryWeight, product of:\n1.2769271 = boost\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.023464676 = queryNorm\n0.44393742 = fieldWeight in 1056, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.09375 = fieldNorm(doc=1056)\n0.019006802 = weight(abstract_txt:that in 1056) [ClassicSimilarity], result of:\n0.019006802 = score(doc=1056,freq=1.0), product of:\n0.0846631 = queryWeight, product of:\n1.506732 = boost\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.023464676 = queryNorm\n0.22449924 = fieldWeight in 1056, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.09375 = fieldNorm(doc=1056)\n0.1485546 = weight(abstract_txt:meaning in 1056) [ClassicSimilarity], result of:\n0.1485546 = score(doc=1056,freq=2.0), product of:\n0.1995308 = queryWeight, product of:\n1.5142777 = boost\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.023464676 = queryNorm\n0.7445196 = fieldWeight in 1056, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.09375 = fieldNorm(doc=1056)\n0.23983976 = weight(abstract_txt:indexers in 1056) [ClassicSimilarity], result of:\n0.23983976 = score(doc=1056,freq=2.0), product of:\n0.27459967 = queryWeight, product of:\n1.77644 = boost\n6.5877166 = idf(docFreq=159, maxDocs=42740)\n0.023464676 = queryNorm\n0.87341607 = fieldWeight in 1056, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n6.5877166 = idf(docFreq=159, maxDocs=42740)\n0.09375 = fieldNorm(doc=1056)\n0.13358085 = weight(abstract_txt:term in 1056) [ClassicSimilarity], result of:\n0.13358085 = score(doc=1056,freq=1.0), product of:\n0.295077 = queryWeight, product of:\n2.6042533 = boost\n4.8287816 = idf(docFreq=928, maxDocs=42740)\n0.023464676 = queryNorm\n0.4526983 = fieldWeight in 1056, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.8287816 = idf(docFreq=928, maxDocs=42740)\n0.09375 = fieldNorm(doc=1056)\n0.28 = coord(7/25)\n```\n4. Turner, J.M.: Comparing user-assigned terms with indexer-assigned terms for storage and retrieval of moving images : research results (1995) 0.20\n```0.19552971 = sum of:\n0.19552971 = product of:\n0.81470716 = sum of:\n0.047657117 = weight(abstract_txt:them in 3900) [ClassicSimilarity], result of:\n0.047657117 = score(doc=3900,freq=1.0), product of:\n0.117809705 = queryWeight, product of:\n1.1635661 = boost\n4.3149467 = idf(docFreq=1552, maxDocs=42740)\n0.023464676 = queryNorm\n0.40452623 = fieldWeight in 3900, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.3149467 = idf(docFreq=1552, maxDocs=42740)\n0.09375 = fieldNorm(doc=3900)\n0.048504815 = weight(abstract_txt:indexing in 3900) [ClassicSimilarity], result of:\n0.048504815 = score(doc=3900,freq=1.0), product of:\n0.119202614 = queryWeight, product of:\n1.1704246 = boost\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.023464676 = queryNorm\n0.40691066 = fieldWeight in 3900, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.09375 = fieldNorm(doc=3900)\n0.030402344 = weight(abstract_txt:used in 3900) [ClassicSimilarity], result of:\n0.030402344 = score(doc=3900,freq=1.0), product of:\n0.096090436 = queryWeight, product of:\n1.2134168 = boost\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.023464676 = queryNorm\n0.31639302 = fieldWeight in 3900, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.09375 = fieldNorm(doc=3900)\n0.22165217 = weight(abstract_txt:supplied in 3900) [ClassicSimilarity], result of:\n0.22165217 = score(doc=3900,freq=2.0), product of:\n0.22759888 = queryWeight, product of:\n1.3205048 = boost\n7.3454022 = idf(docFreq=74, maxDocs=42740)\n0.023464676 = queryNorm\n0.97387195 = fieldWeight in 3900, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n7.3454022 = idf(docFreq=74, maxDocs=42740)\n0.09375 = fieldNorm(doc=3900)\n0.22665092 = weight(abstract_txt:came in 3900) [ClassicSimilarity], result of:\n0.22665092 = score(doc=3900,freq=2.0), product of:\n0.23100807 = queryWeight, product of:\n1.3303579 = boost\n7.400211 = idf(docFreq=70, maxDocs=42740)\n0.023464676 = queryNorm\n0.9811386 = fieldWeight in 3900, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n7.400211 = idf(docFreq=70, maxDocs=42740)\n0.09375 = fieldNorm(doc=3900)\n0.23983976 = weight(abstract_txt:indexers in 3900) [ClassicSimilarity], result of:\n0.23983976 = score(doc=3900,freq=2.0), product of:\n0.27459967 = queryWeight, product of:\n1.77644 = boost\n6.5877166 = idf(docFreq=159, maxDocs=42740)\n0.023464676 = queryNorm\n0.87341607 = fieldWeight in 3900, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n6.5877166 = idf(docFreq=159, maxDocs=42740)\n0.09375 = fieldNorm(doc=3900)\n0.24 = coord(6/25)\n```\n5. Luhn, H.P.: Keyword-in-context index for technical literature (1985) 0.19\n```0.19210008 = sum of:\n0.19210008 = product of:\n0.48025018 = sum of:\n0.028082225 = weight(abstract_txt:them in 4639) [ClassicSimilarity], result of:\n0.028082225 = score(doc=4639,freq=2.0), product of:\n0.117809705 = queryWeight, product of:\n1.1635661 = boost\n4.3149467 = idf(docFreq=1552, maxDocs=42740)\n0.023464676 = queryNorm\n0.23836938 = fieldWeight in 4639, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n4.3149467 = idf(docFreq=1552, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.03500533 = weight(abstract_txt:indexing in 4639) [ClassicSimilarity], result of:\n0.03500533 = score(doc=4639,freq=3.0), product of:\n0.119202614 = queryWeight, product of:\n1.1704246 = boost\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.023464676 = queryNorm\n0.29366246 = fieldWeight in 4639, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n4.34038 = idf(docFreq=1513, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.025335286 = weight(abstract_txt:used in 4639) [ClassicSimilarity], result of:\n0.025335286 = score(doc=4639,freq=4.0), product of:\n0.096090436 = queryWeight, product of:\n1.2134168 = boost\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.023464676 = queryNorm\n0.26366085 = fieldWeight in 4639, product of:\n2.0 = tf(freq=4.0), with freq of:\n4.0 = termFreq=4.0\n3.3748589 = idf(docFreq=3975, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.058684938 = weight(abstract_txt:index in 4639) [ClassicSimilarity], result of:\n0.058684938 = score(doc=4639,freq=5.0), product of:\n0.14188325 = queryWeight, product of:\n1.2769271 = boost\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.023464676 = queryNorm\n0.41361427 = fieldWeight in 4639, product of:\n2.236068 = tf(freq=5.0), with freq of:\n5.0 = termFreq=5.0\n4.7353325 = idf(docFreq=1019, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.010399067 = weight(abstract_txt:which in 4639) [ClassicSimilarity], result of:\n0.010399067 = score(doc=4639,freq=1.0), product of:\n0.09075054 = queryWeight, product of:\n1.318407 = boost\n2.9334934 = idf(docFreq=6181, maxDocs=42740)\n0.023464676 = queryNorm\n0.11458959 = fieldWeight in 4639, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n2.9334934 = idf(docFreq=6181, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.06677767 = weight(abstract_txt:came in 4639) [ClassicSimilarity], result of:\n0.06677767 = score(doc=4639,freq=1.0), product of:\n0.23100807 = queryWeight, product of:\n1.3303579 = boost\n7.400211 = idf(docFreq=70, maxDocs=42740)\n0.023464676 = queryNorm\n0.28907073 = fieldWeight in 4639, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.400211 = idf(docFreq=70, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.017708544 = weight(abstract_txt:that in 4639) [ClassicSimilarity], result of:\n0.017708544 = score(doc=4639,freq=5.0), product of:\n0.0846631 = queryWeight, product of:\n1.506732 = boost\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.023464676 = queryNorm\n0.20916483 = fieldWeight in 4639, product of:\n2.236068 = tf(freq=5.0), with freq of:\n5.0 = termFreq=5.0\n2.3946586 = idf(docFreq=10595, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.043768317 = weight(abstract_txt:meaning in 4639) [ClassicSimilarity], result of:\n0.043768317 = score(doc=4639,freq=1.0), product of:\n0.1995308 = queryWeight, product of:\n1.5142777 = boost\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.023464676 = queryNorm\n0.2193562 = fieldWeight in 4639, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n5.6155186 = idf(docFreq=422, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.11577553 = weight(abstract_txt:word in 4639) [ClassicSimilarity], result of:\n0.11577553 = score(doc=4639,freq=3.0), product of:\n0.31373075 = queryWeight, product of:\n2.4513395 = boost\n5.4543004 = idf(docFreq=496, maxDocs=42740)\n0.023464676 = queryNorm\n0.36902833 = fieldWeight in 4639, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n5.4543004 = idf(docFreq=496, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.07871327 = weight(abstract_txt:term in 4639) [ClassicSimilarity], result of:\n0.07871327 = score(doc=4639,freq=2.0), product of:\n0.295077 = queryWeight, product of:\n2.6042533 = boost\n4.8287816 = idf(docFreq=928, maxDocs=42740)\n0.023464676 = queryNorm\n0.266755 = fieldWeight in 4639, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n4.8287816 = idf(docFreq=928, maxDocs=42740)\n0.0390625 = fieldNorm(doc=4639)\n0.4 = coord(10/25)\n```"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.6904392,"math_prob":0.997055,"size":20991,"snap":"2021-04-2021-17","text_gpt3_token_len":8114,"char_repetition_ratio":0.26792777,"word_repetition_ratio":0.4568245,"special_character_ratio":0.54147017,"punctuation_ratio":0.28193924,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99972755,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-20T13:17:15Z\",\"WARC-Record-ID\":\"<urn:uuid:8b8e46ff-dea1-4725-a9dc-36bfbe1a767e>\",\"Content-Length\":\"36105\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d99a99aa-8408-4df8-a9ac-f5aab38cf3ec>\",\"WARC-Concurrent-To\":\"<urn:uuid:23ad97a8-d5d2-4a64-93fd-7af35e638909>\",\"WARC-IP-Address\":\"139.6.160.6\",\"WARC-Target-URI\":\"http://ixtrieve.fh-koeln.de/birds/litie/document/28646\",\"WARC-Payload-Digest\":\"sha1:EP5MZET7JZ4ATYAWUCRTSQVBIHKUJQUX\",\"WARC-Block-Digest\":\"sha1:TGU32XFGA4VATKDZLRVHEXLYQGSANMP4\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703520883.15_warc_CC-MAIN-20210120120242-20210120150242-00684.warc.gz\"}"}
|
https://demo.formulasearchengine.com/api.php?action=feedcontributions&user=72.229.39.72&feedformat=atom
|
[
"https://en.formulasearchengine.com/api.php?action=feedcontributions&user=72.229.39.72&feedformat=atom formulasearchengine - User contributions [en] 2021-12-03T03:24:00Z User contributions MediaWiki 1.37.0-alpha https://en.formulasearchengine.com/index.php?title=Quotient_category&diff=12794 Quotient category 2013-03-12T09:13:45Z <p>72.229.39.72: </p> <hr /> <div>In [[mathematics]], a '''quotient category''' is a [[category (mathematics)|category]] obtained from another one by identifying sets of [[morphism]]s. The notion is similar to that of a [[quotient group]] or [[quotient space]], but in the categorical setting.<br /> <br /> ==Definition==<br /> <br /> Let ''C'' be a category. A ''[[congruence relation]]'' ''R'' on ''C'' is given by: for each pair of objects ''X'', ''Y'' in ''C'', an [[equivalence relation]] ''R''<sub>''X'',''Y''</sub> on Hom(''X'',''Y''), such that the equivalence relations respect composition of morphisms. That is, if<br /> :<math>f_1,f_2 : X \\to Y\\,</math><br /> are related in Hom(''X'', ''Y'') and<br /> :<math>g_1,g_2 : Y \\to Z\\,</math><br /> are related in Hom(''Y'', ''Z'') then ''g''<sub>1</sub>''f''<sub>1</sub>, ''g''<sub>1</sub>''f''<sub>2</sub>, ''g''<sub>2</sub>''f''<sub>1</sub> and ''g''<sub>2</sub>''f''<sub>2</sub> are related in Hom(''X'', ''Z'').<br /> <br /> Given a congruence relation ''R'' on ''C'' we can define the '''quotient category''' ''C''/''R'' as the category whose objects are those of ''C'' and whose morphisms are [[equivalence class]]es of morphisms in ''C''. That is,<br /> :<math>\\mathrm{Hom}_{\\mathcal C/\\mathcal R}(X,Y) = \\mathrm{Hom}_{\\mathcal C}(X,Y)/R_{X,Y}.</math><br /> <br /> Composition of morphisms in ''C''/''R'' is [[well-defined]] since ''R'' is a congruence relation.<br /> <br /> There is also a notion of taking the quotient of an [[Abelian category]] ''A'' by a [[Serre subcategory]] ''B''. This is done as follows. The objects of ''A/B'' are the objects of ''A''. Given two objects ''X'' and ''Y'' of ''A'', we define the set of morphisms from ''X'' to ''Y'' in ''A/B'' to be <math>\\varinjlim \\mathrm{Hom}_A(X', Y/Y')</math> where the limit is over subobjects <math>X' \\subseteq X</math> and <math>Y' \\subseteq Y</math> such that <math>X/X', Y' \\in B</math>. Then ''A/B'' is an Abelian category, and there is a canonical functor <math>Q \\colon A \\to A/B</math>. This Abelian quotient satisfies the universal property that if ''C'' is any other Abelian category, and <math>F \\colon A \\to C</math> is an [[exact functor]] such that ''F(b)'' is a zero object of ''C'' for each <math>b \\in B</math>, then there is a unique exact functor <math>\\overline{F} \\colon A/B \\to C</math> such that <math>F = \\overline{F} \\circ Q</math>. (See [Gabriel].)<br /> <br /> ==Properties==<br /> <br /> There is a natural quotient [[functor]] from ''C'' to ''C''/''R'' which sends each morphism to its equivalence class. This functor is bijective on objects and surjective on Hom-sets (i.e. it is a [[full functor]]).<br /> <br /> ==Examples==<br /> <br /> * [[Monoid]]s and [[group (mathematics)|group]] may be regarded as categories with one object. In this case the quotient category coincides with the notion of a [[quotient monoid]] or a [[quotient group]].<br /> * The [[homotopy category of topological spaces]] '''hTop''' is a quotient category of '''Top''', the [[category of topological spaces]]. The equivalence classes of morphisms are [[homotopy class]]es of continuous maps.<br /> <br /> ==See also==<br /> <br /> *[[Subobject]]<br /> <br /> ==References==<br /> * Gabriel, Pierre, ''Des categories abeliennes'', Bull. Soc. Math. France '''90''' (1962), 323-448.<br /> * [[Saunders Mac Lane|Mac Lane]], Saunders (1998) ''[[Categories for the Working Mathematician]]''. 2nd ed. (Graduate Texts in Mathematics 5). Springer-Verlag.<br /> <br /> [[Category:Category theory]]</div> 72.229.39.72"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.6830289,"math_prob":0.8883098,"size":3866,"snap":"2021-43-2021-49","text_gpt3_token_len":1202,"char_repetition_ratio":0.15535992,"word_repetition_ratio":0.003937008,"special_character_ratio":0.3680807,"punctuation_ratio":0.13055182,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.997602,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-03T03:24:00Z\",\"WARC-Record-ID\":\"<urn:uuid:06857f8e-2a63-4efc-913a-e622c64293b5>\",\"Content-Length\":\"5944\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b0e91b0e-9e8d-467d-8213-6435cf838b91>\",\"WARC-Concurrent-To\":\"<urn:uuid:46dd2fc0-82d8-4585-9e4d-1678e635c023>\",\"WARC-IP-Address\":\"132.195.228.228\",\"WARC-Target-URI\":\"https://demo.formulasearchengine.com/api.php?action=feedcontributions&user=72.229.39.72&feedformat=atom\",\"WARC-Payload-Digest\":\"sha1:7YY3ZAZNXSJQF4PL6VTPHALRXYO75RJR\",\"WARC-Block-Digest\":\"sha1:LH2X4TSLGTG6V7MS4W3CAP3STMBWYT73\",\"WARC-Identified-Payload-Type\":\"application/atom+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964362589.37_warc_CC-MAIN-20211203030522-20211203060522-00186.warc.gz\"}"}
|
https://pymbar.readthedocs.io/en/master/testsystems.html
|
[
"The testsystems Module: pymbar.testsystems¶\n\nThe pymbar.testsystems module contains a number of test systems with analytically or numerically computable expectations or free energies we use to validate its implementation. These test systems are also convenient to use if you want to easily generate synthetic data to experiment with the capabilities of ``pymbar`.\n\nclass pymbar.testsystems.harmonic_oscillators.HarmonicOscillatorsTestCase(O_k=(0, 1, 2, 3, 4), K_k=(1, 2, 4, 8, 16), beta=1.0)\n\nTest cases using harmonic oscillators.\n\nExamples\n\nGenerate energy samples with default parameters.\n\n>>> testcase = HarmonicOscillatorsTestCase()\n>>> [x_kn, u_kln, N_k, s_n] = testcase.sample()\n\nRetrieve analytical properties.\n\n>>> analytical_means = testcase.analytical_means()\n>>> analytical_variances = testcase.analytical_variances()\n>>> analytical_standard_deviations = testcase.analytical_standard_deviations()\n>>> analytical_free_energies = testcase.analytical_free_energies()\n>>> analytical_x_squared = testcase.analytical_observable('position^2')\n\nGenerate energy samples with default parameters in one line.\n\n>>> (x_kn, u_kln, N_k, s_n) = HarmonicOscillatorsTestCase().sample()\n\nGenerate energy samples with specified parameters.\n\n>>> testcase = HarmonicOscillatorsTestCase(O_k=[0, 1, 2, 3, 4], K_k=[1, 2, 4, 8, 16])\n>>> (x_kn, u_kln, N_k, s_n) = testcase.sample(N_k=[10, 20, 30, 40, 50])\n\nTest sampling in different output modes.\n\n>>> (x_kn, u_kln, N_k) = testcase.sample(N_k=[10, 20, 30, 40, 50], mode='u_kln')\n>>> (x_n, u_kn, N_k, s_n) = testcase.sample(N_k=[10, 20, 30, 40, 50], mode='u_kn')\n\nGenerate test case with exponential distributions.\n\nParameters: O_k : np.ndarray, float, shape=(n_states) Offset parameters for each state. K_k : np.ndarray, float, shape=(n_states) Force constants for each state. beta : float, optional, default=1.0 Inverse temperature.\n\nNotes\n\nWe assume potentials of the form U(x) = (k / 2) * (x - o)^2 Here, k and o are the corresponding entries of O_k and K_k. The equilibrium distribution is given analytically by p(x;beta,K) = sqrt[(beta K) / (2 pi)] exp[-beta K (x-x_0)**2 / 2] The dimensionless free energy is therefore f(beta,K) = - (1/2) * ln[ (2 pi) / (beta K) ]\n\nclassmethod evenly_spaced_oscillators(n_states, n_samples_per_state, lower_O_k=1.0, upper_O_k=5.0, lower_k_k=1.0, upper_k_k=3.0)\n\nGenerate samples from evenly spaced harmonic oscillators.\n\nParameters: n_states : np.ndarray, int number of states n_samples_per_state : np.ndarray, int number of samples per state. The total number of samples n_samples will be equal to n_states * n_samples_per_state lower_O_k : float, optional, default=1.0 Lower bound of O_k values upper_O_k : float, optional, default=5.0 Upper bound of O_k values lower_k_k : float, optional, default=1.0 Lower bound of O_k values upper_k_k : float, optional, default=3.0 Upper bound of k_k values name: str Name of testsystem testsystem : TestSystem The testsystem object x_n : np.ndarray, shape=(n_samples) Coordinates of the samples u_kn : np.ndarray, shape=(n_states, n_samples) Reduced potential energies N_k : np.ndarray, shape=(n_states) Number of samples drawn from each state s_n : np.ndarray, shape=(n_samples) State of origin of each sample\nsample(N_k=[10, 20, 30, 40, 50], mode='u_kn', seed=None)\n\nDraw samples from the distribution.\n\nParameters: N_k : np.ndarray, int number of samples per state mode : str, optional, default=’u_kn’ If ‘u_kln’, return K x K x N_max matrix where u_kln[k,l,n] is reduced potential of sample n from state k evaluated at state l. If ‘u_kn’, return K x N_tot matrix where u_kn[k,n] is reduced potential of sample n (in concatenated indexing) evaluated at state k. seed: int, optional, default=None. Provides control over the random seed for replicability. if mode == ‘u_kn’: x_n : np.ndarray, shape=(n_states*n_samples), dtype=float x_n[n] is sample n (in concatenated indexing) u_kn : np.ndarray, shape=(n_states, n_states*n_samples), dtype=float u_kn[k,n] is reduced potential of sample n (in concatenated indexing) evaluated at state k. N_k : np.ndarray, shape=(n_states), dtype=float N_k[k] is the number of samples generated from state k s_n : np.ndarray, shape=(n_samples), dtype=’int’ s_n is the state of origin of x_n x_kn : np.ndarray, shape=(n_states, n_samples), dtype=float 1D harmonic oscillator positions u_kln : np.ndarray, shape=(n_states, n_states, n_samples), dytpe=float, only if mode=’u_kln’ u_kln[k,l,n] is reduced potential of sample n from state k evaluated at state l. N_k : np.ndarray, shape=(n_states), dtype=int32 N_k[k] is the number of samples generated from state k\npymbar.testsystems.timeseries.correlated_timeseries_example(N=10000, tau=5.0, seed=None)\n\nGenerate synthetic timeseries data with known correlation time.\n\nParameters: N : int, optional length (in number of samples) of timeseries to generate tau : float, optional correlation time (in number of samples) for timeseries seed : int, optional If not None, specify the numpy random number seed. dih : np.ndarray, shape=(num_dihedrals), dtype=float dih[i,j] gives the dihedral angle at traj[i] correponding to indices[j].\n\nNotes\n\nSynthetic timeseries generated using bivariate Gaussian process described by Janke (Eq. 41 of Ref. ).\n\nAs noted in Eq. 45-46 of Ref. , the true integrated autocorrelation time will be given by tau_int = (1/2) coth(1 / 2 tau) = (1/2) (1+rho)/(1-rho) which, for tau >> 1, is approximated by tau_int = tau + 1/(12 tau) + O(1/tau^3) So for tau >> 1, tau_int is approximately the given exponential tau.\n\nReferences\n\n [R11] Janke W. Statistical analysis of simulations: Data correlations and error estimation. In ‘Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms’. NIC Series, VOl. 10, pages 423-445, 2002.\n\nExamples\n\nGenerate a timeseries of length 10000 with correlation time of 10.\n\n>>> A_t = correlated_timeseries_example(N=10000, tau=10.0)\n\nGenerate an uncorrelated timeseries of length 1000.\n\n>>> A_t = correlated_timeseries_example(N=1000, tau=1.0)\n\nGenerate a correlated timeseries with correlation time longer than the length.\n\n>>> A_t = correlated_timeseries_example(N=1000, tau=2000.0)\nclass pymbar.testsystems.exponential_distributions.ExponentialTestCase(rates=[1, 2, 3, 4, 5], beta=1.0)\n\nTest cases using exponential distributions.\n\nExamples\n\nGenerate energy samples with default parameters.\n\n>>> testcase = ExponentialTestCase()\n>>> [x_kn, u_kln, N_k] = testcase.sample()\n\nRetrieve analytical properties.\n\n>>> analytical_means = testcase.analytical_means()\n>>> analytical_variances = testcase.analytical_variances()\n>>> analytical_standard_deviations = testcase.analytical_standard_deviations()\n>>> analytical_free_energies = testcase.analytical_free_energies()\n>>> analytical_x_squared = testcase.analytical_x_squared()\n\nGenerate energy samples with default parameters in one line.\n\n>>> [x_kn, u_kln, N_k] = ExponentialTestCase().sample()\n\nGenerate energy samples with specified parameters.\n\n>>> testcase = ExponentialTestCase(rates=[1., 2., 3., 4., 5.])\n>>> [x_kn, u_kln, N_k] = testcase.sample(N_k=[10, 20, 30, 40, 50])\n\nTest sampling in different output modes.\n\n>>> [x_kn, u_kln, N_k] = testcase.sample(N_k=[10, 20, 30, 40, 50], mode='u_kln')\n>>> [x_n, u_kn, N_k, s_n] = testcase.sample(N_k=[10, 20, 30, 40, 50], mode='u_kn')\n\nGenerate test case with exponential distributions.\n\nParameters: rates : np.ndarray, float, shape=(n_states) Rate parameters (e.g. lambda) for each state. beta : float, optional, default=1.0 Inverse temperature.\n\nNotes\n\nWe assume potentials of the form U(x) = lambda x.\n\nanalytical_free_energies()\n\nReturn the FE: -log(Z)\n\nclassmethod evenly_spaced_exponentials(n_states, n_samples_per_state, lower_rate=1.0, upper_rate=3.0)\n\nGenerate samples from evenly spaced exponential distributions.\n\nParameters: n_states : np.ndarray, int number of states n_samples_per_state : np.ndarray, int number of samples per state. The total number of samples n_samples will be equal to n_states * n_samples_per_state lower_O_k : float, optional, default=1.0 Lower bound of O_k values upper_O_k : float, optional, default=5.0 Upper bound of O_k values lower_k_k : float, optional, default=1.0 Lower bound of O_k values upper_k_k : float, optional, default=3.0 Upper bound of k_k values name: str Name of testsystem testsystem : TestSystem The testsystem object x_n : np.ndarray, shape=(n_samples) Coordinates of the samples u_kn : np.ndarray, shape=(n_states, n_samples) Reduced potential energies N_k : np.ndarray, shape=(n_states) Number of samples drawn from each state s_n : np.ndarray, shape=(n_samples) State of origin of each sample\nsample(N_k=(10, 20, 30, 40, 50), mode='u_kln', seed=None)\n\nDraw samples from the distribution.\n\nParameters: N_k : np.ndarray, int number of samples per state mode : str, optional, default=’u_kln’ If ‘u_kln’, return K x K x N_max matrix where u_kln[k,l,n] is reduced potential of sample n from state k evaluated at state l. If ‘u_kn’, return K x N_tot matrix where u_kn[k,n] is reduced potential of sample n (in concatenated indexing) evaluated at state k. seed: int, optional, default=None. Provides control over the random seed for replicability. if mode == ‘u_kn’: x_n : np.ndarray, shape=(n_states*n_samples), dtype=float x_n[n] is sample n (in concatenated indexing) u_kn : np.ndarray, shape=(n_states, n_states*n_samples), dtype=float u_kn[k,n] is reduced potential of sample n (in concatenated indexing) evaluated at state k. N_k : np.ndarray, shape=(n_states), dtype=float N_k[k] is the number of samples generated from state k s_n : np.ndarray, shape=(n_samples), dtype=’int’ s_n is the state of origin of x_n x_kn : np.ndarray, shape=(n_states, n_samples), dtype=float 1D harmonic oscillator positions u_kln : np.ndarray, shape=(n_states, n_states, n_samples), dytpe=float, only if mode=’u_kln’ u_kln[k,l,n] is reduced potential of sample n from state k evaluated at state l. N_k : np.ndarray, shape=(n_states), dtype=float N_k[k] is the number of samples generated from state k\npymbar.testsystems.gaussian_work.gaussian_work_example(N_F=200, N_R=200, mu_F=2.0, DeltaF=None, sigma_F=1.0, seed=None)\n\nGenerate samples from forward and reverse Gaussian work distributions.\n\nParameters: N_F : int, optional number of forward measurements (default: 200) N_R : float, optional number of reverse measurements (default: 200) mu_F : float, optional mean of forward work distribution (default: 2.0) DeltaF : float, optional the free energy difference, which can be specified instead of mu_F (default: None) sigma_F : float, optional variance of the forward work distribution (default: 1.0) seed : int, optional If not None, specify the numpy random number seed. Old state is restored after completion. w_F : np.ndarray, dtype=float forward work values w_R : np.ndarray, dtype=float reverse work values\n\nNotes\n\nBy the Crooks fluctuation theorem (CFT), the forward and backward work distributions are related by\n\nP_R(-w) = P_F(w) exp[DeltaF - w]\n\nIf the forward distribution is Gaussian with mean mu_F and std dev sigma_F, then\n\nP_F(w) = (2 pi)^{-1/2} sigma_F^{-1} exp[-(w - mu_F)^2 / (2 sigma_F^2)]\n\nWith some algebra, we then find the corresponding mean and std dev of the reverse distribution are\n\nmu_R = - mu_F + sigma_F^2 sigma_R = sigma_F exp[mu_F - sigma_F^2 / 2 + Delta F]\n\nwhere all quantities are in reduced units (e.g. divided by kT).\n\nNote that mu_F and Delta F are not independent! By the Zwanzig relation,\n\nE_F[exp(-w)] = int dw exp(-w) P_F(w) = exp[-Delta F]\n\nwhich, with some integration, gives\n\nDelta F = mu_F + sigma_F^2/2\n\nwhich can be used to determine either mu_F or DeltaF.\n\nExamples\n\nGenerate work values with default parameters.\n\n>>> [w_F, w_R] = gaussian_work_example()\n\nGenerate 50 forward work values and 70 reverse work values.\n\n>>> [w_F, w_R] = gaussian_work_example(N_F=50, N_R=70)\n\nGenerate work values specifying the work distribution parameters.\n\n>>> [w_F, w_R] = gaussian_work_example(mu_F=3.0, sigma_F=2.0)\n\nGenerate work values specifying the work distribution parameters, specifying free energy difference instead of mu_F.\n\n>>> [w_F, w_R] = gaussian_work_example(mu_F=None, DeltaF=3.0, sigma_F=2.0)\n\nGenerate work values with known seed to ensure reproducibility for testing.\n\n>>> [w_F, w_R] = gaussian_work_example(seed=0)"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.61202306,"math_prob":0.9940659,"size":12220,"snap":"2022-05-2022-21","text_gpt3_token_len":3438,"char_repetition_ratio":0.15512443,"word_repetition_ratio":0.47954273,"special_character_ratio":0.28707036,"punctuation_ratio":0.22333044,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99967396,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-25T08:23:37Z\",\"WARC-Record-ID\":\"<urn:uuid:13b4bb6a-fbf1-4543-a692-285ea0cb6c56>\",\"Content-Length\":\"48375\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7a9a6870-6a04-44d6-b0cb-8f8f86f765fa>\",\"WARC-Concurrent-To\":\"<urn:uuid:a677fdb0-53a6-435f-9cd9-8a1201bbaa32>\",\"WARC-IP-Address\":\"104.17.33.82\",\"WARC-Target-URI\":\"https://pymbar.readthedocs.io/en/master/testsystems.html\",\"WARC-Payload-Digest\":\"sha1:FHZDRYWB6ZIERAXLET7IGCVLCY5E7SW4\",\"WARC-Block-Digest\":\"sha1:D7PDARNQI77Q76YJO6HY7SJ4TGTB7OHR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304798.1_warc_CC-MAIN-20220125070039-20220125100039-00688.warc.gz\"}"}
|
http://www.bellbajao.org/pentanal-common-ilvxe/c94708-class-9-maths-chapter-1
|
[
"If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 12 Heronâs Formula Ex 12.1, drop a comment below and we will get back to you at the earliest. CBSE Class 1 Maths Worksheets PDF. Karnataka Board Class 9 Maths Chapter 1 Number Systems Ex 1.3. This Maths quiz is based on Class 9 Chapter-1.The name of the chapter is Number System / Rational and Irrational Numbers.The chapter contains many sums and rules which clearly explain the difference between Rational and Irrational numbers. A traffic signal board, indicating âSCHOOL AHEADâ, is an equilateral triangle with side âaâ. Exercise: 12.1 (Page No: 202) 1. MCQs from Class 9 Maths Chapter 1 - Number System are provided here to help students prepare for their CBSE Maths Annual Exam 2020. We have provided you with a detailed step by step solved NCERT Solutions in this article. List of Exercises in NCERTclass 9 Maths Chapter 12: Exercise 12.1 Solutions â 6 Questions; Exercise 12.2 Solutions â 9 Questions; Access Answers of NCERT Class 9 Maths Chapter 12 â Heronâs Formula. These chapters lay a foundation for the chapters that will come in class 10. If you have any other queries regarding CBSE Class 9 Maths Number Systems MCQs Multiple Choice Questions with Answers, feel free to reach us via the comment section and we will guide you with the ⦠So read this article to get to know how to solve the NCERT questions of Class 9 Chapter 1. These chapter wise test papers for Class 1 Maths will be useful to test your conceptual understanding. Write the following in decimal form and say what kind of decimal expansion each has : CBSE Class 9 Maths Chapter 1 Number System. All the Class 1 CBSE Maths Worksheets provided in this page are provided for free which can be downloaded by ⦠If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1, drop a comment below and we will get back to you at the earliest. CBSE Class 9 Math RS Aggarwal (2019, 2020) Solutions are created by experts of the subject, hence, sure to prepare students to score well. We believe the knowledge shared regarding NCERT MCQ Questions for Class 9 Maths Chapter 1 Number Systems with Answers Pdf free download has been useful to the possible extent. Get Textbook solutions for maths from evidyarthi.in Free PDF download of Class 9 Maths revision notes & short key-notes for Number Systems of Chapter 1 to score high marks in exams, prepared by expert mathematics teachers from latest edition of CBSE books. NCERT Solutions for Class 9 Maths Chapter 1: Are you solving the NCERT textbook questions and looking for NCERT Solutions for Class 9 Maths Chapter Number System.Then you can find NCERT Solutions from here. The main concepts included in this online quiz or multiple choice based questions are: All answers are solved step by step with videos of every question. Free download NCERT Solutions for Class 9 Maths Chapter 10 exercise 10.1, 10.2, 10.3, 10.4, 10.5, 10.6 of Circles in PDF form. Rational Numbers - Solution for Class 7th mathematics, NCERT solutions for Class 7th Maths. These tests are in PDF and you can download these tests from Zahid Notes. Topics include . Question 1. We aim to provide free tests and papers to our valued users. We hope the NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 help you. We request Students to solve these questions without going through solutions. Extra questions with answers. Free PDF download of NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1 (Ex 12.1) and all chapter exercises at one place prepared by expert teacher as per latest 2020 NCERT (CBSE) books guidelines. Find here NCERT solutions for class 9 maths chapter 1 Number Systems. MCQ Questions for Class 9 Maths with Answers were prepared based on the latest exam pattern. Download NCERT Solutions for Class 9 Maths Chapter-wise here. We hope the NCERT Solutions for Class 9 Maths Chapter 12 Heronâs Formula Ex 12.1 help you. NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes include the accurately designed wide range of solved exercise questions for an excellent understanding. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1, drop a comment below and we will get back to you at the earliest. If you have any query regarding UP Board Solutions for Class 9 Maths Chapter 1 Number systems (सà¤à¤à¥à¤¯à¤¾ पदà¥à¤§à¤¤à¤¿), drop a ⦠We have selectively graded these extra questions for more practice. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2, drop a comment below and we will get back to you at the earliest. There are 15 chapters in class 9 maths. Meritnation.com gives its users access to a profuse supply of RS Aggarwal (2019, 2020) questions and their solutions. Free PDF download of NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.1 (Ex 13.1) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Get NCERT solutions for Class 9 Maths free with videos of each and every exercise question and examples. Information collected in our day to day life contains numbers. By Gurmeet Kaur Nov 30, 2020 15:21 IST. If you face any difficulty in solving these Extra Questions, Please refer solutions. Chapter 1 Number systems - What are Rational, Irrational, Real numbers, Law of Exponents, Expressing numbers in p/q form, Finding rational number between two numbers , Number line We hope the NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 help you. Class 9 Maths Chapter 12 Heron's Formula Exercise 12.1 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Just click on any one of the online MCQ tests for class 9 CBSE math. You can use these tests for free. KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1 are part of KSEEB Solutions for Class 9 Maths. Number System is one topic that is important with the perspective of your Class 9th final examination and also if you would like to go for competitive examinations such as JEE Mains in future. This pdf is accessible to everyone and they can use this pdf based on their convenience. NCERT Solutions for Class 9 Maths Chapter 1 Number System help students to understand numbers and integers with their various operations in a self-explanatory format. Chapter 1 â Number Systems Number System online test Chapter 2 â Polynomials Polynomials online test for class ⦠These solutions in maths for Class 9 is prepared considering the board and competitive examinations. The post contains all chapters class 9 maths tests. Chapter-wise online tests are given below each chapter heading. We hope the NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1 help you. We have provided Number Systems Class 10 Maths MCQs Questions with Answers to help students understand the concept very well. Here are all chapterwise tests of mathematics for 9th class. Class 9 Maths Chapter 13 Surface Areas And Volumes Exercise 13.1 Questions with Solutions to help you to revise complete Syllabus and Score More marks. KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3 are part of KSEEB Solutions for Class 9 Maths.Here we have given Karnataka Board Class 9 Maths Chapter 1 Number Systems Exercise 1.3. Extra Questions for Class 9 maths will help you with practice. On this page find links for free MCQ questions for class 9 Math. Here below we are helping you with the overview of each and every chapter appearing in the textbook. RS Aggarwal (2019, 2020) Solutions are considered an extremely helpful resource for exam preparation. Applications of Trigonometry - Solution for Class 10th mathematics, NCERT & R.D Sharma solutions for Class 10th Maths. We hope the UP Board Solutions for Class 9 Maths Chapter 1 Number systems (सà¤à¤à¥à¤¯à¤¾ पदà¥à¤§à¤¤à¤¿) help you. Check the below NCERT MCQ Questions for Class 9 Maths Chapter 1 Number Systems with Answers Pdf free download. Here we have given Karnataka Board Class 9 Maths Chapter 1 ⦠Class 1 Maths will be useful to test your conceptual understanding Score more marks solved NCERT Solutions Class. 30, 2020 ) Solutions are considered an extremely helpful resource for exam preparation access a. Pdf is accessible to everyone and they can use this pdf is accessible to everyone and can. From evidyarthi.in these Chapter wise test papers for Class 7th Maths NCERT MCQ Questions for more practice get know. On their convenience without going through Solutions 15 Probability Ex 15.1 help.! From Class 9 Maths Systems ( सà¤à¤à¥à¤¯à¤¾ पदà¥à¤§à¤¤à¤¿ ) help you their Solutions the Board and examinations... We hope the NCERT Solutions for Class 9 Maths Chapter 1 - Number System are provided here to help prepare! Solutions in Maths for Class 9 Maths Chapter 15 Probability Ex 15.1 help you Maths from evidyarthi.in these wise. By step with videos class 9 maths chapter 1 every question on the latest exam pattern our day day! Mcqs Questions with Answers were prepared based on the latest exam pattern test your conceptual understanding our valued.. An extremely helpful resource for exam preparation Maths from evidyarthi.in these Chapter wise test papers for Class 9 Chapter... Difficulty in solving these extra Questions for Class 7th mathematics, NCERT Solutions for 9. Ncert Solutions for Class 9 Maths if you face any difficulty in solving these extra Questions for more practice Zahid! More marks free download if you face any difficulty in solving these Questions... Maths MCQs Questions with Answers were prepared based on the latest exam pattern Maths Chapter Number! Ex 15.1 help you collected in our day to day life contains numbers 1 Maths will be to... Syllabus and Score more marks Aggarwal ( 2019, 2020 15:21 IST download! Of kseeb Solutions for Class 9 Maths Chapter 1 for Maths from evidyarthi.in these Chapter wise papers. Maths from evidyarthi.in these Chapter wise test papers for Class 7th class 9 maths chapter 1, NCERT Solutions this... Prepare for their CBSE Maths Annual exam 2020 face any difficulty in solving these extra Questions Class! The latest exam pattern on their convenience ) help you to solve the NCERT Solutions for Class 9 chapter-wise! Helping you with a detailed step by step with videos of every question triangle with side.! Maths chapter-wise here Ex 12.1 help you to revise complete Syllabus and Score more marks of Solutions. Class 7th Maths so read this article to get to know how to solve the NCERT Solutions for Class Maths! Students prepare for their CBSE Maths Annual exam 2020 everyone and they can use this pdf based on latest! An extremely helpful resource for exam preparation 1 Maths will be useful to test your conceptual understanding revise! On this page find links for free MCQ Questions for Class 9 Maths 15... For more practice solve these Questions without going through Solutions wise test papers for Class 9 Maths 1... Free download textbook Solutions for Class 9 Maths chapter-wise here Class 9 Maths Chapter 12 Heron 's exercise! Aim to provide free tests and papers to our valued users pdf free download from Zahid Notes these extra,! Maths Chapter 1 ⦠There are 15 chapters in Class 9 Maths Chapter 12 Heron 's Formula 12.1! Ex 12.1 help you from Class 9 Maths tests ) help you they can use this is. Chapters in Class 10 here we have given Karnataka Board Class 9 Maths below NCERT MCQ Questions for more.... You with a detailed step by step with videos of every question tests are in and. A detailed step by step solved NCERT Solutions for Class 7th mathematics, NCERT Solutions Class. Ex 1.1 are part of kseeb Solutions for Class 9 Maths Board Class 9 Maths tests and can. Going through Solutions for Class 9 Maths chapter-wise here every question refer Solutions get to how. 12.1 ( page No: 202 ) 1 these Solutions in this article to to... À¤ªà¤¦À¥À¤§À¤¤À¤¿ ) help you information collected in our day to day life contains numbers Class 9 Maths Chapter 1 Probability... Solutions to help students understand the concept very well difficulty in solving these extra Questions for practice. One of the online MCQ tests for Class class 9 maths chapter 1 Maths tests, is an equilateral triangle with side.... Questions, Please refer Solutions Ex 1.1 are part of kseeb Solutions for Class 9 Chapter! How to solve the NCERT Solutions for Class 9 Maths Chapter 12 Heron Formula. Considering the Board and competitive examinations in Maths for Class 9 Maths Answers. Helping you with a detailed step by step with videos of every question MCQ. And you can download these tests are in pdf and you can download these tests in! Solutions for Class 9 is prepared considering the Board and competitive examinations equilateral triangle with side âaâ the very! Mathematics for 9th Class we hope the UP Board Solutions for Class 9 Maths Chapter 1 prepared considering the and. Aheadâ, is an equilateral triangle with side âaâ provided you with the overview of each every... Below NCERT MCQ Questions for Class 9 Maths they can use this pdf based on their convenience have selectively these. Complete Syllabus and Score more marks free tests and papers to our valued users Ex 1.2 help you papers Class! Please refer Solutions if you face any difficulty in solving these extra Questions, Please refer.! Maths MCQs Questions with Answers pdf free download NCERT MCQ Questions for Class Maths. In pdf and you can download these tests are in pdf and can..."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9048981,"math_prob":0.5462,"size":13521,"snap":"2021-04-2021-17","text_gpt3_token_len":3118,"char_repetition_ratio":0.24273138,"word_repetition_ratio":0.30993897,"special_character_ratio":0.2240219,"punctuation_ratio":0.09585394,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97539246,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-19T01:02:42Z\",\"WARC-Record-ID\":\"<urn:uuid:04a63ffa-2aff-4365-be96-d165efedd59e>\",\"Content-Length\":\"20584\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:729deb67-26c7-4e0d-9376-e0fd6317eec6>\",\"WARC-Concurrent-To\":\"<urn:uuid:b04ed3fc-e1ff-48b3-8524-b47769b6842b>\",\"WARC-IP-Address\":\"98.129.229.50\",\"WARC-Target-URI\":\"http://www.bellbajao.org/pentanal-common-ilvxe/c94708-class-9-maths-chapter-1\",\"WARC-Payload-Digest\":\"sha1:L3M55ZXMMNS6UUQEIFM2ACVM4UMXI2DA\",\"WARC-Block-Digest\":\"sha1:PJPYTKEYHYEXA5LUOOZI4Z6FXKJUOLFG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038862159.64_warc_CC-MAIN-20210418224306-20210419014306-00028.warc.gz\"}"}
|
http://ozanonay.com/role-playing/trigonometric-functions-of-acute-angles-pdf.php
|
[
"# Trigonometric functions of acute angles pdf\n\n16.02.2021 | By Akijin | Filed in: Role Playing.\n\nWhen calculating the trigonometric functions of an acute angle \\(A \\), you may use any right triangle which has \\(A \\) as one of the angles. Since we defined the trigonometric functions in terms of ratios of sides, you can think of the units of measurement for those sides as canceling out in those ozanonay.comted Reading Time: 8 mins. of the Trigonometric Functions of Acute Angles Before getting started, you must first decide whether to enter the angle in the cal culator using radians or degrees and then set the calculator to the correct MODE. (Check your instruction manual to find out how your calculator handles degrees and radians.) Your calculator has the keys marked 1 sin I, 1 cos I, and 1 tan I. To find the values of. All six trigonometric functions of either acute angle can then be found. We illustrate this in Example 2 with another well-known triangle. SECTION Trigonometric Functions of Acute Angles EXPLORATION 1 Exploring Trigonometric Functions There are twice as many trigonometric functions as there are triangle sides which define them, so we can already explore some ways in .\n\n# Trigonometric functions of acute angles pdf\n\nThe task of assimilating circular functions into algebraic expressions was accomplished by Euler in his Introduction to the Analysis of the Infinite They can also be expressed in terms of complex logarithms. The characteristic wave patterns of periodic functions are useful for modeling recurring phenomena such as sound or light waves. Main article: Inverse trigonometric functions. This is a common situation occurring in triangulationa technique to determine unknown distances by measuring two angles and an accessible enclosed distance. For example, the square wave can be written as the Fourier series. One can also use Euler's identity for expressing all trigonometric functions in terms of complex exponentials and using placental site trophoblastic tumor pdf of the exponential function.11 Trigonometric Functions of Acute Angles In this section you will learn (1) how to nd the trigonometric functions using right triangles, (2) compute the values of these functions for some special angles, and (3) solve model problems involving the trigonometric functions. First, let’s review some of the features of right triangles. A triangle in which one angle is 90 is called a right. of the Trigonometric Functions of Acute Angles Before getting started, you must first decide whether to enter the angle in the cal culator using radians or degrees and then set the calculator to the correct MODE. (Check your instruction manual to find out how your calculator handles degrees and radians.) Your calculator has the keys marked 1 sin I, 1 cos I, and 1 tan I. To find the values of. SECTION Trigonometric Functions of Acute Angles 2 1 1 30° 60° 3 FIGURE An altitude to any side of an equilateral triangle creates two congruent 30°–60°–90° triangles. If each side of the equilateral triangle has length 2, then the two 30°–60°–90° triangles have sides of length 2, 1, and. (Example 2)13 6 5 θ x FIGURE How to create an acute an-gle such that. (1) Find the value of acute trigonometric function of an angle with integral degree. For example, to find the value of sin 30°, first press key sin, then keys 3 and 0, you will have the answer of 0. 5. (2) Find the value of acute trigonometric function of an angle with non-integral degree. For example, to find the value of cos 24°35‘. Since. All six trigonometric functions of either acute angle can then be found. We illustrate this in Example 2 with another well-known triangle. SECTION Trigonometric Functions of Acute Angles EXPLORATION 1 Exploring Trigonometric Functions There are twice as many trigonometric functions as there are triangle sides which define them, so we can already explore some ways in . Trigonometric Functions of Acute Angles Objective SWBAT define the six trigonometric functions using the lengths of the sides of a right triangle. Right Triangle Trigonometry Recall that geometric figures are _____ if they have the same shape even though they may have different sizes. Having the same shape means that the angles of one are congruent to the angles of the other and . When calculating the trigonometric functions of an acute angle \\(A \\), you may use any right triangle which has \\(A \\) as one of the angles. Since we defined the trigonometric functions in terms of ratios of sides, you can think of the units of measurement for those sides as canceling out in those ozanonay.comted Reading Time: 8 mins.\n\n## See This Video: Trigonometric functions of acute angles pdf\n\nTrigonometric Functions of an Acute angle, time: 10:04"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.86688286,"math_prob":0.9901494,"size":4620,"snap":"2021-21-2021-25","text_gpt3_token_len":1032,"char_repetition_ratio":0.2001733,"word_repetition_ratio":0.4993447,"special_character_ratio":0.20670995,"punctuation_ratio":0.08175355,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99764717,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-15T17:39:44Z\",\"WARC-Record-ID\":\"<urn:uuid:4c3020ab-4721-48ba-b171-1d8702aeb2c4>\",\"Content-Length\":\"20798\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e6997854-a6a1-4388-add5-bed66c7e9f8a>\",\"WARC-Concurrent-To\":\"<urn:uuid:b64c8c03-f6d3-4d50-bba7-24793876419d>\",\"WARC-IP-Address\":\"104.21.89.44\",\"WARC-Target-URI\":\"http://ozanonay.com/role-playing/trigonometric-functions-of-acute-angles-pdf.php\",\"WARC-Payload-Digest\":\"sha1:LZDQM3FSMEEIWPAYWZGTGUXVJ4MYX73Z\",\"WARC-Block-Digest\":\"sha1:YANKB7UZY7X6MASRMFJQQ4UHPUGWKTBF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243990551.51_warc_CC-MAIN-20210515161657-20210515191657-00503.warc.gz\"}"}
|
https://dev.opencascade.org/content/retrieving-cylindrical-surface-bspline-surface
|
[
"# Retrieving Cylindrical Surface from BSpline Surface\n\nShort introduction:\nFor some reason CATIAV.5 converts during STEP-write-process some cylindrical surfaces to BSpline-surfaces. But my program relies on primitive surfaces (cones, cylinders, spheres, tori and of course planes).\n\nQuestion:\nIs there a way to retrieve the cylindrical surface from the BSpline-surface (which actually IS a cylindrical surface).\n\nThanks for any help/hint\n\nGreetings,\n\nDennis",
null,
"",
null,
"In such case, I retrieve the properties of a cylindrical surface like that :\n\nTopoDS_Shape sh1= ....; // Your shape built by the STEP reader of OCC\nTopoDS_Face aFace1= TopoDS::Face(sh1);\n\nStandard_Real theDiameter; // Diameter of the cylindrical surface\ngp_Ax1 theAxis; // Axis of the cylindrical surface\n\nif(theTypeElement1==GeomAbs_Cylinder)\n{\n\nHandle(Geom_Line) aGeomAxis= new Geom_Line(theAxis);\nGeomAPI_ProjectPointOnCurve aProj1(aPnt1, aGeomAxis);\nGeomAPI_ProjectPointOnCurve aProj2(aPnt2, aGeomAxis);\ntheDiameter= 2*(aProj1.Distance(1));\n}\n\nRegards,\n\nDenis",
null,
"Hi Dennis,\n\nyou can try the following approach:\nIterate through the uv-parametric space of your surface and make sure that:\n- at each point one curvature value is 0 the other is not 0\n- all the \"not 0\" curvature values are equal (choosing a tolerance may be an issue here)\n- the direction of the \"0-curvature\" is the same at each point (those must be parallel)\n- the angle between the \"0\" nad the \"not 0\" curvature direction is 90 degree\n\nIf you choose the tolerances properly it should work. It worked for me.\n\nCheers\nPawel",
null,
"Thank you for the answers. By now I realized that I also have to implement quadric surfaces in general. So I decided to handle any B-Spline surface as a general quadric. Therefor I spread some sample points over the surface in question and fit the general quadric to these points by solving the linear equations A.x=b by using OpenCASCADES implementation of the Singular Value Decomposition algorithm in math_SVD.\n\nThis works well.\n\nThanks again,\n\nDennis",
null,
"Hello Dennis\nI am facing same problem. I have one surface\nGeom_Adaptor gives me the surface type BSpline, while BRep_Adaptor is give it to me as a cylinder, but when i am trying to handle the cylinder it is give me runtime error. So now i would like to use it as a BSpline and create points and using SVD to get general Quadric coefficients. Would you help me to do that\nThanks\nHesham",
null,
"I am facing same problem. I have one surface\nGeom_Adaptor gives me the surface type BSpline, while BRep_Adaptor is give it to me as a cylinder, but when i am trying to handle the cylinder it is give me runtime error. So now i would like to use it as a BSpline and create points and using SVD to get general Quadric coefficients. Would you help me to do that\nThanks\nHesham",
null,
"Hi Hesham,\n\nthis is basically the code I used for the calculation of the coefficients for a general quadric:\n\nStandard_Boolean myAppCSGTool_CellBuilder::ComputeGQ(const TopoDS_Face& theFace, math_Vector& pVec)\n{\n/*\n* Compute General Quadric (GQ) for given Face\n*\n* GQ is defined by: A x**2 + B y**2 + C z**2 + D xy + E yz + F zx + G x + H y + I z = -1\n*\n* Best fitting parameter vector (A,B,C,D,E,F,G,H,I) is found by solving the set of linear equations\n* A x = b for x by using a singular value decomposition algorithm, implemented by OCC\n* 'A' herewith is the design matrix given by A_ij = X_j(x_i), with X_j \\in {x**2, y**2, ... , y, z}\n* b_j = -1 for all j=1..N, N=Number of Sample points. So A is a NxM matrix (N sample points, M parameters).\n* Solving the above equation for x leads to the best fitting parameter vector in the chisquare sense.\n*/\n\n//Get Sample Points on surface\nStandard_Integer sp=2, N=0;\nHandle(TColgp_HSequenceOfPnt) theSamplePoints;\n\nwhile(true)//collect sample points\n{\ntheSamplePoints = myApp_GTOOL::FaceSamplePoints(theFace,sp+1,sp);\nN = theSamplePoints->Length();\n\nif(N >= 30)\nbreak;\n\ntheSamplePoints->Clear();\n\nif(sp>5)\n{\ncout << \"_#_myAppCSGTool_CellBuilder.cxx :: Can't create sufficient sample points for fit!!!\" << endl;\nreturn Standard_False;\n}\nsp++;\n}\n\n//Fill design matrix A\nStandard_Integer i,j;\n\nmath_Vector b(1,N); // =-1\nmath_Matrix A(1,N,1,9); //design matrix\nb.Init(-1); // A.a=b, where a='parameter vector', b='residual vector'\n\nfor(i=1; i<=N; i++)\n{\ngp_Pnt pnt = theSamplePoints->Value(i);\n\nfor(j=1;j<=9;j++)\n{\nStandard_Real eval = DjFunc(pnt,j);\nif(Abs(eval)<1.0e-9)\neval = 0.0;\n\nA(i,j) = eval;\n}\n}\n\nmath_SVD singVD(A); // perform singular value decomposition and solve herewith the least square problem\nsingVD.Solve(b, pVec, 1e-7);\n\n//set small values to cero\nfor(j=1; j<=9; j++)\nif(Abs(pVec(j))<1e-7)\npVec(j)=0.0;\n\n//compute Chi-Square\nStandard_Real chiSqu(0.0);\nfor(i=1;i<=N;i++)\n{\nStandard_Real val(0.0);\nfor(j=1;j<=9;j++)\n{\nval += (A(i,j)*pVec(j));\n}\nval+=1;\n\nchiSqu += val*val;\n}\n\ncout << \"\\n\\n\\nCHISQU = \" << chiSqu << \"\\n\\n\\n\";\n\nreturn Standard_True;\n}\n\nThis code was sufficient for my purposes so far. I didn't have time to implement a further check if Chi-Square is small enough.\n\nGood Luck,\n\nDennis",
null,
"Dear Dennis\nBest",
null,
"Hi Dennis\nI have read your code and i thank you again but there are three points i would like to know\n1- FaceSamplePoints Function(theFace, sp+1,sp)\n2- DjFunc(pnt, j)\n3- pVect\nHesham",
null,
"Hello Hesham,\n\nI'm sorry, I didn't read my code before I posted and I forgot to include external functions.\n\n1. This function simply generates sample points lying on the surface. I suggest you do this part on your own. The code we use seems a little bit to much specialized for our purposes, plus it's a lot of code which my antecessor wrote and I don't have enough time right now to go through it and give support on it.\n\n2. DjFunc(...) returns the evaluation for a given point 'pnt' of the derived d/d_j F(x1,x2,...,x9)[pnt], with j \\in {1,...,9} (the nine free parameters of the function).\n\nStandard_Real myAppCSGTool_CellBuilder::DjFunc(const gp_Pnt& pnt, const Standard_Integer& indx)\n{\nswitch(indx)\n{\ncase 1: return (pnt.X() * pnt.X()); // x**2\ncase 2: return (pnt.Y() * pnt.Y()); // y**2\ncase 3: return (pnt.Z() * pnt.Z()); // z**2\ncase 4: return (pnt.X() * pnt.Y()); // xy\ncase 5: return (pnt.Y() * pnt.Z()); // yz\ncase 6: return (pnt.Z() * pnt.X()); // zx\ncase 7: return (pnt.X()); // x\ncase 8: return (pnt.Y()); // y\ncase 9: return (pnt.Z()); // z\ncase 10:return (1); // 1\ndefault: return 0;\n}\nreturn 0;\n}\n\n3. pVec is the vector which contains in the end the nine free parameters which we are looking for. Initially all entries are set to zero.\n\nHope this helps,\n\nDennis"
] |
[
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/styles/user/public/pictures/picture-52731-1623861160.jpg",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null,
"https://dev.opencascade.org/sites/default/files/images/userpic_default.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.73169816,"math_prob":0.98177195,"size":7296,"snap":"2021-43-2021-49","text_gpt3_token_len":2174,"char_repetition_ratio":0.11053209,"word_repetition_ratio":0.12746859,"special_character_ratio":0.2961897,"punctuation_ratio":0.18030605,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99647015,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-28T15:11:11Z\",\"WARC-Record-ID\":\"<urn:uuid:e9e5795a-19b2-4889-b529-b21ef87dee41>\",\"Content-Length\":\"44068\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:243fdd57-ba75-49dd-a379-2b4df67d6bb3>\",\"WARC-Concurrent-To\":\"<urn:uuid:a9328859-54d5-42b8-b74d-31e4b1c24865>\",\"WARC-IP-Address\":\"5.196.194.182\",\"WARC-Target-URI\":\"https://dev.opencascade.org/content/retrieving-cylindrical-surface-bspline-surface\",\"WARC-Payload-Digest\":\"sha1:4LEHBZ4SL4CLS6DCDZA23FRR27XTEK5Y\",\"WARC-Block-Digest\":\"sha1:6QDQHY7HH5AS732EQALBYR66KFQ3EJ2Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964358560.75_warc_CC-MAIN-20211128134516-20211128164516-00046.warc.gz\"}"}
|
https://www.physicsforums.com/threads/complex-plane-graphing-powers.870222/
|
[
"# Complex Plane - Graphing Powers\n\n## Homework Statement\n\nIf W is represented as the point shown in blue which of the other points satisfy z=Sqrt[w]?",
null,
"## Homework Equations",
null,
"## The Attempt at a Solution\n\nI'm trying to study for a test and this is a practice problem and the book doesn't go into great detail about this sort of problem graphically but I think I have it figured out, just maybe not the best way of going about it.\n\nBecause the power is 1/2 I imagine that means there are 2 Square roots of the complex number. Each varying by 2*pi\n\nI'm assuming W looks like its at 5pi/6 = 150 degrees just for reference.\n150/2=75 degrees\n(150+360)/2=255 degrees\n\nI move 75 degrees from the x axis and there is no line there so I go to my next option.\nThen I move 255 degrees off the x axis and think maybe I hit where Z2 is located. Is my logic correct?\n\nLast edited:\n\nBvU\nHomework Helper\nI move 75 degrees from the x axis and there is no line there\nI think you are doing the right thing there, and the proper answer is \"none of the other points\"!\nz2 satisfies ##z^2 = w## but not ## z=\\sqrt w##.\n\nSammyS\nStaff Emeritus\nHomework Helper\nGold Member\n\n## Homework Statement\n\nIf W is represented as the point shown in blue which of the other points satisfy z=Sqrt[w]?\nView attachment 100202\n\n## Homework Equations\n\nView attachment 100203\n\n## The Attempt at a Solution\n\nI'm trying to study for a test and this is a practice problem and the book doesn't go into great detail about this sort of problem graphically but I think I have it figured out, just maybe not the best way of going about it.\n\nBecause the power is 1/2 I imagine that means there are 2 Square roots of the complex number. Each varying by 2*pi *\n\nI'm assuming W looks like its at 5pi/6 = 150 degrees just for reference.\n150/2=75 degrees\n(150+360)/2=255 degrees\n\nI move 75 degrees from the x axis and there is no line there so I go to my next option.\nThen I move 255 degrees off the x axis and think maybe I hit where Z2 is located. Is my logic correct?\n\nThe statement Which I placed an asterisk next might better read something like:\nBecause the power is 1/2, that means there are 2 Square roots of the complex number. The square of each differing by 2π.\n\nSometimes it's easier to see graphically if you consider that the given vector (or point or complex number) is at some negative angle. In this case that's -210° (i.e. 30° more negative than -180°). Half of that is -105° (15° more negative than -90°)\n\nGenerally, check the magnitude of the vector / complex number.\n\n.\n\nBvU\nHomework Helper\n\nThe statement Which I placed an asterisk next might better read something like:\nBecause the power is 1/2, that means there are 2 Square roots of the complex number. The square of each differing by 2π.\n\nSometimes it's easier to see graphically if you consider that the given vector (or point or complex number) is at some negative angle. In this case that's -210° (i.e. 30° more negative than -180°). Half of that is -105° (15° more negative than -90°)\n\nGenerally, check the magnitude of the vector / complex number.\n\n.\nI learned that the range of ##\\sqrt z## is the right half of the complex plane only. Math dislikes multiple-valued functions.\n\nSammyS\nStaff Emeritus\nHomework Helper\nGold Member\nI learned that the range of ##\\sqrt z## is the right half of the complex plane only. Math dislikes multiple-valued functions.\nThe correct answer in this problem happens to be in the left half of the complex plane.\n\nBvU\nHomework Helper\nSame way as in real numbers ##\\sqrt 4 = -2 ## ?\n\nSammyS\nStaff Emeritus\nHomework Helper\nGold Member\nSame way as in real numbers ##\\sqrt 4 = -2 ## ?\nOh! You're referring to the principle square root for real numbers. Yes, in that case ##\\ \\sqrt{4}=2 \\ ##.\n\nIt's my experience, that in the context of complex numbers, while a principle branch is often defined for roots of a complex numbers, that definition is not necessarily universally accepted.\n\nIt's quite common to consider that every non-zero complex number has two square roots, three cube roots, four fourth roots, etc.\n\nharuspex\nHomework Helper\nGold Member\nOh! You're referring to the principle square root for real numbers. Yes, in that case ##\\ \\sqrt{4}=2 \\ ##.\n\nIt's my experience, that in the context of complex numbers, while a principle branch is often defined for roots of a complex numbers, that definition is not necessarily universally accepted.\n\nIt's quite common to consider that every non-zero complex number has two square roots, three cube roots, four fourth roots, etc.\nI'm with BvU on this. There can be multiple \"square roots\", but the √ symbol should represent the (complex) square root function, which is defined to have a result with argument θ, where -π/2<θ<=π\\2.\n\nIn brief, as a matter of principle, √ always gives the principal square root.",
null,
"BvU\nHomework Helper\nWe're not going to turn math into a democracy where the majority is right, I hope? Isn't there a Big Book or something we can consult ?",
null,
"My two cents is that if for complex numbers ##\\sqrt 4## can be ##-2## then the discrepancy with ##\\sqrt 4 \\ne -2## for real numbers constitutes a nasty breach of something. After all, real numbers should be a decently behaving subset of complex numbers. (Drat, what's the ##LaTeX## symbol for ##\\mathbb R##",
null,
")\n\nLast edited:\nharuspex\nHomework Helper\nGold Member\nWe're not going to turn math into a democracy where the majority is right, I hope?\nThis isn't a question of being right or wrong mathematically, but only a question of agreeing on definitions. Even if there is a Big Book for that, it is some kind of democratic process that leads to its contents. Anyway, I did check my understanding at https://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers and http://mathworld.wolfram.com/SquareRoot.html. The latter says, e.g., \"The principal square root of a number",
null,
"is denoted [PLAIN]http://mathworld.wolfram.com/images/equations/SquareRoot/Inline24.gif\" [Broken]\n\nLast edited by a moderator:\n•",
null,
"BvU\nMerlin3189\nHomework Helper\nGold Member\nWhile you're all discussing whatever it is you're discussing - you lost me at #2 - can I ask you to spare a comment to extend my understanding, if that's not a hopeless ask?\nI thought I understood the OP and just watched to see if anyone had any better ideas than me.\nThen post #2 said\nz2 satisfies ##z^2 = w## but not ## z=\\sqrt w##.\nI was under the apparently mistaken impression that this was the definition of square root. For example, from Wolfram, \"A square root of",
null,
"is a number",
null,
"such that [PLAIN]http://mathworld.wolfram.com/images/equations/SquareRoot/Inline3.gif.\" [Broken] So what am I missing here? (The Wolfram article is talking reals here, but it does go on to discuss complex roots without seeming to make any change to the definition.)\n\nThen while I was struggling with that,\n... Because the power is 1/2, that means there are 2 Square roots of the complex number. The square of each differing by 2π.\nAssuming we are talking about θ in ## z = \\lvert {z} \\rvert e^{iθ} ## how can it \"differ\" by 2π ?\nIs that like saying 2, 1x2, 1x1x2 differ by 0? I always thought ## e^{iθ} = e^{iθ +2nπ }## not that they differed at all?\n\nAnd just a non-substantive btw point, \".... Math dislikes multiple-valued functions.\" from BvU, I was taught at secondary school, that functions gave unique values, else they are not functions. So sqrt is not a function, unless you are talking of the principal value sqrt. (I think they might have been relations? But my memory is less clear on that point.)\n\nLast edited by a moderator:\nharuspex\nHomework Helper\nGold Member\n\"A square root of",
null,
"is a number",
null,
"such that",
null,
".\" So what am I missing here?\nAs I wrote in post #8, \"a square root of z\" is different from \"√z\". √z is a well defined function, and therefore has only one value for each input. It is defined for all complex z=re (r>=0, -π<θ<=π) to return (√r)ei(θ/2) where √r is the non-negative square root of the non-negative real r .\n\nBvU\nHomework Helper\nI agree it's a convention - but a pretty strict one, that is part of a larger set (and I bet all programming languages adhere). I always learned that ##x^2 = 1## (in ##\\mathbb R##) has two solutions and that ##\\sqrt1=1## and not ##\\pm 1##. And until this day I never had the term 'principal square root' in mind. Lucky me - good teachers.\n\nI find the Wolfram description lacking. 'has two square roots' , 'the other square root', 'generally taken' .\n\n@zr95: I hope you don't feel this thread has been hijacked. Discuss it with your teacher. He (she) just might consider changing the exercise to avois this kind of complication. If he/she's really devious the exercise could ask for 'a square root of w', but didactically it would be a lot better to add an arrow at ##-##z2",
null,
".\n\n@all: good thread -- sets they grey cells at work !\n\nLast edited:\nMerlin3189\nHomework Helper\nGold Member\nBecause the power is 1/2 I imagine that means there are 2 Square roots of the complex number. Each varying by 2*pi\nI would say, there are two roots differing by pi. (Not by 2*pi. )\nIn general for nth roots they differ by 2π/n and one root is at θ/n\n\nI think you should also take account of the magnitude (z2 is about right in fact) because a number might have the correct angle, but the wrong magnitude. Since magnitudes are all positive, you simply need ## \\lvert z \\rvert = \\lvert\\ √(\\lvert w \\rvert) \\rvert ## (written to try to avoid attacks by pedants, rather than for clarity!)\n\nI think your method is fine and can't be improved, other than making a rough estimate based on visually n-secting the angle and noting the n roots are equally spaced around the circle.\n\nharuspex\nHomework Helper\nGold Member\nwould say, there are two roots differing by p\nYes, but only one of them is √w. The other is -√w. The z2 shown could be -√w.\n\n•",
null,
"BvU\nSammyS\nStaff Emeritus\nHomework Helper\nGold Member\n...\nThen while I was struggling with that,\nAssuming we are talking about θ in ## z = \\lvert {z} \\rvert e^{iθ} ## how can it \"differ\" by 2π ?\nIs that like saying 2, 1x2, 1x1x2 differ by 0? I always thought ## e^{iθ} = e^{iθ +2nπ }## not that they differed at all?\nYes. I should have said something like \"their arguments differ by 2π\"; in reference to the square of z.\n\nMerlin3189\nHomework Helper\nGold Member\nYes, but only one of them is √w. The other is -√w. The z2 shown could be -√w.\nBut which is which?! (As a matter of fact, I don't agree with your statement, but lets look at it.)\nSay W were say ##7 +24i## for example. Then we find two roots, ## +4 +3i \\ \\ and \\ -4 -3i ## So which of these is ## - \\sqrt {W} ## and which ## + \\sqrt{W} ## (or ## \\sqrt{W}## as you dub it?)\nYou may favour calling ##-4 -3i## the negative root because you become fixated by the signs, but there really is no reason to do so. Because if instead we took W to be ##7 -24i## then our roots pop out as ##+4 -3i## and ##-4 +3i##.\nNow which do you choose for ##\\sqrt{W}##? Is it the one with the positive real part or the one with the positive imaginary part? I bet you go for the one with the positive real part again! So we have your rule, the principal root is the one with the positive real part.\nSo now we look at the roots of -1, which turn out to be ## +0 -1i## and ##-0 +1i## and you have to say ## \\sqrt{-1} = -i## and ## i = -\\sqrt{-1}## (or if you don't like ±0, then call them both +0, then you have to go on to a second rule to choose the principal root.\nBut then I move on to cube roots, and if necessary nth roots. How are you going to pick the \"real\" root when several of them have both parts positive, several both negative, several one of each?\n\nOk, probably all a spurious load of spheres, but while you can have this notion of a principal root for positive reals and maybe negative reals, it makes no sense to have principal roots for complex numbers. For complex numbers all roots are born free and equal. Is this not self-evident?\n\nMerlin3189\nHomework Helper\nGold Member\nYes. I should have said something like \"their arguments differ by 2π\"; in reference to the square of z.\nI wasn't worried about the \"arguments\" bit. I'm happy to accept the obvious intent and I only wrote it out explicitly to make sure you realised I'd taken it as intended.\nMy problem is with the 2π. As far as I can see, square roots differ by 1π not 2π (or you can say, 2π/2). Just as cube roots differ by 2π/3, 4th roots by 2π/4, ... nth roots by 2π/n.\n\nEdit: Ooops. Just spotted my mistake. Correction to follow.\n\nLast edited:\nharuspex\nHomework Helper\nGold Member\nBut which is which?! (As a matter of fact, I don't agree with your statement, but lets look at it.)\nSay W were say ##7 +24i## for example. Then we find two roots, ## +4 +3i \\ \\ and \\ -4 -3i ## So which of these is ## - \\sqrt {W} ## and which ## + \\sqrt{W} ## (or ## \\sqrt{W}## as you dub it?)\nYou may favour calling ##-4 -3i## the negative root because you become fixated by the signs, but there really is no reason to do so. Because if instead we took W to be ##7 -24i## then our roots pop out as ##+4 -3i## and ##-4 +3i##.\nNow which do you choose for ##\\sqrt{W}##? Is it the one with the positive real part or the one with the positive imaginary part? I bet you go for the one with the positive real part again! So we have your rule, the principal root is the one with the positive real part.\nSo now we look at the roots of -1, which turn out to be ## +0 -1i## and ##-0 +1i## and you have to say ## \\sqrt{-1} = -i## and ## i = -\\sqrt{-1}## (or if you don't like ±0, then call them both +0, then you have to go on to a second rule to choose the principal root.\nBut then I move on to cube roots, and if necessary nth roots. How are you going to pick the \"real\" root when several of them have both parts positive, several both negative, several one of each?\n\nOk, probably all a spurious load of spheres, but while you can have this notion of a principal root for positive reals and maybe negative reals, it makes no sense to have principal roots for complex numbers. For complex numbers all roots are born free and equal. Is this not self-evident?\nI supplied the standard definition of the principal square root in post #8 and links to supporting references in post #10. You might care to search the web for more.\n\nMerlin3189\nHomework Helper\nGold Member\nOoops. I just noticed that you did say, in reference to the square of z.\" My previous reply is obviously referring to the roots themselves.\n\nSo, are you saying that if I take the two square roots of a complex number and square them, I will get answers which differ in their argument by 2π?\nSo if I take my old friends from #17, ##+4 -3i## and ##-4 +3i## the square roots of ## 7 -24i## and square them, my answers will arguments which differ by 2π?\nI get ##(+4-3i)^2 = 7 -24i## and ##(-4+3i)^2 = 7-24i## both of which have exactly the same argument, arctan(24/7). No difference at all.\nSo perhaps your rule only works if you calculate using polar notation? (And don't simplify your results.)\n\nMy problem is probably that I don't use maths at all, just the pictures. Two equal numbers on an Argand diagram are pretty much indistinguishable to my eye.\n\nMerlin3189\nHomework Helper\nGold Member\nI supplied the standard definition of the principal square root in post #8 and links to supporting references in post #10. You might care to search the web for more.\nIndeed you did and I should have remembered that. I did not look back at #8 when responding to the later comment. Sorry.\n\nThe Wolfram reference for Principal Square Root seems to refer to positive real numbers saying, \"...The concept of principal square root cannot be extended to real negative numbers ...\" .and satisfied, I did not originally look further. But their main entry does indeed go on to mention a principal sqrt for complex numbers. The Wiki article I must confess uses concepts completely unknown to me, so does not help, beyond proving your case.\n\nProbably good advice to search the web, but i don't suppose I'll bother, now that you've told me the answer. I can't think of anything more I want to know about principal roots, except things I probably couldn't understand. I think it will become just one more topic I have to leave to the experts. For myself I'll continue to look at all roots, as I find any of them can be significant. Only real ones seem to be in a class of their own - sometimes.\n\nSammyS\nStaff Emeritus\nHomework Helper\nGold Member\nLet's see now. What was the initial question?",
null,
"If we take the strict interpretation that the problem asks us to use a strict interpretation of ##\\ \\sqrt{w}\\ ## as the principle square root, that is the square root in the right half-plane or on the positive imaginary axis, then none of the vectors is correct.\n\nIf we take the problem to mean, \"Find ##z##, such that ##\\ z^2=w\\ ##,\" then ##\\ z_2 \\ ## is the solution as OP found.\n\nI was merely trying to give OP an alternate way to find that solution.\n\nMerlin3189\nHomework Helper\nGold Member\nYour non-strict interpretation is fine by me. Like you I was looking at how the original question could be answered.\n\nAlthough I'd never come across the notion of √ z meaning \"the principal square root of z\", I'm quite happy to believe that some people use it that way.\nBut if someone told me that, say -2 is not = √4 , I would not ( will not) believe them, irrespective of context, as all my experience tells me that it is. If they say that answer gives a solution outside some boundary condition for a particular problem, fine, but you need to have considered that value to decide.\n\nReflecting on my own practice I see that, I will normally write, ## (x^2=y)⇒x=±√y ## as a sort of reminder not to lose the other root in my algebraic manipulation, but normally just ## (x^2=2) ⇒ (x=√2) ⇒(x=±1.414)## leaving the two roots implicit until the end in arithmetic.\n\nI can't think of any situation where you'd be better off assuming √ means principal root, than √ means both roots. At worst you end up with ±(±n) for an answer, which is no problem. If you end up with +n only, that could be bad.\n\nI don't know what zr95 thinks, but it seems to me that the more correct answer is not the more helpful answer here.\n\nBvU"
] |
[
null,
"https://www.physicsforums.com/attachments/upload_2016-5-3_16-20-19-png.100202/",
null,
"https://www.physicsforums.com/attachments/upload_2016-5-3_16-21-45-png.100203/",
null,
"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
null,
"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
null,
"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
null,
"https://www.physicsforums.com/attachments/inline23-gif.200093/",
null,
"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
null,
"https://www.physicsforums.com/attachments/inline1-gif.200094/",
null,
"https://www.physicsforums.com/attachments/inline2-gif.200095/",
null,
"https://www.physicsforums.com/attachments/proxy-php-image-http-3a-2f-2fmathworld-wolfram-com-2fimages-2fequations-2fsquareroot-2finline1-png.202835/",
null,
"https://www.physicsforums.com/attachments/proxy-php-image-http-3a-2f-2fmathworld-wolfram-com-2fimages-2fequations-2fsquareroot-2finline2-png.202836/",
null,
"https://www.physicsforums.com/attachments/proxy-php-image-http-3a-2f-2fmathworld-wolfram-com-2fimages-2fequations-2fsquareroot-2finline3-png.202837/",
null,
"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
null,
"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7",
null,
"https://www.physicsforums.com/attachments/upload_2016-5-3_16-20-19-png-100202-png.187505/",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9603482,"math_prob":0.8561274,"size":910,"snap":"2022-05-2022-21","text_gpt3_token_len":242,"char_repetition_ratio":0.10375276,"word_repetition_ratio":0.0,"special_character_ratio":0.2758242,"punctuation_ratio":0.05612245,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97415227,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"im_url_duplicate_count":[null,2,null,2,null,null,null,null,null,null,null,2,null,null,null,2,null,2,null,2,null,2,null,2,null,null,null,null,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-28T05:02:54Z\",\"WARC-Record-ID\":\"<urn:uuid:8c687973-01fb-442a-a5c9-df07b046c68b>\",\"Content-Length\":\"179726\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0d13cd2e-44d4-42a4-964d-92424e82b59d>\",\"WARC-Concurrent-To\":\"<urn:uuid:20acfaf8-003e-42e0-81ef-66826a7ae8e2>\",\"WARC-IP-Address\":\"104.26.15.132\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/complex-plane-graphing-powers.870222/\",\"WARC-Payload-Digest\":\"sha1:V23KQIU6OYOBD2F5VFHCF3Y4EO3RQQ5B\",\"WARC-Block-Digest\":\"sha1:RAPPNWRZFXL5CPZHT26WTUNA5HHZXUCH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652663012542.85_warc_CC-MAIN-20220528031224-20220528061224-00041.warc.gz\"}"}
|
http://ec.citizendium.org/wiki/Idempotence
|
[
"# Idempotence",
null,
"",
null,
"Main Article Discussion Related Articles [?] Bibliography [?] External Links [?] Citable Version [?] This editable Main Article is under development and subject to a disclaimer. [edit intro]\n\nIn mathematics and computer science idempotence is the property of an operation that repeated application has no further effect.\n\n## In mathematics\n\nA binary operation $\\star$",
null,
"is idempotent if\n\n$x\\star x=x$",
null,
"for all x:\n\nequivalently, every element is an idempotent element for $\\star$",
null,
".\n\nExamples of idempotent binary operations include join and meet in a lattice; union and intersection on sets; disjunction and conjunction in propositional logic.\n\nA unary operation (a function from a set to itself) π is idempotent if it is an idempotent element for function composition, $\\pi \\circ \\pi =\\pi$",
null,
".\n\n## In computing\n\nIn applications such as databases and transaction processing, idempotent operations are those for which the intended effect is that repeated application should have no effect, such as inserting a record into a file, an element into a set, or sending a message. Implementations must therefore be constructed in such a way that the intended effect is actually carried into practice. For example, messages might have unique sequence numbers with duplicates being discarded on receipt; a set might be implemented as a bit vector, and member insertion implemented by an idempotent mathematical operation such as inclusive or with a bit mask.\n\nWhen a particular unit of work (i.e., transaction), has the idempotent property, relaxation of the ACID properties usually required for reliable transaction processing, can be relaxed."
] |
[
null,
"https://s9.addthis.com/button1-share.gif",
null,
"http://ec.citizendium.org/wiki/images/4/4f/Statusbar2.png",
null,
"https://wikimedia.org/api/rest_v1/media/math/render/svg/bd316a21eeb5079a850f223b1d096a06bfa788c0",
null,
"https://wikimedia.org/api/rest_v1/media/math/render/svg/e02411b7c727d9ea6eab85ada89e212ace3a6401",
null,
"https://wikimedia.org/api/rest_v1/media/math/render/svg/bd316a21eeb5079a850f223b1d096a06bfa788c0",
null,
"https://wikimedia.org/api/rest_v1/media/math/render/svg/2b989f38eb9ffbd07ec93a5aa47eb668544532d4",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9281984,"math_prob":0.7748589,"size":1386,"snap":"2022-27-2022-33","text_gpt3_token_len":271,"char_repetition_ratio":0.14761215,"word_repetition_ratio":0.009478673,"special_character_ratio":0.17748918,"punctuation_ratio":0.10878661,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9680162,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,3,null,null,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-17T07:13:08Z\",\"WARC-Record-ID\":\"<urn:uuid:c51f6d6a-9d39-4efe-b893-dafefcd0a6bf>\",\"Content-Length\":\"33061\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0071932c-dec0-46e8-b38a-a8476a44974b>\",\"WARC-Concurrent-To\":\"<urn:uuid:d60fa3ae-b1a6-4a42-8e51-8ab8000d13b0>\",\"WARC-IP-Address\":\"208.100.31.41\",\"WARC-Target-URI\":\"http://ec.citizendium.org/wiki/Idempotence\",\"WARC-Payload-Digest\":\"sha1:OQLFWT6VH2GR4DI3B2NCQVJUE5ZWUQKU\",\"WARC-Block-Digest\":\"sha1:OYNWAKTZO5TF25XLW3HKQBU65KEBYO4X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572870.85_warc_CC-MAIN-20220817062258-20220817092258-00721.warc.gz\"}"}
|
http://forums.wolfram.com/mathgroup/archive/2001/Apr/msg00294.html
|
[
"",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"cylindrical vector plot\n\n• To: mathgroup at smc.vnet.net\n• Subject: [mg28490] cylindrical vector plot\n• From: Julian Sweet <jsweet at engineering.ucsb.edu>\n• Date: Sun, 22 Apr 2001 01:30:21 -0400 (EDT)\n• Sender: owner-wri-mathgroup at wolfram.com\n\n```\tI am trying to create a 3D vector field plot, but in\ncylindrical coordinates. My vector equation has two components, \"phi\"\nand \"z\". Both of these components are dependent on radius, \"r\". I\nguess I'm trying to figure out how to graph this in cylindrical\ncoordinates, as plotfield3D assumes cartesian coordinates. Ultimately\nI would end up with a cylindrical vector field plot with arrows\npointing in some \"phi\" and \"z\" direction -- each arrow's magnitude and\ndirection is dependent upon r....\n\nemail response appreciated: jsweet at engineering.ucsb.edu\n\n```\n\n• Prev by Date: RE: PC - Mac Compatibility\n• Next by Date: help to plot..please\n• Previous by thread: Re: Echelon form of a matrix\n• Next by thread: Re: cylindrical vector plot"
] |
[
null,
"http://forums.wolfram.com/mathgroup/images/head_mathgroup.gif",
null,
"http://forums.wolfram.com/mathgroup/images/head_archive.gif",
null,
"http://forums.wolfram.com/mathgroup/images/numbers/2.gif",
null,
"http://forums.wolfram.com/mathgroup/images/numbers/0.gif",
null,
"http://forums.wolfram.com/mathgroup/images/numbers/0.gif",
null,
"http://forums.wolfram.com/mathgroup/images/numbers/1.gif",
null,
"http://forums.wolfram.com/mathgroup/images/search_archive.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9032561,"math_prob":0.6658456,"size":796,"snap":"2020-34-2020-40","text_gpt3_token_len":198,"char_repetition_ratio":0.125,"word_repetition_ratio":0.0,"special_character_ratio":0.2512563,"punctuation_ratio":0.18064517,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98880124,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-09T13:54:59Z\",\"WARC-Record-ID\":\"<urn:uuid:9d905d00-587c-439c-98e1-d7e5a79f3b95>\",\"Content-Length\":\"44058\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0458d35a-2e4d-4125-8590-9faa91317295>\",\"WARC-Concurrent-To\":\"<urn:uuid:149eca15-d7a4-4c17-a849-0a193cf9020f>\",\"WARC-IP-Address\":\"140.177.205.73\",\"WARC-Target-URI\":\"http://forums.wolfram.com/mathgroup/archive/2001/Apr/msg00294.html\",\"WARC-Payload-Digest\":\"sha1:U3LUTTF5VEGMA7ZLHMDD3Y2BXQW4CEVA\",\"WARC-Block-Digest\":\"sha1:B5EK45DT3W4FG6GFJFBFZWJMEH6NQAJ6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738555.33_warc_CC-MAIN-20200809132747-20200809162747-00465.warc.gz\"}"}
|
https://cran.ma.ic.ac.uk/web/packages/apexcharter/readme/README.html
|
[
"# apexcharter\n\nHtmlwidget for apexcharts.js : A modern JavaScript charting library to build interactive charts and visualizations with simple API. See the online demo for examples.\n\n:warning: Use RStudio >= 1.2 to properly display charts\n\n## Installation\n\nInstall from CRAN with:\n\n``install.packages(\"apexcharter\")``\n\nOr install the development version from GitHub with:\n\n``````# install.packages(\"devtools\")\ndevtools::install_github(\"dreamRs/apexcharter\")``````\n\n## Quick Charts\n\nUse `apex` function to quickly create visualizations :\n\n``````library(apexcharter)\ndata(\"mpg\", package = \"ggplot2\")\napex(data = mpg, type = \"bar\", mapping = aes(manufacturer))``````",
null,
"With datetime:\n\n``````data(\"economics\", package = \"ggplot2\")\napex(data = economics, type = \"line\", mapping = aes(x = date, y = uempmed)) %>%\nax_stroke(width = 1)``````",
null,
"## Full API\n\nAll methods from ApexCharts are available with function like `ax_*` compatible with pipe from `magrittr` :\n\n``````library(apexcharter)\ndata(mpg, package = \"ggplot2\")\n\napexchart() %>%\nax_chart(type = \"bar\") %>%\nax_plotOptions(bar = bar_opts(\nhorizontal = FALSE,\nendingShape = \"flat\",\ncolumnWidth = \"70%\",\ndataLabels = list(\nposition = \"top\"\n))\n) %>%\nax_grid(\nshow = TRUE,\nposition = \"front\",\nborderColor = \"#FFF\"\n) %>%\nax_series(list(\nname = \"Count\",\ndata = tapply(mpg\\$manufacturer, mpg\\$manufacturer, length)\n)) %>%\nax_colors(\"#112446\") %>%\nax_xaxis(categories = unique(mpg\\$manufacturer)) %>%\nax_title(text = \"Number of models\") %>%\nax_subtitle(text = \"Data from ggplot2\")``````",
null,
"## Raw API\n\nPass a list of parameters to the function:\n\n``````apexchart(ax_opts = list(\nchart = list(\ntype = \"line\"\n),\nstroke = list(\ncurve = \"smooth\"\n),\ngrid = list(\nborderColor = \"#e7e7e7\",\nrow = list(\ncolors = c(\"#f3f3f3\", \"transparent\"),\nopacity = 0.5\n)\n),\ndataLabels = list(\nenabled = TRUE\n),\nmarkers = list(style = \"inverted\", size = 6),\nseries = list(\nlist(\nname = \"High\",\ndata = c(28, 29, 33, 36, 32, 32, 33)\n),\nlist(\nname = \"Low\",\ndata = c(12, 11, 14, 18, 17, 13, 13)\n)\n),\ntitle = list(\ntext = \"Average High & Low Temperature\",\nalign = \"left\"\n),\nxaxis = list(\ncategories = month.abb[1:7]\n),\nyaxis = list(\ntitle = list(text = \"Temperature\"),\nlabels = list(\nformatter = htmlwidgets::JS(\"function(value) {return value + '\\u00b0C';}\")\n)\n)\n))``````",
null,
""
] |
[
null,
"https://cran.ma.ic.ac.uk/web/packages/apexcharter/readme/man/figures/apex-bar.png",
null,
"https://cran.ma.ic.ac.uk/web/packages/apexcharter/readme/man/figures/apex-line.png",
null,
"https://cran.ma.ic.ac.uk/web/packages/apexcharter/readme/man/figures/apexcharter-full-bar.png",
null,
"https://cran.ma.ic.ac.uk/web/packages/apexcharter/readme/man/figures/raw-api.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.51820934,"math_prob":0.99697477,"size":2008,"snap":"2021-43-2021-49","text_gpt3_token_len":588,"char_repetition_ratio":0.13323353,"word_repetition_ratio":0.0065146578,"special_character_ratio":0.34611553,"punctuation_ratio":0.19753087,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99129754,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-17T19:06:54Z\",\"WARC-Record-ID\":\"<urn:uuid:393b5814-06c1-4cf7-a1d8-178d97354ada>\",\"Content-Length\":\"16787\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dcc3d2a0-3291-4a48-9cd7-6e0481c52607>\",\"WARC-Concurrent-To\":\"<urn:uuid:c67d18ea-4f70-49f4-af01-d92105f16919>\",\"WARC-IP-Address\":\"155.198.195.11\",\"WARC-Target-URI\":\"https://cran.ma.ic.ac.uk/web/packages/apexcharter/readme/README.html\",\"WARC-Payload-Digest\":\"sha1:DF35DHCBHIPZJ3YT2DPFSMIRG2Y7L7CZ\",\"WARC-Block-Digest\":\"sha1:IJHCJP6S7CLVL74WM53NBVVRQPQ7XLTU\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585181.6_warc_CC-MAIN-20211017175237-20211017205237-00126.warc.gz\"}"}
|
https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/statug_logistic_sect018.htm
|
[
"OUTPUT Statement\nOUTPUT <OUT=SAS-data-set><options> ;\n\nThe OUTPUT statement creates a new SAS data set that contains all the variables in the input data set and, optionally, the estimated linear predictors and their standard error estimates, the estimates of the cumulative or individual response probabilities, and the confidence limits for the cumulative probabilities. Regression diagnostic statistics and estimates of cross validated response probabilities are also available for binary response models. If you specify more than one OUTPUT statement, only the last one is used. Formulas for the statistics are given in the sections Linear Predictor, Predicted Probability, and Confidence Limits and Regression Diagnostics, and, for conditional logistic regression, in the section Conditional Logistic Regression.\n\nIf you use the single-trial syntax, the data set also contains a variable named _LEVEL_, which indicates the level of the response that the given row of output is referring to. For instance, the value of the cumulative probability variable is the probability that the response variable is as large as the corresponding value of _LEVEL_. For details, see the section OUT= Output Data Set in the OUTPUT Statement.\n\nThe estimated linear predictor, its standard error estimate, all predicted probabilities, and the confidence limits for the cumulative probabilities are computed for all observations in which the explanatory variables have no missing values, even if the response is missing. By adding observations with missing response values to the input data set, you can compute these statistics for new observations or for settings of the explanatory variables not present in the data without affecting the model fit. Alternatively, the SCORE statement can be used to compute predicted probabilities and confidence intervals for new observations.\n\nTable 53.8 lists the available options, which can be specified after a slash (/). The statistic and diagnostic options specify the statistics to be included in the output data set and name the new variables that contain the statistics. If a STRATA statement is specified, only the PREDICTED=, DFBETAS=, and H= options are available; see the section Regression Diagnostic Details for details.\n\nTable 53.8 OUTPUT Statement Options\n\nOption\n\nDescription\n\nSpecifies",
null,
"for the",
null,
"confidence intervals\n\nNames the output data set\n\nStatistic Options\n\nNames the lower confidence limit\n\nPREDICTED=\n\nNames the predicted probabilities\n\nPREDPROBS=\n\nRequests the individual, cumulative, or cross validated predicted probabilities\n\nNames the standard error estimate of the linear predictor\n\nNames the upper confidence limit\n\nNames the linear predictor\n\nDiagnostic Options for Binary Response\n\nNames the confidence interval displacement\n\nNames the confidence interval displacement\n\nNames the standardized deletion parameter differences\n\nNames the deletion chi-square goodness-of-fit change\n\nNames the deletion deviance change\n\nNames the leverage\n\nNames the Pearson chi-square residual\n\nNames the deviance residual\n\nNames the likelihood residual\n\nSTDRESCHI=\n\nNames the standardized Pearson chi-square residual\n\nSTDRESDEV=\n\nNames the standardized deviance residual\n\nThe following list describes these options.\n\nALPHA=number\n\nsets the level of significance",
null,
"for",
null,
"% confidence limits for the appropriate response probabilities. The value of number must be between 0 and 1. By default, number is equal to the value of the ALPHA= option in the PROC LOGISTIC statement, or 0.05 if that option is not specified.\n\nC=name\n\nspecifies the confidence interval displacement diagnostic that measures the influence of individual observations on the regression estimates.\n\nCBAR=name\n\nspecifies the confidence interval displacement diagnostic that measures the overall change in the global regression estimates due to deleting an individual observation.\n\nDFBETAS=_ALL_\nDFBETAS=var-list\n\nspecifies the standardized differences in the regression estimates for assessing the effects of individual observations on the estimated regression parameters in the fitted model. You can specify a list of up to",
null,
"variable names, where",
null,
"is the number of explanatory variables in the MODEL statement, or you can specify just the keyword _ALL_. In the former specification, the first variable contains the standardized differences in the intercept estimate, the second variable contains the standardized differences in the parameter estimate for the first explanatory variable in the MODEL statement, and so on. In the latter specification, the DFBETAS statistics are named DFBETA_",
null,
", where",
null,
"is the name of the regression parameter. For example, if the model contains two variables X1 and X2, the specification DFBETAS=_ALL_ produces three DFBETAS statistics: DFBETA_Intercept, DFBETA_X1, and DFBETA_X2. If an explanatory variable is not included in the final model, the corresponding output variable named in DFBETAS=var-list contains missing values.\n\nDIFCHISQ=name\n\nspecifies the change in the chi-square goodness-of-fit statistic attributable to deleting the individual observation.\n\nDIFDEV=name\n\nspecifies the change in the deviance attributable to deleting the individual observation.\n\nH=name\n\nspecifies the diagonal element of the hat matrix for detecting extreme points in the design space.\n\nLOWER=name\nL=name\n\nnames the variable containing the lower confidence limits for",
null,
", where",
null,
"is the probability of the event response if events/trials syntax or single-trial syntax with binary response is specified; for a cumulative model,",
null,
"is cumulative probability (that is, the probability that the response is less than or equal to the value of _LEVEL_); for the generalized logit model, it is the individual probability (that is, the probability that the response category is represented by the value of _LEVEL_). See the ALPHA= option to set the confidence level.\n\nOUT=SAS-data-set\n\nnames the output data set. If you omit the OUT= option, the output data set is created and given a default name by using the DATA",
null,
"convention.\n\nPREDICTED=name\nPRED=name\nPROB=name\nP=name\n\nnames the variable containing the predicted probabilities. For the events/trials syntax or single-trial syntax with binary response, it is the predicted event probability. For a cumulative model, it is the predicted cumulative probability (that is, the probability that the response variable is less than or equal to the value of _LEVEL_); and for the generalized logit model, it is the predicted individual probability (that is, the probability of the response category represented by the value of _LEVEL_).\n\nPREDPROBS=(keywords)\n\nrequests individual, cumulative, or cross validated predicted probabilities. Descriptions of the keywords are as follows.\n\nINDIVIDUAL | I\n\nrequests the predicted probability of each response level. For a response variable Y with three levels, 1, 2, and 3, the individual probabilities are Pr(Y",
null,
"1), Pr(Y",
null,
"2), and Pr(Y",
null,
"3).\n\nCUMULATIVE | C\n\nrequests the cumulative predicted probability of each response level. For a response variable Y with three levels, 1, 2, and 3, the cumulative probabilities are Pr(Y",
null,
"1), Pr(Y",
null,
"2), and Pr(Y",
null,
"3). The cumulative probability for the last response level always has the constant value of 1. For generalized logit models, the cumulative predicted probabilities are not computed and are set to missing.\n\nCROSSVALIDATE | XVALIDATE | X\n\nrequests the cross validated individual predicted probability of each response level. These probabilities are derived from the leave-one-out principle—that is, dropping the data of one subject and reestimating the parameter estimates. PROC LOGISTIC uses a less expensive one-step approximation to compute the parameter estimates. This option is valid only for binary response models; for nominal and ordinal models, the cross validated probabilities are not computed and are set to missing.\n\nSee the section Details of the PREDPROBS= Option at the end of this section for further details.\n\nRESCHI=name\n\nspecifies the Pearson (chi-square) residual for identifying observations that are poorly accounted for by the model.\n\nRESDEV=name\n\nspecifies the deviance residual for identifying poorly fitted observations.\n\nRESLIK=name\n\nspecifies the likelihood residual for identifying poorly fitted observations.\n\nSTDRESCHI=name\n\nspecifies the standardized Pearson (chi-square) residual for identifying observations that are poorly accounted for by the model.\n\nSTDRESDEV=name\n\nspecifies the standardized deviance residual for identifying poorly fitted observations.\n\nSTDXBETA=name\n\nnames the variable containing the standard error estimates of XBETA. See the section Linear Predictor, Predicted Probability, and Confidence Limits for details.\n\nUPPER=name\nU=name\n\nnames the variable containing the upper confidence limits for",
null,
", where",
null,
"is the probability of the event response if events/trials syntax or single-trial syntax with binary response is specified; for a cumulative model,",
null,
"is cumulative probability (that is, the probability that the response is less than or equal to the value of _LEVEL_); for the generalized logit model, it is the individual probability (that is, the probability that the response category is represented by the value of _LEVEL_). See the ALPHA= option to set the confidence level.\n\nXBETA=name\n\nnames the variable containing the estimates of the linear predictor",
null,
", where",
null,
"is the corresponding ordered value of _LEVEL_.\n\n### Details of the PREDPROBS= Option\n\nYou can request any of the three types of predicted probabilities. For example, you can request both the individual predicted probabilities and the cross validated probabilities by specifying PREDPROBS=(I X).\n\nWhen you specify the PREDPROBS= option, two automatic variables, _FROM_ and _INTO_, are included for the single-trial syntax and only one variable, _INTO_, is included for the events/trials syntax. The variable _FROM_ contains the formatted value of the observed response. The variable _INTO_ contains the formatted value of the response level with the largest individual predicted probability.\n\nIf you specify PREDPROBS=INDIVIDUAL, the OUT= data set contains",
null,
"additional variables representing the individual probabilities, one for each response level, where",
null,
"is the maximum number of response levels across all BY groups. The names of these variables have the form IP_xxx, where xxx represents the particular level. The representation depends on the following situations:\n\n• If you specify events/trials syntax, xxx is either ‘Event’ or ‘Nonevent’. Thus, the variable containing the event probabilities is named IP_Event and the variable containing the nonevent probabilities is named IP_Nonevent.\n\n• If you specify the single-trial syntax with more than one BY group, xxx is 1 for the first ordered level of the response, 2 for the second ordered level of the response, and so forth, as given in the \"Response Profile\" table. The variable containing the predicted probabilities Pr(Y=1) is named IP_1, where Y is the response variable. Similarly, IP_2 is the name of the variable containing the predicted probabilities Pr(Y=2), and so on.\n\n• If you specify the single-trial syntax with no BY-group processing, xxx is the left-justified formatted value of the response level (the value might be truncated so that IP_xxx does not exceed 32 characters). For example, if Y is the response variable with response levels ‘None’, ‘Mild’, and ‘Severe’, the variables representing individual probabilities Pr(Y=’None’), P(Y=’Mild’), and P(Y=’Severe’) are named IP_None, IP_Mild, and IP_Severe, respectively.\n\nIf you specify PREDPROBS=CUMULATIVE, the OUT= data set contains",
null,
"additional variables representing the cumulative probabilities, one for each response level, where",
null,
"is the maximum number of response levels across all BY groups. The names of these variables have the form CP_xxx, where xxx represents the particular response level. The naming convention is similar to that given by PREDPROBS=INDIVIDUAL. The PREDPROBS=CUMULATIVE values are the same as those output by the PREDICT= option, but are arranged in variables on each output observation rather than in multiple output observations.\n\nIf you specify PREDPROBS=CROSSVALIDATE, the OUT= data set contains",
null,
"additional variables representing the cross validated predicted probabilities of the",
null,
"response levels, where",
null,
"is the maximum number of response levels across all BY groups. The names of these variables have the form XP_xxx, where xxx represents the particular level. The representation is the same as that given by PREDPROBS=INDIVIDUAL except that for the events/trials syntax there are four variables for the cross validated predicted probabilities instead of two:\n\nXP_EVENT_R1E\n\nis the cross validated predicted probability of an event when a current event trial is removed.\n\nXP_NONEVENT_R1E\n\nis the cross validated predicted probability of a nonevent when a current event trial is removed.\n\nXP_EVENT_R1N\n\nis the cross validated predicted probability of an event when a current nonevent trial is removed.\n\nXP_NONEVENT_R1N\n\nis the cross validated predicted probability of a nonevent when a current nonevent trial is removed.\n\nThe cross validated predicted probabilities are precisely those used in the CTABLE option. See the section Predicted Probability of an Event for Classification for details of the computation."
] |
[
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0007.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0106.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0007.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0031.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0127.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0009.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0128.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0129.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0024.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0024.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0024.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0040.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0026.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0026.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0026.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0130.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0130.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0130.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0024.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0024.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0024.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0131.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0091.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0018.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0018.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0018.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0018.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0018.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0018.png",
null,
"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/images/statug_logistic0018.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8306116,"math_prob":0.961304,"size":12688,"snap":"2021-31-2021-39","text_gpt3_token_len":2437,"char_repetition_ratio":0.18700725,"word_repetition_ratio":0.2668435,"special_character_ratio":0.18308638,"punctuation_ratio":0.09826046,"nsfw_num_words":6,"has_unicode_error":false,"math_prob_llama3":0.99635786,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60],"im_url_duplicate_count":[null,6,null,4,null,6,null,4,null,1,null,null,null,1,null,1,null,7,null,7,null,7,null,null,null,null,null,null,null,null,null,3,null,3,null,3,null,7,null,7,null,7,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-20T23:23:05Z\",\"WARC-Record-ID\":\"<urn:uuid:e47ab4a2-6fe7-44c0-9709-602954698b59>\",\"Content-Length\":\"46899\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:410ce7dc-c563-4a42-a989-b10a47e83b40>\",\"WARC-Concurrent-To\":\"<urn:uuid:d79ff4fe-e04b-4174-9b67-a36e14b55859>\",\"WARC-IP-Address\":\"23.39.179.94\",\"WARC-Target-URI\":\"https://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/statug_logistic_sect018.htm\",\"WARC-Payload-Digest\":\"sha1:NKOSMR4FGOYJQPXHDTIMIDXBIVYET3SN\",\"WARC-Block-Digest\":\"sha1:BXKMP3EOVATTVFYIWJELFDYJRUSZJ52E\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057119.85_warc_CC-MAIN-20210920221430-20210921011430-00088.warc.gz\"}"}
|
https://kmhtomph.com/88-kmh-to-mph/
|
[
"KMHtoMPH | MPG Calculator\n\n# 88 KMH to MPH\n\n88 KMH = 54.6821 MPH\n\n88 kilometers per hour are equal to 54.6821 miles per hour\n\nOpen converter: KMH MPH\n\n## How many miles per hour is 88 KMH?\n\nThere are 54.6821 miles per hour in 88 kilometers per hour.\n\n## How to convert 88 KMH to miles per hour?\n\nTo convert KMH to MPH you need to divide KMH value by 1.6093. In our case to convert 88 KMH to MPH you need to: 88 / 1.6093 = 54.6821 mph As you can see the result will be 54.6821 MPH.\n\n#### Related questions:\n\n• What is mph? See\n• How much is km in miles per hour? See"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8519283,"math_prob":0.88731915,"size":414,"snap":"2022-27-2022-33","text_gpt3_token_len":138,"char_repetition_ratio":0.19756098,"word_repetition_ratio":0.047058824,"special_character_ratio":0.38647342,"punctuation_ratio":0.12264151,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9896222,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-11T11:16:53Z\",\"WARC-Record-ID\":\"<urn:uuid:ab4885ab-c0f3-412b-a8b3-56fcbea0f8cc>\",\"Content-Length\":\"29617\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:406e7287-c522-4294-bda2-6af15726f62b>\",\"WARC-Concurrent-To\":\"<urn:uuid:812687a0-4601-4f87-9e62-7fd43b6e2896>\",\"WARC-IP-Address\":\"108.156.28.41\",\"WARC-Target-URI\":\"https://kmhtomph.com/88-kmh-to-mph/\",\"WARC-Payload-Digest\":\"sha1:EZGT6J7ZMVX2ZKAB52FJHH772CYQSQIT\",\"WARC-Block-Digest\":\"sha1:Q635PVLX3ULMVCBJNYLVCQ25JT7RHV5P\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571284.54_warc_CC-MAIN-20220811103305-20220811133305-00784.warc.gz\"}"}
|
https://vaguevagaries.blogspot.com/2006/12/
|
[
"## Saturday, December 23, 2006\n\n### Roujin Z?\n\nI think the caption \"Robots are looked on as a solution to Japan's ageing population\" under the first photo in this BBC article is a bit misleading.\n\n## Wednesday, December 13, 2006\n\n1.\n\n(a) The complex conjugate of a complex number is the number with the same real value and imaginary magnitude, but the imaginary part is opposite in sign.\n\n...\n\n3.\n* scale plots/images\n\nA convolution is the result of the application of an impulse response function to an input signal.\nThe input signal consists of a series of samples (impulses) of various magnitudes. Each input produces a corresponding input response function\n\nSince 'B' is composed of horizontal line samples, it appears as a horizontal broken line in the fourier transform. Conversely, the 'A' being composed of vertical lines appears as a vertical line in the fourier transform.\n\nThe diagonal crosspieces of the 'A' show up as rotated diagonals in the fourier transform, while the curving edges of the 'B' show up most as the vaguely rounded shapes at the edges of the horizontal line in the centre of the plot.\n\nclear;\n\nsubplot(3,2,1), image(final);\ncolormap(gray(256));\ny = fft2(final);\nsubplot(3,2,2), image(256*log(abs(y))/max(max(log(abs(y)))));\nydim = size(y, 1);\n\nxdim = size(y, 2);\nmsize = 140;\n\nya = ifft2(y2);\n\nyb = ifft2(y3);\n\nsubplot(3,2,3), image(abs(ya));\nsubplot(3,2,4), image(256*log(abs(y2))/max(max(log(abs(y2)))));\n\nsubplot(3,2,5), image(abs(yb));\nsubplot(3,2,6), image(256*log(abs(y3))/max(max(log(abs(y3)))));\n\n----\n\nlenna....\n\nclear;\nsubplot(2,3,1), image(xx);\ncolormap(gray(256));\n\nynew = 512;\nxnew = 512;\n\nscaled = zeros(ynew, xnew);\nscaled(1:2:ynew, 1:2:xnew) = xx;\n\ny = fft2(scaled);\n\nsubplot(2,3,2), image(256*log(abs(y))/max(max(log(abs(y)))));\nsubplot(2,3,3), image(ifft2(y));\nmsize = 128;\n\nsubplot(2,3,4), image(256*log(abs(ya))/max(max(log(abs(ya)))));\nscaledimg = abs(ifft2(ya));\nsubplot(2,3,5), image(256*scaledimg/max(max(scaledimg)));\n\n### the 'ultimate' partner?\n\nMeanwhile, nine out of ten women look for a man who can make her laugh and 73% want someone who will \"automatically\" pay for a meal.\n\nLooks like 73% of women are greedy twats, then.\n\nWhat a disgusting attitude that is, to expect men to 'automatically' pay for all meals. Why shouldn't they pay for it? Selfish arseholes.\n\n## Friday, December 08, 2006\n\n### Atari Falcon emulator\n\n...And when I say emulator, I mean emulator, not what people often think they mean when they mention Aranym, which isn't one.\n\nHatari in CVS now has the beginnings of support for TT and Falcon emulation - no software that could emulate these machines successfully has ever been released or even publically mentioned before as far as I know.\n\nUnfortunately, Hatari is only developed for Unix systems and the source doesn't seem very easily portable to Windows as yet (okay, I haven't looked at the source, but I'm guessing that that's the case). However, it compiles and runs just fine in Ubuntu and performs well. What a bombshell!\n\nHere's the announcement on the great atari-forum.com site."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8306944,"math_prob":0.9849061,"size":6409,"snap":"2021-43-2021-49","text_gpt3_token_len":1881,"char_repetition_ratio":0.12302888,"word_repetition_ratio":0.82522124,"special_character_ratio":0.31081292,"punctuation_ratio":0.20097357,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.976915,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-23T02:42:09Z\",\"WARC-Record-ID\":\"<urn:uuid:c049944a-7ac6-4848-8b28-0d18cd75e93e>\",\"Content-Length\":\"67651\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2cb9aaf4-9c81-4898-8981-0b16560a53a4>\",\"WARC-Concurrent-To\":\"<urn:uuid:53d6d821-6fa1-46e6-b002-122dcbb7d1e2>\",\"WARC-IP-Address\":\"142.251.33.193\",\"WARC-Target-URI\":\"https://vaguevagaries.blogspot.com/2006/12/\",\"WARC-Payload-Digest\":\"sha1:HT36WMAU4L4ZXJF3SBJTLYGK7X7SGMCI\",\"WARC-Block-Digest\":\"sha1:JDU2ULDMAO7LQ5MXDA32ZN7EUTCBNRTB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585537.28_warc_CC-MAIN-20211023002852-20211023032852-00707.warc.gz\"}"}
|
http://www.effortmark.co.uk/confidence-interval-want-one/
|
[
"# What is a confidence interval and why would you want one?\n\nWhat is a confidence interval? I wanted to know that recently and turned to one of my favourite books: Measuring the User Experience, by Tom Tullis and Bill Albert. And here’s what they say:\n\n“Confidence intervals are extremely valuable for any usability professional. A confidence interval is a range that estimates the true population value for a statistic.”\n\nThen they go on to explain how you calculate a confidence interval in Excel. Which is fine, but I have to admit that I wasn’t entirely sure that once I’d calculated it, I really knew what I’d done or what it meant. So I trawled through various statistics books to gain a better understanding of confidence intervals, and this column is the result.\n\n## The starting point: the need for a measurement\n\nAre you more comfortable working with qualitative data than quantitative data? If so, you’re like most UX people – including me. Once we’ve seen three or four test participants in a row fail for the same reason, we just want to get on with fixing the problem.\n\nBut sooner or later, we’ll have to tangle with some quantitative data. Let’s say, for example, that we have this goal for a new product: On average, we want users to be able to do a key task within 60 seconds. We’ve fixed all the show-stoppers and tested with eight participants—all of whom can do the task. Yay! But have we met the goal? Assuming we remembered to record the time it took each participant to complete the task, we might have data that looks like this:\n\nParticipant\nTime to Complete Task (in seconds)\n\nA\n\n40\n\nB\n\n75\n\nC\n\n98\n\nD\n\n40\n\nE\n\n84\n\nF\n\n10\n\nF\n\n33\n\nH\n\n52\n\nTo get the arithmetic average—which statisticians call the mean—you add up all the times and divide by the number of participants. Or use the AVERAGE formula in Excel. Either way, the average time for these participants was 54.0 seconds. Figure 1 shows the same data with the average as a straight line in red.\n\nSo, can we relax and plan the launch party?\n\nWell, maybe. If our product has only eight users, then we’ve tested with all of them, and yes, we’re done. But what if we’re aiming at everyone? Or, let’s say we’re being more precise, and we’ve defined our target market as follows: English-speaking Internet users in the US, Canada, and UK. Would the data from eight test participants be enough to represent the experience of all users?\n\n## True population value compared to our sample\n\nOur challenge, therefore, is to work out whether we can consider the average we’ve calculated from our sample as representative of our target audience.\n\nOr to put that into Tullis and Albert’s terms: in this case, our average is the statistic, and we want to use that data to estimate the true population value – that is, the average we would get if we got everyone in our target audience to try the task for us.\n\nOne way to improve our estimate would be to run more usability tests. So let’s test with eight more participants, giving us the following data:\n\nParticipant\nTime to Complete Task (in seconds)\n\nI\n\n130\n\nJ\n\n61\n\nK\n\n5\n\nL\n\n53\n\nM\n\n126\n\nN\n\n58\n\nO\n\n117\n\nP\n\n15\n\nThen, we can calculate a new mean.\n\nOh, dear… For this sample, the arithmetic average comes out to 74.6 seconds, so we’ve blown our target. Perhaps we need to run more tests or do more work on the product design. Or is there a quicker way?\n\n## Arithmetic averages have a bit of magic: the Central Limit Theorem\n\nLuckily for us, means have a bit of magic: a special mathematical property that may get us out of taking the obvious, but expensive course – running a lot more usability tests.\n\nThat bit of magic is the Central Limit Theorem, which says: if you take a bunch of samples, then calculate the mean of each sample, most of the sample means cluster close to the true population mean.\n\nLet’s see how this might work for our time-on-task problem. Figure 2 shows data from ten samples: the two we’ve just been discussing, plus eight more. Nine of these samples met the 60-second target, one did not. The data varies about from 10 to 130 seconds, but the means are in a much narrower range.\n\nThe chance that any individual mean is way off from the true population mean is quite small. In fact, the Central Limit Theorem also says that means are normally distributed, as in the bell-curve normal distribution shown in Figure 3.",
null,
"Figure 3—A normal distribution with the mean in red and the standard deviation in blue\n\nNormal distributions also have very convenient mathematical properties:\n\n• Two things define them:\n• where the peak is – that is, the mean, which is also the most likely value\n• how spread out the values are – which the standard deviation – also known as sigma – defines\n• The probability of getting any particular value depends on only these two parameters – the mean and the standard deviation.\n\nFigure 4 shows two normal distributions. The one on the left has a smaller mean and standard deviation than the one on the right.\n\n## Using the Central Limit Theorem to find a confidence interval\n\nIf you’re still with me, let’s get back to our challenge: deciding whether our original mean of 54.0 seconds from the first eight participants was sufficiently convincing to show that we’d met our target of an average time on task of less than 60 seconds and would allow us to launch. We’d rather not run nine more rounds of usability tests; instead, we want to estimate the true population mean.\n\nFortunately, the Central Limit Theorem lets us do that. Any mean from a random sample is likely to be quite close to the true population mean, and a normal distribution models the chance that it might be different from the true population mean. Some values of the true population mean would make it very likely that I’d get this sample mean, while other values would make it very unlikely. The likely values represent the confidence interval, which is the range of values for the true population mean that could plausibly give me my observed value.\n\nTo do the calculation, the first thing to decide is what we’re prepared to accept as likely. In other words, how much risk are we willing to run of being wrong? If we’re aiming for a level of risk that is often stated asstatistical significance at p < 0.05, the risk is a 5% chance of being wrong, or one in 20, but there is a 95% chance of being right.\n\nThe next thing we need is a standard deviation. The only one we have is the standard deviation of our sample, which is 29.40 seconds. (I used Excel’s STDEV.S command to work that out.)\n\nFinally, we plug in the mean, which is 54.0 seconds, and the number of participants, which is 8.\n\nYou can work this out with formulas and a calculator, but let’s use Excel. The CONFIDENCE command does it, giving us a value that we can\n\n• subtract from the sample mean to get the lowest true population mean that our observed mean could plausibly have come from\n• add to the sample mean to get the highest true population mean that our observed value could plausibly have come from\n\nThe result: the 95% confidence interval for the mean is 29.4 to 78.6 seconds, in comparison to our target of 60 seconds.\n\nThis is unfortunate. If the true population mean were as high as 78.6 seconds, we could still have obtained our sample mean of 49.4 seconds with a 95% probability. Oh, dear. That would be 18.6 seconds greater than our task-time target, which is disappointing all around. But we wouldn’t be nearly as worried if the true population mean happened to fall at the low end of the range. That would mean we’ve met our target.\n\n## Confidence intervals aren’t always correct\n\nRemember that 95%, which says that about one time in 20 you’re likely to get it wrong? You wouldn’t know whether this time is the one time in 20. If that makes you feel uncomfortable, you’ll need to increase your confidence level, which will also increase the range of the confidence interval, so you’ll have a greater chance of catching the true population value within it.\n\nHere are the confidence intervals for this sample, for some typical levels of risk:\n\nConfidence Interval (in seconds)\nRisk of Being Wrong\nConfidence Level\nLower End\nUpper End\n\n20%\n\n80%\n\n39.3\n\n68.7\n\n10%\n\n90%\n\n34.3\n\n73.7\n\n5%\n\n95%\n\n29.4\n\n78.6\n\n1%\n\n99%\n\n17.6\n\n90.4\n\nYou can see that, as we reduce the risk, we increase the confidence level and end up with a wider confidence interval – and in this example, also have an increasing level of depression about that launch date.\n\nHave you come across Six Sigma, the quality improvement program that Motorola originated, which is now popular in many manufacturing companies? They wanted to be very, very sure that they knew the risk of manufacturing poor-quality products and chose a confidence level of 99.99966% – that is, 3.4 chances in a million. I didn’t bother calculating the confidence interval for our sample to get a Six-Sigma level of risk, because it would constitute the whole range of our data.\n\n## Confidence intervals depend on sample size\n\nWhat to do if you want to get a higher confidence level, but also need to be sure you’ve met your target for the mean? Increase the sample size.\n\nThe more data in your sample, the smaller your confidence interval. That’s because with more data, you have more chance of the sample being a pretty good match to the whole population and, therefore, of its mean being similar to the true population value.\n\nIn my example, I’ve got 80 participants overall. The mean for all of the participants is 47.1 seconds, and the 95% confidence interval is (39.8, 54.4). So if I’d tested with a lot more people, I would indeed have proven that we’re okay to launch, because the highest plausible value is less than my target of 60 seconds.\n\nThat’s part of the fun of confidence intervals: we want to calculate a confidence interval so we don’t have to do as much sampling, but to get a narrow confidence interval, we need to do more sampling.\n\n## The Central Limit Theorem works only on random samples\n\nI recently read an article on sample sizes that asserted, “One thousand sessions provide a sufficiently narrow margin of error (plus or minus 2.5% at a 90% confidence level).”\n\nThis is true, but only if the sample is a random sample. For example, let’s say we wanted the average time it took to complete the New York Marathon across 45,000 runners. If we took a random sample of just 1000 runners, we would get a narrow confidence interval. But if we took the times of the first 1000 runners across the finish line, we’d get something very far indeed from the true population mean.\n\n## The mean is convenient, but not always helpful\n\nSo far, I’ve used the example of a target for a mean value: The average time on task must be less than a specified target.But would that be a good target to have?\n\nFigure 5 shows a set of data that is quite typical for user experience: a peak at low values – for example, task times – then a long tail with a few values that are much higher. It’s the overall data set that our samples have so far come from. The mean is 50.3 seconds, which is lower than the target of 60 seconds.\n\nBut how useful is the mean? Suppose we advertised: On average, you’ll be able to do this task in less than 60 seconds. In fact, some of our participants’ task times are much longer than the target – 8% of the data set has values over twice as long, and the largest value is over five times as long. Okay, so that’s only five minutes, and maybe no one would notice. But what if we were working in minutes instead of seconds? Many people would indeed notice if a task that they anticipated taking less than an hour actually took over two hours. So, in user experience, we often need to know the range – and you can’t calculate a confidence interval for that.\n\nAlso, look at the way most of the values pile up at the shorter end. Those users ought to be happy – the time it took them to complete the task is much shorter than the advertised time. But to ensure that a high volume of users can achieve those task times once the system gets rolled out, we’ll have to make sure that the system can cope with that high peak of very fast task times. So our colleagues who are managing system performance are likely to be far more interested in the most frequent value, which is the mode, than in the mean. But you can’t calculate a confidence interval for the mode either.\n\nOf course, Excel can take any numbers you put in and shove them through the calculation – so if you mistakenly try to run a CONFIDENCE formula on a mode, you’ll get an output. But it won’t be meaningful, because there is no Central Limit Theorem or any equivalent for modes.\n\n## Summary: confidence intervals can save you effort\n\nThe confidence interval for the mean helps you to estimate the true population mean and lets you avoid the additional effort that gathering a lot of extra data would require. You can compare the confidence interval you calculated with the target you were aiming for.\n\nOnce you have worked out what level of risk you are willing to accept, confidence intervals for the mean are easy to calculate. You’ll need these formulas in Excel:\n\n• AVERAGE – to get the mean of your sample\n• STDEV.S, in Excel 2010, or STDEV, in earlier versions – to get the standard deviation of your sample\n• CONFIDENCE – to calculate the amount to subtract from the mean to get the lower end of the confidence interval and to add to the mean to get the upper end."
] |
[
null,
"https://i1.wp.com/www.uxmatters.com/mt/archives/2011/11/images/normal-with-mean-and-sd.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.93529004,"math_prob":0.93971604,"size":13120,"snap":"2021-31-2021-39","text_gpt3_token_len":2983,"char_repetition_ratio":0.14928332,"word_repetition_ratio":0.017026577,"special_character_ratio":0.23422256,"punctuation_ratio":0.10188959,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98218197,"pos_list":[0,1,2],"im_url_duplicate_count":[null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-17T01:41:02Z\",\"WARC-Record-ID\":\"<urn:uuid:b58afe01-4fa9-4088-b9ea-06ff9f4764b4>\",\"Content-Length\":\"84982\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6f514639-f6a9-41f5-9d89-b5b20e46d54d>\",\"WARC-Concurrent-To\":\"<urn:uuid:3ea540d1-676c-4783-9ca5-edcd9bf22774>\",\"WARC-IP-Address\":\"188.94.75.28\",\"WARC-Target-URI\":\"http://www.effortmark.co.uk/confidence-interval-want-one/\",\"WARC-Payload-Digest\":\"sha1:CZB3UQ67KF4JZ7DC2QCPN3XO3NMU3E3T\",\"WARC-Block-Digest\":\"sha1:NMOJEDSPF6OFMLUL52LYXBOTDT6MAN4S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780053918.46_warc_CC-MAIN-20210916234514-20210917024514-00109.warc.gz\"}"}
|
https://research.tue.nl/en/publications/interference-minimization-in-asymmetric-sensor-networks-2
|
[
"Interference minimization in asymmetric sensor networks\n\nY. Brise, K. Buchin, D. Eversmann, M. Hoffmann, W. Mulzer\n\nAbstract\n\nA fundamental problem in wireless sensor networks is to connect a given set of sensors while minimizing the \\emph{receiver interference}. This is modeled as follows: each sensor node corresponds to a point in $\\mathbb{R}^d$ and each \\emph{transmission range} corresponds to a ball. The receiver interference of a sensor node is defined as the number of transmission ranges it lies in. Our goal is to choose transmission radii that minimize the maximum interference while maintaining a strongly connected asymmetric communication graph. For the two-dimensional case, we show that it is NP-complete to decide whether one can achieve a receiver interference of at most $5$. In the one-dimensional case, we prove that there are optimal solutions with nontrivial structural properties. These properties can be exploited to obtain an exact algorithm that runs in quasi-polynomial time. This generalizes a result by Tan et al. to the asymmetric case.\nOriginal language English s.n. 15 Published - 2014\n\nPublication series\n\nName arXiv 1406.7753 [cs.CG]\n\nFingerprint\n\nDive into the research topics of 'Interference minimization in asymmetric sensor networks'. Together they form a unique fingerprint."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8681404,"math_prob":0.83902895,"size":1087,"snap":"2022-05-2022-21","text_gpt3_token_len":228,"char_repetition_ratio":0.09695291,"word_repetition_ratio":0.0,"special_character_ratio":0.20883165,"punctuation_ratio":0.08421053,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.975773,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-17T07:57:55Z\",\"WARC-Record-ID\":\"<urn:uuid:62e827c2-4d19-42c3-89cf-1fbea9262954>\",\"Content-Length\":\"45281\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7bb8b859-177c-4b3c-8f13-a14c9b9422dc>\",\"WARC-Concurrent-To\":\"<urn:uuid:f3098d54-5ecf-4955-bb7d-d0157d256a7a>\",\"WARC-IP-Address\":\"34.248.98.230\",\"WARC-Target-URI\":\"https://research.tue.nl/en/publications/interference-minimization-in-asymmetric-sensor-networks-2\",\"WARC-Payload-Digest\":\"sha1:OULPLERO2DETQF4LKDNM27DRFPWSXKM3\",\"WARC-Block-Digest\":\"sha1:RPHARAFSURX52CUSCOZX25LIJIVYRWTZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320300343.4_warc_CC-MAIN-20220117061125-20220117091125-00212.warc.gz\"}"}
|
https://carbatecstage.customer-self-service.com/brands/robert-sorby/robert-sorby-sharpening-grinding-and-polishing
|
[
"My Store:\nChange Store\nMy Store:\nChange Store\n\n# Sharpening, Grinding & Polish\n\nGrid List\n\\$359.00 inc GST (EACH)\nQty Each\n\\$7.95 inc GST (EACH)\nQty Each\n\\$7.95 inc GST (EACH)\nQty Each\n\\$7.95 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$8.95 inc GST (EACH)\nQty Each\n\\$8.95 inc GST (EACH)\nQty Each\n\\$12.95 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$12.95 inc GST (EACH)\nQty Each\n\\$26.95 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$26.95 inc GST (EACH)\nQty Each\n\\$26.95 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$46.95 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$64.95 inc GST (EACH)\nQty Each\n\\$64.95 inc GST (EACH)\nQty Each\n\\$159.00 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$159.00 inc GST (EACH)\nIncrease value Decrease value\nQty Each\nRobert Sorby Standard Proedge Plus Sharpening System RSB-WPEB01D Usually ships within 91 days\n\\$749.00 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$949.00 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$22.95 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$29.95 inc GST (EACH)\nIncrease value Decrease value\nQty Each\n\\$35.95 inc GST (EACH)\nQty Each\n\\$35.95 inc GST (EACH)\nQty Each\n\\$35.95 inc GST (EACH)\nQty Each\n\\$45.95 inc GST (EACH)\nQty Each\nGrid List"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5803641,"math_prob":0.96288586,"size":9394,"snap":"2021-43-2021-49","text_gpt3_token_len":2740,"char_repetition_ratio":0.22662407,"word_repetition_ratio":0.7882775,"special_character_ratio":0.22727273,"punctuation_ratio":0.022793688,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98770905,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T08:35:21Z\",\"WARC-Record-ID\":\"<urn:uuid:60c47ed9-f515-4901-b3bd-bb06527f9608>\",\"Content-Length\":\"392558\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d289bdc8-2da5-4908-b421-0e27e5d38e26>\",\"WARC-Concurrent-To\":\"<urn:uuid:430343f2-da52-4609-88a5-6f8b8c12c038>\",\"WARC-IP-Address\":\"103.139.229.33\",\"WARC-Target-URI\":\"https://carbatecstage.customer-self-service.com/brands/robert-sorby/robert-sorby-sharpening-grinding-and-polishing\",\"WARC-Payload-Digest\":\"sha1:L6PSETA3PZFZZTYIE7QEKKBKIZHX3265\",\"WARC-Block-Digest\":\"sha1:3SD7MFX6XWBMDYAJRZYY6V7FK435PJXZ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363149.85_warc_CC-MAIN-20211205065810-20211205095810-00241.warc.gz\"}"}
|
https://www.12000.org/my_notes/CAS_integration_tests/reports/rubi_4_16_1_graded/test_cases/0_Independent_test_suites/Stewart_Problems/rese264.htm
|
[
"### 3.264 $$\\int \\frac{x}{\\sqrt{1-x^2}} \\, dx$$\n\nOptimal. Leaf size=13 $-\\sqrt{1-x^2}$\n\n[Out]\n\n-Sqrt[1 - x^2]\n\n________________________________________________________________________________________\n\nRubi [A] time = 0.0022397, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, $$\\frac{\\text{number of rules}}{\\text{integrand size}}$$ = 0.077, Rules used = {261} $-\\sqrt{1-x^2}$\n\nAntiderivative was successfully verified.\n\n[In]\n\nInt[x/Sqrt[1 - x^2],x]\n\n[Out]\n\n-Sqrt[1 - x^2]\n\nRule 261\n\nInt[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(a + b*x^n)^(p + 1)/(b*n*(p + 1)), x] /; FreeQ\n[{a, b, m, n, p}, x] && EqQ[m, n - 1] && NeQ[p, -1]\n\nRubi steps\n\n\\begin{align*} \\int \\frac{x}{\\sqrt{1-x^2}} \\, dx &=-\\sqrt{1-x^2}\\\\ \\end{align*}\n\nMathematica [A] time = 0.0013003, size = 13, normalized size = 1. $-\\sqrt{1-x^2}$\n\nAntiderivative was successfully verified.\n\n[In]\n\nIntegrate[x/Sqrt[1 - x^2],x]\n\n[Out]\n\n-Sqrt[1 - x^2]\n\n________________________________________________________________________________________\n\nMaple [A] time = 0., size = 17, normalized size = 1.3 \\begin{align*}{ \\left ( -1+x \\right ) \\left ( 1+x \\right ){\\frac{1}{\\sqrt{-{x}^{2}+1}}}} \\end{align*}\n\nVerification of antiderivative is not currently implemented for this CAS.\n\n[In]\n\nint(x/(-x^2+1)^(1/2),x)\n\n[Out]\n\n(-1+x)*(1+x)/(-x^2+1)^(1/2)\n\n________________________________________________________________________________________\n\nMaxima [A] time = 0.956916, size = 15, normalized size = 1.15 \\begin{align*} -\\sqrt{-x^{2} + 1} \\end{align*}\n\nVerification of antiderivative is not currently implemented for this CAS.\n\n[In]\n\nintegrate(x/(-x^2+1)^(1/2),x, algorithm=\"maxima\")\n\n[Out]\n\n-sqrt(-x^2 + 1)\n\n________________________________________________________________________________________\n\nFricas [A] time = 1.87824, size = 23, normalized size = 1.77 \\begin{align*} -\\sqrt{-x^{2} + 1} \\end{align*}\n\nVerification of antiderivative is not currently implemented for this CAS.\n\n[In]\n\nintegrate(x/(-x^2+1)^(1/2),x, algorithm=\"fricas\")\n\n[Out]\n\n-sqrt(-x^2 + 1)\n\n________________________________________________________________________________________\n\nSympy [A] time = 0.125356, size = 8, normalized size = 0.62 \\begin{align*} - \\sqrt{1 - x^{2}} \\end{align*}\n\nVerification of antiderivative is not currently implemented for this CAS.\n\n[In]\n\nintegrate(x/(-x**2+1)**(1/2),x)\n\n[Out]\n\n-sqrt(1 - x**2)\n\n________________________________________________________________________________________\n\nGiac [A] time = 1.05779, size = 15, normalized size = 1.15 \\begin{align*} -\\sqrt{-x^{2} + 1} \\end{align*}\n\nVerification of antiderivative is not currently implemented for this CAS.\n\n[In]\n\nintegrate(x/(-x^2+1)^(1/2),x, algorithm=\"giac\")\n\n[Out]\n\n-sqrt(-x^2 + 1)"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.62941855,"math_prob":0.9999994,"size":2148,"snap":"2023-40-2023-50","text_gpt3_token_len":647,"char_repetition_ratio":0.35494402,"word_repetition_ratio":0.35655737,"special_character_ratio":0.5502793,"punctuation_ratio":0.13826367,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998888,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-30T00:47:52Z\",\"WARC-Record-ID\":\"<urn:uuid:a3f53e06-42ae-41c7-87d5-dd6dc2af049b>\",\"Content-Length\":\"15582\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:423f7831-d944-40e5-b5bb-fee9c6610b5d>\",\"WARC-Concurrent-To\":\"<urn:uuid:81901924-a235-45b4-96d6-efaebb77b2fb>\",\"WARC-IP-Address\":\"192.249.121.28\",\"WARC-Target-URI\":\"https://www.12000.org/my_notes/CAS_integration_tests/reports/rubi_4_16_1_graded/test_cases/0_Independent_test_suites/Stewart_Problems/rese264.htm\",\"WARC-Payload-Digest\":\"sha1:ZPB3FYVHXKFPA2C6RKVFYY6EJD2T224L\",\"WARC-Block-Digest\":\"sha1:YXHZQST4L7HVWR27DZKZATCXWH23SLZ4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510529.8_warc_CC-MAIN-20230929222230-20230930012230-00875.warc.gz\"}"}
|
https://www.tongzhuo100.com/v/2015-10/33852.html
|
[
"### 九年级数学上册第4章《一元二次方程》4.3 用公式法解一元二次方程（第二课时）\n\n• 同步课程\n• 本节重点\n• 主讲老师\n\n4.3 用公式法解一元二次方程\n\nx²+3=",
null,
"x.\n\nx²-",
null,
"x+3=0，\na=1，b=-",
null,
"，c=3.\n\n∵b²-4ac=（-",
null,
"）²-4×1×3=0，",
null,
"（x+1）（3x-1）=1.\n\n3x²+2x-2=0，\n\n∵b²-4ac=2²-4×3×（-2）=28＞0，",
null,
"1.用公式法解下列方程：\n（1）x²-12x+20=0；（2）2x²+11x+5=0；\n（3）5x²-",
null,
"+3=0； （4）5x²+10x-6=0.\n2.用公式法解方程2x²-6x+3=0，并求根的近似值（精确到0.01）。\n3.一个三角形的两边长分别是8和6，第三边的长是一元二次方程x²-16x+60=0的一个实数根，求该三角形的面积",
null,
"4.已知实数x，y满足（x²+y²）（x²+y²-1）=2，试求x²+y²的值。\n（x²+y²）（x²+y²-1）=2\n\na·（a-1）=2\na²-a=2\na²-a+1/4=2+1/4\n（a-1/2）²=9/4\na-1/2=±3/2\n∴a1=2 a2=-1",
null,
"",
null,
""
] |
[
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145246348.jpg",
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145246348.jpg",
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145246348.jpg",
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145246348.jpg",
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145425485.jpg",
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145326004.jpg",
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145346761.jpg",
null,
"http://www.tongzhuo100.com/uploads/2016/04/20160405145731083.jpg",
null,
"https://www.tongzhuo100.com/upload/icon/6cbc66f9b657d1ca587d07af8a546508.jpg",
null,
"https://www.tongzhuo100.com/v/2015-10/33852.html",
null
] |
{"ft_lang_label":"__label__zh","ft_lang_prob":0.89986086,"math_prob":0.99870616,"size":909,"snap":"2021-43-2021-49","text_gpt3_token_len":1025,"char_repetition_ratio":0.27403316,"word_repetition_ratio":0.0,"special_character_ratio":0.2739274,"punctuation_ratio":0.097222224,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98411614,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,4,null,4,null,4,null,4,null,1,null,1,null,1,null,1,null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-28T10:59:58Z\",\"WARC-Record-ID\":\"<urn:uuid:d3ca28be-09e9-4b73-9ff1-ffa68ec7762a>\",\"Content-Length\":\"40030\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e88e6364-a6c0-4f9f-8d61-61284a4cac27>\",\"WARC-Concurrent-To\":\"<urn:uuid:66892124-6b44-4bba-9310-628e82906699>\",\"WARC-IP-Address\":\"112.132.32.81\",\"WARC-Target-URI\":\"https://www.tongzhuo100.com/v/2015-10/33852.html\",\"WARC-Payload-Digest\":\"sha1:77X6UGQXFGDH6XB554GPUNUAUM7VCZZ6\",\"WARC-Block-Digest\":\"sha1:2UB6AWUHNT4QN6DZB7TPTVP6FQ2F4Y72\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588284.71_warc_CC-MAIN-20211028100619-20211028130619-00032.warc.gz\"}"}
|
https://math.stackexchange.com/questions/1976143/if-a-and-b-are-relatively-prime-prove-that-a-2b-and-2ab-are-also-rel
|
[
"If $a$ and $b$ are relatively prime, prove that $a + 2b$ and $2a+b$ are also relatively prime or have a gcd of $3$.\n\nIf $a$ and $b$ are relatively prime, prove that $a + 2b$ and $2a+b$ are also relatively prime or have a $\\gcd$ of $3$.\n\nI'm very new to number theory so please don't assume I am familiar with some of the terminology.\n\nHint $\\$ By Cramer's rule (or elimination) we infer\n$$\\begin{eqnarray} \\ a\\, +\\, 2\\ b &=& A\\\\ \\\\ 2\\ a\\, +\\, \\ b &\\ =\\ & B\\end{eqnarray} \\quad\\Rightarrow\\quad \\begin{array}\\ 3 \\ a\\ = \\, -A\\, +\\, 2\\ B \\\\\\\\ 3\\ b\\ =\\ \\ 2\\ A\\, -\\, \\ B \\end{array}$$\nHence, by the RHS system: $\\ n\\mid A,B\\,\\Rightarrow\\,n\\mid 3a,3b\\,\\Rightarrow\\,n\\mid (3a,3b) = 3(a,b) = 3$\nRemark $\\$ In the same way we can prove more generally\nTheorem $\\$ If $\\rm\\,(x,y)\\overset{A}\\mapsto (X,Y)\\,$ is linear then $\\: \\rm\\gcd(x,y)\\mid \\gcd(X,Y)\\mid \\Delta \\gcd(x,y),\\ \\ \\ \\Delta := {\\rm det}\\, A$\nHint: $\\gcd(a + 2b, 2a + b) = \\gcd(a + 2b, (2a + b) - 2(a + 2b)) = \\gcd(a + 2b, -3b)$."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.78835315,"math_prob":1.0000093,"size":1280,"snap":"2019-43-2019-47","text_gpt3_token_len":469,"char_repetition_ratio":0.10188088,"word_repetition_ratio":0.31092438,"special_character_ratio":0.3921875,"punctuation_ratio":0.15412186,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999992,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-19T19:28:01Z\",\"WARC-Record-ID\":\"<urn:uuid:88110e9a-1377-4eb5-bf16-c8d706571c5e>\",\"Content-Length\":\"146644\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3bfa3f99-b698-462f-8afd-76318856680e>\",\"WARC-Concurrent-To\":\"<urn:uuid:987743a6-fb51-477d-9da0-7852ed73d7d0>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/1976143/if-a-and-b-are-relatively-prime-prove-that-a-2b-and-2ab-are-also-rel\",\"WARC-Payload-Digest\":\"sha1:GQAZF2URXHMNAX3NFAZ4SBKHDROQYELD\",\"WARC-Block-Digest\":\"sha1:HJDKNDDNSJGUINIQNNTHWKF6LK3KT6YJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986697760.44_warc_CC-MAIN-20191019191828-20191019215328-00547.warc.gz\"}"}
|
https://pms.plainfieldschools.org/for_parents/math_what_you_should_know
|
[
"• Select a School\n• Language\n• District Home\n\n## Math (What you should know)\n\nImportant Things to Know about CT Math Core Standards\n\n Grade Required Fluency K Add/Subtract within 5 1 Add/Subtract within 10 2 Add/Subtract within 20 Add/Subtract within 100 (pencil and paper) 3 Multiply/divide within 100 Add/subtract within 1000 4 Add/subtract within 1,000,000 5 Multi-digit multiplication 6 Multi-digit division Multi-digit decimal operations 7 Solve px + q = r, p(x +q) = r 8 Solve simple 2x2 systems by inspection\n\nWays Parents Can Help\n\n Students Must… Parents Can… Spend time practicing lots of problems on the same idea Push children to know/memorize basic math facts Understand why the math works. Make the math work. Notice whether your child really knows why the answer is what it is. Talk about why the math works. Advocate for the time your child needs to learn key math. Prove that they know why and how the math works. Provide time for your child to work hard with math at home. Apply math in real world situations. Know which math to use for which situation. Ask your child to do the math that comes up in your daily life."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8362459,"math_prob":0.8059649,"size":1116,"snap":"2022-40-2023-06","text_gpt3_token_len":303,"char_repetition_ratio":0.14928058,"word_repetition_ratio":0.0,"special_character_ratio":0.27867383,"punctuation_ratio":0.0631068,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98887825,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-25T01:06:29Z\",\"WARC-Record-ID\":\"<urn:uuid:ed0a5757-bb02-438e-a2cd-2235b6fc3705>\",\"Content-Length\":\"69649\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a17ee2bf-d298-48c4-b3c8-e226e4d275a0>\",\"WARC-Concurrent-To\":\"<urn:uuid:cdff5658-7257-4540-85de-ca2ed5361178>\",\"WARC-IP-Address\":\"172.64.151.177\",\"WARC-Target-URI\":\"https://pms.plainfieldschools.org/for_parents/math_what_you_should_know\",\"WARC-Payload-Digest\":\"sha1:QJVPR4DW45DG6HHJVQPQ4FRDICR7T5GC\",\"WARC-Block-Digest\":\"sha1:MWEPJN6DNMVN5CXN5ZDVWL2CTEO7GO4P\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334332.96_warc_CC-MAIN-20220925004536-20220925034536-00229.warc.gz\"}"}
|
https://www.laboratorynotes.com/2-butanol-sec-butanol-c2h5chohch3-molecular-weight-calculation/
|
[
"# 2-Butanol (sec-butanol) [C2H5CH(OH)CH3] Molecular Weight Calculation\n\nThe molecular weight of 2-Butanol [C2H5CH(OH)CH3] is 74.1222.",
null,
"To calculate molecular weight of any compound, the first step is to know the constituent atoms and their number in that particular compound. Then calculate the total weight of each atom by multiplying its atomic weight by its number. The sum of total weight of all constituent atoms will be the molecular weight of the compound. Note that the value of atomic weight may differ slightly from different sources.\n\n# CALCULATION PROCEDURE: 2-Butanol [C2H5CH(OH)CH3] Molecular Weight Calculation\n\nStep 1: Find out the chemical formula and determine constituent atoms and their number in a 2-Butanol molecule.\nFrom the chemical formula, you will know different atoms and their number in a 2-Butanol molecule. Chemical formula of 2-Butanol is C4H10O. From the chemical formula of 2-Butanol, you can find that one molecule of 2-Butanol has four Carbon (C) atoms, ten Hydrogen (H) atoms and one Oxygen (O) atom.\n\nStep 2: Find out atomic weights of each atom (from periodic table).\n\nAtomic weight of Carbon (C): 12.0107 (Ref: Jlab-ele006)\nAtomic\nweight of Hydrogen (H) : 1.008 (Ref: Lanl-1)\nAtomic weight of Oxygen (O) : 15.9994 (Ref: Jlab-ele008)\n\nStep 3: Calculate the total weight of each atom present in a 2-Butanol molecule by multiplying its atomic weight by its number.\n\nNumber of Carbon atoms in 2-Butanol: 4\nAtomic weight of Carbon: 12.0107\nTotal weight of Carbon atoms in 2-Butanol: 12.0107 x 4 = 48.0428\n\nNumber of Hydrogen atoms in 2-Butanol: 10\nAtomic weight of Hydrogen: 1.008\nTotal weight of Hydrogen atoms in 2-Butanol: 1.008 x 10 = 10.08\n\nNumber of Oxygen atoms in 2-Butanol: 1\nAtomic weight of Oxygen: 15.9994\nTotal weight of Oxygen atoms in 2-Butanol: 15.9994 x 1 = 15.9994\n\nStep 4: Calculate the molecular weight of 2-Butanol by adding up the total weight of all atoms.\n\nMolecular weight of 2-Butanol: 48.0428 (Carbon) + 10.08 (Hydrogen) + 15.9994 (Oxygen) = 74.1222\n\nSo the molecular weight of 2-Butanol is 74.1222.\n\n2-Butanol [C2H5CH(OH)CH3] Molecular Weight Calculation\n\n## REFERENCES:\n\n• Lanl-1: https://periodic.lanl.gov/1.shtml\n• Pubchem-Hydrogen : https://pubchem.ncbi.nlm.nih.gov/element/Hydrogen\n• Jlab-ele006; https://education.jlab.org/itselemental/ele006.html\n• Pubchem-6: https://pubchem.ncbi.nlm.nih.gov/element/6\n• Jlab-ele008: https://education.jlab.org/itselemental/ele008.html\n• Pubchem-8: https://pubchem.ncbi.nlm.nih.gov/element/8",
null,
""
] |
[
null,
"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NDIiIGhlaWdodD0iMzU4IiB2aWV3Qm94PSIwIDAgNTQyIDM1OCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgc3R5bGU9ImZpbGw6I2NmZDRkYjtmaWxsLW9wYWNpdHk6IDAuMTsiLz48L3N2Zz4=",
null,
"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4MCIgaGVpZ2h0PSI4MCIgdmlld0JveD0iMCAwIDgwIDgwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg==",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7210645,"math_prob":0.9457383,"size":2642,"snap":"2022-27-2022-33","text_gpt3_token_len":839,"char_repetition_ratio":0.20128885,"word_repetition_ratio":0.08730159,"special_character_ratio":0.30847842,"punctuation_ratio":0.1740675,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.995367,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-30T07:58:53Z\",\"WARC-Record-ID\":\"<urn:uuid:bf517aa0-5364-4863-aba3-b40111fff286>\",\"Content-Length\":\"67023\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:604d7aee-8bc7-4a73-b41c-83d3cc6eed00>\",\"WARC-Concurrent-To\":\"<urn:uuid:5d1c3402-9535-431f-a6a7-14c0ccd2b736>\",\"WARC-IP-Address\":\"160.153.129.217\",\"WARC-Target-URI\":\"https://www.laboratorynotes.com/2-butanol-sec-butanol-c2h5chohch3-molecular-weight-calculation/\",\"WARC-Payload-Digest\":\"sha1:AYB2ORO5WVF2SVMZDKJXHPILBFQYLQ5Z\",\"WARC-Block-Digest\":\"sha1:NRUGREQ2GNWNGEU4XWVR7HKN7E2RTQTK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103669266.42_warc_CC-MAIN-20220630062154-20220630092154-00181.warc.gz\"}"}
|
https://allendowney.blogspot.com/2011/11/
|
[
"Wednesday, November 30, 2011\n\nAre first babies more likely to be light?\n\nWay back in February I analyzed data from the National Survey of Family Growth (NSFG) and answered the question \"Are first babies more likely to be late?\" Now I am getting back to that data to look at the related question, \"Are first babies more likely to be light?\"\n\nIn Think Stats (Chapter 7), I showed that the mean birth weight for first babies is lower than the mean for others by about 2 ounces, and that difference is statistically significant. But there is also a relationship between birth weight and mother's age, and the mothers of first babies tend to be younger. So the question is: if we control for the age of the mother, are first babies still lighter?\n\nSeveral students in my class are working on projects involving multiple regression, so I want to use this question as an example. I will follow the steps I recommend to my students:\n\n1) Before looking at relationships between variables, look at each variable in isolation. In particular, characterize the distributions and identify issues like outliers or long tails.\n\n2) Look at the variables pairwise. For each pair, look at CDFs and scatterplots, and compute correlations and/or least squares fits.\n\n3) If there seem to be relationships among the variables, look for ways to separate the effects, either by breaking the data into subsets or doing multiple regression.\n\nSo let's proceed.\n\nOne variable at a time\n\nThe variables I'll use are\n1. Mother's age in years,\n2. Birth weight in ounces, and\n3. first, which is a dummy variable, 1 for first babies and 0 for others.\nFor live births we have 9148 records with valid ages; here is the distribution:\nIt looks like there is a little skew to the right, but other than that, nothing to worry about.\n\nWe have 9038 records with valid weights, with this distribution:\nThe middle of the distribution is approximately normal, with some jaggies due to round-off. In the tails there are some values that are are certainly errors, but it is hard to draw a clear line between exceptional cases and bad data. It might be a good idea to exclude some extreme values, but for the analysis below I did not.\n\nThere are only two values for first, so it's not much of a distribution, but with categorical data, we should check that we have enough values in each bin. As it turns out, there are 4413 first babies and 4735 others, so that's just fine.\n\nOne pair at a time\n\nTo characterize the relationship between weight and first, we compare the CDF of weights for first babies and others:\nThere is some space between the distributions, and the difference in means is 2 ounces. It's not obvious whether that difference is statistically significant, but it is, with p < 0.001.\n\nSimilarly we can compare the CDF of mother's age for first babies and others:\nHere there is clearly space between the distributions. The difference in means is 3.6 years, which is significant (no surprise this time).\n\nIt is not as easy to see the relationship between age and birthweight. I often tell my students to start with a scatterplot:\nBut in this case it's not much help. If there is a relationship there, it is hard to see. An alternative is to break the age range into bins and compute the mean in each bin. Here's what that looks like with 2-year bins:\nWe can't take the first and last points too seriously; there are not many cases in those bins. And ideally I should represent the variability in each bin so we have a sense of whether the apparent differences are real. Based on this figure, it looks like there is a relationship, but it might be nonlinear.\n\nPearson's coefficient of correlation between age and birthweight is 0.07, which is small but statistically significant. Spearman's coefficient of correlation is 0.10; the difference between the two coefficients is another warning that the relationship is nonlinear.\n\nIf we ignore the non-linearity for now, we can compute a least squares fit for birthweight as a function of age. The slope is 0.28, which means that we expect an additional 0.28 ounces per year of age. Since first mothers are 3.6 years younger than others, we expect their babies to be 1.0 ounces lighter. In fact, they are 2.0 ounces lighter, so the linear model of weight vs age accounts for 50% of the observed difference.\n\nMultiple regression\n\nSo far I have been using the thinkstats libraries to compute correlation coefficients and least squares fits. But for multiple regression I am going to break out rpy, which is the Python interface to R a \"language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories.\" To see how it works, you can download the code I used in this section: age_lm.py\n\nThe first model I ran is the same linear model we were just looking at:\n\nweight = intercept + slope * age\n\nIn R's shorthand, that's:\n\nweights ~ ages\n\nHere are the results:\n\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 109.28635 1.08775 100.470 < 2e-16 ***\nages 0.27926 0.04258 6.559 5.72e-11 ***\n\nMultiple R-squared: 0.004738, Adjusted R-squared: 0.004628\n\nThe intercept is 109 ounces; the slope is 0.28 ounces per year, which what we saw before---comparing my implementation to R makes me more confident that R is correct :)\n\nThe standard error provides a confidence interval for the estimates; plus or minus 2 standard errors is (roughly) a 95% confidence interval.\n\nThe last column is the p-value, which is very small, indicating that the slope and intercept are significantly different from 0. The t-value is the test statistic used to compute the p-value, but I don't know why it gets reported; it doesn't mean much.\n\nSince the p-values are so small, it might be surprising that R2 is so low, only 0.0047. But there is no contradiction. We can say with high confidence that there is a relationship between these variables; nevertheless, birth weight is highly variable, and even if you know the age of the mother, that does not reduce the variability by much.\n\nTo understand adjusted R2, consider this: if you add more explanatory variables to a model, R2 usually goes up even if there is no real relationship. The adjusted R2 takes this into account, which makes it more meaningful to compare models with a different number of variables.\n\nNow let's add first as an explanatory variable, so the model looks like this:\n\nweights ~ first + ages\n\nHere are the results:\n\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 110.62791 1.24198 89.073 < 2e-16 ***\nfirst -1.11688 0.49940 -2.236 0.0253 *\nages 0.24708 0.04493 5.499 3.93e-08 ***\n\nMultiple R-squared: 0.005289, Adjusted R-squared: 0.005069\n\nThe coefficient for first is -1.1, which means that we expect first babies to be 1.1 ounces lighter, controlling for age. The p-value for this estimate is 2.5%, which I consider borderline significant.\n\nThe coefficient for ages is about the same as before, and significant. And R2 is a little higher, but still small.\n\nBut remember that the relationship between weight and age is non-linear. We can explore that by introducing a new variable:\n\nages2 = ages^2\n\nNow if we run this model:\n\nweights ~ ages + ages2\n\nWe are effectively fitting a parabola to the weight vs age curve.\n\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 89.151237 4.407677 20.226 < 2e-16 ***\nages 1.898151 0.346071 5.485 4.25e-08 ***\nages2 -0.031002 0.006577 -4.714 2.47e-06 ***\n\nMultiple R-squared: 0.00718, Adjusted R-squared: 0.00696\n\nEstimates for both variables are significant. The coefficient for ages2 is negative, which means that the parabola has downward curvature, as expected. And R2 is a little bigger.\n\nFinally, we can bring it all together:\n\nweights ~ first + ages + ages2\n\nWith this model we get:\n\nEstimate Std. Error t value Pr(>|t|)\n(Intercept) 91.07627 4.56813 19.937 < 2e-16 ***\nfirst -0.80708 0.50373 -1.602 0.109\nages 1.79807 0.35163 5.113 3.23e-07 ***\nages2 -0.02953 0.00664 -4.447 8.80e-06 ***\n\nMultiple R-squared: 0.007462, Adjusted R-squared: 0.007132\n\nWhen we include the parabolic model of weight and age, the coefficient for first gets smaller, and the p-value is 11%.\n\nI conclude that the difference in weight for first babies is explained by the difference in mothers' ages. When we control for age, the difference between first babies and others is no longer statistically significant. It is still possible that there is a small difference in weight for first babies, but this dataset provides little evidence for it.\n\nMonday, November 28, 2011\n\nEstimating the age of renal tumors\n\nUPDATE April 2, 2012: I wrote a paper describing this work and submitted it to arXiv. You can download it here.\n\nAbstract: We present a Bayesian method for estimating the age of a renal tumor given its size. We use a model of tumor growth based on published data from observations of untreated tumors. We find, for example, that the median age of a 5 cm tumor is 20 years, with interquartile range 16-23 and 90% confidence interval 11-30 years.\n\n-----\n\nA few weeks ago I read this post on reddit.com/r/statistics:\n\"I have Stage IV Kidney Cancer and am trying to determine if the cancer formed before I retired from the military. ... Given the dates of retirement and detection is it possible to determine when there was a 50/50 chance that I developed the disease? Is it possible to determine the probability on the retirement date? My tumor was 15.5 cm x 15 cm at detection. Grade II.\"\nI contacted the original poster and got more information; I learned that veterans get different benefits if it is \"more likely than not\" that a tumor formed while they were in military service (among other considerations).\n\nBecause renal tumors grow slowly, and often do not cause symptoms, they are often left untreated. As a result, we can observe the rate of growth for untreated tumors by comparing scans from the same patient at different times. Several papers have reported these growth rates.\n\nI collected data from a paper by Zhang et al. I contacted the authors to see if I could get raw data, but they refused on grounds of medical privacy. Nevertheless, I was able to extract the data I needed by printing one of their graphs and measuring it with a ruler. It's silly, but it works.\n\nThey report growth rates in reciprocal doubling time (RDT), which is in units of doublings per year. So a tumor with RDT=1 doubles in volume each year; with RDT=2 it quadruples in the same time, and with RDT=-1, it halves. The following figure shows the distribution of RDT for 53 patients:\n\nThe squares are the data points from the paper; the line is a model I fit to the data. The positive tail fits an exponential distribution well, so I used a mixture of two exponentials.\n\nAs a simple model of tumor growth, I chose the median value of RDT, which is 0.45, and used that to estimate the age of a tumor with maximum dimension 15.5 cm. Here's what I wrote in my letter to the Veterans Benefits Administration:\n1. In the largest study I reviewed (53 patients) the median volume doubling time is 811 days. By definition of median, 50% of observed tumors grew faster and 50% slower. By geometry, the doubling time for the maximum linear dimension is approximately (811)(3) = 2433 days or 6.7 years. Therefore, for a tumor with maximum linear dimension 15.5 cm on [diagnosis date], it is as likely as not that the size on [discharge date] was 6 cm.\n2. If the diameter of the tumor on [discharge date] were 1 mm and it grew to 15.5 cm by [diagnosis date], the effective volume doubling time would be 150 days. Fewer than half of the tumors in the studies I reviewed grew at this rate or faster, so it is more likely than not that the tumor grew more slowly.\nBased on this analysis, I conclude that it is more likely than not that this tumor formed prior to [discharge date].\nI think this model is sufficient to answer the question as posed, but it occurred to me later (in the shower, where all good ideas come from) that we can do better. By sampling from the distribution of growth rates and generating simulated tumor histories, we can estimate the distribution of size as a function of time and then, using Bayes's Theorem, get the distribution of age as a function of size.\n\nHere's how. The simulation starts with a small tumor (0.3 cm) and runs these steps:\n1. Choose a growth rate from the distribution of RDT.\n2. Compute the size of the tumor at the end of an 8 month interval (that's the median interval between measurements in the data source).\n3. Repeat until the tumor is 20 cm in diameter.\nThis figure shows 100 simulated growth trajectories:\nThe line at 10 cm shows the range of ages for tumors at that size: the fastest-growing tumor gets there in 8 years; the slowest takes more than 35.\n\nBy drawing the line at different sizes, we can estimate the distribution of age as a function of size. There's an implicit use of Bayes's Theorem in there, but because I did everything discretely, I didn't have to think too hard. This figure shows the distribution of age for a few different sizes:\nNot surprisingly, bigger tumors are likely to be older. For any size, we can generate the CDF and compute the median, interquartile range, and 90% confidence interval. Here's what that looks like (with size on a log scale):\nThe points are data from simulation, which produces some variability due to discrete approximation. The lines are fitted to the data.\n\nWith these results, doctors can look up the size of a tumor and get the distribution of ages; for example, the median age of a 15 cm tumor is 27 years, with interquartile range 22-31 and 90% confidence interval 16-39 years.\n\nThis model yields more detail than the simple model I started with, but the results are qualitatively similar; a tumor this size is more likely than not to have formed prior to the original poster's date of discharge. It looks like there is also a good chance that it formed prior to enlistment, but I don't know what the VBA makes of that.\n\n-----\n\nI think this model makes the best use of the available data, but there are several limitations:\n\n1) The factors that limit tumor growth are different for very small tumors, so the observed data doesn't apply. We can extrapolate back to when the tumor was small (I chose 0.3 cm, a bit smaller than the smallest tumor in the study). That gives us a lower bound on the age of the tumor, but we can't say much about when the first cancer cell appeared.\n\n2) The distribution of growth rates is based on a sample of 53 patients. A different sample would yield a different distribution. I could use resampling to characterize this source of error, but haven't.\n\n3) The growth model does not take into account tumor subtype or grade, which is consistent with the conclusion of Zhang et al: “Growth rates in renal tumors of different sizes, subtypes and grades represent a wide range and overlap substantially.”\n\n4) In our model of tumor growth, the growth rate during each interval is independent of previous growth rates. It is plausible that, in reality, tumors that have grown quickly in the past are more likely to grow quickly.\n\nIf this correlation exists, it affects the location and spread of the results. For example, running simulations with ρ = 0.4 increases the estimated median age by about a year, and the interquartile range\nby about 3 years. However, if there were a strong serial correlation in growth rate, there would be also be a correlation between tumor volume and growth rate, and prior work has shown no such relationship.\n\nThere could still be a weak serial correlation, but since there is currently no evidence for it, I ran these simulations with ρ = 0.\n\nMonday, November 21, 2011\n\nComment on \"Racism and Meritocracy\"\n\nEric Ries wrote an article for TechCrunch last week, talking about racism and meritocracy among Silicon Valley entrepreneurs. It's a good article; you should read it and then come back.\n\nAlthough I mostly agree with him, Ries undermines his argument with a statistical bait-and-switch: he starts out talking about race, but most of the article (and the slide deck he refers to) are about gender. Unfortunately, for both his argument and the world, the race gap is bigger than the gender gap, and it is compounded because racial minorities, unlike women, are minorities.\n\nTo quantify the size of the gap, I use data from Academically Adrift",
null,
", a recent book that reports the results from the Collegiate Learning Assessment (CLA) database, collected by the Council for Aid to Education, \"a national nonprofit organization ... established in 1952 to advance corporate support of education and to conduct policy research on higher education...\"\n\n\"The CLA consists of three types of prompts within two types of task: the Performance Task and the Analytic Writing Task...The Analytic Writing Task includes a pair of prompts called Make-an-Argument and Critique-an-Argument.\n\"The CLA uses direct measures of skills in which students perform cognitively demanding tasks... All CLA measures are administered online and contain open-ended prompts that require constructed responses. There are no multiple-choice questions. The CLA tasks require that students integrate critical thinking and written communication skills. The holistic integration of these skills on the CLA tasks mirrors the requirements of serious thinking and writing tasks faced in life outside of the classroom. \"\nThis is not your father's SAT. The exam simulates realistic workplace tasks and assesses skills that are relevant to many jobs, including (maybe especially) entrepreneurship.\n\nOn this assessment, the measured differences between black and white college students are stark. For white college students, the mean and standard deviation are 1170 ± 179. For black students, they are 995 ± 167.\n\nTo get a sense of what that difference looks like, suppose there are just two groups, which I call \"blue\" and \"green\" as a reminder that I am presenting an abstract model and not a realistic description. This figure shows Gaussian distributions with the parameters reported in Academically Adrift",
null,
":\n\nThe difference in means is 175 points, which is about one standard deviation. If we select people from the upper tail, the majority are blue. But the situation is even worse if greens are a minority. If greens make up 20% of the population, the picture looks like this:\n\nThe fraction of greens in the upper tail is even smaller. If, as Ries suggests, \"Here in Silicon Valley, we’re looking for the absolute best and brightest, the people far out on the tail end of aptitude,\" the number of greens in that tail is very small.\n\nHow small? That depends on where we draw the line. If we select people who score above 1200, which includes 37% of the population, we get 6% greens (remember that they are 20% of the hypothetical population). Above 1300 the proportion of greens is 3%, and above 1400 only 2%.\n\nAnd that's not very \"far out on the tail end of aptitude.\" Above 1500, we are still talking about 3% of the general population, but more than 99% of them are blue. So in this hypothetical world of blues and greens, perfect meritocracy does not lead to proportional representation.\n\nRies suggests that blind screening of applicants might help. I think the system he proposes is a good idea, because it improves fairness and also the perception of fairness. But if the racial gap in Y Combinator's applicant pool is similar to the racial gap in CLA scores, making the selection process more meritocratic won't make a big difference.\n\nThese numbers are bad. I'm sorry to be reporting them, and if I know the Internet, some people are going to call me a racist for doing it. But I didn't make them up, and I'm pretty sure I did the math right. Of course, you are welcome to disagree with my conclusions.\n\nHere are some of the objections I expect:\n\n1) The CLA does not capture the full range of skills successful entrepreneurs need.\n\nOf course it doesn't; no test could. But I chose the CLA because I think it assesses thinking skills better than other standardized tests, and because the database includes \"over 200,000 student results across hundreds of colleges.\" I can't think of a better way to estimate the magnitude of the racial gap in the applicant pool.\n\n2) The application process is biased against racial minorities and women.\n\nThe statistics I am reporting here, and my analysis of them, don't say anything about whether or not the application process is biased. But they do suggest (a) We should not assume that because racial minorities are underrepresented among Silicon Valley entrepreneurs, racial bias explains a large part of the effect, and (b) We should not assume that eliminating bias from the process will have a large effect.\n\nOf course, trying to eliminate bias is the right thing to do, whether the effect is big or small.\n\n-----\n\nNOTE: The range of scores for the CLA was capped at 1600 until 2007, which changed the shape of the distribution at the high end. For those years, the Gaussian distributions in the figures are not exactly right, but I don't think it affects my analysis much. Since 2007, scores are no longer capped, but I don't know what the tail of the distribution looks like now.\n\nEDIT 11-28-11: I revised a few sentences to clarify whether I was talking about representation or absolute numbers. The fraction of greens in the population affects the absolute numbers in the tail but not their representation.\n\nThursday, November 10, 2011\n\nGirl Named Florida solutions\n\nIn The Drunkard's Walk, Leonard Mlodinow presents \"The Girl Named Florida Problem\":\n\"In a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?\"\nI like this problem, and I use it on the first day of my class to introduce the topic of conditional probability. But I've decided that it's too easy. To give it a little more punch, I've decided to combine it with the Red-Haired Problem from last week:\nIn a family with two children, what are the chances, if at least one of the children is a girl with red hair, that both children are girls?\nJust like last week, you can make some simplifying assumptions:\nAbout 2% of the world population has red hair. You can assume that the alleles for red hair are purely recessive. Also, you can assume that the Red Hair Extinction theory is false, so you can apply the Hardy–Weinberg principle. And you can ignore the effect of identical twins.\nBefore I present my solution, I want to sneak up on it with a series of warm-up problems.\n1. P[GG | two children]: if a family has two children, what is the chance that they have two girls?\n2. P[GG | two children, at least one girl]: if we know they have at least one girl, what is the chance that they have two girls?\n3. P[GG | two children, older child is a girl]: if the older child is a girl, what is the chance that they have two girls?\n4. P[GG | two children, at least one is a girl named Florida].\n5. P[GG | two children, at least one is a girl with red hair, and the parents have brown hair].\n6. P[GG | two children, at least one is a girl with red hair].\n\nProblem 1: P[GG | two children]\n\nIf we assume that the probability that each child is a girl is 50%, then P[GG | two children] = 1/4.\n\nProblem 2: P[GG | two children, at least one girl]\n\nThere are four equally-likely kinds of two child families: BB, BG, GB and GG. We know that BB is out, so the conditional probability is\n\nP[GG | at least one girl] = P[GG and at least one girl] / P[at least one girl] = 1/3.\n\nProblem 3: P[GG | two children, older child is a girl]\n\nNow there are only two possible families, GB and GG, so the conditional probability is 1/2. Informally we can argue that once we know about the older child we can treat the younger child as independent. But if there's one thing we learn from this problem, it's that our intuition for independence is not reliable.\n\nProblem 4: P[GG | two children, at least one girl named Florida]\n\nHere's the one that makes people's head hurt. For each child, there are three possibilities, boy, girl not named Florida, and girl named Florida, with these probabilities:\n\nB: 1/2\nG: 1/2 - x\nGF: x\n\nwhere x is the unknown percentage of people who are girls named Florida. Of families with at least one girl named Florida, there are these possible combinations, with these probabilities\n\nB GF: 1/2 x\nGF B: 1/2 x\nG GF: x (1/2 - x)\nGF G: x (1/2 - x)\nGF GF: x^2\n\nThe highlighted cases have two girls, so the probability we want is the sum of the highlighted cases over the sum of all cases. With a little algebra, we get:\n\nP(GG | at least one girl named Florida) = (1 - x) / (2 - x)\n\nAssuming that Florida is not a common name, x approaches 0 and the answer approaches 1/2. So it turns out, surprisingly, that the name of the girl is relevant information.\n\nAs x approaches 1/2, the answer converges on 1/3. For example, if we know that at least one child is a girl with two X chromosomes, x is close to 1/2 and the problem reduces to Problem 2.\n\nIf this problem is still making your head hurt, this figure might help:\nHere B a boy, Gx is a girl with some property X, and G is a girl who doesn't have that property. If we select all families with at least one Gx, we get the five blue squares (light and dark). The families with two girls are the three dark blue squares.\n\nIf property X is common, the ratio of dark blue to all blue approaches 1/3. If X is rare, the same ratio approaches 1/2.\n\nProblem 5: P[GG | two children, at least one girl with red hair, parents have brown hair]\n\nIf the parents have brown hair and one of their children has red hair, we know that both parents are heterozygous, so their chance of having a red-haired girl is 1/8.\n\nUsing the girl-named-Florida formula, we get\n\nP[GG | two children, at least one girl with red hair, parents have brown hair] = (1 - 1/8) / (2 - 1/8) = 7/15.\n\nAnd finally:\n\nProblem 6: P[GG | two children, at least one girl with red hair]\n\nIn this case we don't know the genotype of the parents. There are three possibilities: Aa Aa, Aa aa, and aa aa.\n\n1) Use the prevalence of red hair to compute the prior probabilities of each parental genotype.\n\n2) Use the evidence (at least one girl with red hair) to compute the posteriors.\n\n3) For each combination, compute the conditional probability. We have already computed\n\nP(GG | two children, at least one with red hair, Aa Aa) = 7/15\n\nThe others are\n\nP(GG | two children, at least one with red hair, Aa aa) = 3/7\nP(GG | two children, at least one with red hair, aa aa) = 1/3\n\n4) Apply the law of total probability to get the answer.\n\nI'm too lazy to do the algebra, so I got Mathematica to do it for me. Here is the notebook with the answer.\n\nIn general, if p is the prevalence of red hair alleles,\n\nP(GG | two children, at least one with red hair) = (p^2 + 2p - 7) / (p^2 + 2p - 15)\n\nIf the prevalence of red hair is 0.02, then p = sqrt(0.02) = 0.141, and\n\nP(GG | two children, at least one with red hair) = 45.6%\n\nCongratulations to Professor Ted Bunn at the University of Richmond, the only person who submitted a correct answer before the deadline!\n\nAt least, I think it's the right answer. Maybe we both made the same mistake.\n\nFor more fun with probability, see Chapter 5 of my book, Think Stats, which you can read here, or buy here.\n\nMonday, November 7, 2011\n\nThe red-haired girl named Florida\n\nIn The Drunkard's Walk, Leonard Mlodinow presents \"The Girl Named Florida Problem\":\n\"In a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?\"\nI like this problem, and I use it on the first day of my class to introduce the topic of conditional probability. But I've decided that it's too easy. To give it a little more punch, I've decided to combine it with the Red-Haired Problem from last week:\nIn a family with two children, what are the chances, if at least one of the children is a girl with red hair, that both children are girls?\n[Edit: I clarified the wording to say that at least one of the children is a girl with red hair. To be even more precise, I am looking for the conditional probability P(two girls | at least one girl with red hair).]\n\nJust like last week, you can make some simplifying assumptions:\nAbout 2% of the world population has red hair. You can assume that the alleles for red hair are purely recessive. Also, you can assume that the Red Hair Extinction theory is false, so you can apply the Hardy–Weinberg principle. And you can ignore the effect of identical twins.\nHere is my solution.\n\nFor more fun with probability, see Chapter 5 of my book, Think Stats, which you can read here, or buy here.\n\nThursday, November 3, 2011\n\nSomebody bet on the Bayes\n\nIn last week's post I wrote solutions to some of my favorite Bayes's Theorem problems, and posed this new problem:\nIf you meet a man with (naturally) red hair, what is the probability that neither of his parents has red hair?\nHints: About 2% of the world population has red hair. You can assume that the alleles for red hair are purely recessive. Also, you can assume that the Red Hair Extinction theory is false, so you can apply the Hardy–Weinberg principle.\nGiven the prevalence of red hair, we know what fraction of the population is homozygous recessive. To solve the problem, we also need to know how many are heterozygous and homozygous dominant.\n\nI'll use a to represent the recessive allele (or alleles) for red hair, and A for the dominant alleles that code for other colors. p is the prevalence of a and q is the prevalence of A, so p+q = 1.\n\nIf these prevalences are not changing over time, and they don't affect people's mating decisions, we can invoke the Hardy-Weinberg principle to get:\n\nP(AA) = prevalence of homozygous dominant = q**2\nP(Aa) = prevalence of heterozygous = 2 * p * q\nP(aa) = prevalence of homozygous recessive = p**2\n\nAnd P(AA) + P(Aa) + P(aa) = 1.\n\nGiven (aa), we can compute p, q and:\n\nP(Aa) = 0.243\nP(AA) = 0.737\n\nNow if a child has red hair, both parents have at least one recessive allele, so the possible combinations are (Aa Aa), (Aa aa), and (aa aa). If we assume, again, that mating decisions are not based on hair color, we can get the prevalence of each parental pair:\n\nP(Aa Aa) = Aa**2\nP(Aa aa) = 2 Aa aa\nP(aa aa) = aa**2\n\nAnd we can use those as the priors. The evidence is\n\nE: the child has red hair\n\nTo get the likelihoods, we apply Mendelian genetics:\n\nP(E | Aa Aa) = 0.25\nP(E | Aa aa) = 0.5\nP(E | aa aa) = 1.0\n\nFinally, applying Bayes's Theorem, we have\n\nP(Aa Aa | E) = P(Aa Aa) P(E | Aa Aa) / P(E)\n\nAnd the answer is 0.737. With a little algebra we can show that\n\nP(Aa Aa | E) = P(AA)\n\nThat is, the probability that neither parent has red hair is exactly the fraction of the population that is homozygous dominant.\n\nAlmost 75% of red-haired people come from parents with non-red hair, which might explain why a \"red haired child\" is a metaphor for a child that doesn't resemble his parents. In the expression, \"beat like a red haired step child,\" some of the humor (for people who find child abuse funny) comes from the suggestion that the parentage of a red haired child is suspect.\n\nBut why should red hair be funnier than blue eyes or blonde hair? It turns out that we can answer this question mathematically. If the prevalence of red hair were higher, say 10%, most red haired people would have at least one red-haired parent, and that would be less funny.\n\nIn general, as the prevalence of the recessive phenotype increases, the potential for amusing insinuations of infidelity decreases; near 0 it drops off steeply, as shown in this figure:\n\nSince I believe I am the first person to quantify this effect, I humbly submit that it should be called \"Downey's inverse law of mailman jokes.\"\n\nFor more fun with probability, see Chapter 5 of my book, Think Stats, which you can read here, or buy here.\n\n-----\n\nIf you don't get the title of this post, it is a play on \"Somebody bet on the bay,\" a lyric from the minstrel song \"Camptown Races.\" A bay is a horse with a reddish-brown coat, so I thought it was a pretty good fit."
] |
[
null,
"https://lh5.googleusercontent.com/proxy/h6obgzslYtl3OgZ3Rp9ZXk_LfTw6l8hNjOU_joPnJ73joMRjFFv2y00VV0X_sX_SNY7ZrjdrT0mYIs_dwH_lALWPR5nMPACmDx-UQHVSGpslJNg3YmwRxCmtoNUnbNBEOX2oOq51J_tZ1gGIgBgo8V6Tvb35-b_TDeg=s0-d",
null,
"https://lh5.googleusercontent.com/proxy/h6obgzslYtl3OgZ3Rp9ZXk_LfTw6l8hNjOU_joPnJ73joMRjFFv2y00VV0X_sX_SNY7ZrjdrT0mYIs_dwH_lALWPR5nMPACmDx-UQHVSGpslJNg3YmwRxCmtoNUnbNBEOX2oOq51J_tZ1gGIgBgo8V6Tvb35-b_TDeg=s0-d",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.92524177,"math_prob":0.9177286,"size":7129,"snap":"2022-05-2022-21","text_gpt3_token_len":1760,"char_repetition_ratio":0.12898245,"word_repetition_ratio":0.11996644,"special_character_ratio":0.27254874,"punctuation_ratio":0.14256619,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9614257,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,6,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-20T20:30:02Z\",\"WARC-Record-ID\":\"<urn:uuid:1aeca12d-0c7b-4aad-98e1-a13c3fadf47b>\",\"Content-Length\":\"173929\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e40b5466-53be-4813-8e9d-5c72df2bbb4d>\",\"WARC-Concurrent-To\":\"<urn:uuid:5a30ec10-9c01-4712-9b2a-dd64d6bf750b>\",\"WARC-IP-Address\":\"172.217.1.193\",\"WARC-Target-URI\":\"https://allendowney.blogspot.com/2011/11/\",\"WARC-Payload-Digest\":\"sha1:OIS75UDTD6GNCRZZQYIM37T6MXEUUBKT\",\"WARC-Block-Digest\":\"sha1:LOEOGEWS6F5HKQ3ZFFAWPDK3SZFZW4VM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320302622.39_warc_CC-MAIN-20220120190514-20220120220514-00152.warc.gz\"}"}
|
https://www.cis.upenn.edu/~cis194/fall16/hw/04-typeclasses.html
|
[
"# Homework 4: Graph algorithms\n\nCIS 194: Homework 4\nDue Tuesday, September 27\n\nThe general remarks about style and submittion from the first week still apply.\n\n## Exercise 0: Import the list of mazes\n\nWe have collected your submitted mazes from last week. You can download the code of the mazes. It contains a list of mazes (mazes) and a longer list including broken mazes (extraMazes). Paste them into your file, at the very end.\n\nBecause the starting position is relevant, we added a data type to go along with the maze:\n\ndata Maze = Maze Coord (Coord -> Tile)\nmazes :: List Maze\nmazes = …\nextraMazes :: List Maze\nextraMazes = …\n\n## Exercise 1: More polymorphic list function\n\nImplement these generally useful functions:\n\nelemList :: Eq a => a -> List a -> Bool\nappendList :: List a -> List a -> List a\nlistLength :: List a -> Integer\nfilterList :: (a -> Bool) -> List a -> List a\nnth :: List a -> Integer -> a\n\nThese should do what their name and types imply:\n\n• elemList x xs is True if and only if at least one entry in xs equals to x.\n• appendList xs ys should be the list containing the entries of xs followed by those of ys, in that order.\n• listLength xs should be the number of entries in xs.\n• filterList p xs should be the list containing those entries x of xs for which p x is true.\n• nths xs n extracts the $$n$$th entry of the list (start counting with 1). If $$n$$ is too large, you may abort the program (by writing error \"list too short\", which is an expression that can be used at any type). This is not good style, but shall do for now.\n\n(Read exercise 3 first, to have understand why this is an interesting function.)\n\nThe algorithm you have to implement below can be phrased very generally, and we want it to be general. So implement a function\n\nisGraphClosed :: Eq a => a -> (a -> List a) -> (a -> Bool) -> Bool\n\nso that in a call isGraphClosed initial adjacent isOk, where the parameters are\n\n• initial, an initial node,\n• adjacent, a function that for every node lists all walkable adjacent nodes and\n• isOk, which checks if the node is ok to have in the graph,\n\nthe function returns True if all reachable nodes are “ok” and False otherwise.\n\nNote that the graph described by adjacent can have circles, and you do not want your program to keep running in circles. So you will have to remember what nodes you have already visted.\n\nThe algorithm follows quite naturally from handling the various cases in a local helper function go that takes two arguments, namely a list of seen nodes and a list of nodes that need to be handled. If the latter list is empty, you are done. If it is not empty, look at the first entry. Ignore it if you have seen it before. Otherwise, if it is not ok, you are also donw. Otherwise, add its adjacent elements to the list of nodes to look ak.\n\nYou might find it helpful to define a list allDirections :: List Direction and use mapList and filterList when implementing adjacent.\n\n## Exercise 3: Check closedness of mazes\n\nWrite a function\n\nisClosed :: Maze -> Bool\n\nthat checks whether the maze is closed. A maze is closed if\n\n• the starting position is either Ground or Storage and\n• every reachable tile is either Ground, Storage or Box.\n\nUse isGraphClosed to do the second check. Implement adjacent so that isGraphClosed walks everywhere where there is not a Wall (including Blank). Implement isOk so that Blank tiles are not ok.\n\nWith the following function you can visualize a list of booleans:\n\npictureOfBools :: List Bool -> Picture\npictureOfBools xs = translated (-fromIntegral k /2) (fromIntegral k) (go 0 xs)\nwhere n = listLength xs\nk = findK 0 -- k is the integer square of n\nfindK i | i * i >= n = i\n| otherwise = findK (i+1)\ngo _ Empty = blank\ngo i (Entry b bs) =\ntranslated (fromIntegral (i mod k))\n(-fromIntegral (i div k))\n(pictureOfBool b)\n& go (i+1) bs\n\npictureOfBool True = colored green (solidCircle 0.4)\npictureOfBool False = colored red (solidCircle 0.4)\n\nLet exercise3 :: IO () be the visualization of isClosed applied to every element of extraMazes. Obviously, mapList wants to be used here.\n\n## Exercise 4: Multi-Level Sokoban\n\nExtend your game from last week (or the code from the lecture) to implement multi-level sokoban.\n\n• Extend the State with a field of type Integer, to indicate the current level (start counting at 1).\n• The initial state should start with level 1. The initial coordinate is obtained read from the entry in maze.\n• Your handle and draw functions will now need to take an additional argument, the current maze, of type Coord -> Tile, instead of refering to a top-level maze function. Any helper functions (e.g. noBoxMaze) will also have to take this as an argument. This requires many, but straight-forward changes to the code: You can mostly, without much thinking:\n\n• Check the compier errors for an affected function, say foo.\n• Add (Coord -> Tile) -> to the front of foo’s type signature, .\n• Add a new first parameter maze to foo\n• Everywhere where foo is called, add maze as an argument.\n• Repeat.\n\nTo get the current maze, use nth from exercise 1. Of course, make sure you never use nth with a too-short list. A variant nthMaze :: Integer -> (Coord -> Tile) that gets the maze component of the corresponding entry in mazes will also be handy whenever you have the State, but need a maze :: Coord -> Tile.\n\n• If the level is solved and the current level is not the last (use listLength from above) the space bar should load the next level.\n\nThere is some code to be shared with the calculation of the initial state! Maybe the same function loadLevel :: Integer -> State can be used in both situations.\n• If the level is solved and the current leve is the last, show a differnt message (e.g. “All done” instead of “You won”).\n\nLet exercise4 :: IO () be this interaction, wrapped in withUndo, withStartScreen and resetable."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.84148246,"math_prob":0.8753116,"size":5828,"snap":"2019-43-2019-47","text_gpt3_token_len":1477,"char_repetition_ratio":0.10645604,"word_repetition_ratio":0.02743614,"special_character_ratio":0.24193548,"punctuation_ratio":0.124333926,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96263,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-19T01:29:42Z\",\"WARC-Record-ID\":\"<urn:uuid:aa58d19b-6899-45c2-b5ad-7250e7a75829>\",\"Content-Length\":\"12538\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a7b25ac1-ae3f-42ed-a838-933ba4b62043>\",\"WARC-Concurrent-To\":\"<urn:uuid:42276793-3908-46f6-8301-2d8cfd6deb59>\",\"WARC-IP-Address\":\"158.130.69.163\",\"WARC-Target-URI\":\"https://www.cis.upenn.edu/~cis194/fall16/hw/04-typeclasses.html\",\"WARC-Payload-Digest\":\"sha1:DHGHS3DJYNQG66KKVVBMXRKFAXPCW2WC\",\"WARC-Block-Digest\":\"sha1:TFUOQGXZGZSTAJUMAS755CZAYSKLHJIY\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496669868.3_warc_CC-MAIN-20191118232526-20191119020526-00174.warc.gz\"}"}
|
https://www.cpalms.org/PreviewCourse/Export/13029
|
[
"",
null,
"# Geometry (#1206310)\n\nThis document was generated on CPALMS - www.cpalms.org\nYou are not viewing the current course, please click the current year’s tab.\n\n#### Course Standards\n\nName Description\nMAFS.912.G-C.1.1: Prove that all circles are similar.\nMAFS.912.G-C.1.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.\nMAFS.912.G-C.1.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.\nMAFS.912.G-C.2.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.\nMAFS.912.G-CO.1.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.\nMAFS.912.G-CO.1.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).\nMAFS.912.G-CO.1.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.\nMAFS.912.G-CO.1.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.\nMAFS.912.G-CO.1.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.\nMAFS.912.G-CO.2.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.\nMAFS.912.G-CO.2.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.\nMAFS.912.G-CO.2.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.\nMAFS.912.G-CO.3.9: Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.\nMAFS.912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.\nMAFS.912.G-CO.3.11: Prove theorems about parallelograms; use theorems about parallelograms to solve problems. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.\nMAFS.912.G-CO.4.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.\n\n Clarifications:Geometry - Fluency Recommendations Fluency with the use of construction tools, physical and computational, helps students draft a model of a geometric phenomenon and can lead to conjectures and proofs.\nMAFS.912.G-CO.4.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.\nMAFS.912.G-GMD.1.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.\nMAFS.912.G-GMD.1.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.\nMAFS.912.G-GMD.2.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.\nMAFS.912.G-GPE.1.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.\nMAFS.912.G-GPE.2.4: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).\n\n Clarifications:Geometry - Fluency Recommendations Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.\nMAFS.912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).\n\n Clarifications:Geometry - Fluency Recommendations Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.\nMAFS.912.G-GPE.2.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.\nMAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.\n Clarifications:Geometry - Fluency Recommendations Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.\nMAFS.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).\nMAFS.912.G-MG.1.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).\nMAFS.912.G-MG.1.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).\nMAFS.912.G-SRT.1.1: Verify experimentally the properties of dilations given by a center and a scale factor:\n1. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.\n2. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.\nMAFS.912.G-SRT.1.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.\nMAFS.912.G-SRT.1.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.\nMAFS.912.G-SRT.2.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.\nMAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.\n\n Clarifications:Geometry - Fluency Recommendations Fluency with the triangle congruence and similarity criteria will help students throughout their investigations of triangles, quadrilaterals, circles, parallelism, and trigonometric ratios. These criteria are necessary tools in many geometric modeling tasks.\nMAFS.912.G-SRT.3.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.\nMAFS.912.G-SRT.3.7: Explain and use the relationship between the sine and cosine of complementary angles.\nMAFS.912.G-SRT.3.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.\nMAFS.K12.MP.1.1:\n\nMake sense of problems and persevere in solving them.\n\nMathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.\n\nMAFS.K12.MP.2.1:\n\nReason abstractly and quantitatively.\n\nMathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.\n\nMAFS.K12.MP.3.1:\n\nConstruct viable arguments and critique the reasoning of others.\n\nMathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.\n\nMAFS.K12.MP.4.1:\n\nModel with mathematics.\n\nMathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.\n\nMAFS.K12.MP.5.1: Use appropriate tools strategically.\n\nMathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.\nMAFS.K12.MP.6.1:\n\nAttend to precision.\n\nMathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.\n\nMAFS.K12.MP.7.1:\n\nLook for and make use of structure.\n\nMathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.\n\nMAFS.K12.MP.8.1:\n\nLook for and express regularity in repeated reasoning.\n\nMathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.\n\nLAFS.910.RST.1.3: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.\nLAFS.910.RST.2.4: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.\nLAFS.910.RST.3.7: Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.\nLAFS.910.SL.1.1: Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.\n1. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.\n2. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.\n3. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.\n4. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.\nLAFS.910.SL.1.2: Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source.\nLAFS.910.SL.1.3: Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence.\nLAFS.910.SL.2.4: Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task.\nLAFS.910.WHST.1.1: Write arguments focused on discipline-specific content.\n1. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence.\n2. Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form and in a manner that anticipates the audience’s knowledge level and concerns.\n3. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.\n4. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.\n5. Provide a concluding statement or section that follows from or supports the argument presented.\nLAFS.910.WHST.2.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.\nLAFS.910.WHST.3.9: Draw evidence from informational texts to support analysis, reflection, and research.\nELD.K12.ELL.MA.1: English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.\nELD.K12.ELL.SI.1: English language learners communicate for social and instructional purposes within the school setting.\n\n## General Course Information and Notes\n\n### VERSION DESCRIPTION\n\nThe fundamental purpose of the course in Geometry is to formalize and extend students' geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school standards. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The critical areas, organized into five units are as follows.\n\nUnit 1-Congruence, Proof, and Constructions: In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal proof. Students prove theorems using a variety of formats and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.\n\nUnit 2- Similarity, Proof, and Trigonometry: Students apply their earlier experience with dilation and proportional reasoning to build a formal understanding of similarity. They identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean theorem. Students develop the Laws of Sines and Cosines in order to find missing measures of general (not necessarily right) triangles, building on students work with quadratic equations done in the first course. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles.\n\nUnit 3- Extending to Three Dimensions: Students' experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line.\n\nUnit 4- Connecting Algebra and Geometry Through Coordinates: Building on their work with the Pythagorean theorem in 8th grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in the first course. Students continue their study of quadratics by connecting the geometric and algebraic definitions of the parabola.\n\nUnit 5-Circles With and Without Coordinates: In this unit students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations, which relates back to work done in the first course, to determine intersections between lines and circles or parabolas and between two circles.\n\n### GENERAL NOTES\n\nEnglish Language Development ELD Standards Special Notes Section:\nTeachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL's need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:\n\nA.V.E. for Success Collection is provided by the Florida Association of School Administrators: http://www.fasa.net/4DCGI/cms/review.html?Action=CMS_Document&DocID=139. Please be aware that these resources have not been reviewed by CPALMS and there may be a charge for the use of some of them in this collection.\n\nFlorida Standards Implementation Guide Focus Section:\n\nThe Mathematics Florida Standards Implementation Guide was created to support the teaching and learning of the Mathematics Florida Standards. The guide is compartmentalized into three components: focus, coherence, and rigor.Focus means narrowing the scope of content in each grade or course, so students achieve higher levels of understanding and experience math concepts more deeply. The Mathematics standards allow for the teaching and learning of mathematical concepts focused around major clusters at each grade level, enhanced by supporting and additional clusters. The major, supporting and additional clusters are identified, in relation to each grade or course. The cluster designations for this course are below.\n\nMajor Clusters\n\nMAFS.912.G-CO.2 Understand congruence in terms of rigid motions.\n\nMAFS.912.G-CO.3 Prove geometric theorems.\n\nMAFS.912.G-SRT.1 Understand similarity in terms of similarity transformations.\n\nMAFS.912.G-SRT.2 Prove theorems involving similarity.\n\nMAFS.912.G-SRT.3 Define trigonometric ratios and solve problems involving right triangles.\n\nMAFS.912.G-GPE.2 Use coordinates to prove simple geometric theorems algebraically.\n\nMAFS.G-MG.1 Apply geometric concepts in modeling situations.\n\nSupporting Clusters\n\nMAFS.912.G-CO.1 Experiment with transformations in the plane.\n\nMAFS.G-CO.4 Make geometric constructions.\n\nMAFS.912.G-C.1 Understand and apply theorems about circles.\n\nMAFS.912.G-C.2 Find arc lengths and areas of sectors of circles.\n\nMAFS.912.G-GPE.1 Translate between the geometric description and the equation of a conic section.\n\nMAFS.912.G-GMD.1 Explain volume formulas and use them to solve problems.\n\nMAFS.912.G-GMD.2 Visualize relationships between two-dimensional and three-dimensional objects.\n\nNote: Clusters should not be sorted from major to supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting and additional clusters.\n\n### General Information\n\n Course Number: 1206310 Course Path: Section: Grades PreK to 12 Education Courses > Grade Group: Grades 9 to 12 and Adult Education Courses > Subject: Mathematics > SubSubject: Geometry > Abbreviated Title: GEO Number of Credits: One (1) credit Course Attributes: Class Size Core Required Highly Qualified Teacher (HQT) Required Florida Standards Course Course Type: Core Academic Course Course Level: 2 Course Status: Course Approved Grade Level(s): 9,10,11,12 Graduation Requirement: Geometry\n\n#### Educator Certifications\n\n Carnegie Learning FL High School Math Solution, Geometry with HonorsSandy Bartle Finocchi and Amy Jones Lewis - Carnegie Learning, Inc. dba EMC Publishing & Mondo Ed - 1st - 2023",
null,
"enVision Florida B.E.S.T. GeometryKennedy, Milou, Thomas, Zbiek & Cuoco - Savvas Learning Company LLC, formerly known as Pearson K12 Learning LLC. - 1 - 2023",
null,
"Florida GeometryAgile Mind, the Charles A. Dana Center at the University of Texas at Austin - Agile Mind Educational Holdings, Inc. - 2021 - 2021",
null,
"Florida Reveal GeometryCathy L. Seeley , Ed.D; Raj Shah, Ph.D.; Cheryl R. Tobey, M.Ed.; Dinah Zike, M.Ed.; Walter Secada, Ph.D. - McGraw Hill LLC - 1 - 2023",
null,
"Florida's B.E.S.T. Standards for MATH Geometry with CalcChat® and CalcView®Ron Larson and Laurie Boswell - Big Ideas Learning, LLC - 1 - 2023",
null,
"Math Nation: Florida's B.E.S.T. GeometryMath Nation - Math Nation (a division of Study Edge) - 1 - 2023",
null,
"MATHSPACE FLORIDA: Geometry B.E.S.T. 2022 editionHoyt, A., et al. - Mathspace Inc. - 1 - 2022",
null,
""
] |
[
null,
"https://www.cpalms.org/Content/Images/cpalms_color.png",
null,
"https://www.flimadoption.org/https://flimmedia.blob.core.windows.net/flim/bids/a68beff9-79a4-eb11-94b2-0003ff50178a/_thumbnails/2021-MATHbook-FL-TIG-Geo-Vol1[2].jpg",
null,
"https://www.flimadoption.org/https://flimmedia.blob.core.windows.net/flim/bids/9e88b944-f5a9-eb11-94b2-0003ff504e11/_thumbnails/Geometry Front_Cover.jpg",
null,
"https://www.flimadoption.org/https://flimmedia.blob.core.windows.net/flim/bids/59ceabb9-c09e-eb11-85aa-0003ff506bfc/_thumbnails/Florida_thumbs_geometry.jpg",
null,
"https://www.flimadoption.org/https://flimmedia.blob.core.windows.net/flim/bids/8b771483-12b1-eb11-94b2-0003ff504e11/_thumbnails/RM_TE_F_COVER_GEOM_VOL1_1264436122 .jpg",
null,
"https://www.flimadoption.org/https://flimmedia.blob.core.windows.net/flim/bids/261e7d0f-3799-eb11-85aa-0003ff506bfc/_thumbnails/FL_geo_hs_se_cvr.jpg",
null,
"https://www.flimadoption.org/https://flimmedia.blob.core.windows.net/flim/bids/5e4126f2-31b1-eb11-94b2-0003ff504e11/_thumbnails/GEO FINAL.jpg",
null,
"https://www.flimadoption.org/https://flimmedia.blob.core.windows.net/flim/bids/f8ed032a-80a1-eb11-85aa-0003ff502929/_thumbnails/FLORIDA MATH [email protected]",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.88098353,"math_prob":0.9066204,"size":28235,"snap":"2022-05-2022-21","text_gpt3_token_len":6100,"char_repetition_ratio":0.13927951,"word_repetition_ratio":0.019598236,"special_character_ratio":0.20563132,"punctuation_ratio":0.16911487,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97183055,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,null,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-24T12:47:05Z\",\"WARC-Record-ID\":\"<urn:uuid:d85345e5-2319-4c7b-82ad-c3ea685977f8>\",\"Content-Length\":\"111419\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f638cddf-ed48-4b02-b85f-592d7edfee1e>\",\"WARC-Concurrent-To\":\"<urn:uuid:1c89a670-c1d2-447d-93d0-ea1275bfeb64>\",\"WARC-IP-Address\":\"20.49.104.5\",\"WARC-Target-URI\":\"https://www.cpalms.org/PreviewCourse/Export/13029\",\"WARC-Payload-Digest\":\"sha1:NHR6MY3OIFN2MIRI5XQL6E2PNTH6PIWB\",\"WARC-Block-Digest\":\"sha1:JKWHMWF6NBBY3FTBRHJA6OGAI523ZKHN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662572800.59_warc_CC-MAIN-20220524110236-20220524140236-00154.warc.gz\"}"}
|
https://file.scirp.org/Html/2-9801635_60462.htm
|
[
" Comparison of Excitation of Acoustic-Electromagnetic Wave in Piezoelecric Crystal and Crystal with Potential of Deformation\n\nJournal of Electromagnetic Analysis and Applications\nVol.07 No.10(2015), Article ID:60462,5 pages\n10.4236/jemaa.2015.710027\n\nComparison of Excitation of Acoustic-Electromagnetic Wave in Piezoelecric Crystal and Crystal with Potential of Deformation\n\nS. Koshevaya, V. Grimalsky, Y. Kotsarenko, J. Escobedo-Alatorre\n\nAutonomous University of Morelos State, CIICAp, Cuernavaca, Mexico\n\nEmail: [email protected]",
null,
"",
null,
"",
null,
"Received 29 July 2015; accepted 19 October 2015; published 22 October 2015\n\nABSTRACT\n\nIn this article, the comparison of excitation in high frequencies of acoustic-electromagnetic wave in piezoelecric crystal and crystal with potential of deformation GaAs is investigating. Possible mechanisms of coupling different hybrid waves are the piezoeffect and the deformation potential. As a model it is analyzing a film of crystal places between two symmetrical substrates with the other materials without an acoustic contact. This film includes 2D electron gas with a high negative differential conductivity and uniform initial distribution of electrons. The hybrid acoustic-electromagnetic wave and hybrid space charge wave interact. Amplification of space charge wave takes place due to negative differential conductivity in GaAs. This amplification of space charge waves is causing the amplification of acoustic-electromagnetic wave. It is to show that the symmetric modes, emerging as transverse ones, interact more effectively with the space charge waves. Another important result is the following: at the frequencies f ≈ 10 GHz, the excitation efficiency of acoustic-electromagnetic wave with transverse displacement due to piezoeffect is more effective, but at higher frequencies, the deformation potential is dominating.\n\nKeywords:\n\nPiezoelectric Crystal, Deformation Potential, Acoustic-Electromagnetic and Space Charge Waves",
null,
"1. Introduction\n\nThe amplification of the acoustic-electromagnetic waves is very important problem . A possible solution of this problem is the resonant coupling of acoustic waves with the microwave electric field of space charge waves (SCW) in materials possessing negative differential conductivity (NDC) like GaAs . Namely, under pro- pagation in the bias electric field higher than the critical value for observing negative differential conductivity (NDC), the SCW is subject to amplification, and its microwave electric field can achieve high values. Due to piezoeffect or deformation potential, this microwave electric field excites hypersonic acoustic-electromagnetic waves (AEW). In , it is demonstrated that this excitation has a resonant character with respect to the frequency and the thickness of the GaAs film. The critical value of bias electric field in GaAs is Ec = 3.5 kV/cm that it is good for analysis of amplification in different mechanisms like piezoeffect or deformation potential so as other materials have very big critical field like crystal InP and GaN.\n\nThe present paper is focused on theoretical research of excitation of acoustic-electromagnetic waves (AEW) in GaAs films of a sub-micron thickness placed between non-piezoelectric substrates. The spatial increments of SCW due to NDC have been calculated for two mechanisms like piezoeffect and deformation potential. An amplification of SCW is possible for frequencies from 10 GHz for case of piezoeffect. For deformation potential the frequencies range increase from 10 GHz to 30 GHz, so the mechanism of deformation potential is more useful in high frequencies.\n\nThe thin GaAs film plays the role in a transducer of acoustic electromagnetic waves. The amplification has a resonant character, and the intensities of energy may reach the values of 10 W/cm2. The realization of the good amplification has showed that usefulness of hybrid waves in high frequencies range more f ≈ 10 GHz is very important for application in communication, medicine and control systems. The analysis of basic mechanisms of amplification is given in this article. The resonance excitation and amplification of acoustic-electromagnetic wave with space mode in structure of GaAs is analyzing for two cases of piezoeffect and deformation potential, but the amplification of high frequencies are realizing only in case of deformation potential.\n\n2. Model of Amplification Due to Piezoeffect\n\nLet us to consider a thin film of n-GaAs located between two mediums, the substrates are from material without piezoeffect, and the transversal wave passed along z axis. The component of displacement U is in direction of the y axis. The film consists of a 2D gas with a high negative differential mobility. The value L is the length of the element (along axis OZ), h is the thickness of film (see Figure 1). This film has a substrates with depth d. The hybrid wave is decreasing in the substrate, then, all its energy is in the very thin film with 2D electron beam. The effective size of the waveguide is describing by the parameter 2H = 2(h + d/2), d is the depth of substrate.\n\nLet us to analyze the simplest transversal in displacements u mode using elastic theory equation with the pie-\n\nzoeffect . It is necessary to use the variable electric field",
null,
"(in direction of axes Z) determined by\n\npotential",
null,
",",
null,
"1(a)\n\nFigure 1. Geometry of waveguide for computing simulation of amplification acoustic-electromagnetic wave where 2 h is the transversal size of guide in x direction and L is the length of the guide. In direction y the model of guide has size going to infinitive value.",
null,
"1(b)",
null,
", 1(c)\n\nwhere s » 3 × 105 cm/s is the sound velocity,",
null,
"is the module of coefficient of piezoeffect,",
null,
"is the density parameter,",
null,
"is the potential determined the electric field",
null,
"- .\n\nThe boundary conditions are in (Equation 1(c)). In the case of free very thin film it is",
null,
". In this\n\ncase it is necessary to consider the viscosity coefficient",
null,
"for the simulation. The wave process shows that the amplification realizes if the synchronism between the acoustic-electromagnetic wave with transversal displacement mode and the space charge wave ,",
null,
"(2)\n\nwhere",
null,
"is the frequency of synchronism, s,",
null,
"is sound and space charges waves velocities, respectively; index",
null,
"), H must have also an optimal value.\n\nResonance condition must hold true,\n\nwhere\n\n.\n\nParameters are given by\n\nand\n\n.\n\nThese conditions for the amplification are better for the symmetric modes if the displacement\n\n.\n\nBoundary conditions are taken in case of the absent of the acoustic contact of the film with the environment (Equation 1(c)).\n\nIn the simulation it is to use Equation (1) and the resonance condition (2). It is necessary to take into account the 2D electron gas of n-GaAs thin film and the equations for slow changing amplitudes of acoustic-electro- magnetic hybrid wave with potential. The computer modeling shows the effective amplification of waves in the presence of the negative differential mobility (conductivity). The following parameters have been chosen n0 » 1015 cm−3, the electron concentration in the film, v0 » 2 × 107 cm/s, the electron velocity, L = 0.1 cm, the length of the film H = 1 mm. The intensity of wave can reach value of 10 W/cm2 at microwave frequencies w = 5 × 1010 - 2 × 1011 s1. In the Figures 2-4, the amplification of the acoustic-electromagnetic wave in microwave range is to present.\n\nTraditional construction for realization of acoustic-electromagnetic amplification is in Figure 3. This construction is for high frequencies f » 1011 Hz ranges too.\n\nAdditionally, in simulations it is considering the electric variable field distribution in input antenna like Gauss impulse.\n\nFigure 2. Distribution of the amplitude of acoustic deformation along the film in direction z for time t = 4 ns. The resonant excitation is given at frequency w = 1011 s−1 of the hybrid acoustic-electromagnetic mode, and the size of the waveguide is H = 1 μm.\n\nFigure 3. Traditional structure for exiting of acoustic-electromagnetic waves. It is necessary to prepare the cathode and anode 1, and the input 3 and the output 4 antennas; the film of n-GaAs is in i-GaAs substrate.\n\nFigure 4. Distribution of the displacements deformation amplitude along the film in direction z at time t = 4 ns with a size of wave guide H = 0.1 μm.\n\nElectric variable field distribution in input antenna has parameters: z1 = 0.001 cm, z0 = 0.0001 cm; y1 = 0.05 cm, y0 = 0.02 cm; t1 = 2.5 ns, t0 = 1.25 ns; E10 = 200 V/cm and EB = 4.56 kV/cm, the drift field, n0 = 1011 cm−2, the 2D concentration of electron gas, and q, the transverse wave number (index m equal 5) of the acoustic-electro- magnetic mode.\n\nExcitation of the acoustic-electromagnetic wave due to deformation potential is in the Lamb’s acoustic mode , which possess longitudinal component of mechanic displacement, has the electric field too and interacts with space charge waves due to the deformation potential. The equation for the elastic displacement components of the Lamb’s wave u = (u1, 0, u3) takes a form.\n\n(3)\n\nHere are the components of tensor of deformation potential; cij are the elastic constants , the term is due to dissipation, as in the Equation (3). Note that the partial concentrations nL, nG for the valleys G, L are present in the Equations (3).\n\nAs in the case of piezoactive transverse modes, the effective excitation of acoustic-electromagnetic waves with displacement like in Equations (3) takes place near cut-off frequency. It is shown that the symmetric modes emerging as transverse ones interact more effectively with the space charge waves. A distribution of the displacements near cut-off is\n\n, (4)\n\nhere sl » 5.5 × 105 cm/s is the longitudinal sound velocity in GaAs .\n\nThe computer modeling in the base of Equations (3) and (4) is the same like for case the piezoeffect. This modeling has demonstrated that the distributions in the plane of the film of excited acoustic-electromagnetic waves are very similar to those obtained for piezoeffect. But it is shown ¡ that the efficiency of excitation due to deformation potential becomes dominating at higher frequencies f > 30 GHz.\n\n3. Conclusion\n\nThe resonant interaction of space charge waves with acoustic-electromagnetic waves in thin GaAs films can be used for effective in microwave wave range. At the frequencies f < 30 GHz efficiency of excitation of acoustic- electromagnetic due to piezoeffect is more effective, but at higher frequencies, deformation potential is dominating. An intensity of acoustic-electromagnetic waves can reach 10 W/cm2 at microwave frequencies range f = 10 GHz ÷ 30 GHz. To increase a frequency of excited wave to millimeter range, it is possible to choose the resonant excitation of acoustic-electromagnetic waves at the second harmonic of the input signal.\n\nAcknowledgements\n\nAuthors thank SEP-CONACyT for the support of our work.\n\nCite this paper\n\nS.Koshevaya,V.Grimalsky,Y.Kotsarenko,J.Escobedo-Alatorre, (2015) Comparison of Excitation of Acoustic-Electromagnetic Wave in Piezoelecric Crystal and Crystal with Potential of Deformation. Journal of Electromagnetic Analysis and Applications,07,259-264. doi: 10.4236/jemaa.2015.710027\n\nReferences\n\n1. 1. Dieulesaint, E. and Royer, D. (2000) Elastic Waves in Solids. Springer, New York.\n\n2. 2. Grimalsky, V., Gutierrez-D., E., Garcia-B., A. and Koshevaya, S. (2004) Resonant Excitation of Microwave Acoustic Modes in n-GaAs Film. Proceedings of International. Conference on Microelectronics ICM-2004, Tunis, 6-8 December 2004, 72-75.\nhttp://dx.doi.org/10.1109/icm.2004.1434209\n\n3. 3. Grimalsky, V., Gutierrez-D., E., Garcia-B., A. and Koshevaya, S. (2006) Resonant Excitation of Microwave Acoustic Modes in n-GaAs. Microelectronics Journal, 37, 395-403.\nhttp://dx.doi.org/10.1016/j.mejo.2005.06.003\n\n4. 4. Mitin, V.V., Kochelap, V.A. and Stroscio, A. (1999) Quantum Heterostructures: Microelectronics and Optoelectronics. Cambridge University Press, Cambridge.\n\n5. 5. Shur, M. (1989) GaAs Devices and Circuits. Plenum Press, New York.\n\n6. 6. Carnez, B. (1980) Modeling of Submicrometer Gate FET Including Effect of Nonstationary Dynamics. Journal of Applied Physics, 51, 784-790.\n\n7. 7. Koshevaya, S.V., Grimalsky, V.V., Garcia-B., A. and Díaz-A., M.F. (2006) Amplification of Hypersonic by GaAs Crystals. Ukrainian Journal of Physics, 51, 594-598."
] |
[
null,
"http://html.scirp.org/file/9-2500537x3.png",
null,
"http://html.scirp.org/file/9-2500537x2.png",
null,
"http://html.scirp.org/file/2-9801635x3.png",
null,
"http://html.scirp.org/file/2-9801635x4.png",
null,
"http://html.scirp.org/file/2-9801635x5.png",
null,
"http://html.scirp.org/file/2-9801635x6.png",
null,
"http://html.scirp.org/file/2-9801635x7.png",
null,
"http://html.scirp.org/file/2-9801635x9.png",
null,
"http://html.scirp.org/file/2-9801635x10.png",
null,
"http://html.scirp.org/file/2-9801635x11.png",
null,
"http://html.scirp.org/file/2-9801635x12.png",
null,
"http://html.scirp.org/file/2-9801635x13.png",
null,
"http://html.scirp.org/file/2-9801635x14.png",
null,
"http://html.scirp.org/file/2-9801635x15.png",
null,
"http://html.scirp.org/file/2-9801635x16.png",
null,
"http://html.scirp.org/file/2-9801635x17.png",
null,
"http://html.scirp.org/file/2-9801635x18.png",
null,
"http://html.scirp.org/file/2-9801635x19.png",
null,
"http://html.scirp.org/file/2-9801635x20.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.84962195,"math_prob":0.9466326,"size":12355,"snap":"2020-10-2020-16","text_gpt3_token_len":2944,"char_repetition_ratio":0.16646425,"word_repetition_ratio":0.041884817,"special_character_ratio":0.22840954,"punctuation_ratio":0.13469921,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9574801,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],"im_url_duplicate_count":[null,null,null,null,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-27T09:01:21Z\",\"WARC-Record-ID\":\"<urn:uuid:8ea6f9e3-9773-4354-be72-d8d7a8efdc42>\",\"Content-Length\":\"42169\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:de4ff3f9-aa53-4b25-9eb4-f7cb5747833a>\",\"WARC-Concurrent-To\":\"<urn:uuid:26126f50-f7a0-4420-9a80-8ec18bc05a11>\",\"WARC-IP-Address\":\"104.149.186.66\",\"WARC-Target-URI\":\"https://file.scirp.org/Html/2-9801635_60462.htm\",\"WARC-Payload-Digest\":\"sha1:ZF43GSA2OJ4VOLLWDJYJXY7I4KUY6KQ2\",\"WARC-Block-Digest\":\"sha1:TSLFXQ76G2PZMKMTMFVKLJ4Q266NTD27\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875146665.7_warc_CC-MAIN-20200227063824-20200227093824-00503.warc.gz\"}"}
|
https://www.hpmuseum.org/forum/thread-7318.html
|
[
"[REQUEST] terminal view for CAS mode\n11-26-2016, 09:30 PM (This post was last modified: 12-07-2016 03:52 PM by compsystems.)\nPost: #1",
null,
"compsystems",
null,
"Senior Member Posts: 1,326 Joined: Dec 2013\n[REQUEST] terminal view for CAS mode\nHello hp-prime community\n\nThe current terminal view was created for numerical mode (HOME MODE), for this reason the output expressions are not symbolic. The numerical results, do not need readable printing.\n\nFor those we program in CAS MODE we need or require PRETTY PRINT\n\nA comparison of the view & a practical example",
null,
"simplify flag: off\nincreasing flag: off\ncas mode: on\n\nScript on history view\nPHP Code:\nassume(a>0);(a*x^2+b*x+c) = 0;Ans*4*a; // ((a*x^2+b*x+c)*4*a) = 0expand(Ans); // (4*a^2*x^2+4*a*b*x+4*a*c) = 0Ans+b^2; // (4*a^2*x^2 +4*a*b*x + 4*a*c+b^2 ) = (b^2)Ans-4*a*c; // (4*a^2*x^2+4*a*b*x+4*a*c+b^2-4*a*c) = (b^2-4*a*c)simplify(Ans); // (4*a^2*x^2+4*a*b*x+b^2) = (-4*a*c+b^2) factor(Ans); // (2*a*x+b)^2) = (-4*a*c+b^2)√(Ans); // (abs(2*a*x+b)) = (√(-4*a*c+b^2))assume(b>0);assume(c>0);expr(replace(string(Ans),\"abs\",\"\")); // (2*a*x+b) = (√(-4*a*c+b^2))Ans-b; // (2*a*x+b-b) = (√(-4*a*c+b^2)-b)simplify(Ans); // (2*a*x-b) = (√(-4*a*c+b^2)-2*b)Ans/(2*a); // (2*a*x/(2*a)) = (-b+√(-4*a*c+b^2))/(2*a)simplify(Ans); // x = (-b+√(-4*a*c+b^2))/(2*a)part(Ans,1)=reorder(part(Ans,2),[b,a,c]); // x = (-b+√[b^2-4*a*c])/(2*a)expr(replace(string(Ans),\"-b+\",\"-b-\")); // x = (-b-√[b^2-4*a*c])/(2*a)\n\nCAS prgm\nPHP Code:\n#cas deductionQuadformula():= begin local equation; assume(a>0); print; // Clear Terminal Window print( \"Use cursor keys ↑↓ to move the output screen\" ); print( \"Another key to continue after PAUSE\" ); print( \"\" ); print( \"[PAUSE]\" ); wait(); print; // Clear Terminal Window again print( \"***** Deduction Quadratic Formula *****\" ); // Title print( \"\" ); equation:= (a*x^2+b*x+c) = 0; print( string( equation ) ); print( \"\" ); print( \"Ans*4*a\" ); equ := equ * 4*a; // ((a*x^2+b*x+c)*4*a) = 0 print( string( equ ) ); print( \"\" ); print( \"expand(Ans)\" ); equ := expand( equ ); // (4*a^2*x^2+4*a*b*x+4*a*c) = 0 print( string( equ ) ); print( \"\" ); print( \"Ans+b^2\" ); equ := equ + b^2; // (4*a^2*x^2 +4*a*b*x + 4*a*c+b^2 ) = (b^2) print( string( equ ) ); print( \"\" ); print( \"Ans-4*a*c\" ); equ := equ - 4*a*c; // (4*a^2*x^2+4*a*b*x+4*a*c+b^2-4*a*c) = (b^2-4*a*c) print( string( equ ) ); print( \"\" ); print( \"simplify(Ans)\" ); equ := simplify( equ ); // (4*a^2*x^2+4*a*b*x+b^2) = (-4*a*c+b^2) print( string( equ ) ); print( \"\" ); print( \"factor(Ans)\" ); equ := factor( equ ); // (2*a*x+b)^2) = (-4*a*c+b^2) print( string( equ ) ); print( \"\" ); print( \"√(Ans)\" ); assume( b>0 ); assume( c>0 ); equ := √( equ ); // (abs(2*a*x+b)) = (√(-4*a*c+b^2)) // Should not show ABS print( string( equ ) ); print( \"\" ); // patch equ := expr( replace( string( equ ), \"abs\", \"\" ) ); // (2*a*x+b) = (√(-4*a*c+b^2)) print( string( equ ) ); print( \"\" ); print( \"Ans-b\" ); equ := equ - b; // (2*a*x+b-b) = (√(-4*a*c+b^2)-b) print( string( equ ) ); print( \"\" ); print( \"simplify(Ans)\" ); equ := simplify( equ ); // (2*a*x-b) = (√(-4*a*c+b^2)-2*b) print( string( equ ) ); print( \"\" ); print( \"Ans/(2*a)\" ); equ := equ / ( 2*a ); // (2*a*x/(2*a)) = (-b+√(-4*a*c+b^2))/(2*a) print( string( equ ) ); print( \"\" ); print( \"simplify(Ans)\" ); equ := simplify( equ ); // x1 = (-b+√(-4*a*c+b^2))/(2*a) equ := expr( replace( string( equ ), \"x\", \"x1\" ) ); print( string( equ ) ); print( \"\" ); print( \"expr(replace(string(equ),\"-b+\",\"-b-\"))\" ); equ1 := expr( replace( string( equ ), \"-b+\", \"-b-\" ) ); // x2 = (-b-√[b^2-4*a*c])/(2*a) equ1 := expr( replace( string( equ1 ), \"x1\", \"x2\" ) ); print( string( equ1 ) ); print( \"[PAUSE]\" ); wait( ); return \"done\"; end;#end\n\nSurvey:\nDo you really need a new terminal view with pretty print?\n\n11-27-2016, 03:55 AM\nPost: #2\n toml_12953",
null,
"Senior Member Posts: 1,709 Joined: Dec 2013\nRE: terminal view for CAS mode\n(11-26-2016 09:30 PM)compsystems Wrote: Survey:\nDo you really need a new terminal view with pretty print?"
] |
[
null,
"https://www.hpmuseum.org/forum/uploads/avatars/avatar_176.jpg",
null,
"https://www.hpmuseum.org/forum/images/buddy_offline.gif",
null,
"http://eonicasys.com.co/public/math/CAS/hp_prime/libraries/script/image/script_hp_prime_image02.png",
null,
"https://www.hpmuseum.org/forum/images/buddy_offline.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.80656666,"math_prob":0.99793875,"size":1074,"snap":"2021-31-2021-39","text_gpt3_token_len":301,"char_repetition_ratio":0.1317757,"word_repetition_ratio":0.027173912,"special_character_ratio":0.2905028,"punctuation_ratio":0.13777778,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000004,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,8,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-26T15:12:01Z\",\"WARC-Record-ID\":\"<urn:uuid:7931e81d-54e1-4502-9191-e278955313f8>\",\"Content-Length\":\"48051\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9c687d2a-ffb5-4c6a-a902-32043a383695>\",\"WARC-Concurrent-To\":\"<urn:uuid:fb51e4a5-5efe-4c2a-b98f-0a83e3c25bb2>\",\"WARC-IP-Address\":\"209.197.117.170\",\"WARC-Target-URI\":\"https://www.hpmuseum.org/forum/thread-7318.html\",\"WARC-Payload-Digest\":\"sha1:S3EMCZJ2IYRD72UZFBRJ6Y6VFCWWKAFS\",\"WARC-Block-Digest\":\"sha1:EDW4OZDRI3WVBNMWVTOCLJKAG7JDCY44\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057882.56_warc_CC-MAIN-20210926144658-20210926174658-00393.warc.gz\"}"}
|
https://thriveglobal.com/stories/derivatives-and-their-real-world-applications/
|
[
"Community//\n\n# Derivatives and their real world applications\n\n## What you need to know about derivatives & integrals.\n\nThe Thrive Global Community welcomes voices from many spheres on our open platform. We publish pieces as written by outside contributors with a wide range of opinions, which don’t necessarily reflect our own. Community stories are not commissioned by our editorial team and must meet our guidelines prior to being published.\n\nHave you ever heard of the term derivative? Well! It’s a fundamental tool of calculus. What makes it unique, is the fact that this tool can compute the change of a function at any point. In calculus, this concept is equally important as integral, which is the reverse of derivative also called anti-derivative.\n\nThe rate of change concept, makes it a valuable asset in many real life applications. For instance, the diversity of temperature can be checked using this notion. In this article, we will discuss in detail, its definition along with the real life utility.\n\nNow let’s get started, at first we will try to understand the concepts of derivative and differentiation.\n\nDefinition:\n\nThe derivative of a variable is defined as a measure to compute the rate of change of a function’s output value as it varies from the initial value or input. Here, an important thing is the time factor, the variation in input and output value as time changes.\n\nLet’s consider an example of a moving object, the location of that object starting from the initial point, with respect to time is considered as object’s velocity. This tells us the relative swiftness of the object as it deviates from its position, as time advances.\n\nHere, the image above, illustrates a tangent line. The slope of the tangent line at the marked point represents the derivative of a function. The variation can be projected by the ratio of change of function Y (dependent variable) to that of the variable x (independent variable).\n\nNotation\n\nA German mathematician, Gottfried Wilhelm Leibniz’s introduced a notation, in which symbols were given; dx, dy, and dy/dx. It is commonly used in case an equation y=f(x) is viewed as an association of dependent and independent variables.\n\nIt uses these symbols to define the infinitesimal (very small) increments. On the other hand, symbols such as Δx and Δy are used to represent the finite increments of x and y.\n\nDifferentiation:\n\nIt is a process that helps in calculating the derivative, just like integration computes an integral. This operation is reverse of integration.\n\nLet’s assume y a linear function of x. In this example, y = f(x) = mx + b, let m and b the real numbers, slope m is expressed as\n\nSlope = m = change in y / change in x = Δy/ Δx\n\nHere, Δy = f(x + Δx) – f(x), the above equation is because;\n\n= y+ Δy = f(x + Δx)\n\n=m(x + Δx) + b = mx + mΔx + b = y + mΔx\n\nThis gives us the slope of line, Δy = mΔx\n\nIt applies to a straight line, if the graph is not linear, then the change varies over a considerable range. The differentiation is an efficient method to compute this change over a specific value of x.\n\nPractical Applications:\n\nThis tool isn’t just limited to mathematical problems, it has a broad range of practical utility. Nothing is useless in this world, when we say something can’t be used, we actually don’t know how to use it. The one who knows its utility, won’t stop thinking about it.\n\nThe uniqueness of this concept is its predictive ability to evaluate the change in quantities. Whether its speed, momentum, temperature and even the business speculations, all the variations can be worked out using derivative.\n\nUse in Physics:\n\nAs we mentioned above, the example of a moving body’s relative position can help us calculate the velocity.\n\nIn the same way, derivatives of acceleration and momentum can be found.\n\nUse in Chemistry:\n\nIn chemistry, the concentration of an element involved in a reaction, the change in concentration can be predicted.\n\nSimilarly, to measure the rate of chemical reactions and to check the contribution and loss of a compound during the reaction.\n\nUse in Economics:\n\nNowadays, the decision making in economics has become more mathematical. Statistical and mathematical principles are applied in making decisions regarding possible gain or loss in investment.\n\nConfronted with massive statistical data, dependent on lots of variables, there was a need of some tool that could assist the analysts.\n\nHere, calculus proved to be beneficial. It implemented the derivative concepts to predict the results of different investment possibilities.\n\nUltimately, this enabled the analysts to select the one possibility that might prove to be productive in terms of profitability.\n\nIn the end, I hope this article will help you understand and apply the calculus concepts in practical fields. If you are interested in methods to calculate this fundamental of calculus, try this derivative calculator. You can also make a relevant calculation on integral function on this integral calculator."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.91544145,"math_prob":0.9737393,"size":4519,"snap":"2020-45-2020-50","text_gpt3_token_len":948,"char_repetition_ratio":0.12026578,"word_repetition_ratio":0.002610966,"special_character_ratio":0.20491259,"punctuation_ratio":0.11494253,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9965625,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-23T23:17:48Z\",\"WARC-Record-ID\":\"<urn:uuid:01010a7d-58df-4b53-9d88-0782cddd257c>\",\"Content-Length\":\"194849\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2182287b-5447-4ad4-9540-814a9ce6273f>\",\"WARC-Concurrent-To\":\"<urn:uuid:915f5c4a-c0c1-4efb-bbb0-6960e3586b06>\",\"WARC-IP-Address\":\"104.22.30.175\",\"WARC-Target-URI\":\"https://thriveglobal.com/stories/derivatives-and-their-real-world-applications/\",\"WARC-Payload-Digest\":\"sha1:KGNKSVVF2ELGNVPN6CFMDYNA5VRJFP2U\",\"WARC-Block-Digest\":\"sha1:5JV6SFXYWGNRPF3ZMSSM37O7DA2QO2IN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141168074.3_warc_CC-MAIN-20201123211528-20201124001528-00071.warc.gz\"}"}
|
https://www.lsuagcenter.com/portals/our_offices/departments/ode/research-and-data/quantitative-data-basics
|
[
"# Quantitative Data Basics",
null,
"## What is Quantitative Data?\n\nQuantitative data is information that can be counted or measured and given a numerical value. Quantitative data can be used for mathematical calculations and statistical analysis. Program impact can be evaluated, and programming decisions can be made based on these mathematical derivations. Quantitative data can be used to determine:\n\n• How many\n• How much\n• How often\n\n## Quantitative Methods\n\nQuantitative data is usually collected using surveys, experiments, phone interviews, polls, or questionnaires. Questionnaires and surveys are standard methods for collecting quantitative data.\n\n## Quantitative Data Analysis\n\nQuantitative data should be properly analyzed to report program impact and make future programming decisions. Analyzing quantitative data can involve the following steps:\n\n#### Step 1: Transform raw data into quantifiable data.\n\nThe data will need to be converted into quantifiable data by quantitative analysis. This involves organizing data properly to give it meaning. Data must be entered into a spreadsheet, organized, and coded.\n\n#### Step 2: Relate measurement scales with variables.\n\nThis step involves associating measurement scales such as nominal, ordinal, interval, and ratio with the variables. This step is essential and helps arrange data in proper order within your spreadsheet.\n\n#### Step 3: Descriptive statistics.\n\nIt can be challenging to establish a pattern in the raw data; therefore, descriptive statistics help researchers find patterns within the data. Some commonly used descriptive statistics include:\n\n• Mean: an average of values for a variable\n• Median: the midpoint of the value scale for a variable\n• Mode: the most common value of a variable\n• Frequency: the number of times a particular value is observed in the scale\n• Minimum and Maximum: the lowest and highest scale values\n• Percentages: a format to express scores and set of values for variables.\n\n#### Step 4: Inferential Statistics.\n\nThese complex forms of analysis show the relationships between multiple variables to generalize results and make predictions. This can include:\n\n• Correlation: describes the relationship between two variables\n• Regression: helps to determine whether one variable is the predictor of another variable\n• Analysis of variance: use it to determine if there is any difference between the means of different groups."
] |
[
null,
"https://www.lsuagcenter.com/~/media/system/1/2/8/f/128f0d9a1e42dbac822e2dfd3c269ae6/quanitativedatajpg.jpg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.87648314,"math_prob":0.9204074,"size":1584,"snap":"2023-14-2023-23","text_gpt3_token_len":272,"char_repetition_ratio":0.14050633,"word_repetition_ratio":0.00913242,"special_character_ratio":0.16161616,"punctuation_ratio":0.12741312,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98927677,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-04-02T09:55:35Z\",\"WARC-Record-ID\":\"<urn:uuid:682d56f5-e0d2-4767-b395-210c102f7c71>\",\"Content-Length\":\"81231\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:36ce85c9-0c2d-4b79-be95-1ff08008809b>\",\"WARC-Concurrent-To\":\"<urn:uuid:b57d609f-e8de-4a6b-8618-59ee9bbf5ada>\",\"WARC-IP-Address\":\"130.39.23.83\",\"WARC-Target-URI\":\"https://www.lsuagcenter.com/portals/our_offices/departments/ode/research-and-data/quantitative-data-basics\",\"WARC-Payload-Digest\":\"sha1:7MZUDOR64R3TO43FPRSC6F6EAXQWJK2H\",\"WARC-Block-Digest\":\"sha1:3HAU5GLSBU5XATMXCPJ4ZZ25G37W7EGN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296950422.77_warc_CC-MAIN-20230402074255-20230402104255-00649.warc.gz\"}"}
|
https://learn.careers360.com/school/question-need-solution-for-rd-sharma-maths-class-12-chapter-algebra-of-matrices-exercise-4-point-3-question-67-sub-question-iii-math/?question_number=67.3
|
[
"",
null,
"",
null,
"#### Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 67 sub question (iii) math",
null,
"Hint: Matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.\n\nGiven: A and B be square matrices of same order\n\n[using distributive properties]\n\nSince, in general matrix multiplication is not always commutative\n\nSo,\n\n#### infoexpert22",
null,
""
] |
[
null,
"https://cdn.entrance360.com/static/images/exam/products_page_bg.12f7f177de52.png",
null,
"https://cdn.entrance360.com/static/images/qna.a449b2e8236a.png",
null,
"https://cdn.entrance360.com/static/images/best_answer.7f977deb01a8.png",
null,
"https://learn.careers360.com/static/images/cuet_ads.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8058964,"math_prob":0.9804937,"size":415,"snap":"2023-40-2023-50","text_gpt3_token_len":90,"char_repetition_ratio":0.11922141,"word_repetition_ratio":0.0,"special_character_ratio":0.20481928,"punctuation_ratio":0.103896104,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99798054,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-28T03:19:20Z\",\"WARC-Record-ID\":\"<urn:uuid:1fae6c11-ee41-40b3-a0a9-39f727ce1d6c>\",\"Content-Length\":\"603538\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:23bd879d-1c3f-4b09-8b8c-5b75d78f299a>\",\"WARC-Concurrent-To\":\"<urn:uuid:361987d2-00ad-405c-a800-c56f0723f960>\",\"WARC-IP-Address\":\"3.109.250.236\",\"WARC-Target-URI\":\"https://learn.careers360.com/school/question-need-solution-for-rd-sharma-maths-class-12-chapter-algebra-of-matrices-exercise-4-point-3-question-67-sub-question-iii-math/?question_number=67.3\",\"WARC-Payload-Digest\":\"sha1:WFYKFDQ5ZZPRIZI3V3J5KQVDHJBRK3US\",\"WARC-Block-Digest\":\"sha1:GHIULDABNMT3G6DEA4MYKO53XHQMUPZE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510358.68_warc_CC-MAIN-20230928031105-20230928061105-00013.warc.gz\"}"}
|
https://data.intrinio.com/data-tags/product/zacks-long-term-growth-estimates
|
[
"# Zacks Long-Term Growth Estimates\n\n### What is a data tag?\n\nIntrinio data is categorized using “data tags”, such as marketcap , netincome , and close_price . A data tag combined with a corresponding entity (security, company, index, bank, etc), will allow you to retrieve current and historical values from our system. For example, to retrieve the historical daily volume for Apple, you would use the volume data tag in conjuction with the AAPL ticker symbol.\n\n### Data Tags\n\nName Tag Type Units\nLong-Term Growth (LTG) high estimate\nltg_est_high\nLtg Estimate Stat Number\nLong-Term Growth (LTG) low estimate\nltg_est_low\nLtg Estimate Stat Number\nLong-Term Growth (LTG) mean estimate\nltg_est_mean\nLtg Estimate Stat Number\nLong-Term Growth (LTG) mean estimate 1 month ago\nltg_est_mean_1m_ago\nLtg Estimate Trend Number\nLong-Term Growth (LTG) mean estimate 1 week ago\nltg_est_mean_1w_ago\nLtg Estimate Trend Number\nLong-Term Growth (LTG) mean estimate 2 months ago\nltg_est_mean_2m_ago\nLtg Estimate Trend Number\nLong-Term Growth (LTG) mean estimate 3 months ago\nltg_est_mean_3m_ago\nLtg Estimate Trend Number\nLong-Term Growth (LTG) median estimate\nltg_est_median\nLtg Estimate Stat Number\nLong-Term Growth (LTG) number of estimates\nltg_est_cnt\nLtg Estimate Stat Number\nLong-Term Growth (LTG) number of estimates revised downward in 1 month for the period\nltg_est_cnt_rev_down_1m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised downward in 1 week for the period\nltg_est_cnt_rev_down_1w\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised downward in 2 months for the period\nltg_est_cnt_rev_down_2m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised downward in 3 months for the period\nltg_est_cnt_rev_down_3m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised downward in 4 months for the period\nltg_est_cnt_rev_down_4m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised downward in 5 months for the period\nltg_est_cnt_rev_down_5m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised upward in 1 month for the period\nltg_est_cnt_rev_up_1m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised upward in 1 week for the period\nltg_est_cnt_rev_up_1w\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised upward in 2 months for the period\nltg_est_cnt_rev_up_2m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised upward in 3 months for the period\nltg_est_cnt_rev_up_3m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised upward in 4 months for the period\nltg_est_cnt_rev_up_4m\nLtg Estimate Trend Number\nLong-Term Growth (LTG) number of estimates revised upward in 5 months for the period\nltg_est_cnt_rev_up_5m\nLtg Estimate Trend Number\nLong-term growth (LTG) number of revisions down for the period\nltg_est_cnt_rev_down\nLtg Estimate Stat Number\nLong-term growth (LTG) number of revisions up for the period\nltg_est_cnt_rev_up\nLtg Estimate Stat Number\nLong-term growth (LTG) standard deviation of estimate for the period\nltg_est_std_dev\nLtg Estimate Stat Number\nLong-Term Growth Rate\nlong_term_growth_rate\nLtg Estimate Stat Percentage"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5351817,"math_prob":0.9537534,"size":3322,"snap":"2020-34-2020-40","text_gpt3_token_len":922,"char_repetition_ratio":0.23387583,"word_repetition_ratio":0.4451477,"special_character_ratio":0.24202287,"punctuation_ratio":0.026639344,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98029757,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-30T04:59:51Z\",\"WARC-Record-ID\":\"<urn:uuid:3097facc-1f6b-48cb-98bd-e1ef1794aec5>\",\"Content-Length\":\"78194\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a7f8f9f1-7f28-438a-bf44-f3ab89097a1b>\",\"WARC-Concurrent-To\":\"<urn:uuid:f481fefb-573d-4db7-9b91-f3d6b087922f>\",\"WARC-IP-Address\":\"54.88.63.64\",\"WARC-Target-URI\":\"https://data.intrinio.com/data-tags/product/zacks-long-term-growth-estimates\",\"WARC-Payload-Digest\":\"sha1:PESOHDOIDPYVCBWYYESD3L3Y7Q5JZ3YY\",\"WARC-Block-Digest\":\"sha1:DMLM32IIIKAUZ2OSJYITXS5EKV6IV44J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600402118004.92_warc_CC-MAIN-20200930044533-20200930074533-00651.warc.gz\"}"}
|
https://fr.slideshare.net/ssuser002675/progressionsdocx
|
[
"Publicité",
null,
"",
null,
"",
null,
"",
null,
"Publicité",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"Publicité",
null,
"",
null,
"Prochain SlideShare",
null,
"Progression & Series-01-Theory.pdf\nChargement dans ... 3\n1 sur 11\nPublicité\n\n### progressions.docx\n\n1. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com General Term of an A.P.. (1) Let ‘a’ be the first term and ‘d’ be the common difference of an A.P. Then its nth term is d n a ) 1 ( . d n a Tn ) 1 ( (2) pth term of an A.P. from the end : Let ‘a’ be the first term and ‘d’ be the common difference of an A.P. having n terms. Then pth term from the end is th p n ) 1 ( term from the beginning. d p n a T p p n th ) ( end the from term ) 1 ( Important Tips General term (Tn) is also denoted by l (last term). Common difference can be zero, +ve or –ve. n (number of terms) always belongs to set of natural numbers. If Tk and Tp of any A.P. are given, then formula for obtaining Tn is k p T T k n T T k p k n . If pTp = qTq of an A.P., then Tp + q = 0. If pth term of an A.P. is q and the qth term is p, then Tp + q = 0 and Tn = p + q – n. If the pth term of an A.P. is q 1 and the qth term is p 1 , then its pqth term is 1. If Tn =pn + q, then it will form an A.P. of common difference p and first term p + q. Selection of Terms in an A.P.. When the sum is given, the following way is adopted in selecting certain number of terms : Number of terms Terms to be taken 3 a – d, a, a + d 4 a – 3d, a – d, a + d, a + 3d 5 a – 2d, a – d, a, a + d, a + 2d In general, we take a – rd, a – (r – 1)d, ……., a – d, a, a + d, ……, a + (r – 1)d, a + rd, in case we have to take (2r + 1) terms (i.e. odd number of terms) in an A.P. And, d r a d a d a d r a d r a ) 1 2 ( ......., , , ......., , ) 3 2 ( , ) 1 2 ( , in case we have to take 2r terms in an A.P. When the sum is not given, then the following way is adopted in selection of terms. Number of terms Terms to be taken 3 d a d a a 2 , , 4 d a d a d a a 3 , 2 , , 5 d a d a d a d a a 4 , 3 , 2 , , Sum of n terms of an A.P. : The sum of n terms of the series } ) 1 ( { ....... ) 2 ( ) ( d n a d a d a a is given by ] ) 1 ( 2 [ 2 d n a n Sn Also, ) ( 2 l a n Sn , where l = last term = d n a ) 1 ( Important Tips\n2. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com The common difference of an A.P is given by 1 2 2S S d where 2 S is the sum of first two terms and 1 S is the sum of first term or the first term. The sum of infinite terms 0 when , 0 when , d d . If sum of n terms n S is given then general term 1 n n n S S T , where 1 n S is sum of (n – 1) terms of A.P. Sum of n terms of an A.P. is of the form Bn An 2 i.e. a quadratic expression in n, in such case, common difference is twice the coefficient of 2 n i.e. 2A. If for the different A.P’s n n n n f S S , then ) 1 2 ( ) 1 2 ( n n f T T n n If for two A.P.’s D Cn B An T T n n then D n C B n A S S n n 2 1 2 1 Some standard results Sum of first n natural numbers 2 ) 1 ( ........ 3 2 1 1 n n r n n r Sum of first n odd natural numbers 2 1 ) 1 2 ( ) 1 2 ( ..... 5 3 1 n r n n r Sum of first n even natural numbers n r n n r n 1 ) 1 ( 2 2 ...... 6 4 2 If for an A.P. sum of p terms is q and sum of q terms is p, then sum of (p + q) terms is {–(p + q)}. If for an A.P., sum of p terms is equal to sum of q terms, then sum of (p + q) terms is zero. If the pth term of an A.P. is q 1 and qth term is p 1 , then sum of pq terms is given by ) 1 ( 2 1 pq Spq Arithmetic Mean. (1) Definitions (i) If three quantities are in A.P. then the middle quantity is called Arithmetic mean (A.M.) between the other two. If a, A, b are in A.P., then A is called A.M. between a and b. (ii) If b A A A A a n , ,....., , , , 3 2 1 are in A.P., then n A A A A ......, , , , 3 2 1 are called n A.M.’s between a and b. (2) Insertion of arithmetic means (i) Single A.M. between a and b : If a and b are two real numbers then single A.M. between a and b 2 b a (ii) n A.M.’s between a and b : If n A A A A ......., , , , 3 2 1 are n A.M.’s between a and b, then 1 1 n a b a d a A , 1 2 2 2 n a b a d a A , 1 3 3 3 n a b a d a A , ……., 1 n a b n a nd a An Important Tips Sum of n A.M.’s between a and b is equal to n times the single A.M. between a and b. i.e. 2 .......... 3 2 1 b a n A A A A n If 1 A and 2 A are two A.M.’s between two numbers a and b, then ) 2 ( 3 1 ), 2 ( 3 1 2 1 b a A b a A . Between two numbers, n m n m s A.M.' of Sum s A.M.' of Sum .\n3. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com If number of terms in any series is odd, then only one middle term exists which is th n 2 1 term. If number of terms in any series is even then there are two middle terms, which are given by th n 2 and th n 1 2 term Properties of A.P.. (1) If ..... , , 3 2 1 a a a are in A.P. whose common difference is d, then for fixed non-zero number K R. (i) ,..... , , 3 2 1 K a K a K a will be in A.P., whose common difference will be d. (ii) ........ , , 3 2 1 Ka Ka Ka will be in A.P. with common difference = Kd. (iii) ...... , , 3 2 1 K a K a K a will be in A.P. with common difference = d/K. (2) The sum of terms of an A.P. equidistant from the beginning and the end is constant and is equal to sum of first and last term. i.e. .... 2 3 1 2 1 n n n a a a a a a (3) Any term (except the first term) of an A.P. is equal to half of the sum of terms equidistant from the term i.e. ) ( 2 1 k n k n n a a a , k < n. (4) If number of terms of any A.P. is odd, then sum of the terms is equal to product of middle term and number of terms. (5) If number of terms of any A.P. is even then A.M. of middle two terms is A.M. of first and last term. (6) If the number of terms of an A.P. is odd then its middle term is A.M. of first and last term. (7) If n a a a ...... , , 2 1 and n b b b ...... , , 2 1 are the two A.P.’s. Then n n b a b a b a ...... , , 2 2 1 1 are also A.P.’s with common difference 2 1 d d , where 1 d and 2 d are the common difference of the given A.P.’s. (8) Three numbers a, b, c are in A.P. iff c a b 2 . (9) If 1 , n n T T and 2 n T are three consecutive terms of an A.P., then 2 1 2 n n n T T T . (10) If the terms of an A.P. are chosen at regular intervals, then they form an A.P. Geometric progression(G.P.) Definition. A progression is called a G.P. if the ratio of its each term to its previous term is always constant. This constant ratio is called its common ratio and it is generally denoted by r. Example: The sequence 4, 12, 36, 108, ….. is a G.P., because 3 ..... 36 108 12 36 4 12 , which is constant. Clearly, this sequence is a G.P. with first term 4 and common ratio 3. The sequence .... , 8 9 , 4 3 , 2 1 , 3 1 is a G.P. with first term 3 1 and common ratio 2 3 3 1 2 1 General Term of a G.P.. (1) We know that, 1 3 2 ..... , , , , n ar ar ar ar a is a sequence of G.P. Here, the first term is ‘a’ and the common ratio is ‘r’. The general term or nth term of a G.P. is 1 n n ar T It should be noted that,\n4. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com ...... 2 3 1 2 T T T T r (2) pth term from the end of a finite G.P. : If G.P. consists of ‘n’ terms, pth term from the end th p n ) 1 ( term from the beginning p n ar . Also, the pth term from the end of a G.P. with last term l and common ratio r is 1 1 n r l Important Tips If a, b, c are in G.P. b c a b or ac b 2 If Tk and Tp of any G.P. are given, then formula for obtaining Tn is k p k p k n k n T T T T 1 1 If a, b, c are in G.P. then b c a b c b c b b a b a or b a c b b a or b a c b b a Let the first term of a G.P be positive, then if r > 1, then it is an increasing G.P., but if r is positive and less than 1, i.e. 0< r < 1, then it is a decreasing G.P. Let the first term of a G.P. be negative, then if r > 1, then it is a decreasing G.P., but if 0< r < 1, then it is an increasing G.P. If a, b, c, d,… are in G.P., then they are also in continued proportion i.e. r d c c b b a 1 .... Sum of First ‘n’ Terms of a G.P.. If a be the first term, r the common ratio, then sum n S of first n terms of a G.P. is given by r r a S n n 1 ) 1 ( , |r|< 1 1 ) 1 ( r r a S n n , |r|> 1 na Sn , r = 1 Selection of Terms in a G.P.. (1) When the product is given, the following way is adopted in selecting certain number of terms : Number of terms Terms to be taken 3 ar a r a , , 4 3 3 , , , ar ar r a r a 5 2 2 , , , , ar ar a r a r a (2) When the product is not given, then the following way is adopted in selection of terms Number of terms Terms to be taken\n5. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com 3 2 , , ar ar a 4 3 2 , , , ar ar ar a 5 4 3 2 , , , , ar ar ar ar a Sum of Infinite Terms of a G.P.. (1) When |r|< 1, (or ) 1 1 r r a S 1 (2) If r 1, then S doesn’t exist Geometric Mean. (1) Definition : (i) If three quantities are in G.P., then the middle quantity is called geometric mean (G.M.) between the other two. If a, G, b are in G.P., then G is called G.M. between a and b. (ii) If b G G G G a n , ,.... , , , 3 2 1 are in G.P. then n G G G G ,.... , , 3 2 1 are called n G.M.’s between a and b. (2) Insertion of geometric means : (i) Single G.M. between a and b : If a and b are two real numbers then single G.M. between a and b ab (ii) n G.M.’s between a and b : If n G G G G ......, , , , 3 2 1 are n G.M.’s between a and b, then 1 1 1 n a b a ar G , 1 2 2 2 n a b a ar G , 1 3 3 3 n a b a ar G , ……………….., 1 n n n n a b a ar G Important Tips Product of n G.M.’s between a and b is equal to nth power of single geometric mean between a and b. i.e. n n ab G G G G ) ( ...... 3 2 1 G.M. of n a a a a ...... 3 2 1 is n n a a a a / 1 3 2 1 ) ..... ( If 1 G and 2 G are two G.M.’s between two numbers a and b is 3 / 1 2 2 3 / 1 2 1 ) ( , ) ( ab G b a G . The product of n geometric means between a and a 1 is 1. If n G.M.’s inserted between a and b then 1 1 n a b r Properties of G.P.. (1) If all the terms of a G.P. be multiplied or divided by the same non-zero constant, then it remains a G.P., with the same common ratio. (2) The reciprocal of the terms of a given G.P. form a G.P. with common ratio as reciprocal of the common ratio of the original G.P. (3) If each term of a G.P. with common ratio r be raised to the same power k, the resulting sequence also forms a G.P. with common ratio k r . (4) In a finite G.P., the product of terms equidistant from the beginning and the end is always the same and is equal to the product of the first and last term. i.e., if n a a a a ...... , , , 3 2 1 be in G.P. Then 1 3 2 3 1 2 1 . .......... r n r n n n n n a a a a a a a a a a\n6. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com (5) If the terms of a given G.P. are chosen at regular intervals, then the new sequence so formed also forms a G.P. (6) If ...... ....., , , , 3 2 1 n a a a a is a G.P. of non-zero, non-negative terms, then ...... , log ..... , log , log , log 3 2 1 n a a a a is an A.P. and vice-versa. (7) Three non-zero numbers a, b, c are in G.P. iff ac b 2 . (8) Every term (except first term) of a G.P. is the square root of terms equidistant from it. i.e. p r p r r T T T ; [r > p] (9) If first term of a G.P. of n terms is a and last term is l, then the product of all terms of the G.P. is 2 / ) ( n al . (10) If there be n quantities in G.P. whose common ratio is r and m S denotes the sum of the first m terms, then the sum of their product taken two by two is 1 1 n n S S r r . Harmonic progression(H.P.) Definition. A progression is called a harmonic progression (H.P.) if the reciprocals of its terms are in A.P. Standard form : .... 2 1 1 1 d a d a a Example: The sequence ,... 9 1 , 7 1 , 5 1 , 3 1 , 1 is a H.P., because the sequence 1, 3, 5, 7, 9, ….. is an A.P. General Term of an H.P.. If the H.P. be as .... , 2 1 , 1 , 1 d a d a a then corresponding A.P. is ..... , 2 , , d a d a a n T of A.P. is d n a ) 1 ( n T of H.P. is d n a ) 1 ( 1 In order to solve the question on H.P., we should form the corresponding A.P. Thus, General term : d n a Tn ) 1 ( 1 or A.P. of 1 H.P. of n n T T Harmonic Mean. (1) Definition : If three or more numbers are in H.P., then the numbers lying between the first and last are called harmonic means (H.M.’s) between them. For example 1, 1/3, 1/5, 1/7, 1/9 are in H.P. So 1/3, 1/5 and 1/7 are three H.M.’s between 1 and 1/9. Also, if a, H, b are in H.P., then H is called harmonic mean between a and b. (2) Insertion of harmonic means : (i) Single H.M. between a and b b a ab 2 (ii) H, H.M. of n non-zero numbers n a a a a ...., , , , 3 2 1 is given by n a a a H n 1 ..... 1 1 1 2 1 .\n7. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com (iii) Let a, b be two given numbers. If n numbers n H H H ...... , , 2 1 are inserted between a and b such that the sequence b H H H H a n , ...... , , , 3 2 1 is an H.P., then n H H H ...... , , 2 1 are called n harmonic means between a and b. Now, b H H H a n , ...... , , , 2 1 are in H.P. b H H H a n 1 , 1 ...... , 1 , 1 , 1 2 1 are in A.P. Let D be the common difference of this A.P. Then, 2 term ) 2 ( 1 n th T n b D n a b ) 1 ( 1 1 ab n b a D ) 1 ( Thus, if n harmonic means are inserted between two given numbers a and b, then the common difference of the corresponding A.P. is given by ab n b a D ) 1 ( Also, D a H 1 1 1 , D a H 2 1 1 2 ,……., nD a Hn 1 1 where ab n b a D ) 1 ( Important Tips If a, b, c are in H.P. then c a ac b 2 . If 1 H and 2 H are two H.M.’s between a and b, then b a ab H 2 3 1 and b a ab H 2 3 2 Properties of H.P.. (1) No term of H.P. can be zero. (2) If a, b, c are in H.P., then c a c b b a . (3) If H is the H.M. between a and b, then (i) b a b H a H 1 1 1 1 (ii) 2 ) 2 )( 2 ( H b H a H (iii) 2 b H b H a H a H Arithmetico-geometric progression(A.G.P.) nth Term of A.G.P.. If ...... , ......, , , , 3 2 1 n a a a a is an A.P. and ...... , ......, , , 2 1 n b b b is a G.P., then the sequence , , , 3 3 2 2 1 1 b a b a b a ..... , ......, n nb a is said to be an arithmetico-geometric sequence. Thus, the general form of an arithmetico geometric sequence is ..... , ) 3 ( , ) 2 ( , ) ( , 3 2 r d a r d a r d a a From the symmetry we obtain that the nth term of this sequence is 1 ] ) 1 ( [ n r d n a\n8. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com Also, let ..... , ) 3 ( , ) 2 ( , ) ( , 3 2 r d a r d a r d a a be an arithmetico-geometric sequence. Then, r d a a ) ( ... ) 3 ( ) 2 ( 3 2 r d a r d a is an arithmetico-geometric series. Sum of A.G.P.. (1) Sum of n terms : The sum of n terms of an arithmetico-geometric sequence , ) 2 ( , ) ( , 2 r d a r d a a ..... , ) 3 ( 3 r d a is given by 1 when ], ) 1 ( 2 [ 2 n 1 when , 1 } ) 1 ( { ) 1 ( ) 1 ( 1 2 1 r d n a r r r d n a r r dr r a S n n n (2) Sum of infinite sequence : Let |r|< 1. Then 0 , 1 n n r r as n and it can also be shown that 0 . n r n as n . So, we obtain that 2 ) 1 ( 1 r dr r a Sn , as n . In other words, when |r|< 1 the sum to infinity of an arithmetico-geometric series is 2 ) 1 ( 1 r dr r a S Method for Finding Sum. This method is applicable for both sum of n terms and sum of infinite number of terms. First suppose that sum of the series is S, then multiply it by common ratio of the G.P. and subtract. In this way, we shall get a G.P., whose sum can be easily obtained. Method of Difference. If the differences of the successive terms of a series are in A.P. or G.P., we can find nth term of the series by the following steps : Step I: Denote the nth term by n T and the sum of the series upto n terms by n S . Step II: Rewrite the given series with each term shifted by one place to the right. Step III: By subtracting the later series from the former, find n T . Step IV: From n T , n S can be found by appropriate summation Miscellaneous series Special Series. There are some series in which nth term can be predicted easily just by looking at the series. If n n n Tn 2 3 Then n n n n n n n n n n n n n n n n n n n n T S 1 1 1 2 1 3 1 2 3 1 1 ) ( \n9. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com n n n n n n n n 2 ) 1 ( 6 ) 1 2 )( 1 ( 2 ) 1 ( 2 Note : Sum of squares of first n natural numbers 6 ) 1 2 )( 1 ( ....... 3 2 1 1 2 2 2 2 2 n n n r n n r Sum of cubes of first n natural numbers 2 1 3 3 3 3 3 3 2 ) 1 ( ....... 4 3 2 1 n n r n n r Vn Method. (1) To find the sum of the series 1 1 1 3 2 3 2 1 ..... 1 ..... ..... 1 ..... 1 r n n n r r a a a a a a a a a a Let d be the common difference of A.P. Then d n a an ) 1 ( 1 . Let n S and n T denote the sum to n terms of the series and nth term respectively. 1 1 1 3 2 2 1 ..... 1 ..... ..... 1 ..... 1 r n n n r r n a a a a a a a a a S 1 1..... 1 r n n n n a a a T Let 1 2 1 ..... 1 r n n n n a a a V ; 2 1 1 ..... 1 r n n n n a a a V 1 1 1 2 1 1 2 1 1 ..... ..... 1 ..... 1 r n n n r n n r n n n r n n n n n a a a a a a a a a a a V V n r n n n T r d a a a d r n a d n a ) 1 ( ..... ] } 1 ) 1 {( [ ] ) 1 ( [ 1 1 1 1 } { ) 1 ( 1 1 n n n V V r d T , ) ( ) 1 ( 1 0 1 n n n n n V V r d T S 1 2 1 1 2 1 1 2 ...... 1 .... 1 ) )( 1 ( 1 r n n n r n a a a a a a a a r S Example: If n a a a ..... , , 2 1 are in A.P., then 2 1 2 1 1 2 2 1 4 3 2 3 2 1 1 1 ) ( 2 1 1 ... 1 1 n n n n n a a a a a a a a a a a a a a a (2) If 1 1 1 3 2 2 1 ... .... ..... ..... r n n n r r n a a a a a a a a a S 1 1 ..... r n n n n a a a T Let r n r n n n n a a a a V 1 1 .... , 1 1 1 1 ...... r n n n n a a a V d r T d n a d r n a T a a a a a a V V n n n r n r n n n n n n ) 1 ( ]} ) 2 ( [ ] ) 1 ( {[ ) ( ..... 1 1 1 1 2 1 1 d r V V T n n n ) 1 ( 1 )} .... ( ) .... {( ) 1 ( 1 ) ( ) 1 ( 1 ) ( ) 1 ( 1 1 0 1 0 1 1 1 r r n n n n n n n n n n n n a a a a a a d r V V d r V V d r T S \n10. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com } ..... .... { ) )( 1 ( 1 1 0 1 1 2 r r n n n a a a a a a a a r Properties of Arithmetic, Geometric and Harmonic means between Two given Numbers. Let A, G and H be arithmetic, geometric and harmonic means of two numbers a and b. Then, ab G b a A , 2 and b a ab H 2 These three means possess the following properties : (1) H G A ab G b a A , 2 and b a ab H 2 0 2 ) ( 2 2 b a ab b a G A G A …..(i) 0 ) ( 2 2 2 b a b a ab b a ab b a ab b a ab ab H G H G …..(ii) From (i) and (ii), we get H G A Note that the equality holds only when a = b (2) A, G, H from a G.P., i.e. AH G 2 2 2 ) ( 2 2 G ab ab b a ab b a AH Hence, AH G 2 (3) The equation having a and b as its roots is 0 2 2 2 G Ax x The equation having a and b its roots is 0 ) ( 2 ab x b a x 0 2 2 2 G Ax x ab G b a A and 2 The roots a, b are given by 2 2 G A A (4) If A, G, H are arithmetic, geometric and harmonic means between three given numbers a, b and c, then the equation having a, b, c as its roots is 0 3 3 3 3 2 3 G x H G Ax x 3 / 1 ) ( , 3 abc G c b a A and 3 1 1 1 1 c b a H 3 , 3 G abc A c b a and ca bc ab H G 3 3 The equation having a, b, c as its roots is 0 ) ( ) ( 2 3 abc x ca bc ab x c b a x\n11. FIITJEE INDEFINITE INTEGRATION FIITJEE Mumbai Centre (Andheri, Chembur, Dadar, Kandivali, Thane, Vashi) Phone: 022- 42378100, 32911892, 32383438, 41617777, 41581500, 9987686970 email: [email protected] web: www.fiitjee.com 0 3 3 3 3 2 3 G x H G Ax x Relation between A.P., G.P. and H.P.. (1) If A, G, H be A.M., G.M., H.M. between a and b, then 1 when 2 / 1 when 0 when 1 1 n H n G n A b a b a n n n n (2) If 2 1 , A A be two A.M.’s; 2 1 ,G G be two G.M.’s and 2 1 , H H be two H.M.’s between two numbers a and b then 2 1 2 1 2 1 2 1 H H A A H H G G (3) Recognization of A.P., G.P., H.P. : If a, b, c are three successive terms of a sequence. Then if, a a c b b a , then a, b, c are in A.P. If, b a c b b a , then a, b, c are in G.P. If, c a c b b a , then a, b, c are in H.P. (4) If number of terms of any A.P./G.P./H.P. is odd, then A.M./G.M./H.M. of first and last terms is middle term of series. (5) If number of terms of any A.P./G.P./H.P. is even, then A.M./G.M./H.M. of middle two terms is A.M./G.M./H.M. of first and last terms respectively. (6) If pth , qth and rth terms of a G.P. are in G.P. Then p, q, r are in A.P. (7) If a, b, c are in A.P. as well as in G.P. then c b a . (8) If a, b, c are in A.P., then c b a x x x , , will be in G.P. ) 1 ( x\nPublicité"
] |
[
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-1-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-2-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-3-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-4-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-5-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-6-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-7-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-8-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-9-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-10-320.jpg",
null,
"https://image.slidesharecdn.com/progressions-230326160957-232faa5c/85/progressionsdocx-11-320.jpg",
null,
"https://cdn.slidesharecdn.com/ss_thumbnails/02-progressionseries-theory-230524123407-8bb88f76-thumbnail.jpg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.81101245,"math_prob":0.99646425,"size":21414,"snap":"2023-14-2023-23","text_gpt3_token_len":9618,"char_repetition_ratio":0.16683793,"word_repetition_ratio":0.27323186,"special_character_ratio":0.43140003,"punctuation_ratio":0.23392318,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9989452,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-02T16:53:37Z\",\"WARC-Record-ID\":\"<urn:uuid:3e6f2650-d5a8-4a28-9ec6-3f9a34e83bbd>\",\"Content-Length\":\"527758\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:acf5f1e8-e076-4f74-86c0-942b6a19afa1>\",\"WARC-Concurrent-To\":\"<urn:uuid:c7b7fb9d-73f1-48c0-9fb7-19fd0ce25202>\",\"WARC-IP-Address\":\"146.75.38.152\",\"WARC-Target-URI\":\"https://fr.slideshare.net/ssuser002675/progressionsdocx\",\"WARC-Payload-Digest\":\"sha1:RN2WVLGAT7USL6NV2CQTCIWMDGK6GMV7\",\"WARC-Block-Digest\":\"sha1:LDC4MYBIDA4UBKE7BMTIHC45CCHTBLUY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224648695.4_warc_CC-MAIN-20230602140602-20230602170602-00442.warc.gz\"}"}
|
https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-5-section-5-3-proving-triangles-similar-exercises-page-230/7
|
[
"## Elementary Geometry for College Students (6th Edition)\n\n$SAS \\sim$\nWe are given that one set of corresponding angles is congruent. We are also given that the corresponding sides on the 'left' side of the angles are proportional AND the corresponding sides on the 'right' side of the angles are equally proportional. Since the congruent angles are INBETWEEN the two sets of proportional corresponding sides, the two triangles are congruent by $SAS \\sim$."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8898339,"math_prob":0.9930178,"size":422,"snap":"2022-05-2022-21","text_gpt3_token_len":93,"char_repetition_ratio":0.17942584,"word_repetition_ratio":0.060606062,"special_character_ratio":0.19668247,"punctuation_ratio":0.054054055,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98936635,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-20T10:52:50Z\",\"WARC-Record-ID\":\"<urn:uuid:bfc7605a-eb09-4d82-9a38-8387988a2e57>\",\"Content-Length\":\"58478\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a688e85c-e536-4e7e-88fb-7b9b0dd5c0dc>\",\"WARC-Concurrent-To\":\"<urn:uuid:8437446d-acaa-46bc-b21d-38e63e9ecdea>\",\"WARC-IP-Address\":\"3.227.56.233\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-5-section-5-3-proving-triangles-similar-exercises-page-230/7\",\"WARC-Payload-Digest\":\"sha1:3XELVOWB2S6MYWCUKSSTJZUIBOMHE5FX\",\"WARC-Block-Digest\":\"sha1:IIRZ7DPAZ7TPJJVZIOB576AKUVSL77YE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662531779.10_warc_CC-MAIN-20220520093441-20220520123441-00676.warc.gz\"}"}
|
https://juejin.im/post/5949d85f61ff4b006c0de98b
|
[
"# JavaScript专题之数组去重\n\nJavaScript 专题系列第三篇，讲解各种数组去重方法，并且跟着 underscore 写一个 unique API\n\n## 双层循环\n\n``````var array = [1, 1, '1', '1'];\n\nfunction unique(array) {\n// res用来存储结果\nvar res = [];\nfor (var i = 0, arrayLen = array.length; i < arrayLen; i++) {\nfor (var j = 0, resLen = res.length; j < resLen; j++ ) {\nif (array[i] === res[j]) {\nbreak;\n}\n}\n// 如果array[i]是唯一的，那么执行完循环，j等于resLen\nif (j === resLen) {\nres.push(array[i])\n}\n}\nreturn res;\n}\n\nconsole.log(unique(array)); // [1, \"1\"]复制代码``````\n\n## indexOf\n\n``````var array = [1, 1, '1'];\n\nfunction unique(array) {\nvar res = [];\nfor (var i = 0, len = array.length; i < len; i++) {\nvar current = array[i];\nif (res.indexOf(current) === -1) {\nres.push(current)\n}\n}\nreturn res;\n}\n\nconsole.log(unique(array));复制代码``````\n\n## 排序后去重\n\n``````var array = [1, 1, '1'];\n\nfunction unique(array) {\nvar res = [];\nvar sortedArray = array.concat().sort();\nvar seen;\nfor (var i = 0, len = sortedArray.length; i < len; i++) {\n// 如果是第一个元素或者相邻的元素不相同\nif (!i || seen !== sortedArray[i]) {\nres.push(sortedArray[i])\n}\nseen = sortedArray[i];\n}\nreturn res;\n}\n\nconsole.log(unique(array));复制代码``````\n\n## unique API\n\n``````var array1 = [1, 2, '1', 2, 1];\nvar array2 = [1, 1, '1', 2, 2];\n\n// 第一版\nfunction unique(array, isSorted) {\nvar res = [];\nvar seen = [];\n\nfor (var i = 0, len = array.length; i < len; i++) {\nvar value = array[i];\nif (isSorted) {\nif (!i || seen !== value) {\nres.push(value)\n}\nseen = value;\n}\nelse if (res.indexOf(value) === -1) {\nres.push(value);\n}\n}\nreturn res;\n}\n\nconsole.log(unique(array1)); // [1, 2, \"1\"]\nconsole.log(unique(array2, true)); // [1, \"1\", 2]复制代码``````\n\n## 优化\n\n``````var array3 = [1, 1, 'a', 'A', 2, 2];\n\n// 第二版\n// iteratee 英文释义：迭代 重复\nfunction unique(array, isSorted, iteratee) {\nvar res = [];\nvar seen = [];\n\nfor (var i = 0, len = array.length; i < len; i++) {\nvar value = array[i];\nvar computed = iteratee ? iteratee(value, i, array) : value;\nif (isSorted) {\nif (!i || seen !== value) {\nres.push(value)\n}\nseen = value;\n}\nelse if (iteratee) {\nif (seen.indexOf(computed) === -1) {\nseen.push(computed);\nres.push(value);\n}\n}\nelse if (res.indexOf(value) === -1) {\nres.push(value);\n}\n}\nreturn res;\n}\n\nconsole.log(unique(array3, false, function(item){\nreturn typeof item == 'string' ? item.toLowerCase() : item\n})); // [1, \"a\", 2]复制代码``````\n\narray：表示要去重的数组，必填\n\nisSorted：表示函数传入的数组是否已排过序，如果为 true，将会采用更快的方法进行去重\n\niteratee：传入一个函数，可以对每个元素进行重新的计算，然后根据处理的结果进行去重\n\n## filter\n\nES5 提供了 filter 方法，我们可以用来简化外层循环：\n\n``````var array = [1, 2, 1, 1, '1'];\n\nfunction unique(array) {\nvar res = array.filter(function(item, index, array){\nreturn array.indexOf(item) === index;\n})\nreturn res;\n}\n\nconsole.log(unique(array));复制代码``````\n\n``````var array = [1, 2, 1, 1, '1'];\n\nfunction unique(array) {\nreturn array.concat().sort().filter(function(item, index, array){\nreturn !index || item !== array[index - 1]\n})\n}\n\nconsole.log(unique(array));复制代码``````\n\n## Object 键值对\n\n``````var array = [1, 2, 1, 1, '1'];\n\nfunction unique(array) {\nvar obj = {};\nreturn array.filter(function(item, index, array){\nreturn obj.hasOwnProperty(item) ? false : (obj[item] = true)\n})\n}\n\nconsole.log(unique(array)); // [1, 2]复制代码``````\n\n``````var array = [1, 2, 1, 1, '1'];\n\nfunction unique(array) {\nvar obj = {};\nreturn array.filter(function(item, index, array){\nreturn obj.hasOwnProperty(typeof item + item) ? false : (obj[typeof item + item] = true)\n})\n}\n\nconsole.log(unique(array)); // [1, 2, \"1\"]复制代码``````\n\n## ES6\n\n``````var array = [1, 2, 1, 1, '1'];\n\nfunction unique(array) {\nreturn Array.from(new Set(array));\n}\n\nconsole.log(unique(array)); // [1, 2, \"1\"]复制代码``````\n\n``````function unique(array) {\nreturn [...new Set(array)];\n}复制代码``````\n\n``var unique = (a) => [...new Set(a)]复制代码``\n\n``````function unique (arr) {\nconst seen = new Map()\nreturn arr.filter((a) => !seen.has(a) && seen.set(a, 1))\n}复制代码``````\n\n## 特殊类型比较\n\n``````var str1 = '1';\nvar str2 = new String('1');\n\nconsole.log(str1 == str2); // true\nconsole.log(str1 === str2); // false\n\nconsole.log(null == null); // true\nconsole.log(null === null); // true\n\nconsole.log(undefined == undefined); // true\nconsole.log(undefined === undefined); // true\n\nconsole.log(NaN == NaN); // false\nconsole.log(NaN === NaN); // false\n\nconsole.log(/a/ == /a/); // false\nconsole.log(/a/ === /a/); // false\n\nconsole.log({} == {}); // false\nconsole.log({} === {}); // false复制代码``````\n\n``var array = [1, 1, '1', '1', null, null, undefined, undefined, new String('1'), new String('1'), /a/, /a/, NaN, NaN];复制代码``\n\nfor循环[1, \"1\", null, undefined, String, String, /a/, /a/, NaN, NaN]对象和 NaN 不去重\nindexOf[1, \"1\", null, undefined, String, String, /a/, /a/, NaN, NaN]对象和 NaN 不去重\nsort[/a/, /a/, \"1\", 1, String, 1, String, NaN, NaN, null, undefined]对象和 NaN 不去重 数字 1 也不去重\nfilter + indexOf [1, \"1\", null, undefined, String, String, /a/, /a/]对象不去重 NaN 会被忽略掉\nfilter + sort[/a/, /a/, \"1\", 1, String, 1, String, NaN, NaN, null, undefined]对象和 NaN 不去重 数字 1 不去重\n\nSet[1, \"1\", null, undefined, String, String, /a/, /a/, NaN]对象不去重 NaN 去重\n\n``````// demo1\nvar arr = [1, 2, NaN];\narr.indexOf(NaN); // -1复制代码``````\n\nindexOf 底层还是使用 === 进行判断，因为 NaN ==== NaN的结果为 false，所以使用 indexOf 查找不到 NaN 元素\n\n``````// demo2\nfunction unique(array) {\nreturn Array.from(new Set(array));\n}\nconsole.log(unique([NaN, NaN])) // [NaN]复制代码``````\n\nSet 认为尽管 NaN === NaN 为 false，但是这两个元素是重复的。\n\n## 专题系列\n\nJavaScript专题系列目录地址：github.com/mqyqingfeng…\n\nJavaScript专题系列预计写二十篇左右，主要研究日常开发中一些功能点的实现，比如防抖、节流、去重、类型判断、拷贝、最值、扁平、柯里、递归、乱序、排序等，特点是研(chao)究(xi) underscore 和 jQuery 的实现方式。"
] |
[
null
] |
{"ft_lang_label":"__label__zh","ft_lang_prob":0.6152639,"math_prob":0.9940732,"size":6922,"snap":"2020-24-2020-29","text_gpt3_token_len":3310,"char_repetition_ratio":0.16926858,"word_repetition_ratio":0.2892473,"special_character_ratio":0.34180874,"punctuation_ratio":0.23770492,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9740129,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-29T01:22:04Z\",\"WARC-Record-ID\":\"<urn:uuid:2a978962-6d2a-4deb-a869-c67624a0301b>\",\"Content-Length\":\"77493\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:78c21279-e2bb-4e81-9fd8-c3c46fe14136>\",\"WARC-Concurrent-To\":\"<urn:uuid:0c2b23c3-f9b8-48a5-a03c-f8e716ed4b95>\",\"WARC-IP-Address\":\"139.198.2.223\",\"WARC-Target-URI\":\"https://juejin.im/post/5949d85f61ff4b006c0de98b\",\"WARC-Payload-Digest\":\"sha1:BHEPFCNZKA6YJGJDINVSSSXYDOUKKMHL\",\"WARC-Block-Digest\":\"sha1:TKZJNVMZKFUXUHVRQVWRD457GDFCSP6S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347401004.26_warc_CC-MAIN-20200528232803-20200529022803-00475.warc.gz\"}"}
|
https://www.colorhexa.com/22cd15
|
[
"# #22cd15 Color Information\n\nIn a RGB color space, hex #22cd15 is composed of 13.3% red, 80.4% green and 8.2% blue. Whereas in a CMYK color space, it is composed of 83.4% cyan, 0% magenta, 89.8% yellow and 19.6% black. It has a hue angle of 115.8 degrees, a saturation of 81.4% and a lightness of 44.3%. #22cd15 color hex could be obtained by blending #44ff2a with #009b00. Closest websafe color is: #33cc00.\n\n• R 13\n• G 80\n• B 8\nRGB color chart\n• C 83\n• M 0\n• Y 90\n• K 20\nCMYK color chart\n\n#22cd15 color description : Strong lime green.\n\n# #22cd15 Color Conversion\n\nThe hexadecimal color #22cd15 has RGB values of R:34, G:205, B:21 and CMYK values of C:0.83, M:0, Y:0.9, K:0.2. Its decimal value is 2280725.\n\nHex triplet RGB Decimal 22cd15 `#22cd15` 34, 205, 21 `rgb(34,205,21)` 13.3, 80.4, 8.2 `rgb(13.3%,80.4%,8.2%)` 83, 0, 90, 20 115.8°, 81.4, 44.3 `hsl(115.8,81.4%,44.3%)` 115.8°, 89.8, 80.4 33cc00 `#33cc00`\nCIE-LAB 72.265, -70.576, 68.343 22.625, 44.054, 8.02 0.303, 0.59, 44.054 72.265, 98.243, 135.921 72.265, -65.69, 86.496 66.373, -55.307, 39.297 00100010, 11001101, 00010101\n\n# Color Schemes with #22cd15\n\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #c015cd\n``#c015cd` `rgb(192,21,205)``\nComplementary Color\n• #7ecd15\n``#7ecd15` `rgb(126,205,21)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #15cd64\n``#15cd64` `rgb(21,205,100)``\nAnalogous Color\n• #cd157e\n``#cd157e` `rgb(205,21,126)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #6415cd\n``#6415cd` `rgb(100,21,205)``\nSplit Complementary Color\n• #cd1522\n``#cd1522` `rgb(205,21,34)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #1522cd\n``#1522cd` `rgb(21,34,205)``\nTriadic Color\n• #cdc015\n``#cdc015` `rgb(205,192,21)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #1522cd\n``#1522cd` `rgb(21,34,205)``\n• #c015cd\n``#c015cd` `rgb(192,21,205)``\nTetradic Color\n• #16880e\n``#16880e` `rgb(22,136,14)``\n• #1a9f10\n``#1a9f10` `rgb(26,159,16)``\n• #1eb613\n``#1eb613` `rgb(30,182,19)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #26e417\n``#26e417` `rgb(38,228,23)``\n• #39e92c\n``#39e92c` `rgb(57,233,44)``\n• #4fec43\n``#4fec43` `rgb(79,236,67)``\nMonochromatic Color\n\n# Alternatives to #22cd15\n\nBelow, you can see some colors close to #22cd15. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #50cd15\n``#50cd15` `rgb(80,205,21)``\n• #41cd15\n``#41cd15` `rgb(65,205,21)``\n• #31cd15\n``#31cd15` `rgb(49,205,21)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #15cd17\n``#15cd17` `rgb(21,205,23)``\n• #15cd27\n``#15cd27` `rgb(21,205,39)``\n• #15cd36\n``#15cd36` `rgb(21,205,54)``\nSimilar Colors\n\n# #22cd15 Preview\n\nText with hexadecimal color #22cd15\n\nThis text has a font color of #22cd15.\n\n``<span style=\"color:#22cd15;\">Text here</span>``\n#22cd15 background color\n\nThis paragraph has a background color of #22cd15.\n\n``<p style=\"background-color:#22cd15;\">Content here</p>``\n#22cd15 border color\n\nThis element has a border color of #22cd15.\n\n``<div style=\"border:1px solid #22cd15;\">Content here</div>``\nCSS codes\n``.text {color:#22cd15;}``\n``.background {background-color:#22cd15;}``\n``.border {border:1px solid #22cd15;}``\n\n# Shades and Tints of #22cd15\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #020901 is the darkest color, while #f7fef6 is the lightest one.\n\n• #020901\n``#020901` `rgb(2,9,1)``\n• #041b03\n``#041b03` `rgb(4,27,3)``\n• #072d05\n``#072d05` `rgb(7,45,5)``\n• #0a3f06\n``#0a3f06` `rgb(10,63,6)``\n• #0d5008\n``#0d5008` `rgb(13,80,8)``\n• #10620a\n``#10620a` `rgb(16,98,10)``\n• #13740c\n``#13740c` `rgb(19,116,12)``\n• #16860e\n``#16860e` `rgb(22,134,14)``\n• #199810\n``#199810` `rgb(25,152,16)``\n• #1ca911\n``#1ca911` `rgb(28,169,17)``\n• #1fbb13\n``#1fbb13` `rgb(31,187,19)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #25df17\n``#25df17` `rgb(37,223,23)``\nShade Color Variation\n• #2fe821\n``#2fe821` `rgb(47,232,33)``\n• #40ea33\n``#40ea33` `rgb(64,234,51)``\n• #50ec45\n``#50ec45` `rgb(80,236,69)``\n• #61ee56\n``#61ee56` `rgb(97,238,86)``\n• #72f068\n``#72f068` `rgb(114,240,104)``\n• #82f17a\n``#82f17a` `rgb(130,241,122)``\n• #93f38c\n``#93f38c` `rgb(147,243,140)``\n• #a4f59e\n``#a4f59e` `rgb(164,245,158)``\n• #b4f7af\n``#b4f7af` `rgb(180,247,175)``\n• #c5f9c1\n``#c5f9c1` `rgb(197,249,193)``\n• #d6fad3\n``#d6fad3` `rgb(214,250,211)``\n• #e6fce5\n``#e6fce5` `rgb(230,252,229)``\n• #f7fef6\n``#f7fef6` `rgb(247,254,246)``\nTint Color Variation\n\n# Tones of #22cd15\n\nA tone is produced by adding gray to any pure hue. In this case, #6d766c is the less saturated color, while #13de04 is the most saturated one.\n\n• #6d766c\n``#6d766c` `rgb(109,118,108)``\n• #657f63\n``#657f63` `rgb(101,127,99)``\n• #5e875b\n``#5e875b` `rgb(94,135,91)``\n• #569052\n``#569052` `rgb(86,144,82)``\n• #4f9949\n``#4f9949` `rgb(79,153,73)``\n• #47a240\n``#47a240` `rgb(71,162,64)``\n• #40aa38\n``#40aa38` `rgb(64,170,56)``\n• #38b32f\n``#38b32f` `rgb(56,179,47)``\n• #31bc26\n``#31bc26` `rgb(49,188,38)``\n• #29c41e\n``#29c41e` `rgb(41,196,30)``\n• #22cd15\n``#22cd15` `rgb(34,205,21)``\n• #1bd60c\n``#1bd60c` `rgb(27,214,12)``\n• #13de04\n``#13de04` `rgb(19,222,4)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #22cd15 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.55661774,"math_prob":0.71758866,"size":3682,"snap":"2019-13-2019-22","text_gpt3_token_len":1633,"char_repetition_ratio":0.122349106,"word_repetition_ratio":0.011090573,"special_character_ratio":0.5602933,"punctuation_ratio":0.23783186,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9788964,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-24T11:46:23Z\",\"WARC-Record-ID\":\"<urn:uuid:d2800fa6-de26-4f0d-afe2-23fad6f477fe>\",\"Content-Length\":\"36400\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:199032af-dfa2-470d-af20-65fba88f3e9c>\",\"WARC-Concurrent-To\":\"<urn:uuid:6346982b-d264-4d93-9750-e553431141a4>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/22cd15\",\"WARC-Payload-Digest\":\"sha1:R2BUBUEQON3KHJAZTZ2UKMT3KK2KCUGT\",\"WARC-Block-Digest\":\"sha1:ITGBNO7VRJBAF7GAURUOD65I6DPSNNDD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232257605.76_warc_CC-MAIN-20190524104501-20190524130501-00255.warc.gz\"}"}
|
https://arvimal.blog/2017/02/
|
[
"# Selection Sort – Algorithm Study\n\nSelection Sort is a sorting algorithm used to sort a data set either in incremental or decremental order.\n\nIt goes through the entire elements one by one and hence it’s not a very efficient algorithm to work on large data sets.\n\n## How does Selection sort work?\n\nSelection sort starts with an unsorted data set. With each iteration, it builds up a sub dataset with the sorted data.\n\nBy the end of the sorting process, the sub dataset contains the entire elements in a sorted order.\n\n1. Iterate through the data set one element at a time.\n2. Find the biggest element in the data set (Append it to another if needed)\n3. Reduce the sample space by the biggest element just found. The new data set becomes `n – 1` compared to the previous iteration.\n4. Start over the iteration again, on the reduced sample space.\n5. Continue till we have a sorted data set, either incremental or decremental\n\n## How does the data sample change in each iteration?\n\nConsider the data set [10, 4, 9, 3, 6, 19, 8]\n\n[10, 4, 9, 3, 6, 19, 8] – Data set\n[10, 4, 9, 3, 6, 8] – – After Iteration 1\n[4, 9, 3, 6, 8] – [10, 19] – After Iteration 2\n[4, 3, 6, 8] – [9, 10, 19] – After Iteration 3\n[4, 3, 6] – [8, 9, 10, 19] – After Iteration 4\n[4, 3] – [6, 8, 9, 10, 19] – After Iteration 5\n – [4, 6, 8, 9, 10, 19] – After Iteration 6\n[3, 4, 6, 8, 9, 10, 19] – After Iteration 7 – Sorted data set\n\nLet’s check what the Selection Sort algorithm has to go through in each iteration.\n\nDataset – [10, 4, 9, 3, 6, 19, 8]\nIter 1 – [10, 4, 9, 3, 6, 8]\nIter 2 – [4, 9, 3, 6, 8]\nIter 3 – [4, 3, 6, 8]\nIter 4 – [4, 3, 6]\nIter 5 – [4, 3]\nIter 6 – \n\nSorted Dataset – [3, 4, 6, 8, 9, 10, 19]\n\n## Performance / Time Complexity\n\nSelection Sort has to go through all the elements in the data set, no matter what.\n\nHence, the Worst case, Best case and Average Time Complexity would be O(n^2).\n\nSince `Selection Sort` takes in `n` elements while starting, and goes through the data set `n` times (each step reducing the data set size by 1 member), the iterations would be:\n\nn + [ (n – 1) + (n – 2) + (n – 3) + (n – 4) + … + 2 + 1 ]\n\nWe are more interested in the worse-case scenario. In a very large data set, an `n – 1`, `n – 2` etc.. won’t make a difference.\n\nHence we can re-write the above iterations as:\n\nn + [n + n + n + n ….. n]\n\nOr also as:\n\nn * n = (n^2)\n\n## Code\n\n```def find_smallest(my_list):\nsmallest = my_list\nsmallest_index = 0\n\nfor i in range(1, len(my_list)):\nif my_list[i] < smallest:\nsmallest = my_list[i]\nsmallest_index = i\nreturn smallest_index\n\ndef selection_sort(my_list):\nnew_list = []\nfor i in range(len(my_list)):\nsmallest = find_smallest(my_list)\nnew_list.append(my_list.pop(smallest))\nreturn new_list\n```\n\n## Observations:\n\n1.Selection Sort is an algorithm to sort a data set, but it is not particularly fast.\n2. It takes `n` iterations in each step to find the biggest element in that iteration.\n3. The next iteration has to run on a data set of `n – 1` elements compared to the previous iteration.\n4. For `n` elements in a sample space, Selection Sort takes `n x n` iterations to sort the data set."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.772347,"math_prob":0.9894772,"size":3183,"snap":"2020-45-2020-50","text_gpt3_token_len":1032,"char_repetition_ratio":0.16451715,"word_repetition_ratio":0.0756579,"special_character_ratio":0.35186931,"punctuation_ratio":0.19645293,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9641518,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-30T15:39:05Z\",\"WARC-Record-ID\":\"<urn:uuid:5a5406c9-fcc8-4c09-b672-5c1613d9d833>\",\"Content-Length\":\"112408\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3b301963-4e89-4365-9131-b7633f8287ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:4ed088e9-9ff7-4c50-946e-73e36f4dbfe9>\",\"WARC-IP-Address\":\"192.0.78.24\",\"WARC-Target-URI\":\"https://arvimal.blog/2017/02/\",\"WARC-Payload-Digest\":\"sha1:3STIRFQJAZT5ZRE4JOQG5IFLAX22LB6C\",\"WARC-Block-Digest\":\"sha1:3SVBIZ636EBK6ERBLN7NSDTORAFDM75V\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107911027.72_warc_CC-MAIN-20201030153002-20201030183002-00021.warc.gz\"}"}
|
https://www.machinelearninginterview.com/topics/natural-language-processing/explain-latent-dirichlet-allocation-where-is-it-typically-used/
|
[
"# Explain latent dirichlet allocation – where is it typically used ?\n\nLatent Dirichlet Allocation is a probabilistic model that models a document as a multinomial mixture of topics and the topics as a multinomial mixture of words. Each of these multinomials have a dirichlet prior. The goal is to learn these multinomial proportions using probabilistic inference techniques based on the observed data which is the words/content in the document.\n\nLet there be $M$ documents, $V$ words in the vocabulary and $K$ be the number of topics we want to find. The LDA can be defined by the following generative process :\n\n→ For each topic $k$, $\\phi_k = (\\phi_{k1}, \\hdots, \\phi_{kV})$ is a topic specific multinomial distribution over $V$ words in the vocabulary. Note that $\\phi_{kv}$ represents the weightage given to word $v$ in topic $k$. The multinomial $\\phi_k$ is generated as $\\phi_k \\sim Dir(\\beta)$.\n\n→ For each document $j, \\theta_j=(\\theta_{j1}, \\hdot, \\theta_{jK})$ is a document specific multinomial where each component $\\theta_{jk}$ represents the weightage of topic $k$ in the document $j$. The multinomial $\\theta_j$ is generated as follows from a dirichlet distribution : $\\theta_j \\sim Dir(\\alpha)$\n\n→ For each word $i$ in document $j$ a topic $z_{ji} \\sim \\theta_j$ is generated from the document specific multinomial $\\theta_j$. Then depending on the topic, a word $w_{ji}$ is generated as $w_{ji} \\sim \\phi_{z_{ji}}$\n\nNow, the learning happens through the task of inference (typically the techniques used for inference are Gibbs Sampling or Variational Inference) to learn the $\\theta_j$s and $\\phi_k$s based on the observed data i.e the words in the document.\n\nThe outcome of LDA is one multinomial for each document which is a low dimensional representation of the document and a multinomial for each topic. One can visualize the topic as a combination of all words whose weight is high in the corresponding multinomial."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8360179,"math_prob":0.99702346,"size":1863,"snap":"2019-51-2020-05","text_gpt3_token_len":456,"char_repetition_ratio":0.17374933,"word_repetition_ratio":0.013745705,"special_character_ratio":0.24369296,"punctuation_ratio":0.07294833,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999347,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-28T07:27:18Z\",\"WARC-Record-ID\":\"<urn:uuid:491097e7-7fc8-4a73-894f-1c3aa301c271>\",\"Content-Length\":\"78065\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:349c3ee7-08ce-4529-b1a6-457fcafeed04>\",\"WARC-Concurrent-To\":\"<urn:uuid:6989b631-88a3-4c43-808c-91437c7a7d76>\",\"WARC-IP-Address\":\"13.127.164.78\",\"WARC-Target-URI\":\"https://www.machinelearninginterview.com/topics/natural-language-processing/explain-latent-dirichlet-allocation-where-is-it-typically-used/\",\"WARC-Payload-Digest\":\"sha1:5CYPTVZHJMECWSM2PJW7L5DEIIJXXN6Q\",\"WARC-Block-Digest\":\"sha1:U4OOKGSBCP66ZACHTDO2G2JUZUTA7AGV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251776516.99_warc_CC-MAIN-20200128060946-20200128090946-00305.warc.gz\"}"}
|
https://www.memrise.com/course/700001/learn-mathematics/256/?action=next
|
[
"Level 255 Level 257\nLevel 256\n\n## Ignore words\n\nCheck the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.\n\nIgnore?\ny = 7\nm = 0, point (4, 7)\ny = 2/5x + 1\nm = 2/5, point (0, 1)\ny = 1/3x - 11/3\nm = 1/3, point (2, -3)\nx = 5\nm = undefined, point (5, -25)\ny = -4x + 7\nm = -4, point (1, 3)\n(1, 5) (-2, -4)\ny = 3x + 2\n(-3, -1) (0, -2)\ny = -1/3x - 2"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.539554,"math_prob":0.999966,"size":452,"snap":"2019-51-2020-05","text_gpt3_token_len":204,"char_repetition_ratio":0.16294643,"word_repetition_ratio":0.0,"special_character_ratio":0.5022124,"punctuation_ratio":0.15517241,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9756394,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-10T02:03:49Z\",\"WARC-Record-ID\":\"<urn:uuid:815d4ced-0dcc-498f-b654-f02d8db8bb91>\",\"Content-Length\":\"146406\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:07b3cdfa-9d3b-4336-8b61-8570b45951b8>\",\"WARC-Concurrent-To\":\"<urn:uuid:2549c226-31e6-4192-baf6-7f5118ea9745>\",\"WARC-IP-Address\":\"3.222.195.117\",\"WARC-Target-URI\":\"https://www.memrise.com/course/700001/learn-mathematics/256/?action=next\",\"WARC-Payload-Digest\":\"sha1:AD4NPICDZCG4LMUCCNQBJAJTC4K4YE2Y\",\"WARC-Block-Digest\":\"sha1:B7B2K2QAGYP5UWAULJPZYXAFFCUWKH5E\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540525781.64_warc_CC-MAIN-20191210013645-20191210041645-00511.warc.gz\"}"}
|
https://www.convertunits.com/from/range/to/inch
|
[
"## ››Convert range to inch\n\n range inch\n\nHow many range in 1 inch? The answer is 2.6304661195286E-6.\nWe assume you are converting between range and inch.\nYou can view more details on each measurement unit:\nrange or inch\nThe SI base unit for length is the metre.\n1 metre is equal to 0.00010356165824916 range, or 39.370078740157 inch.\nNote that rounding errors may occur, so always check the results.\nUse this page to learn how to convert between ranges and inches.\nType in your own numbers in the form to convert the units!\n\n## ››Quick conversion chart of range to inch\n\n1 range to inch = 380160.76032 inch\n\n2 range to inch = 760321.52064 inch\n\n3 range to inch = 1140482.28096 inch\n\n4 range to inch = 1520643.04129 inch\n\n5 range to inch = 1900803.80161 inch\n\n6 range to inch = 2280964.56193 inch\n\n7 range to inch = 2661125.32225 inch\n\n8 range to inch = 3041286.08257 inch\n\n9 range to inch = 3421446.84289 inch\n\n10 range to inch = 3801607.60322 inch\n\n## ››Want other units?\n\nYou can do the reverse unit conversion from inch to range, or enter any two units below:\n\n## Enter two units to convert\n\n From: To:\n\n## ››Definition: Inch\n\nAn inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot. The inch is usually the universal unit of measurement in the United States, and is widely used in the United Kingdom, and Canada, despite the introduction of metric to the latter two in the 1960s and 1970s, respectively. The inch is still commonly used informally, although somewhat less, in other Commonwealth nations such as Australia; an example being the long standing tradition of measuring the height of newborn children in inches rather than centimetres. The international inch is defined to be equal to 25.4 millimeters.\n\n## ››Metric conversions and more\n\nConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3\", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8769214,"math_prob":0.9531198,"size":2275,"snap":"2022-27-2022-33","text_gpt3_token_len":586,"char_repetition_ratio":0.17129017,"word_repetition_ratio":0.0,"special_character_ratio":0.29758242,"punctuation_ratio":0.14042553,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96746904,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-02T07:25:45Z\",\"WARC-Record-ID\":\"<urn:uuid:7337bd66-da91-404a-8a4f-6fa027f6cdc1>\",\"Content-Length\":\"52349\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:62a818ed-342f-43bb-9766-b764010aa92d>\",\"WARC-Concurrent-To\":\"<urn:uuid:cb5f6121-4e6a-4742-9f45-487e6d85bd6c>\",\"WARC-IP-Address\":\"3.213.84.236\",\"WARC-Target-URI\":\"https://www.convertunits.com/from/range/to/inch\",\"WARC-Payload-Digest\":\"sha1:O7SSOWPIRXI5EOFM5EIZXBYLSHPY73QD\",\"WARC-Block-Digest\":\"sha1:7UIJSMAOYBHETMZF4KLM2DKYTBF6O5MP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103989282.58_warc_CC-MAIN-20220702071223-20220702101223-00000.warc.gz\"}"}
|
https://www.tutorialcup.com/interview/string/nth-character-in-concatenated-decimal-string.htm
|
[
"# Nth Character in Concatenated Decimal String\n\nDifficulty Level Medium\nString\n\n## Problem Statement\n\nIn the “Nth Character in Concatenated Decimal String” problem we have given an integer value “n”. Write a program to find the Nth character in the string in which all decimals are concatenated.\n\n## Input Format\n\nThe first and only one line containing an integer value n.\n\n## Output Format\n\nPrint a character at position “n” in the string in which all decimals are concatenated.\n\n• 1<=n<=10^5\n\n## Example\n\n`7`\n`7`\n\nExplanation: Let’s form a string whose length is 7 and all decimals are concatenated in it. So, our string is “1234567”. Now we check the 7th character in the string which is 7. So our final answer is “7”.\n\n`10`\n`1`\n\nExplanation: Let’s form a string in which concatenate 10 numbers. So, our string is “12345678910”. Now we check the 10th character in the string which is 1. So our final answer is “1”.\n\n## Approach\n\nIn this method the main idea is, considering the fact that in decimal 9 numbers are of length 1, 90 numbers are of length 2 and 900 numbers are of length 3 and so on. So skip these numbers according to the given N and find the character\n\n1. Find the length of the number at N\n\n2. Now, get the character at N\n\n### Example\n\nN = 51\n\n1) Finding the length of the number at N\n51 – 9 = 42 // There are 9 numbers with length 1\n42 – 90*2 < 0 // As there are 90 numbers with length 2, we got to know that the length is 2\n\nRabin Karp Algorithm\n\n2) Find the character at N\n42 characters are after max 1 digit number(ie, 9)\nceil(42/2) = 21,so 9+21 = 30. So, 30 is the number at N.\nNow, finding the actual character at N\n42%2 = 0, so take 2nd digit of 30. Therefore, 0 is the character at N\n\n## Implementation\n\n### C++ program for Nth Character in Concatenated Decimal String\n\n```#include <bits/stdc++.h>\nusing namespace std;\n\nint main()\n{\nint n;\ncin>>n;\nint sum=0,nine=9,dist=0,len;\nfor(len=1; ;len++)\n{\nsum+=nine*len;\ndist+=nine;\nif(sum>=n)\n{\nsum-=nine*len;\ndist-=nine;\nn-=sum;\nbreak;\n}\nnine*=10;\n}\nint diff=ceil((double)n/len);\nint d=n%len;\nif(d==0)\n{\nd=len;\n}\nn=dist+diff;\nstring str;\nstringstream ss;\nss<<n;\nss>>str;\ncout<<str[d - 1]<<endl;\nreturn 0;\n}\n```\n\n### Java program for Nth Character in Concatenated Decimal String\n\n```import java.util.Scanner;\n\nclass sum\n{\npublic static void main(String[] args)\n{\nScanner sr = new Scanner(System.in);\nint n=sr.nextInt();\nint sum=0,nine=9,dist=0,len;\nfor(len=1; ;len++)\n{\nsum+=nine * len;\ndist+=nine;\nif(sum>=n)\n{\nsum-=nine*len;\ndist-=nine;\nn-=sum;\nbreak;\n}\nnine*=10;\n}\nint diff=(int)(Math.ceil((double)(n)/(double)(len)));\nint d=n%len;\nif(d==0)\n{\nd=len;\n}\nString str=Integer.toString(dist+diff);\nSystem.out.println(str.charAt(d-1));\n}\n}\n```\n`51`\n\n## Complexity Analysis for Nth Character in Concatenated Decimal String\n\n### Time Complexity\n\nO(Log N) where N is the given integer. Here the base of log is 10.\n\n### Space Complexity\n\nO(1) because we don’t use any extra space here. We simply find the answer using a few operations using few variables."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7164927,"math_prob":0.9912966,"size":2848,"snap":"2021-43-2021-49","text_gpt3_token_len":834,"char_repetition_ratio":0.14135021,"word_repetition_ratio":0.11578947,"special_character_ratio":0.31074437,"punctuation_ratio":0.14576803,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9996315,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T08:22:44Z\",\"WARC-Record-ID\":\"<urn:uuid:9c8c3487-c6df-4dfc-b88d-0191d7c0a694>\",\"Content-Length\":\"181766\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1fe7b17b-24d1-48b1-b332-83daec9812d6>\",\"WARC-Concurrent-To\":\"<urn:uuid:09f04167-1979-463a-95a0-3a139b88567e>\",\"WARC-IP-Address\":\"172.67.176.24\",\"WARC-Target-URI\":\"https://www.tutorialcup.com/interview/string/nth-character-in-concatenated-decimal-string.htm\",\"WARC-Payload-Digest\":\"sha1:62JZXFEWHK6BPDXJXQANDVTYOA6SSLQZ\",\"WARC-Block-Digest\":\"sha1:PHFHFIE6WTTMI4HCRNCP7UYJ3JIGFS62\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363149.85_warc_CC-MAIN-20211205065810-20211205095810-00306.warc.gz\"}"}
|
https://docs.galpy.org/en/v1.6.0/reference/quasidfmeanjr.html
|
[
"# galpy.df.quasiisothermaldf.meanjr¶\n\nquasiisothermaldf.meanjr(R, z, nsigma=None, mc=True, nmc=10000, **kwargs)[source]\n\nNAME:\n\nmeanjr\n\nPURPOSE:\n\ncalculate the mean radial action by marginalizing over velocity\n\nINPUT:\n\nR - radius at which to calculate this (can be Quantity)\n\nz - height at which to calculate this (can be Quantity)\n\nOPTIONAL INPUT:\n\nnsigma - number of sigma to integrate the velocities over"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5600168,"math_prob":0.99470794,"size":590,"snap":"2020-24-2020-29","text_gpt3_token_len":166,"char_repetition_ratio":0.11945392,"word_repetition_ratio":0.102564104,"special_character_ratio":0.23559321,"punctuation_ratio":0.17757009,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99602175,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-28T17:09:49Z\",\"WARC-Record-ID\":\"<urn:uuid:2c5f5f5d-18a9-4ebe-91d3-1a055a5c9e45>\",\"Content-Length\":\"9598\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f34e80a7-71f4-485f-a263-fd966764a611>\",\"WARC-Concurrent-To\":\"<urn:uuid:ee65d9c4-fb02-4dbe-9a68-4a32e95e9d72>\",\"WARC-IP-Address\":\"104.17.33.82\",\"WARC-Target-URI\":\"https://docs.galpy.org/en/v1.6.0/reference/quasidfmeanjr.html\",\"WARC-Payload-Digest\":\"sha1:G2FMUNNHXKRKRCVG6CPMVPQ6E3BZFBZW\",\"WARC-Block-Digest\":\"sha1:P4RYVHZXNYMM4LW2MCUCYSFXX64YJ5LL\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347399830.24_warc_CC-MAIN-20200528170840-20200528200840-00248.warc.gz\"}"}
|
http://www.atombus.biz/2012/08/doppler-effect-basic-information-and.html
|
[
"### DOPPLER EFFECT BASIC INFORMATION AND TUTORIALS\n\nWhat is Doppler Effect?\n\nDoppler effect is an apparent shift of the transmitted frequency which occurs when either the receiver or transmitter is moving. It becomes significant in mobile radio applications towards the higher end of the UHF band and on digitally modulated systems.\n\nWhen a mobile receiver travels directly towards the transmitter each successive cycle of the wave has less distance to travel before reaching the receiving antenna and, effectively, the received frequency is raised. If the mobile travels away from the transmitter, each successive cycle has a greater distance to travel and the frequency is lowered.\n\nThe variation in frequency depends on the frequency of the wave, its propagation velocity and the velocity of the vehicle containing the receiver. In the situation where the velocity of the vehicle is small compared with the velocity of light, the frequency shift when moving directly towards, or away from, the transmitter is given to sufficient accuracy for most purposes by:\n\nfd = V/C fi\n\nwhere\nfd = frequency shift, Hz\nft = transmitted frequency, Hz\nV = velocity of vehicle, m/s\nC = velocity of light, m/s\n\nExamples are:\n• 100 km/hr at 450 MHz, frequency shift = 41.6Hz\n• 100 km/hr at 1.8 GHz – personal communication network (PCN)\nfrequencies – frequency shift = 166.5Hz\n• Train at 250 km/hr at 900MHz – a requirement for the GSM pan- European radio-telephone frequency shift = 208 Hz\n\nWhen the vehicle is travelling at an angle to the transmitter the frequency shift is reduced. It is calculated as above and the result multiplied by the cosine of the angle of travel from the direct approach\n\nIn a radar situation Doppler effect occurs on the path to the target and also to the reflected signal so that the above formula is modified to:\n\nfd = V/C fi\n\nwhere fd is now the total frequency shift."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9047687,"math_prob":0.9741929,"size":1851,"snap":"2020-45-2020-50","text_gpt3_token_len":418,"char_repetition_ratio":0.15592854,"word_repetition_ratio":0.019169329,"special_character_ratio":0.21393842,"punctuation_ratio":0.07941177,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9585903,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-28T01:54:55Z\",\"WARC-Record-ID\":\"<urn:uuid:e2aa874b-a9f7-4eb9-85f5-82a4b3a2c6be>\",\"Content-Length\":\"63901\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2752d58c-3978-4935-9035-ab6e7cbf2756>\",\"WARC-Concurrent-To\":\"<urn:uuid:95eb0928-e7d4-4648-96f3-912cf3463e4e>\",\"WARC-IP-Address\":\"172.217.13.83\",\"WARC-Target-URI\":\"http://www.atombus.biz/2012/08/doppler-effect-basic-information-and.html\",\"WARC-Payload-Digest\":\"sha1:UJN5O4YQ6JYYQWCBV5OVGFEID25AXNMJ\",\"WARC-Block-Digest\":\"sha1:LVWP2K2FP2NRMC3SMYR2SQNFM5SIKMGF\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141194982.45_warc_CC-MAIN-20201128011115-20201128041115-00581.warc.gz\"}"}
|
https://www.open.edu/openlearn/science-maths-technology/linear-programming-the-basic-ideas/content-section-0?active-tab=description-tab
|
[
"Science, Maths & Technology\nFree course\n\n# Linear programming – the basic ideas",
null,
"",
null,
"## Course reviews\n\nThis free course examines the formulation and solution of small linear programming problems. Section 1 deals with the formulation of linear programming models, describing how mathematical models of suitable real-world problems can be constructed. Section 2 looks at graphical representations of two-dimensional models, considers some theoretical implications and examines the graphical solution of such models. Section 3 introduces the simplex method for solving linear programming models and Section 4 uses matrix notation to formalize the simplex method.\n\n## Course learning outcomes\n\nAfter studying this course, you should be able to:\n\n• formulate a given simplified description of a suitable real-world problem as a linear programming model in general, standard and canonical forms\n• sketch a graphical representation of a two-dimensional linear programming model given in general, standard or canonical form\n• classify a two-dimensional linear programming model by the type of its solution\n• solve a two-dimensional linear programming problem graphically\n• use the simplex method to solve small linear programming models by hand, given a basic feasible point.\n\nFirst Published: 12/03/2018\n\nUpdated: 11/07/2019\n\nSkip Rate and Review"
] |
[
null,
"https://www.open.edu/openlearn/pluginfile.php/1135958/tool_ocwmanage/image/0/m373_1_OLHP_786x400.jpg",
null,
"https://www.open.edu/openlearn/theme/image.php/openlearnng/theme_openlearnng/1679481670/icon-copyright-free",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8974261,"math_prob":0.9350465,"size":1161,"snap":"2023-14-2023-23","text_gpt3_token_len":196,"char_repetition_ratio":0.17372516,"word_repetition_ratio":0.0124223605,"special_character_ratio":0.16020672,"punctuation_ratio":0.06557377,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9959644,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,8,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-31T04:39:01Z\",\"WARC-Record-ID\":\"<urn:uuid:613dfae0-8630-4d1a-9d8f-6a7b912f5f45>\",\"Content-Length\":\"97239\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f0a03039-ad77-4316-810c-effe0ff03fd9>\",\"WARC-Concurrent-To\":\"<urn:uuid:205ea695-8152-4567-8b1d-3268b18af0ad>\",\"WARC-IP-Address\":\"108.138.85.39\",\"WARC-Target-URI\":\"https://www.open.edu/openlearn/science-maths-technology/linear-programming-the-basic-ideas/content-section-0?active-tab=description-tab\",\"WARC-Payload-Digest\":\"sha1:74UYC5BVWNA4ELAKQ25VETETMTWLZBON\",\"WARC-Block-Digest\":\"sha1:74YVKNUPOJ4VIS6BJMDYD6VFGT6RWMIC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224646257.46_warc_CC-MAIN-20230531022541-20230531052541-00381.warc.gz\"}"}
|
https://mathematica.stackexchange.com/questions/6304/combining-plots-almost-there?noredirect=1
|
[
"# Combining plots (almost there!) [duplicate]\n\nPossible Duplicate:\n1 Plot, 2 Scale/Axis\n\nI aim to combine two plots in which the YY axes have different scales: one goes PlotRange->{0,100} while the other goes PlotRange->{0,2.5*^-5}. I've been trying to do this for several hours and, although I think I'm almost there, I cant seem to make it.\n\nHere's the input code:\n\n(*not very important, is one of the functions to be plotted*)\nP[st_, base_, int_] :=\nModule[{nper, period, length, tcap, tarteriols, tvenuls, ttotaloxi},\nperiod = 60/((4/3 Pi (0.1/2)^3)/48);\nlength = 2;\nnper = (t - st)/period;\nIf[0 <= (t - st) - period Floor@nper < length, base + int, base]\n]\n\n\nThe problem is in this one for sure:\n\nCombineplots[{hout_, maxrange_}, {t_, t0_, tf_}] :=\nModule[{relgraf, ihgraf, relrange, ih2o2range, relticks,\nih2o2ticks},\nrelgraf =\nPlot[Evaluate[{10 t} /. setpars /. pa[h2o2out]], {t, t0, tf},\nLabelStyle -> {FontFamily -> \"Arial\", Bold, 40},\nPlotStyle -> {{Thickness[0.011],\nDarker[Green, 0.5]}, {Thickness[0.011],\nDarker[Red, 0.2]}, {Thickness[0.007],\nDarker[Blue, 0.3]}, {Thickness[0.007], Darker[Orange, 0.3]}}];\n\nih2o2graf =\nPlot[Pulse[2, 1*^-9, h2o2out], {t, t0, tf},\nLabelStyle -> {FontFamily -> \"Arial\", Bold, 40},\nPlotStyle -> {Thickness[0.007], Black}];\nrelrange = ({0, 100});\nih2o2range = ({0, maxrange});\n\nShow[relgraf,\nih2o2graf /.\nGraphics[graf_, s___] :>\nGraphics[\nGeometricTransformation[graf,\nRescalingTransform[{{0, 10}, ih2o2range}, {{0, 10},\nrelrange}]], s], Axes -> True,\n\nFrame -> {{True, True}, {True, False}},\nFrameStyle -> AbsoluteThickness,\nFrameTicks -> {{Automatic, {{1/200000, \"5\"}, {1/100000, \"10\"}, {3/\n200000, \"15\"}, {1/50000, \"20\"}, {1/40000, \"25\"}, {3/100000,\n\"30\"}}}, {Automatic, None}}, ImageSize -> Medium]]\nCombineplots[{2*^-5, 3*^-5}, {t, 0, 10}]\n\n\nI've been able to plot both together correctly, with exception for the right YY axis:",
null,
"Yet, the ticks theoretically are placed at the correct place (using the same tick marks in a single plot I get the correct marking:)",
null,
"Do you guys think you can give me some clue please? Thanks so much!\n\n• thanks! already looking into it! and I'm sorry if this seems like repeating the same question as the one in the link :S EDIT: indeed, I also tried with Overlayand gives almost the same result with many less code lines than the ones I was using. Superimposition of both graphs isn't perfect yet, but a bit of fine tuning and it works too. Problably playing around with ImagePadding and thats it! thanks again! – Sosi Jun 1 '12 at 10:36\n\nYou rescaled the plot, but you didn't adjusted the position of the tick marks of the right vertical axis. To correct this you could do something like this:\n\nCombineplots[{hout_, maxrange_}, {t_, t0_, tf_}] :=\nModule[{relgraf, ihgraf, relrange, ih2o2range, relticks, ih2o2ticks, newticks},\nrelgraf = Plot[Evaluate[{10 t}], {t, t0, tf},\nLabelStyle -> {FontFamily -> \"Arial\", Bold, 40},\nPlotStyle -> {{Thickness[0.011],\nDarker[Green, 0.5]}, {Thickness[0.011],\nDarker[Red, 0.2]}, {Thickness[0.007],\nDarker[Blue, 0.3]}, {Thickness[0.007], Darker[Orange, 0.3]}}];\n\nih2o2graf = Plot[Pulse[2, 1*^-9, maxrange], {t, t0, tf},\nLabelStyle -> {FontFamily -> \"Arial\", Bold, 40},\nPlotStyle -> {Thickness[0.007], Black}];\nrelrange = ({0, 100});\nih2o2range = ({0, maxrange});\nnewticks = Transpose[{Rescale[Range/200000, ih2o2range, relrange], Range 5}];\nShow[relgraf,\nih2o2graf /. Graphics[graf_, s___] :>\nGraphics[GeometricTransformation[graf,\nRescalingTransform[{{0, 10}, ih2o2range}, {{0, 10}, relrange}]], s],\nAxes -> True,\nFrame -> {{True, True}, {True, False}},\nFrameStyle -> AbsoluteThickness,\nFrameTicks -> {{Automatic, newticks}, {Automatic, None}},\nImageSize -> Medium]]\n\nCombineplots[{2*^-5, 3*^-5}, {t, 0, 10}]",
null,
"• Oh, thanks! Indeed, it was something so simple and I wasn't seeing it. Thanks! – Sosi Jun 1 '12 at 10:32"
] |
[
null,
"https://i.stack.imgur.com/yjGry.png",
null,
"https://i.stack.imgur.com/Iif0I.png",
null,
"https://i.stack.imgur.com/EYZci.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.74430794,"math_prob":0.95423955,"size":2317,"snap":"2019-51-2020-05","text_gpt3_token_len":759,"char_repetition_ratio":0.08949416,"word_repetition_ratio":0.04733728,"special_character_ratio":0.3832542,"punctuation_ratio":0.26746505,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9710792,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,6,null,6,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-11T17:53:34Z\",\"WARC-Record-ID\":\"<urn:uuid:ec95160c-6093-475a-9f46-bf27130e446a>\",\"Content-Length\":\"120421\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:da168c48-7b57-4282-a753-5d95f7e5bf19>\",\"WARC-Concurrent-To\":\"<urn:uuid:7d659dfc-37a3-4180-b663-3bdc6c495d99>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://mathematica.stackexchange.com/questions/6304/combining-plots-almost-there?noredirect=1\",\"WARC-Payload-Digest\":\"sha1:WQD55K25NAJBHXNJQ6DCMH6S5BBIMRKV\",\"WARC-Block-Digest\":\"sha1:2BDYTKXQHMWWCJAEM2SM2B6NNWFTFFSU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540531974.7_warc_CC-MAIN-20191211160056-20191211184056-00046.warc.gz\"}"}
|
https://juliaintervals.github.io/pages/tutorials/tutorialOptimisation/index.html
|
[
"# Interval optimisation tutorial\n\nDownload the notebook for this tutorial.\n\n## Setup\n\nThe IntervalOptimisation.jl package can be installed with\n\njulia> using Pkg; Pkg.add(\"IntervalOptimisation\")\n\nOnce the package is installed, it can be imported. Note that you will need also the IntervalArithmetic.jl package.\n\nusing IntervalArithmetic, IntervalOptimisation\n\n## Function minimisation\n\nThe package two main functions are minimise and maximise. Here we will use minimise as example, however maximise behaves in an analog way. The main syntax is\n\nminimise(f, X, tol=1e-3),\n\nwhere $f:\\mathbb{R}^n↦\\mathbb{R}$ is the function to minimize, $X$ is the interval, or interval box, over which we minimize the function. For example, let's consider the function $f(x)=(x-3)^2$ and let us find its global minimum over its whole domain\n\nminimise(x->(x-3)^2, -∞..∞)\n([0, 7.392914838e-09], IntervalArithmetic.Interval{Float64}[[2.999645979, 3.000182057]])\n\nThe first value of the results tells us that the minimum value of the function is in the interval $[0, 7.39292e-09]$. The second value tells us that this minimum is achieved in the interval $[2.99964, 3.00019]$. If we want to narrow down this interval, we can use a smaller tolerance\n\nminVal, xmin = minimise(x->(x-3)^2, -∞..∞, tol=1e-9)\nxmin, [diam(x) for x in xmin]\n(IntervalArithmetic.Interval{Float64}[[2.999999999, 3.000000001]], [5.109304090922251e-10])\n\nNow the diameter of the minimiser is only $10^{-10}$ and the minimum is guaranteed to be in that interval.\n\n## Multivariate function minimisation\n\nThe package can also be used to minimise multivariate functions. Now, the function $f$ will take an array, and $X$ will be an interval box of dimension $n$. As an example, let us find the minimum of the paraboloid $z=(x-3)^2+(y-3)^2$ over the box $[-100, 100]×[-100, 100]$. First let's define the function\n\nparaboloid(x) = (x-3)^2 + (x-3)^2\nparaboloid (generic function with 1 method)\n\nand our interval box\n\nX = IntervalBox(-100..100, 2)\n[-100, 100] × [-100, 100]\n\nnow we can obtain the minimum\n\nzmin, xmin = minimise(paraboloid, X, tol=1e-10)\n([0, 4.245252e-22], IntervalArithmetic.IntervalBox{2,Float64}[[2.999999999, 3.000000001] × [2.999999999, 3.000000001]])\n\nthe position of the minimum has been found with an accuracy of\n\n[diam(x) for x in xmin]\n1-element Array{Float64,1}:\n9.154810243217071e-11\n\n### Griewank function minimisation\n\nThe $n$-dimensional Griewank function is defined as\n\n$G_n(\\mathbf{x})=1+\\frac{1}{4000}\\sum_{i=1}^n x_i^2 -∏_{i=1}^n \\cos\\left(\\frac{x_i}{\\sqrt{i}}\\right),$\n\nfor example the 1-dimensional Griewank function is\n\n$G_1(x) = 1+\\frac{x^2}{4000}-\\cos(x)$\n\n.\n\nand it is commonly used to test optimisation algorithms. This function has the property to have several regularly distributed local minima, but only one global minimum at the origin. Let's define our function\n\nG(X) = 1 + sum(abs2, X) / 4000 - prod( cos(X[i] / √i) for i in 1:length(X) )\nG (generic function with 1 method)\n\nNow let's verify our package finds the minima in several dimensions\n\nfor N in (1,2, 10, 20, 50)\nres, xmin = minimise(G, IntervalBox(-600..600, N))\n@show N, res, diam(xmin)\nend\n(N, res, diam(xmin)) = (1, [-0, 0], 0.000541404722891739)\n(N, res, diam(xmin)) = (2, [-0, 0], 0.000541404722891739)\n(N, res, diam(xmin)) = (10, [-0, 0], 0.000541404722891739)\n(N, res, diam(xmin)) = (20, [-0, 0], 0.000541404722891739)\n(N, res, diam(xmin)) = (50, [-0, 0], 0.000541404722891739)\n\n\n## Clustering problem\n\nThe clustering problem is an issue arising in global optimisation with interval arithmetic. Let us consider a simple function\n\nf(x) = x^2 - 2x + 1\nf (generic function with 1 method)\n\nYou may recall that interval arithmetic suffers from the dependency problem, i.e. if the same variable is repeated in the expression (as in the example above) then evaluating the function will produce an overestimate. Observe\n\nf(0..2)\n[-3, 5]\n\nusing Interval arithmetic we obtain the range $[-3, 5]$, while the true range is $[0, 1]$. Suppose $x^*$ is a minimiser for $f$, then for an $\\epsilon$ small enough we will have that $f(x^*) \\in f([x^*+\\epsilon, x^*+2\\epsilon])$. Hence, close to the minimiser $x^*$ we will have intervals not containing $x^*$ that cannot be thrown away, because they seem to contain $f(x^*)$. Observe the following example\n\nminval, minimisers = minimise(f, 0..2, tol=1e-3);\n@show length(minimisers)\nlength(minimisers) = 102\n\n\nThe function returns $102$ minimisers, however only of these contains the true minimiser $x=1$. The following picture illustrates this\n\nusing Plots\nplot(f, 1-0.1, 1+0.1, lw=2)\nplot!(IntervalBox.(minimisers, f.(minimisers)), legend=false)",
null,
"Using a stricter tolerance makes things worse, as we will keep bisecting those fake minimisers, obtaining more fake minimisers that cannot be thrown away, Observe\n\nminval, minimisers = minimise(f, 0..2, tol=1e-6);\n@show length(minimisers)\nlength(minimisers) = 2990\n\n\nHow to solve this problem? A solution is the so called mean-value form, instead of computing f(X) with traditional interval arithmetic, we use the following formula\n\n$f(X) = f(m(X)) +f'(X)(X-m(X))$\n\nwhere $m(X)$ denotes the midpoint of $X$. It can be proved that the true range of $f(X)$ is enclosed into the mean value form. It can also be proved that the mean-value form overestimates reduces the overestimate. Let us define a function to compute the mean-value form, using ForwardDiff to compute the derivative\n\nusing ForwardDiff\n\nmean_value_form(f, X) = f(mid(X)) + ForwardDiff.derivative(f, X)*(X - mid(X))\nmean_value_form (generic function with 1 method)\n\nNow let us try to minimise the function using the mean-value form\n\nminval, minimisers = minimise(X -> mean_value_form(f, X), 0..2, tol=1e-6);\n@show length(minimisers)\n@show minimisers\nlength(minimisers) = 3\nminimisers = IntervalArithmetic.Interval{Float64}[[0.999999378, 1.000000281], [1.00000028, 1.000001169], [0.9999984897, 0.9999993781]]\n\n\nAs you can see, the number of minimisers has been reduced from 2990 to 3!"
] |
[
null,
"https://juliaintervals.github.io/assets/pages/tutorials/tutorialOptimisation/code/output/clustering.svg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7091652,"math_prob":0.9987497,"size":5473,"snap":"2021-21-2021-25","text_gpt3_token_len":1568,"char_repetition_ratio":0.16383252,"word_repetition_ratio":0.030150754,"special_character_ratio":0.31920338,"punctuation_ratio":0.17814508,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999144,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-25T07:23:05Z\",\"WARC-Record-ID\":\"<urn:uuid:fde23f82-04cc-475a-b37c-78cf7058e7cf>\",\"Content-Length\":\"57447\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c8bb735c-98a4-4d84-b24e-4a0c09e5f39f>\",\"WARC-Concurrent-To\":\"<urn:uuid:f027f765-1534-43ba-ae34-f4c7aabb24dc>\",\"WARC-IP-Address\":\"185.199.109.153\",\"WARC-Target-URI\":\"https://juliaintervals.github.io/pages/tutorials/tutorialOptimisation/index.html\",\"WARC-Payload-Digest\":\"sha1:ZBBVU2KSHC2NP2TC45S6GGT3IP7GW74T\",\"WARC-Block-Digest\":\"sha1:6GQJFGDRJP2EPVK4XNXSTYLLLX4HMZJ4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487622113.11_warc_CC-MAIN-20210625054501-20210625084501-00088.warc.gz\"}"}
|
https://whiteboyz.xyz/2n2219-transistor-datasheet-96/
|
[
"# 2N2219 TRANSISTOR DATASHEET PDF\n\n2N Transistor Datasheet pdf, 2N Equivalent. Parameters and Characteristics. 2N Silicon NPN Transistor. Data Sheet. Description. Semicoa Semiconductors offers: • Screening and processing per MIL-PRF Appendix E. DATA SHEET NPN switching transistor in a TO metal package. collector- emitter voltage open base. 2N −. V. 2NA. −.",
null,
"Author: Mikazahn Mulkis Country: Norway Language: English (Spanish) Genre: Literature Published (Last): 12 December 2005 Pages: 379 PDF File Size: 2.37 Mb ePub File Size: 20.89 Mb ISBN: 386-3-67849-749-3 Downloads: 94318 Price: Free* [*Free Regsitration Required] Uploader: Fenritaxe",
null,
"As we know the transistor is a current controlled device meaning, we have pass some current I B thorough the base of the transistor to turn it on.",
null,
"Where h FE, is the current gain of the transistor which datashfet our case is The 2N is a NPN transistor and is normally used as a switch in many circuits. TL — Programmable Reference Voltage.\n\nWhere Vcc is the voltage on which the load operates and V BE is the voltage across the Base and Emitter which in our case according to the data sheet 1.\n\nThis resistor is connected to the base pin of the transistor to limit the current flowing through the base. Submitted by admin on 21 June Current Drains out through emitter, normally connected to ground.\n\nWhen this transistor is fully biased then it can allow a maximum of mA to flow across the collector and emitter. Complete Technical Details can be found at the datasheet given at the end of this page. The maximum amount of current that could flow through the Collector pin is mA, hence we cannot connect loads that consume more than mA using this transistor. In our case for a collector current of mA we have to pass a base current of 16mA.\n\nCISCO ISCW PDF\n\n### 2N Datasheet(PDF) – NXP Semiconductors\n\nSo to calculate the resistor value of the base we can use the formulae. So if you looking for an NPN transistor that could switch loads or for decent amplification then 2N might the right choice for your project. Here lets us assume the load here consumes around mA maximum so our collector current I C mA.\n\nOverall it is just another small signal transistor which is commonly used in switching and amplifying circuits. To make this current flow through the transistor the value of base current I B can be calculated using the below formula:. The value of this current can be calculated by the required dxtasheet of current that will be consumed by the load.\n\nWhen base current is removed the transistor becomes fully off, this stage is called as the Cut-off Region and the Base Emitter voltage could be around mV. Amplifier modules like Audio amplifiers, signal Amplifier etc. Since transistor is of NPN the load to be switched should be connected to the collector and the emitter should be connected to the ground datasheeg show in the figure below.\n\n3RV1021 1KA10 PDF\n\n### 2N Datasheet(PDF) – Microsemi Corporation\n\nSo the value if R B will be. But it comes in a metal can package and can operate on voltages slightly higher than what a 2N can handle.",
null,
"This stage is called Saturation Region. Another important thing to keep in mind, while using a transistor as switch is the base resistor.\n\n## 2N2219 Datasheet, Equivalent, Cross Reference Search\n\nCurrent flows in through collector, normally connected to load. To make this current flow through the transistor the value of base current I B can be calculated using the below formula: But this calculation will lead to the closest value to start with.",
null,
"However this vale will not be very accurate because the transistor will have an internal voltage drop across the collector current, so it mostly experimental to get the maximum current from the transistor. To bias a transistor we have to supply current to base pin, this current I B should datashee limited to 5mA by using a transistor to the base pin."
] |
[
null,
"https://alltransistors.com/pdfdatasheet_philips/image/2n2219_2n2219a_3_0002.jpg",
null,
"https://whiteboyz.xyz/download_pdf.png",
null,
"https://www.digchip.com/image-datasheet/456/2N2218-2N2219.jpg",
null,
"https://images.alldatasheet.com/semiconductor/electronic_parts/datasheet/103842/MICROSEMI/2N2219.GIF",
null,
"http://ee223.eeng.dcu.ie/_/rsrc/1468749626385/laboratories/laboratory-session-4---the-transistor/2N2219A Pinout.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8791625,"math_prob":0.85876334,"size":3833,"snap":"2020-10-2020-16","text_gpt3_token_len":867,"char_repetition_ratio":0.15382606,"word_repetition_ratio":0.055555556,"special_character_ratio":0.21497521,"punctuation_ratio":0.09517241,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.954959,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-07T03:19:57Z\",\"WARC-Record-ID\":\"<urn:uuid:be7546f6-ae0d-4631-b54d-673f1d512b25>\",\"Content-Length\":\"38848\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:13aaa91f-a092-4f49-a57d-eb810f6b8dea>\",\"WARC-Concurrent-To\":\"<urn:uuid:b4e71f69-048e-45e0-a2dd-be3c07adf927>\",\"WARC-IP-Address\":\"104.28.10.92\",\"WARC-Target-URI\":\"https://whiteboyz.xyz/2n2219-transistor-datasheet-96/\",\"WARC-Payload-Digest\":\"sha1:5L4E3R5PLILGZCL6NW6D32TFJZW6HMLU\",\"WARC-Block-Digest\":\"sha1:GXY34HDFH2CWHX3H7CSHO6Z3BXQZ7BJU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371665328.87_warc_CC-MAIN-20200407022841-20200407053341-00158.warc.gz\"}"}
|
https://sizespectrum.org/mizer/articles/plotting.html
|
[
"## Introduction\n\nIn this tutorial we will use the ggplot2 package and the\nplotly package for R to visualise the results from mizer simulations.\n\nlibrary(mizer)\nlibrary(ggplot2)\nlibrary(plotly)\n\nMizer provides several functions for calculating summaries of the mizer simulation results, see ?summary_functions. Many of these functions have corresponding plotting functions, see ?plotting_functions. However it is easy to produce customised plots directly using ggplot() or plot_ly(). This gives more flexibility than the built-in plotting functions. Also, you will occasionally want to look at different quantities for which perhaps there is not built-in plotting function. In those cases the examples you see below will provide a useful blueprint.\n\nBoth ggplot2 and plotly works with data frames, and the convenient way to manipulate data frames is the dplyr package.\n\nlibrary(dplyr)\n\nWe create a simple simulation that we will use for our examples below.\n\nparams <- newMultispeciesParams(NS_species_params)\nsim <- project(params, t_max = 10, t_save = 0.5, effort = 0)\n\n## From arrays to data frames\n\nMizer likes to work with arrays indexed by species and time or size. For example the built-in summary functions return such arrays. These arrays need to be converted to data frames before they can be conveniently plotted with either ggplot() or plot_ly. This conversion is achieved by the function melt().\n\nFor example, the function getBiomass() returns a two-dimensional array (matrix) with one dimension corresponding to the time and the second dimension to the species.\n\nbiomass <- getBiomass(sim)\nstr(biomass)\n## num [1:21, 1:12] 8.77e+07 2.52e+09 3.21e+09 7.50e+08 2.09e+08 ...\n## - attr(*, \"dimnames\")=List of 2\n## ..$time: chr [1:21] \"0\" \"0.5\" \"1\" \"1.5\" ... ## ..$ sp : chr [1:12] \"Sprat\" \"Sandeel\" \"N.pout\" \"Herring\" ...\n\nThis array can be converted with the melt() function to a data frame that contains one row for each entry in the array.\n\nbiomass_frame <- melt(biomass)\nstr(biomass_frame)\n## 'data.frame': 252 obs. of 3 variables:\n## $time : num 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ... ##$ sp : Factor w/ 12 levels \"Sprat\",\"Sandeel\",..: 1 1 1 1 1 1 1 1 1 1 ...\n## $value: num 8.77e+07 2.52e+09 3.21e+09 7.50e+08 2.09e+08 ... ## ggplot2 or plotly In this form the information can be handed to plot_ly() and converted to a line plot: pp <- plot_ly(biomass_frame) %>% add_lines(x = ~time, y = ~value, color = ~sp) pp We have specified that the time is plotted along the x axis, the value along the y axis and that the different species are represented by the colours of the lines. Note the American spelling “color” required by plotly. Alternatively we can do the same thing with ggplot(): pg <- ggplot(biomass_frame) + geom_line(aes(x = time, y = value, colour = sp)) pg",
null,
"Notice the different syntax for the ggplot2 and for plotly packages. The underlying ideas are similar: they are both implementations of the grammar of graphics. I recommend learning ggplot2 first, and switching to plotly only when it has clear advantages (in particular for animations, see below). The main advantage of plotly, namely the interactivity of the resulting figures, can be obtained also with the ggplot syntax by running the result of ggplot() through the function ggplotly(): ggplotly(pg) Below we will always for each plot first give the ggplot code and then the plotly code. ## Adding labels We may want to add labels to the figure and to each of the axes. In ggplot this is done with labs(). pg + labs(title = \"Biomass plot\", x = \"Time [years]\", y = \"Biomass [g]\")",
null,
"In plotly we use the layout() function. pp %>% layout( title = \"Biomass plot\", xaxis = list( title = \"Time [years]\" ), yaxis = list( title = \"Biomass [g]\" ) ) ## Filtering out data We can use the filter function to filter out some of the data. For example we could select only the data for specific species: two_species_biomass <- filter(biomass_frame, sp %in% c(\"Gurnard\", \"Herring\")) Now if we plot this reduced data frame we get ggplot(two_species_biomass) + geom_line(aes(x = time, y = value, color = sp))",
null,
"In the above we first converted the array to a data frame with melt() and then selected the data of interest with filter(). We could alternatively have first selected only the desired entries in the array and then created the data frame with melt() from the resulting smaller array: nfr <- melt(getBiomass(sim)[, c(\"Gurnard\", \"Herring\")]) ggplot(nfr) + geom_line(aes(x = time, y = value, color = sp))",
null,
"The result looks almost identical, except that the colours associated to the species have changed. ## Specifying line colours If we want to make sure the same species always has the same colour, we can use the colours specified by the MizerParams object getColours(params) ## Sprat Sandeel N.pout Herring Dab Whiting Sole ## \"#815f00\" \"#6237e2\" \"#8da600\" \"#de53ff\" \"#0e4300\" \"#430079\" \"#6caa72\" ## Gurnard Plaice Haddock Cod Saithe Resource Total ## \"#ee0053\" \"#007957\" \"#b42979\" \"#142300\" \"#a08dfb\" \"green\" \"black\" ## Background Fishing External ## \"grey\" \"red\" \"grey\" To use these colours in ggplot we add scale_colour_manual(): ggplot(biomass_frame) + geom_line(aes(x = time, y = value, color = sp)) + scale_colour_manual(values = getColours(params))",
null,
"In plotly we add colors = getColours(params)r to the add_lines() command: plot_ly(biomass_frame) %>% add_lines(x = ~time, y = ~value, color = ~sp, colors = getColours(params)) Again note the American spelling “colors” required by plotly. ## Plotting spectra Of course mizer has the plotSpectra() function for plotting size spectra. Again it is instructional to create such plots by hand. We can access the abundance spectra of the species via N(sim). This is a three-dimensional array (time x species x size). Let us first look at the abundance at the final time. final_n <- N(sim)[idxFinalT(sim), , , drop = FALSE] The drop = FALSE means that the result will again be a 3 dimensional array. str(final_n) ## num [1, 1:12, 1:100] 1.92e+06 4.81e+12 1.15e+14 3.86e+12 1.12e+11 ... ## - attr(*, \"dimnames\")=List of 3 ## ..$ time: chr \"10\"\n## ..$sp : chr [1:12] \"Sprat\" \"Sandeel\" \"N.pout\" \"Herring\" ... ## ..$ w : chr [1:100] \"0.001\" \"0.00119\" \"0.00142\" \"0.0017\" ...\n\nWe use the melt() function to convert this array into a data frame.\n\nnf <- melt(final_n)\n\nThis has created a data frame with 4 variables and one observation for each of the 1200 entries in the 1 x 12 x rdim(final_n) matrix final_n.\n\nstr(nf)\n## 'data.frame': 1200 obs. of 4 variables:\n## $time : int 10 10 10 10 10 10 10 10 10 10 ... ##$ sp : Factor w/ 12 levels \"Sprat\",\"Sandeel\",..: 1 2 3 4 5 6 7 8 9 10 ...\n## $w : num 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 ... ##$ value: num 1.92e+06 4.81e+12 1.15e+14 3.86e+12 1.12e+11 ...\n\nThe first three variables take their values from the dimension names of the array. Of course the time variable is the same for all observations, because we selected these before creating the data frame. The fourth variable called value is the value of the entry of the array, so the abundance density in our case.\n\nThere are a lot of entries with value 0, which we are not really interested in, so it makes sense to remove them:\n\nnf <- filter(nf, value > 0)\n\nThis leaves a data frame with only 945 observations.\n\nWe can send this data frame to ggplot and add a line for the spectrum for each species, with a different colour for each, and specify that we want both the x axis and the y axis to be on a logarithmic scale.\n\npg <- ggplot(nf) +\ngeom_line(aes(x = w, y = value, color = sp)) +\nscale_x_log10() +\nscale_y_log10()\npg",
null,
"The corresponding syntax for plotly is\n\np <- plot_ly(nf) %>%\nadd_lines(x = ~w, y = ~value, color = ~sp) %>%\nlayout(xaxis = list(type = \"log\", exponentformat = \"power\"),\nyaxis = list(type = \"log\", exponentformat = \"power\"))\np\n\nIn the above we used the pipe operator %>% which feeds the return value of one function into the first argument of the next function.\n\n## Including resource spectrum\n\nWe can include additional lines in the plot by merging several data frames. For example, we can include another line for the resource spectrum. We first convert also the resource abundance at the final time into a data frame and filter out the zero values\n\nnf_pp <- melt(NResource(sim)[idxFinalT(sim), , drop = FALSE]) %>%\nfilter(value > 0)\n\nThis data frame only contains three variables, because it does not have the sp column specifying the species. We add this column with the value “Resource”\n\nnf_pp$sp <- \"Resource\" Now this new data frame has the same columns as the data frame nf and the two can be bound together nf <- rbind(nf, nf_pp) Using this extended data frame gives the following plot: p <- ggplot(nf) + geom_line(aes(x = w, y = value, color = sp)) + scale_colour_manual(values = getColours(params)) + scale_x_log10() + scale_y_log10() p",
null,
"Of course we could use the same data frame also with plotly. ## Limiting the axes We might want to zoom in on the part that includes the fish. There are three ways to achieve this. The first is to use filter() to filter out all the rows in the data frame that have small w and then plot the resulting data frame as usual: nf %>% filter(w > 10^-4) %>% ggplot() + geom_line(aes(x = w, y = value, color = sp)) + scale_colour_manual(values = getColours(params)) + scale_x_log10() + scale_y_log10()",
null,
"The second method is to specify limits for the axes. In ggplot this is done by adding limits to the axis scales: ggplot(nf) + geom_line(aes(x = w, y = value, color = sp)) + scale_colour_manual(values = getColours(params)) + scale_x_log10(limits = c(10^-4, NA)) + scale_y_log10(limits = c(NA, 10^20))",
null,
"The NA means that the existing limits are kept. In plotly we specify the range as follows: plot_ly(nf) %>% add_lines(x = ~w, y = ~value, color = ~sp, colours = getColours(params)) %>% layout(xaxis = list(type = \"log\", exponentformat = \"power\", range = c(-4, 4)), yaxis = list(type = \"log\", exponentformat = \"power\", range = c(-14, 20))) Note how in plotly the range is specified by giving the logarithm to base 10 of the limits. ## Animating spectra Instead of picking out a specific time we can ask plotly to make an animation showing the changing spectra over time. So we melt the entire N(sim) array and use the time variable to specify the frames with the frame = ~time argument to add_lines(): melt(N(sim)) %>% filter(value > 0) %>% plot_ly() %>% add_lines(x = ~w, y = ~value, color = ~sp, colors = getColours(params), frame = ~time, line = list(simplify = FALSE)) %>% layout(xaxis = list(type = \"log\", exponentformat = \"power\"), yaxis = list(type = \"log\", exponentformat = \"power\")) Note how this produces a smooth animation in spite of the fact that we saved the abundances only once a year. That interpolation is facilitated by the line = list(simplify = FALSE) argument. The ggplot package does not provide a similarly convenient way of creating animations. There is the gganimate package, but it is not nearly as convenient. ## Comparing simulations We may also want to make plots contrasting the results of two different simulations, for example with different fishing policies. To illustrate this we create two simulations with different fishing effort: sim1 <- project(params, t_max = 10, t_save = 0.2, effort = 2) sim2 <- project(params, t_max = 10, t_save = 0.2, effort = 4) Let us look at a plot of the fishing yield against time. This is calculated by the getYield() function, which returns an array (time x species) that we can convert to a data frame yield1 <- melt(getYield(sim1)) yield2 <- melt(getYield(sim2)) Let’s look at the plot of the yield from the first simulation: ggplot(yield1) + geom_line(aes(x = time, y = value, colour = sp))",
null,
"To make the plot less cluttered, we keep only the 4 most important species yield1 <- filter(yield1, sp %in% c(\"Saithe\", \"Cod\", \"Haddock\", \"N.pout\")) yield2 <- filter(yield2, sp %in% c(\"Saithe\", \"Cod\", \"Haddock\", \"N.pout\")) and plot again p1 <- ggplot(yield1) + geom_line(aes(x = time, y = value, colour = sp)) p1",
null,
"For simulation 2 the plot looks like this: p2 <- ggplot(yield2) + geom_line(aes(x = time, y = value, colour = sp)) p2",
null,
"Comparison will be easier if we combine these two plots. For that we add an extra variable to the data frames that allow us to distinguish them and then we merge them together. yield1$effort <- as.factor(2)\nyield2\\$effort <- as.factor(4)\nyield <- rbind(yield1, yield2)\n\nIn ggplot we can now use facet_grid() to put the plot for each value of effort side-by-side:\n\nggplot(yield) +\ngeom_line(aes(x = time, y = value,\ncolour = sp)) +\nfacet_grid(cols = vars(effort))",
null,
"Or we can use the linetype aesthetic to represent the different effort values by different line types:\n\nggplot(yield) +\ngeom_line(aes(x = time, y = value,\ncolour = sp,\nlinetype = effort))",
null,
"plotly is less good at faceting, but it can put arbitrary plots side-by-side (or arrange them into a grid) with subplot()\n\nsubplot(p1, p2, shareX = TRUE, shareY = TRUE)\n\nNote how the shareY = TRUE argument to suplot() makes sure the two plots use the same scale on the y axis, and similarly for shareX = TRUE.\n\nAlso in plotly we can now tie the effort variable to the line type.\n\nplot_ly(yield) %>%\nadd_lines(x = ~time, y = ~value,\ncolor = ~sp, linetype = ~effort)\n\nArguably, ggplot2 does a nicer job in this case."
] |
[
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-7-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-9-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-12-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-13-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-15-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-22-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-27-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-28-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-29-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-34-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-36-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-37-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-39-1.png",
null,
"https://sizespectrum.org/mizer/articles/plotting_files/figure-html/unnamed-chunk-40-1.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.73759365,"math_prob":0.99637604,"size":12051,"snap":"2023-14-2023-23","text_gpt3_token_len":3377,"char_repetition_ratio":0.12210509,"word_repetition_ratio":0.10817426,"special_character_ratio":0.29599205,"punctuation_ratio":0.13674852,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9973318,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"im_url_duplicate_count":[null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-11T00:12:38Z\",\"WARC-Record-ID\":\"<urn:uuid:336bd006-a374-4144-a3be-c562813784d3>\",\"Content-Length\":\"812887\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:008d75b5-ccae-410b-9521-d3b1b6ea078b>\",\"WARC-Concurrent-To\":\"<urn:uuid:2231111e-36b2-4aa4-bcd7-5b72ab8afe55>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://sizespectrum.org/mizer/articles/plotting.html\",\"WARC-Payload-Digest\":\"sha1:5V57QJ2QIXWDSLQDHB7TCUSF3FKD4RBY\",\"WARC-Block-Digest\":\"sha1:2WF3Z3V3D7OTYAQQRJB6TF52DBETFOLR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224646652.16_warc_CC-MAIN-20230610233020-20230611023020-00467.warc.gz\"}"}
|
https://www.demedici.be/pebble/Apr-22_22420-volume-loading-formula-in-ball-mill/
|
[
"### Ball Load Formula For Ball Mills - snmarketing.co.in\n\nMeasurement of the vertical distance between the lining and the balls (H/D):\n\n### calculating load on a ball mill – Grinding Mill China\n\n... size to be achieved by your ball mill is an important thing ... this formula can be derived for ball ... in ball mixtures or rationed loading, ...\n\n### ball mill volume calculation - YouTube\n\ncirculating load formula crusher. circulating load formula crusher. Volume in Ball or Rod Mill circulating load calculation crush size of 80% passing the pilot SAG ...\n\ncement mill recirculation load formula calculation. ... calculating of volume in ball mill capacity description grinding volume calculation in a ball mill jan .this ...\n\nWe can calculate the steel charge volume of a ball or rod mill and express it as the % of the volume circulating load formula in ball mill, ...\n\nformula to calculate ball mill volume loading ? Grinding Mill China. … ball mill volume, Grinding mill filling calculation sagmilling. TECHNICAL BULLETIN – DONHAD.\n\n### Ball Load Formula For Ball Mills - snmarketing.co.in\n\nI'm interested to know when sizing a new ball mill, as to why recirculating load has ... Grinding & Classification Circuits. ... ball mills will give you a formula ...\n\n### how to calculate volume in ballmill filling | Mining ...\n\nor the percentage by volume of, ball load levels evolutions inside the mill and provide this key formula to calculate ball mill volume loading . Chat Online.\n\n### circulating load in roll mill calculation - gibma.org\n\nMay 12, 2013· formula to calculate ball mill volume loading – Gold Ore Crusher. How to Calculate Charge Volume in Ball or Rod Mill … circulating load calculation ...\n\n### How to Handle the Charge Volume of a Ball Mill or Rod Mill ...\n\nformula to calculate ball mill volume loading . ... cement mill ball mill china, formula for maximum ball size in cement. MORE. ball mill circulating load ...\n\n### circulating load formula crusher - BINQ Mining\n\nHow to Handle the Charge Volume of a Ball ... The charge volume of a ball or rod mill is expressed ... The percentage loading or change volume can then be ...\n\n### Ball charges calculators - thecementgrindingoffice.com\n\nWe can calculate the steel charge volume of a ball or rod mill and express it as the % of the volume circulating load formula in ball mill, ...\n\ncalculation of ball mill charge ... power calculation formula of sag mill ... Ball top size; Volume load; Mill power; . Read more. Mineral Processing - Slideshare.\n\nLoad Calculation For Ball Mill Circulating . ball mill media load calculation formula. is the best formula calculation recirculating load in a mill to the choice and ...\n\n### Calculate and Select Ball Mill Ball Size for Optimum …\n\nAug 03, 2016· Formula To Calculate Ball Mill Volume Loading | Manganese Crusher equipment is the cylinder overall body New Method to Measure the ... tube mill …\n\nHow to Handle the Charge Volume of a Ball ... The charge volume of a ball or rod mill is expressed ... The percentage loading or change volume can then be ...\n\n### Choosing a SAG Mill to Achieve Design Performance\n\ngrinding mill c capacity formula ??? Grinding Mill China. how to calculate ball mill volume loading - SAMAC Crusher how to calculate ball mill volume Use of this ...\n\n### Calculating Power Draw when sizing Ball Mills - Grinding ...\n\nformula to calculate ball mill volume loading - ball mill capacity calculations Grinding Mill China. How to calculate the production of dry multi-compartment ball ...\n\n### Grinding Volume Calculation In A Ball Mill - carmec.eu\n\ngrinding ball mill load calculation formula - YouTube. Aug 25, 2016 ... This is a simple video slideshow, if you want to know more details, please click on our ...\n\n### ball.load formula for ball mills - BINQ Mining\n\ngrinding ball mill load calculation formula - YouTube. Aug 25, 2016 ... This is a simple video slideshow, ... Aug 30, 2016 ... volume of ball mill ball load ...\n\n### calculation of ball mill charge volume - …\n\nTECHNICAL NOTES 8 GRINDING R. P. King. 8-2 ... steel balls in a ball mill, ... Let Jt be the fraction of the mill volume that is occupied\n\nAug 25, 2016 Circulating Load Calculation In Closed Circuit Ball Mill calculating re formula, Gold Ore Crusher . formula to calculate ball mill volume loading .\n\n### How to Handle the Charge Volume of a Ball Mill or Rod Mill ...\n\nBINQ Mining > Crusher and Mill > ball.load formula for ball mills; Print. ball.load formula for ball mills. Posted at:November 1, ... how do u calculate mill ball ...\n\n### TECHNICAL NOTES 8 GRINDING R. P. King - …\n\nAug 03, 2016· ... calculating of volume in ball mill ... Formula To Calculate Ball Mill Volume Loading ...\n\n### ball mill capacity formulas - crusher in India - YouTube\n\ncalculating load on a ball mill ... formula to calculate ball mill volume loading. How to Calculate Charge Volume in Ball or Rod MillMining and .\n\n### formula for calculation of tph in cement mill - pcclas.org\n\n- Ball top size (bond formula): ... inside the mill and proposes a modification of the ball charge in order to improve the mill ... - Ball charges composition: These ..."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.72267765,"math_prob":0.98158485,"size":6885,"snap":"2021-31-2021-39","text_gpt3_token_len":1449,"char_repetition_ratio":0.30111903,"word_repetition_ratio":0.26253185,"special_character_ratio":0.22890341,"punctuation_ratio":0.18409091,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9956218,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-23T12:04:25Z\",\"WARC-Record-ID\":\"<urn:uuid:767344ad-4216-4e52-92ab-bbf72a6f0e17>\",\"Content-Length\":\"20894\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:be32a538-4022-48cf-a127-79cbda700eaa>\",\"WARC-Concurrent-To\":\"<urn:uuid:763cf078-d6bb-4b88-b1e2-f797906fd8ab>\",\"WARC-IP-Address\":\"172.67.206.150\",\"WARC-Target-URI\":\"https://www.demedici.be/pebble/Apr-22_22420-volume-loading-formula-in-ball-mill/\",\"WARC-Payload-Digest\":\"sha1:L325S4ZNY4VPTIQL2BYHZWNC3LXKDKHP\",\"WARC-Block-Digest\":\"sha1:BGHEGING3TMQVJ4VFN2BDVZORSBO2MHS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057421.82_warc_CC-MAIN-20210923104706-20210923134706-00026.warc.gz\"}"}
|
https://www.stratascratch.com/blog/machine-learning-algorithms-explained-clustering/
|
[
"# Machine Learning Algorithms Explained: Clustering\n\n##### Categories\n\n•",
null,
"Written by:\nNathan Rosidi\nAuthor Bio\n\nIn this article, we are going to learn how different machine learning clustering algorithms try to learn the pattern of the data.\n\nLet’s imagine that on a Saturday night, our friends invite us to a concert by a band that we have never heard of. When they play their music, you notice that there are no lyrics at all in their song. Although you just listened to their music for the very first time, you might guess that their music is one of the instrumental genres.\n\nYour ability to be able to classify music genres as you listen to them for the very first time is one of the examples of clustering in real life. Clustering is one of the unsupervised learning methods in the machine learning paradigm. The main goal of machine learning clustering algorithms is to assign an instance or unseen data point to a particular group without the need to assign a ground-truth label in advance.\n\nThere are a lot of use cases in real life where clustering method will be beneficial, such as:\n\n• Customer and market grouping\n• Image segmentation\n• Social media analysis\n• Search engine result grouping\n• Anomaly detection\n\nTo understand the high-level concept behind machine learning clustering, let’s take a look at the following data points:\n\nAt a first glance, the scattered data points above are just data points, each with its own x-coordinate and y-coordinate. There is no label or ground truth available for each data point. Now, the task of our machine learning algorithm is to try to learn the pattern of these scattered data points by itself and then assign each of the data points to a particular group.\n\nThe clustering result of the scattered data points above might look something like this:\n\nAs you can see in the visualization above, the data points that are considered ‘similar’ by our machine learning model are grouped together into one cluster. Overall, our machine learning model did a great job in two things:\n\n1. Determining the necessary number of clusters\n2. Assigning each data point to the most likely cluster\n\nNow the question that we might ask is, how does our machine learning model determine the optimum number of clusters? How does our machine learning model assign each data point to the most suitable clusters?\n\nDifferent machine learning algorithms have their own way and concept of how to come up with the optimum number of clusters as well as how they assign each data point to the appropriate cluster. In this article, we’re going to learn how different machine learning clustering algorithms try to learn the pattern of the data to come up with the things mentioned above.\n\n## Types of Machine Learning Clustering Algorithms\n\nThere are many types of machine learning clustering algorithms, but in this article we’re going to cover four of the most commonly used clustering algorithms.\n\n### Centroid-Based Clustering\n\nCentroid-based machine learning clustering is a method where the algorithm needs to first randomly initialize a certain amount of centroids that should be defined in advance. This algorithm will then use an iterative approach to find the optimum position for each centroid such that the distance between data points and the centroid is minimized.\n\nThe most crucial part of this method is defining the number of centroids that should be initialized in advance before the iterative step takes place. In the next section, we’re going to take a look at an approach that utilizes centroid-based clustering. There we will learn how we can determine the optimum number of clusters for our use case.\n\n### Distribution-Based Clustering\n\nDistribution-based clustering is a clustering method that uses probability from a particular distribution to group data points into clusters instead of using similarity or distance as the metrics.\n\nSpecifically, it groups data points based on each data point’s likelihood of belonging to a specific probability distribution, which commonly would be the Gaussian distribution. However, you can choose different probability distributions as well, such as Binomial distribution.\n\n### Density-Based Clustering\n\nAs the name suggests, density-based clustering is a clustering algorithm that works by identifying and grouping data points that are located in the same high-density region together.\n\nThis clustering method can cluster data points together in an arbitrary shape, as long as the data points are located close to each other in a dense region.\n\n### Hierarchical-Based Clustering\n\nHierarchical-based clustering is a machine learning clustering algorithm that groups data points into clusters by looking at the distance between each data point and its neighborhood. With this method, each data point is connected to its neighbors depending on their distance and then the data points that have minimal distance among them would be clustered into one group.\n\nTo achieve the purpose above, hierarchical-based clustering uses either one of two different approaches:\n\n• Agglomerative approach: This approach starts by taking a single data point as a single cluster, and merges all of the data points such that in the end, we end up with a single cluster. We’re going to learn more about how this works in the next section.\n• Divisive approach: This approach is the opposite of the agglomerative approach. The idea behind this approach is that we assume that initially, all of the data points belong to one large cluster. Next, this approach tries to split this large cluster into smaller clusters based on specific distance thresholds or until we reach a point where further data splitting is no longer possible.\n\nWe can normally visualize a hierarchical-based approach with the dendrogram visualization that you will also see in more detail in the next section. This method looks similar to the tree-based machine learning method and if you would like to learn more about the tree-based machine learning method, you can read it here: Decision Tree and Random Forest Algorithm Explained.\n\nNow that we know about different kinds of clustering methods, let’s take a look at different types of machine learning clustering algorithms that utilize each of the approaches mentioned above. Let’s start with k-means clustering.\n\n## k-Means Clustering in Machine Learning\n\nk-means clustering in machine learn is one of the algorithms that utilize the centroid-based clustering approach. Among several machine learning algorithms commonly used for clustering purposes, k-means clustering is arguably the most common one to be used. The reason for this is that of course, it normally performs reasonably well and also, the working concept of k-means clustering can be easily explained.\n\nTo understand how k-means clustering actually works, let’s imagine that we have scattered data points as follows:\n\nFrom our perspective, we know how the final clustering should look like: it should have three clusters that looks something like the following:\n\nAnd the visualization above is exactly what we’re going to get after implementing the k-means clustering algorithm. Now the question is, how is the k-means clustering algorithm able to cluster our data points as shown in the visualization above?\n\nBelow is the step-by-step working process of k-means clustering in machine learning:\n\n• The first step of centroid-based clustering is defining the number of clusters, and we need to define it in advance. Each centroid will act as the center of the cluster. As an example, let’s say that we initialize three centroids in the beginning, this means that we have three clusters formed in the end. The centroids that we initialized will then be placed randomly by this algorithm at the start, as you can see in the visualization below:\n\n• After random initialization, now the similarity between each centroid and each data point is calculated. The measure of similarity usually used in centroid-based clustering is the distance, which can be calculated by using Euclidean distance. After calculating the distance, then each data point will be assigned to the nearest centroid, as you can see in the visualization below:\n\n• In the third step, each centroid will move to the average point of data points assigned to it. As already mentioned in the previous section, centroid-based clustering utilizes an iterative approach to come to the optimal solution. This is the end of the first iteration.\n\n• The second iteration follows the same step as the previous iteration. In this step, the similarity or the distance of the data points to the closest centroid that’s already moved to its new position is computed again. Then, same as the previous iteration, each data point will be assigned to the closest centroid.\n\n• Next, each centroid moves to the average of data points assigned to it, as you can see in the visualization below. This step is the end of the second iteration, and the third iteration will follow the same procedure described in the previous steps. In our example case, the algorithm has reached the optimal solution at the end of the second iteration. This means that the position of each centroid will no longer move, even if we run this algorithm for many more iterations.\n\n### Choosing the Number of Centroids\n\nThe letter k in k-means clustering algorithm refers to the number of clusters. As already mentioned in the previous section, the important step of a centroid-based algorithm is to define the number of clusters in advance. The problem is that we don’t normally have any prior information about the optimal number of clusters that we should initialize.\n\nIf we initialize too few centroids, then the clustering result would not lead to a good result. Meanwhile, if we initialize too many centroids, then there would be an overfitting problem such that the clustering result would be meaningless.\n\nHowever, there is an approach commonly used in the k-means clustering algorithm to come up with the optimal number of centroids that need to be initialized, which is called the elbow method. To use this method, we initialize a different number of clusters and then track the sum of in-group errors.\n\nThe in-group error or also commonly called within-group error measures how well is each centroid in approximating our data. More centroids mean lesser in-group error, but in k-means clustering, a lower value of in-group error doesn’t mean that the clustering result becomes better. A very low value of in-group error means that the clustering result is basically meaningless, as you can imagine that one centroid represents only one data point. What we want instead is to find that number of clusters that results in an in-group error that’s low ‘enough’, but not too low.\n\nWith the so-called elbow method, we will normally get the following visualization from the number of clusters vs the in-group error:\n\nThe in-group error keeps decreasing as we increase the number of centroids. However, after a certain number of clusters, the error decreases at a slower rate, which gives us an elbow-shaped visualization. The optimum number of clusters will be the one where the elbow shape is formed, as you can see with the green circle above.\n\n### Implementation of k-Means Clustering\n\nLet’s now implement k-means clustering in Python. In this example, we’re going to use the Scikit-learn library to do so, specifically with the KMeans instance from sklearn.cluster. But first, let’s generate the dataset first.\n\nimport matplotlib.pyplot as plt\nfrom sklearn.datasets import make_blobs\n\n# create dataset\nX, y = make_blobs(\nn_samples=300, n_features=2,\ncenters=3, cluster_std=1,\nshuffle=True, random_state=42\n\nAs you can see from the visualization above, our dataset consists of 300 data points, and from the location of our data points, we would expect that the k-means clustering method will be able to form three clusters. However, if you remember, we need to define the number of centroids in advance. In our case, we know that it should be 3, but in most real-life scenarios, we don’t know how many centroids we should define.\n\nTo solve this, we’re going to use the Elbow method explained in the previous section. So let’s find out if this method will give us 3 as the optimum number of centroids.\n\nfrom sklearn.cluster import KMeans\nfrom matplotlib import pyplot as plt\n\nerrors = []\nfor k in range(1, 10):\nkmeans = KMeans(n_clusters=k)\nkmeans.fit(X)\nerrors.append(kmeans.inertia_)\n\nfig = plt.figure(figsize=(12, 9))\nplt.plot(range(1, 10), errors)\nplt.grid(True)\nplt.xlabel('Error', fontsize=18)\nplt.ylabel('No. of clusters', fontsize=16)\nplt.title('Elbow curve',fontsize=18)\n\nWith the elbow method, we can clearly see that the optimum number of clusters would be 3. So, let’s initialize and train a new k-means clustering model, and then plot the clustering result as well as the location of each centroid.\n\n# Initialize and train k-means model\nkm = KMeans(n_clusters=3)\ny_kmeans = km.fit_predict(X)\n\n# plot the clusters and centroids\nplt.figure(figsize=(12,8))\nplt.scatter(\nX[y_kmeans == 0, 0], X[y_kmeans == 0, 1],\ns=50, c='green',\nmarker='s', edgecolor='black',\nlabel='cluster 1'\n)\n\nplt.scatter(\nX[y_kmeans == 1, 0], X[y_kmeans == 1, 1],\ns=50, c='orange',\nmarker='o', edgecolor='black',\nlabel='cluster 2'\n)\n\nplt.scatter(\nX[y_kmeans == 2, 0], X[y_kmeans == 2, 1],\ns=50, c='blue',\nmarker='v', edgecolor='black',\nlabel='cluster 3'\n)\n\nplt.scatter(\nkm.cluster_centers_[:, 0], km.cluster_centers_[:, 1],\ns=250, marker='*',\nc='red', edgecolor='black',\nlabel='centroids'\n)\nplt.legend(scatterpoints=1)\nplt.grid()\nplt.show()\n\nAs you can see from the visualization above, our k-means clustering algorithm managed to group our data points into 3 clusters perfectly. However, the k-means clustering algorithm has a couple of drawbacks that make this algorithm wouldn’t be the right algorithm to use in a certain use case. We will find out more about this in the next section.\n\n## Gaussian Mixture Model for Clustering in Machine Learning\n\nAs mentioned previously, there are certain drawbacks of using the k-means clustering algorithm. K-means clustering performs best when our dataset has a circular shape, as you can see from the previous example.\n\nIf we have data points that can’t be clustered with circular shape, then the k-means clustering algorithm will perform poorly, as you can see in the following visualization:\n\nAs you can see, the k-means clustering algorithm couldn’t cluster our data points properly as some of the data points are wrongly clustered. Also, k-means clustering results in a hard classification of clusters, which means that each data point will get a result in which cluster it has been assigned to.\n\nGaussian Mixture Model or GMM is a probabilistic-based clustering method that alleviates the problem with k-means clustering above. GMM assumes that each data point comes from a mixture of several Gaussian distributions with unknown parameters (mean and standard deviation).\n\nBelow is the step for how data points can be generated with GMM:\n\n• First, the number of Gaussian distributions needs to be defined, let’s say the number of Gaussian distributions is k and we will call this the number of clusters. The parameters (mean and standard deviation) of each Gaussian distribution are normally assigned randomly\n• One random cluster is picked from a possible k Gaussian distribution for each data point with a certain probability value of choosing i th cluster defined by the cluster’s weight.\n• Finally, the location of each data point is sampled randomly from the chosen Gaussian distribution in the ith cluster with a certain mean and covariance matrix.\n• The parameters (mean, standard deviation, and weight) of each cluster will be updated iteratively based on data points assigned to it.\n\nThe main goal of GNN is to find in which Gaussian distribution a data point is most likely to be generated. To achieve this, GMM uses an iterative approach in order to optimize the Gaussian distributions’ parameters that are normally initialized randomly in the beginning. This involves two steps:\n\n• First, GMM will assign each data point to a cluster (Gaussian distribution) similar to assigning data points to a centroid in the k-means algorithm. This step is also normally called the expectation step. This step tries to answer the following: does the data point look likely to be generated by the ith cluster?\n• Then, the parameters of each cluster will be updated according to the data points assigned to it. This step is also normally called the maximization step.\n\n### Choosing the Number of Clusters\n\nThe similar concept between GMM and k-means clustering is that we need to define the number of clusters in advance. Specifically in GMM, we need to define the number of distributions that we should initialize, whereas in k-means clustering we need to define the centroids.\n\nWith k-means, we know we can use the elbow method to determine the optimal number of centroids. But how about in GMM? The main approach in GMM is that we need to initialize a certain number of clusters such that the so-called theoretical information criterion is minimized. Examples of theoretical information criteria would be Bayesian information criterion (BIC) and Akaike information criterion (AIC).\n\nBelow are the equations for BIC and AIC:\n\n$BIC = log (m)p-2 log(\\hat{L})$\n$AIC = 2p -2 log(\\hat{L})$\n\nwhere:\n\nm: data points\n\np: parameters that need to be optimized by GMM\n\nL: the likelihood function\n\nBy plotting the AIC or BIC against the number of distributions, we will normally get similar visualization as in the elbow method as follows:\n\nThe information criterion keeps decreasing as we increase the number of distributions. However, same as the elbow method in k-means clustering, we want to select the number of distributions where the elbow shape is formed, as you can see in the green dot above.\n\n### Implementation of Gaussian Mixture Model\n\nNow that we know at a high level how GMM works, let’s implement it with the help of Python. Same as before, we’re going to use the scikit-learn library to do so. For this GMM example, we’re going to use the stretched dataset as visualized above.\n\nBut before moving further, the first step that we need to do is to define the number of Gaussian distributions. Same as k-means clustering algorithm, normally we don’t know how many distributions we should define in advance. However intuitively, we know that the optimal number of distributions would be 3. Let’s find out about this by plotting the AIC and BIC criterion vs the number of distributions.\n\nfrom sklearn.mixture import GaussianMixture\nimport numpy as np\n\nrng = np.random.RandomState(52)\nX_stretched = np.dot(X, rng.randn(2, 2))\n\nn_components = np.arange(1, 10)\n\ngm = [GaussianMixture(n, covariance_type='diag', random_state=0).fit(X_stretched) for n in n_components]\n\nplt.figure(figsize=(12,8))\nplt.plot(n_components, [m.bic(X_stretched) for m in gm], label='BIC')\nplt.plot(n_components, [m.aic(X_stretched) for m in gm], label='AIC')\nplt.legend(loc='best')\nplt.xlabel('n_components', fontsize=18);\nplt.ylabel('information criterion', fontsize=16);\nplt.grid(True)\n\nAs you can see in the visualization above, the elbow shape is formed when the number of distributions is 3. Hence, it is safe for us to assume that the optimal number of distributions for our use case is 3.\n\nLet’s initialize and train the GMM model on our data points with 3 clusters. After that, we can visualize the clustering result\n\nfrom matplotlib.patches import Ellipse\n\ndef draw_ellipse(position, covariance, ax=None, **kwargs):\nax = ax or plt.gca()\n\nif covariance.shape == (2, 2):\nU, s, Vt = np.linalg.svd(covariance)\nangle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\nwidth, height = 2 * np.sqrt(s)\nelse:\nangle = 0\nwidth, height = 2 * np.sqrt(covariance)\n\nfor nsig in range(1, 4):\nax.add_patch(Ellipse(position, nsig * width, nsig * height,\nangle, **kwargs))\n\ndef plot_scatter(X, labels, target, color, marker_shape, legend):\n\nplt.scatter(\nX[labels == target, 0], X[labels == target, 1],\ns=50, c=color,\nmarker=marker_shape, edgecolor='black',\nlabel=legend\n)\n\ndef plot_gmm(gmm, X, label=True, ax=None):\nplt.figure(figsize=(12,8))\nax = ax or plt.gca()\nlabels = gmm.fit(X).predict(X)\nif label:\n\nplot_scatter(X, labels, 0, 'green', 's', 'cluster_1')\nplot_scatter(X, labels, 1, 'orange', 'o','cluster_2')\nplot_scatter(X, labels, 2, 'blue', 'v','cluster_3')\n\nax.axis('equal')\nplt.grid(True)\n\nw_factor = 0.2 / gmm.weights_.max()\nfor pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\ndraw_ellipse(pos, covar, alpha=w * w_factor)\n\ngmm = GaussianMixture(n_components=3, covariance_type='full', random_state=42)\nplot_gmm(gmm, X_stretched)\n\nAs you can see, GMM gives us flexibility in terms of the shape of the clusters. Instead of a circular shape cluster, GMM can also capture an ellipsis shape cluster, hence the better clustering result for our use case above.\n\n## Agglomerative Clustering in Machine Learning\n\nThe agglomerative clustering algorithm in machine learning is a hierarchical-based clustering method that we can also use to cluster our data points. One advantage of using agglomerative clustering instead of the previous two algorithms is that we don’t really need to initialize a specific number of clusters in advance if we don’t want to.\n\nHowever, although we don’t really need to initialize a specific number of clusters in advance, the clustering result would be potentially better if we specify the optimal number of clusters in advance. With agglomerative clustering, there is a certain way to find out the optimal number of clusters, which we will discuss in the next section.\n\nIn a nutshell, an agglomerative algorithm works by first assigning each data point as a cluster. Let’s say we have 4 data points, then in the beginning we would have 4 clusters. Next, the algorithm merges the data points iteratively such that in the end, we end up with one single big cluster containing all of the data points.\n\nTo understand more how the agglomerative algorithm works, let’s say that in the beginning we have data with four data points, as you can see below:\n\nIn the first iteration, each data point will be assigned as a single cluster. If we have N data points, then we will have N clusters at this point.\n\nIn the next iteration, the two closest data points will be merged together, such that after this iteration, we have N-1 clusters.\n\nThe steps above will be repeated iteratively until it forms into a single cluster. Once they form into a single cluster, then the merging history in each iteration can be visualized with the dendrogram.\n\nNow the question is, how does this merging of points work? How does the algorithm choose which data points will be merged in each iteration? The distance between two data points across different clusters is normally used, and there are two common metrics that the agglomerative approach uses to calculate this distance:\n\n• Single linkage: The distance is calculated from the closest data points in-between clusters\n• Complete linkage: The distance is calculated from the farthest data points in-between clusters\n• Centroid linkage: The distance is calculated from the centroid of each cluster.\n• Ward linkage: The distance is calculated such that the variance of the clusters being merged is minimized\n\n### Choosing the Number of Clusters\n\nAs mentioned previously, although it’s not mandatory, the clustering result of the agglomerative clustering is often better when we decide the number of clusters in advance. Now the question is, how do we know the optimal number of clusters?\n\nPreviously we have learned how agglomerative clustering works in a nutshell. In the end, we can visualize the merging history in each iteration with the so-called dendrogram. The dendrogram visualization will help us to determine the optimal number of clusters for our use case.\n\nIn general, the visualization of a dendrogram would look something like this:\n\nThe y-axis in the above visualization represents the distance and the x-axis represents our data points. To determine the optimal number of clusters from the visualization above, here is the common step-by-step procedure:\n\n• Draw a horizontal line that will act as a cut-off point on the tallest vertical line that doesn’t intersect with any other cluster.\n• The number of vertical lines that intersect the horizontal line would be the optimal number of clusters. In the following visualization, the optimal number of clusters would be 3\n\nOf course, there is a possibility that we will get a different number of clusters if we choose different cut-off points (distance). This is why we need to adjust this algorithm according to our needs and knowledge about the data.\n\n### Implementation of Agglomerative Algorithm\n\nNow that we know how agglomerative approach works, let’s try to implement this algorithm with Python. We will use the same dataset that we used in the previous two machine learning clustering algorithms.\n\nFirst, let’s visualize the dendrogram of the merging history for our use case in order to determine the optimal number of clusters.\n\nimport pandas as pd\nimport numpy as np\nfrom matplotlib import pyplot as plt\nfrom sklearn.cluster import AgglomerativeClustering\nimport scipy.cluster.hierarchy as sch\n\nplt.figure(figsize=(12, 8))\ndendrogram = sch.dendrogram(sch.linkage(X, method='ward'))\n\nFrom the visualization above, let’s pick the cut-off point at 80. Then we can draw a horizontal line from there and find out that the optimal number of clusters would be 3.\n\nNow let’s instantiate our agglomerative model with 3 clusters and train it on our dataset. Next, we can visualize the clustering result.\n\ndef plot_scatter(X, labels, target, color, marker_shape, legend):\n\nplt.scatter(\nX[labels == target, 0], X[labels == target, 1],\ns=50, c=color,\nmarker=marker_shape, edgecolor='black',\nlabel=legend\n)\n\ndef plot_agglo(agglo, X, label=True, ax=None):\nplt.figure(figsize=(12,8))\nax = ax or plt.gca()\nlabels = agglo.fit_predict(X)\nif label:\n\nplot_scatter(X, labels, 0, 'green', 's', 'cluster_1')\nplot_scatter(X, labels, 1, 'orange', 'o','cluster_2')\nplot_scatter(X, labels, 2, 'blue', 'v','cluster_3')\n\nax.axis('equal')\nplt.grid(True)\n\nplot_agglo(agglo, X)\n\nAs mentioned before, one of the advantages of using the agglomerative ML clustering algorithm is that we don’t need to initialize a certain number of clusters in advance. What we can do instead is to define the threshold distance of the linkage. This means that if the distance between two clusters is above the threshold, then the agglomerative algorithm won’t merge the clusters.\n\nTo make it clearer, let’s do some examples in Python without defining a specific number of clusters. We’re going to specify two different distances: 60 and 140, and then let’s see the difference in the clustering result between these two.\n\nagglo_dist_60 = AgglomerativeClustering(n_clusters=None, distance_threshold=60, affinity='euclidean', linkage='ward')\nagglo_dist_140 = AgglomerativeClustering(n_clusters=None, distance_threshold=140, affinity='euclidean', linkage='ward')\n\nplot_agglo(agglo_dist_60, X)\nplot_agglo(agglo_dist_140, X)\n\nThere is one apparent difference between the two visualizations above: on the left-hand side, we ended up having 3 clusters, while on the right-hand side we ended up having just 2. Indeed, the result from 3 clusters is better than 2, but the question is, why do we end up with a different number of clusters just by changing the distance threshold?\n\nIf you look at the dendrogram visualization above, if our cut-off point is 60 and we draw a horizontal line across the graph, then it will intersect 3 different vertical lines, which corresponds to our visualization result. Meanwhile, if our cut-off point is 140 and we draw the horizontal line, it will intersect only 2 vertical lines, which also corresponds to our visualization result on the right-hand side.\n\nThis is why the threshold distance can be considered as one of several hyperparameters that we should tune in order to get a better clustering result. Other hyperparameters that we can fine-tune are the type of linkage as well as the distance metrics.\n\nAs an example, ward linkage often performs best when we have a cluster with a spherical shape, while with a single linkage, although it might not be robust to the outlier, it performs well in a cluster with an arbitrary shape. Let’s imagine we have the following data points:\n\nNow, if we implement agglomerative clustering with two different linkage methods, ward and single, we will end up with the following results:\n\nOn the left-hand side, the clustering result is not optimal with ward linkage, as it’s generally not suited to find a cluster with arbitrary shape. Meanwhile on the right-hand side, the clustering result is much better when we use single linkage.\n\n## DBSCAN in Machine Learning\n\nDensity-based spatial clustering of applications with noise or DBSCAN is a density-based clustering method that calculates how dense the neighborhood of a data point is. In a nutshell, DBSCAN works similarly to the algorithms mentioned in the previous section. First, it will measure the similarity between data points, and group similar data points into one cluster. One of the best advantages of the DBSCAN clustering algorithm is that it is able to find a cluster with an arbitrary shape.\n\nLet’s imagine that we have data points that look like the moon datasets visualized above. If we’re using k-means clustering, we’ll end up with something like this:\n\nHowever, when we use DBSCAN, you will see in the following section that it can capture arbitrary shapes of clusters. Below is the step-by-step explanation how the DBSCAN algorithm works:\n\n• First, we need to define a couple of parameters in advance: a threshold distance, let’s call it epsilon, and the number of minimum neighbors in a data point, let’s call it min_samples.\n• Now, for each data point, the algorithm will count the neighboring data points that are located within epsilon.\n• If the count of neighbors of a data point is higher than min_samples, then this particular data point will be called a core sample. In the DBSCAN algorithm, a core sample means that a data point is located in a highly dense region.\n• All of the neighboring points of a core sample will be grouped into one cluster. Meanwhile, if there is any data point that is not considered as a core sample nor being a neighbor of any core sample, then the DBSCAN clustering algorithm will consider this data point as an outlier.\n\n### Implementation of DBSCAN Algorithm\n\nNow that we know how the DBSCAN machine learning clustering algorithm works, let’s implement it with Python. To do this, we can use the Scikit-learn library, especially with DBSCAN class. First, let’s generate a dataset for our example.\n\nimport numpy as np\nfrom sklearn.cluster import DBSCAN\nfrom sklearn.datasets import make_moons\nfrom sklearn.preprocessing import StandardScaler\n\nX_moon, labels_true = make_moons(\nn_samples=300, noise = 0.05, random_state=0\n)\n\nAnd below is the visualization of the resulting data points from the code snippet above:\n\nTo implement DBSCAN, first, we need to standardize our data, and then call DBSCAN class from the Scikit-learn library. For our example, we’re going to define the eps value, which is the threshold distance, to 0.3 and the number of minimum neighbors (min_samples) to be 10.\n\nX_moon = StandardScaler().fit_transform(X_moon)\ndb = DBSCAN(eps=0.3, min_samples=10).fit(X_moon)\n\nAfter we train our DBSCAN model on the training data, then we can check to which cluster each of our data points belongs. To do this, we can use labels_ method as you can see in the following code snippet:\n\ndb.labels_\n\nOutput: array([0, 1, 1, ..., 0, 1, 0, 0, 0])\n\nThe result that we will get is an array with the shape equal to the number of data points. Each element of the array is the label of the cluster to which your data point belongs. In our example use case above, the DBSCAN algorithm converges into the result that the optimum number of clusters would be 2, hence the value of either 0 or 1 in each element of the array.\n\nHowever, if we have outliers in our dataset, then the DBSCAN algorithm will give them -1 as the label.\n\nFinally, the visualization of the clustering process using DBSCAN can be seen below:\n\nAs you might have noticed from the working process of the DBSCAN clustering algorithm, there are two important parameters that we can fine-tune in order to improve the performance of the model, which are the epsilon value and the minimum neighbors value. In a more complex dataset, fine-tuning of these two parameters will be important to improve the quality of the clustering result.\n\n### HDBSCAN\n\nThere is one additional machine learning clustering algorithm that is basically an extension of the DBSCAN algorithm called HDBSCAN or Hierarchical DBSCAN. This algorithm has a similar workflow in comparison with DBSCAN with one difference: with HDBSCAN, we don’t need to specify the value of parameter epsilon in advance. This is because HDBSCAN will try to find the optimal clusters based on varying distances.\n\nWith this feature, HDBSCAN maintains all of the positive things about DBSCAN whilst also being able to identify clusters with varying densities. Thus, the only parameter that we need to define in advance is the minimum cluster size.\n\nHDBSCAN has its own library in Python that we can install via pip. The good thing is, the API of this library is similar to the DBSCAN algorithm that we have implemented above with Scikit-learn. Below is an example of how we can implement HDBSCAN:\n\nimport hdbscan\nimport numpy as np\nfrom sklearn.preprocessing import StandardScaler\n\nhdb = hdbscan.HDBSCAN(min_cluster_size=5, gen_min_span_tree=True).fit(X_moon)\n\nAs you can see above, we didn’t explicitly specify the epsilon parameter, as HDBSCAN algorithm doesn’t need a fixed threshold distance value to come up with the optimal clusters. However, we still need to define the minimum cluster size. This parameter defines that if the split occurs when we have fewer points than our minimum cluster size, then instead of splitting them into two different clusters, those data points will be considered to fall out of the cluster.\n\nWe can also see to which cluster each data point belongs with label_ method.\n\nhdb.labels_\n\nOutput: array([1, 0, 0, ..., 0, 1, 1, 1]\n\n### Conclusion\n\nIn this article, we have learned about machine learning clustering methods, which is an unsupervised learning method in the machine learning paradigm. Specifically, we now know different algorithms of clustering methods such as k-Means Clustering, Gaussian Mixture Model, Agglomerative Clustering, and DBSCAN.\n\nThe k-Means clustering method usually performs well when our data points have a circular shape cluster, plus the workflow of this algorithm is easy to follow. Meanwhile, DBSCAN and Gaussian Mixture Model offer us more flexibility in terms of cluster shape. Agglomerative clustering and DBSCAN are good algorithms to use when we don’t really want to deal with the hassle of finding out the optimal cluster for our use case.\n\n##### Categories\n\n•",
null,
"Written by:\nNathan Rosidi\nAuthor Bio\n\nBecome a data expert. Subscribe to our newsletter."
] |
[
null,
"https://cdn.sanity.io/images/oaglaatp/production/64162bd8e019c9dfa4c3a691a677c3348454e8de-398x398.png",
null,
"https://cdn.sanity.io/images/oaglaatp/production/64162bd8e019c9dfa4c3a691a677c3348454e8de-398x398.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.87211275,"math_prob":0.9771339,"size":34970,"snap":"2023-40-2023-50","text_gpt3_token_len":7477,"char_repetition_ratio":0.1811188,"word_repetition_ratio":0.07970883,"special_character_ratio":0.20880754,"punctuation_ratio":0.11716745,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99658203,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-01T21:19:31Z\",\"WARC-Record-ID\":\"<urn:uuid:6cadffc0-e534-42ea-8496-0a5d1d69cee9>\",\"Content-Length\":\"426995\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5f256276-e39a-4a07-a041-ec1a3dde573c>\",\"WARC-Concurrent-To\":\"<urn:uuid:67f8a04f-7a45-479e-ac94-8691e6625fea>\",\"WARC-IP-Address\":\"18.165.83.43\",\"WARC-Target-URI\":\"https://www.stratascratch.com/blog/machine-learning-algorithms-explained-clustering/\",\"WARC-Payload-Digest\":\"sha1:AMYNKWIPAOZRKU5X3DSZJLXWEEWPKBW3\",\"WARC-Block-Digest\":\"sha1:XF4F7G5HYKDGBGFXAH4YISMMCMUCXMHC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510941.58_warc_CC-MAIN-20231001205332-20231001235332-00537.warc.gz\"}"}
|
https://metanumbers.com/30920
|
[
"# 30920 (number)\n\n30,920 (thirty thousand nine hundred twenty) is an even five-digits composite number following 30919 and preceding 30921. In scientific notation, it is written as 3.092 × 104. The sum of its digits is 14. It has a total of 5 prime factors and 16 positive divisors. There are 12,352 positive integers (up to 30920) that are relatively prime to 30920.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 14\n• Digital Root 5\n\n## Name\n\nShort name 30 thousand 920 thirty thousand nine hundred twenty\n\n## Notation\n\nScientific notation 3.092 × 104 30.92 × 103\n\n## Prime Factorization of 30920\n\nPrime Factorization 23 × 5 × 773\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 5 Total number of prime factors rad(n) 7730 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 30,920 is 23 × 5 × 773. Since it has a total of 5 prime factors, 30,920 is a composite number.\n\n## Divisors of 30920\n\n1, 2, 4, 5, 8, 10, 20, 40, 773, 1546, 3092, 3865, 6184, 7730, 15460, 30920\n\n16 divisors\n\n Even divisors 12 4 4 0\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 16 Total number of the positive divisors of n σ(n) 69660 Sum of all the positive divisors of n s(n) 38740 Sum of the proper positive divisors of n A(n) 4353.75 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 175.841 Returns the nth root of the product of n divisors H(n) 7.10192 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 30,920 can be divided by 16 positive divisors (out of which 12 are even, and 4 are odd). The sum of these divisors (counting 30,920) is 69,660, the average is 4,353,.75.\n\n## Other Arithmetic Functions (n = 30920)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 12352 Total number of positive integers not greater than n that are coprime to n λ(n) 772 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3338 Total number of primes less than or equal to n r2(n) 16 The number of ways n can be represented as the sum of 2 squares\n\nThere are 12,352 positive integers (less than 30,920) that are coprime with 30,920. And there are approximately 3,338 prime numbers less than or equal to 30,920.\n\n## Divisibility of 30920\n\n m n mod m 2 3 4 5 6 7 8 9 0 2 0 0 2 1 0 5\n\nThe number 30,920 is divisible by 2, 4, 5 and 8.\n\n• Abundant\n\n• Polite\n\n## Base conversion (30920)\n\nBase System Value\n2 Binary 111100011001000\n3 Ternary 1120102012\n4 Quaternary 13203020\n5 Quinary 1442140\n6 Senary 355052\n8 Octal 74310\n10 Decimal 30920\n12 Duodecimal 15a88\n20 Vigesimal 3h60\n36 Base36 nuw\n\n## Basic calculations (n = 30920)\n\n### Multiplication\n\nn×y\n n×2 61840 92760 123680 154600\n\n### Division\n\nn÷y\n n÷2 15460 10306.7 7730 6184\n\n### Exponentiation\n\nny\n n2 956046400 29560954688000 914024718952960000 28261644310025523200000\n\n### Nth Root\n\ny√n\n 2√n 175.841 31.3868 13.2605 7.90766\n\n## 30920 as geometric shapes\n\n### Circle\n\n Diameter 61840 194276 3.00351e+09\n\n### Sphere\n\n Volume 1.23825e+14 1.2014e+10 194276\n\n### Square\n\nLength = n\n Perimeter 123680 9.56046e+08 43727.5\n\n### Cube\n\nLength = n\n Surface area 5.73628e+09 2.9561e+13 53555\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 92760 4.1398e+08 26777.5\n\n### Triangular Pyramid\n\nLength = n\n Surface area 1.65592e+09 3.48379e+12 25246.1\n\n## Cryptographic Hash Functions\n\nmd5 4d0ef32997e19fccdeacce5d01fd5dec e7330a7a9ce5706f6bc3102951ee698c8cbc68df 5be0f83c6ef2846dd15b6d0e45212d00675703589be4aed4529433b75bd6604b b8b3e7557c895808d888d77655994a914358a51b6cb93b13233a8dd42630b06afeb7afc72562608056896a3c892f9cd0dd2e0147b5331cb11bd5a2b775114cd5 ccb46646b552dd7bac63ae75e0b19bf865738d8a"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.62338066,"math_prob":0.9880173,"size":4473,"snap":"2021-43-2021-49","text_gpt3_token_len":1591,"char_repetition_ratio":0.12038487,"word_repetition_ratio":0.0254491,"special_character_ratio":0.45606974,"punctuation_ratio":0.08226221,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.995511,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-07T09:24:08Z\",\"WARC-Record-ID\":\"<urn:uuid:30c965e7-8808-4231-b5c9-1b47fb7f258f>\",\"Content-Length\":\"39325\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d9d19301-aa46-4c0e-b4ff-60fdc939b774>\",\"WARC-Concurrent-To\":\"<urn:uuid:7cc76e83-45eb-430c-bb63-5d71acb8d83a>\",\"WARC-IP-Address\":\"46.105.53.190\",\"WARC-Target-URI\":\"https://metanumbers.com/30920\",\"WARC-Payload-Digest\":\"sha1:I2KEWAMPGA5RHTUJ2RAV7KBMODJ4KG4C\",\"WARC-Block-Digest\":\"sha1:Y2NRMEHOAW6WZGEAYFMESYDKCFP3HL65\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363337.27_warc_CC-MAIN-20211207075308-20211207105308-00211.warc.gz\"}"}
|
https://code-maven.com/slides/python/operations-on-infinite-lists
|
[
"# Operations on infinite lists\n\nIn this example we can say that the fibonacci() function returns the infinite list of Fibonacci numbers. In normal circumstances only mathematicians can work with \"infinite lists\", programmers are constrained by memory and time. However generators in Python are lazy so they only pretend to be infinite lists. They are only the promise of having an infinite list. So you can do all kinds of interesting operations on them.\n\nIn this example we multiply each value by 2. (I know it is not the most sophisticated mathematical problem, but it will work for this example.)\n\nThe variable double_fibonacci holds the values of the Fibonacci series multiplied by 2. More precisely it holds the possibility to iterate over that infinite list.\n\nSo in reality we don't operate on the infinite lists, only on the \"potential of the lists\", but the former sounds cooler.\n\nTry running it without the if and break statements and see what happens. (Ctrl-C will stop the program.)\n\nexamples/generators/infinite_operations.py\n```def fibonacci():\na, b = 0, 1\nwhile True:\na, b = b, a+b\nyield a\n\ndouble_fibonacci = (value * 2 for value in fibonacci())\n\nfor a in double_fibonacci:\nprint(a)\n\nif a > 200:\nbreak\n\n```\n\n```2\n2\n4\n6\n10\n16\n26\n42\n68\n110\n178\n288\n\n```"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.814433,"math_prob":0.81134856,"size":814,"snap":"2021-21-2021-25","text_gpt3_token_len":207,"char_repetition_ratio":0.12716049,"word_repetition_ratio":0.0,"special_character_ratio":0.27027026,"punctuation_ratio":0.116564415,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99930596,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-17T05:52:12Z\",\"WARC-Record-ID\":\"<urn:uuid:8fb031cc-338a-49fb-9a88-39af0c2aea36>\",\"Content-Length\":\"6206\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e1f22297-ecd8-4048-ba76-d8114036cc6c>\",\"WARC-Concurrent-To\":\"<urn:uuid:40d907bb-c40f-4ddb-9ef8-d5329ccbd66a>\",\"WARC-IP-Address\":\"173.255.196.65\",\"WARC-Target-URI\":\"https://code-maven.com/slides/python/operations-on-infinite-lists\",\"WARC-Payload-Digest\":\"sha1:HL2HGIFF6SFV56PD4XAU6YW6MISIRMW7\",\"WARC-Block-Digest\":\"sha1:RWNRSLK7NBBMD5YGAC6ALB4EVIJ4P4DR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487629209.28_warc_CC-MAIN-20210617041347-20210617071347-00624.warc.gz\"}"}
|
https://czar-ent.com/picts/2-digit-multiplication-worksheets-grade-3.html
|
[
"# 2 Digit Multiplication Worksheets Grade 3",
null,
"### Multiplication double digit x single digit (10 printable",
null,
"### 3rd grade homework sheets printable Large Print 3Digit",
null,
"### Here is a free printable 3digit addition worksheet for",
null,
"### No login or account is needed.\n\n2 digit multiplication worksheets grade 3. 2 digit by 1 digit multiplication worksheets pdf grade 3. 3 digit x 2 digit and 3 gigit x 1 digit multiplication worksheets for 3rd and 4th grade.\n\nRemember to put the extra zero in the ones place on the second line of multiplication. Multiplication interactive and downloadable worksheets.\n\n2 digit multiplication worksheets grade 3 â manuelbustoid.info. Grade 3:mathematics term 2 week 4 worksheet 3:\n\nThere are activities with vertical problems, horizontal problems, and lattice grids. Tap on print pdf or image button to print or download this 4th grade worksheet for practice.\n\nType keywords and hit enter. Practice your multiplication and hone your skills with these printable timestable worksheets for 2 and 3 digits.\n\nAlso have money, decimal, and fraction multiplication. There are activities with vertical problems horizontal problems and lattice grids.",
null,
"",
null,
"### 3.NBT.2 Halloween Themed 3Digit Addition with Regrouping",
null,
"### Multiplication double digit (10 Math Worksheets with",
null,
"### Math Worksheets Adding And Subtracting Three Digit Numbers\n\nSource : pinterest.com"
] |
[
null,
"https://i.pinimg.com/736x/0a/39/dd/0a39dd70a2d714642718c5dac79f1656.jpg",
null,
"https://i.pinimg.com/originals/18/47/1f/18471fe39b136f7750228dcc49466da3.jpg",
null,
"https://i.pinimg.com/originals/26/03/e6/2603e6f4c5b14f19984633fdc38bc224.jpg",
null,
"https://i.pinimg.com/originals/07/18/4d/07184de1387639b53557b9e0eba3de02.jpg",
null,
"https://i.pinimg.com/736x/38/6a/dd/386adda42cbf8e1a93ce996b99e68c5d.jpg",
null,
"https://i.pinimg.com/originals/d0/4d/f0/d04df05804ab01016b31052f971e9c47.jpg",
null,
"https://i.pinimg.com/736x/83/d2/0b/83d20bd5ee2f3d501baada2d79d1a2e0.jpg",
null,
"https://i.pinimg.com/originals/2c/b3/56/2cb356ffa8efd400c40412b0c8983412.jpg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8420373,"math_prob":0.8313926,"size":1356,"snap":"2021-31-2021-39","text_gpt3_token_len":289,"char_repetition_ratio":0.24556214,"word_repetition_ratio":0.04901961,"special_character_ratio":0.20058997,"punctuation_ratio":0.12863071,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98254436,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,7,null,null,null,null,null,null,null,7,null,2,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-08-02T02:16:26Z\",\"WARC-Record-ID\":\"<urn:uuid:38944ae5-d431-4804-a336-6f5fd9806de6>\",\"Content-Length\":\"32789\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a8bc03d8-c48e-432e-b4bd-706ddd08be52>\",\"WARC-Concurrent-To\":\"<urn:uuid:3ed877a7-3a5e-4245-a966-b931d8ecd410>\",\"WARC-IP-Address\":\"104.21.84.51\",\"WARC-Target-URI\":\"https://czar-ent.com/picts/2-digit-multiplication-worksheets-grade-3.html\",\"WARC-Payload-Digest\":\"sha1:O6LVYALK27LFUSBQ6O6YUGLUIYNEHASK\",\"WARC-Block-Digest\":\"sha1:FLZPKBUSTGZVNMRQWPJ2KKRFSSNJYOTN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046154302.46_warc_CC-MAIN-20210802012641-20210802042641-00324.warc.gz\"}"}
|
https://devsenv.com/example/-403-leetcode-frog-jump-solution-in-c,-c++,-java,-javascript,-python,-c-leetcode
|
[
"## Algorithm\n\nProblem Name: 403. Frog Jump\n\nA frog is crossing a river. The river is divided into some number of units, and at each unit, there may or may not exist a stone. The frog can jump on a stone, but it must not jump into the water.\n\nGiven a list of `stones`' positions (in units) in sorted ascending order, determine if the frog can cross the river by landing on the last stone. Initially, the frog is on the first stone and assumes the first jump must be `1` unit.\n\nIf the frog's last jump was `k` units, its next jump must be either `k - 1`, `k`, or `k + 1` units. The frog can only jump in the forward direction.\n\nExample 1:\n\n```Input: stones = [0,1,3,5,6,8,12,17]\nOutput: true\nExplanation: The frog can jump to the last stone by jumping 1 unit to the 2nd stone, then 2 units to the 3rd stone, then 2 units to the 4th stone, then 3 units to the 6th stone, 4 units to the 7th stone, and 5 units to the 8th stone.\n```\n\nExample 2:\n\n```Input: stones = [0,1,2,3,4,8,9,11]\nOutput: false\nExplanation: There is no way to jump to the last stone as the gap between the 5th and 6th stone is too large.\n```\n\nConstraints:\n\n• `2 <= stones.length <= 2000`\n• `0 <= stones[i] <= 231 - 1`\n• `stones == 0`\n• `stones` is sorted in a strictly increasing order.\n\n## Code Examples\n\n### #1 Code Example with C Programming\n\n```Code - C Programming```\n\n``````\ntypedef struct {\nint *p;\nint n;\nint sz;\n} steps_t;\n\nint bs(int *stones, int start, int end, int u) {\nint mid, m;\n\nif (start > end) return -1;\n\nmid = start + (end - start) / 2;\nm = stones[mid];\n\nif (m == u) return mid;\nelse if (m < u) return bs(stones, mid + 1, end, u);\nreturn bs(stones, start, mid - 1, u);\n}\nvoid add_step(int *stones, int sz, steps_t *units, int u, int s) {\nint i, j;\nsteps_t *steps;\n\nif (s == 0) return;\n\ni = bs(stones, 0, sz - 1, u);\n\nif (i == -1) return;\n\nsteps = &units[i];\n\nfor (j = 0; j < steps->n; j ++) {\nif (steps->p[j] == s) return;\n}\n\nif (steps->sz == steps->n) {\nif (steps->sz == 0) steps->sz = 10;\nelse steps->sz *= 2;\nsteps->p = realloc(steps->p, steps->sz * sizeof(int));\n//assert(steps->p);\n}\nsteps->p[steps->n ++] = s;\n}\n\nbool canCross(int* stones, int stonesSize) {\nsteps_t units = { 0 }, *steps;\nint i, j, u, s;\nbool ans = false;\n\nif (stones != 1) return false;\n\nfor (i = 1; i < stonesSize; i ++) {\nu = stones[i];\nsteps = &units[i];\nfor (j = 0; j < steps->n; j ++) {\ns = steps->p[j];\nadd_step(stones, stonesSize, units, u + s - 1, s - 1);\nadd_step(stones, stonesSize, units, u + s, s);\nadd_step(stones, stonesSize, units, u + s + 1, s + 1);\n}\n}\n\nif (units[stonesSize - 1].n > 0) ans = true;\n\nfor (i = 0; i < 1100; i ++) {\nif (units[i].p) free(units[i].p);\n}\n\nreturn ans;\n}\n``````\nCopy The Code &\n\nInput\n\ncmd\nstones = [0,1,3,5,6,8,12,17]\n\nOutput\n\ncmd\ntrue\n\n### #2 Code Example with Java Programming\n\n```Code - Java Programming```\n\n``````\nclass Solution {\npublic boolean canCross(int[] stones) {\nint[][] memo = new int[stones.length][stones.length];\nfor (int[] row : memo) {\nArrays.fill(row, -1);\n}\nreturn helper(stones, 0, 0, memo) == 1;\n}\n\nprivate int helper(int[] stones, int idx, int jumpSize, int[][] memo) {\nif (memo[idx][jumpSize] >= 0) {\nreturn memo[idx][jumpSize];\n}\nfor (int i = idx + 1; i < stones.length; i++) {\nint gap = stones[i] - stones[idx];\nif (gap >= jumpSize - 1 && gap <= jumpSize + 1) {\nif (helper(stones, i, gap, memo) == 1) {\nmemo[idx][gap] = 1;\nreturn 1;\n}\n}\n}\nmemo[idx][jumpSize] = (idx == stones.length - 1) ? 1 : 0;\nreturn memo[idx][jumpSize];\n}\n}\n``````\nCopy The Code &\n\nInput\n\ncmd\nstones = [0,1,3,5,6,8,12,17]\n\nOutput\n\ncmd\ntrue\n\n### #3 Code Example with Javascript Programming\n\n```Code - Javascript Programming```\n\n``````\nconst canCross = function(stones) {\nfor (let i = 3; i < stones.length; i++) {\nif (stones[i] > stones[i - 1] * 2) {\nreturn false\n}\n}\nconst count = new Set(stones)\nconst lastStone = stones[stones.length - 1]\nconst position = \nconst jump = \nwhile (position.length > 0) {\nconst nextPosition = position.pop()\nconst nextDistance = jump.pop()\nfor (let i = nextDistance - 1; i <= nextDistance + 1; i++) {\nif (i <= 0) {\ncontinue\n}\nconst nextStone = nextPosition + i\nif (nextStone == lastStone) {\nreturn true\n} else if (count.has(nextStone)) {\nposition.push(nextStone)\njump.push(i)\n}\n}\n}\nreturn false\n}\n``````\nCopy The Code &\n\nInput\n\ncmd\nstones = [0,1,2,3,4,8,9,11]\n\nOutput\n\ncmd\nfalse\n\n### #4 Code Example with Python Programming\n\n```Code - Python Programming```\n\n``````\nclass Solution:\ndef canCross(self, stones):\nmemo, stones, target = {}, set(stones), stones[-1]\ndef dfs(unit, last):\nif unit == target: return True\nif (unit, last) not in memo:\nmemo[(unit, last)] = any(dfs(unit + move, move) for move in (last - 1, last, last + 1) if move and unit + move in stones)\nreturn memo[(unit, last)]\nreturn dfs(1, 1) if 1 in stones else False\n``````\nCopy The Code &\n\nInput\n\ncmd\nstones = [0,1,2,3,4,8,9,11]\n\nOutput\n\ncmd\nfalse\n\n### #5 Code Example with C# Programming\n\n```Code - C# Programming```\n\n``````\nusing System.Collections.Generic;\n\nnamespace LeetCode\n{\npublic class _0403_FrogJump\n{\npublic bool CanCross(int[] stones)\n{\nvar seen = new HashSet<(int location, int step)>();\nvar stonesSet = new HashSet(stones);\n\nvar last = stones[stones.Length - 1];\n\nvar stack = new Stack<(int location, int step)>();\nstack.Push((0, 0));\nwhile (stack.Count > 0)\n{\n(int location, int step) = stack.Pop();\nif (seen.Contains((location, step))) continue;\n\nif (location == last) return true;\nelse if (location < last)\n{\nfor (int i = step - 1; i < step + 2; i++)\n{\nif (i <= 0) continue;\nif (stonesSet.Contains(location + i))\nstack.Push((location + i, i));\n}\n}\n}\n\nreturn false;\n}\n}\n}\n``````\nCopy The Code &\n\nInput\n\ncmd\nstones = [0,1,3,5,6,8,12,17]\n\nOutput\n\ncmd\ntrue"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.57820755,"math_prob":0.99370736,"size":5413,"snap":"2023-40-2023-50","text_gpt3_token_len":1707,"char_repetition_ratio":0.14679238,"word_repetition_ratio":0.062374245,"special_character_ratio":0.35876593,"punctuation_ratio":0.19861232,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98730546,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-28T06:51:17Z\",\"WARC-Record-ID\":\"<urn:uuid:5dd80731-b3e5-4592-89f9-a7224948b83a>\",\"Content-Length\":\"1049962\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b59f02b2-05b7-43d0-9aef-03a4fe4ac5b4>\",\"WARC-Concurrent-To\":\"<urn:uuid:8c171bb6-868f-4c1d-9f01-f09a82a9cc5f>\",\"WARC-IP-Address\":\"131.153.165.35\",\"WARC-Target-URI\":\"https://devsenv.com/example/-403-leetcode-frog-jump-solution-in-c,-c++,-java,-javascript,-python,-c-leetcode\",\"WARC-Payload-Digest\":\"sha1:XCZNVR37JSN4QIKD76SERH3TKEPMCAWI\",\"WARC-Block-Digest\":\"sha1:BNWGPTF2QNNA3XJWJRGYQXCA5A5ERCT5\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510368.33_warc_CC-MAIN-20230928063033-20230928093033-00418.warc.gz\"}"}
|
https://www.opensourceforu.com/2019/06/deep-learning-of-sequential-data-with-lstm/
|
[
"# Deep Learning of Sequential Data with LSTM\n\n1\n3979\n\nThis brief article presents a method for deep learning of sequential data with LSTM through the use of Keras.\n\n“Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction,” said Yann LeCun, Yoshua Bengio and Geoffrey Hinton in their paper, ‘Deep Learning’ (https://www.nature.com/articles/nature14539).\n\nDeep learning in sequences of data\nSupervised learning with sequences is different when compared to other types of data. Here, we have to consider the sequence and its behaviour. We need to find the correct set of data for each sequence to create and train models. Shown below are the different types of sequencing patterns.\n\n1) Sequence predictions: This is the prediction of the next sequence, based on the sequence model.\n2) Sequence classification: This classifies a sequence based on the sequence model.\n3) Sequence generation: This generates a new sequence based on the sequence pattern.\nHere, we are limiting our focus only to sequence classification — we are going to analyse different sets of patterns and tag them into specific types. Based on this trained model, we will see what the sequence for the test sequence data is. Before getting into implementation, let us look at how we can approach this problem. Based on my analysis on sequence prediction, long short term memory (LSTM) will work better for the sequence classification problem.\n\nLong short term memory (LSTM)\nTraditional neural networks cannot remember more of the past, but only the recent past (short term memory) and this is considered as a shortcoming of these networks. Recurring neural networks (RNN) can fix this problem (more on this at http://karpathy.github.io/2015/05/21/rnn-effectiveness/). LSTM is actually a special kind of RNN which is capable of learning long term dependencies. To solve sequencing classification and prediction modelling, we actually need the neural network to remember the past sequence so that we can classify or predict the sequence. I would recommend reading more about RNN and LSTM if you don’t know much about these topics. The section below explains how we can implement LSTM and solve the sequence classification problem.\n\nLSTM implementation by using Keras: The problem\nThis problem is from Jason Brownlee’s blog and it is about the classification of sentiments expressed in IMDB movie reviews, based on the comments.\n1.",
null,
"Asad Ali"
] |
[
null,
"https://secure.gravatar.com/avatar/18b266cc0d37123341e2c6e21943970f",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9193985,"math_prob":0.80572647,"size":2834,"snap":"2022-05-2022-21","text_gpt3_token_len":574,"char_repetition_ratio":0.14876325,"word_repetition_ratio":0.009569378,"special_character_ratio":0.19160198,"punctuation_ratio":0.10119048,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9598779,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-16T11:25:22Z\",\"WARC-Record-ID\":\"<urn:uuid:27211334-4b88-4fa6-b73a-6cf786ba06d3>\",\"Content-Length\":\"271777\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:526e63dd-8b3d-4962-bb00-e3b1a756fa20>\",\"WARC-Concurrent-To\":\"<urn:uuid:d8f13e2d-2829-4f68-a74e-b5f514d4c043>\",\"WARC-IP-Address\":\"69.163.247.134\",\"WARC-Target-URI\":\"https://www.opensourceforu.com/2019/06/deep-learning-of-sequential-data-with-lstm/\",\"WARC-Payload-Digest\":\"sha1:UZ7OACCEDWN6PM6QV6OEHWNGQNEB5KR4\",\"WARC-Block-Digest\":\"sha1:UX67E75UT5PT4X5YD5XG6HVW3GS2JCZ3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662510117.12_warc_CC-MAIN-20220516104933-20220516134933-00609.warc.gz\"}"}
|
https://lisbdnet.com/what-is-the-linear-speed-of-a-point-on-the-equator-due-to-the-earths-rotation/
|
[
"FAQ\n\nwhat is the linear speed of a point on the equator due to the earth’s rotation?\n\n464 m/s.\n\nWhat is the linear speed of a point on the equator due to the Earth’s rotation Express your answer with the appropriate units?\n\nAt the equator, linear speed with respect to the polar (day/night spin ) axis is 463.82 meter/s = 1521.8 feet/s, At latitude 15oNand15oS , this speed is 447.77 meter/s = 1469.1 feet/s.\n\nWhat is the speed of a point on the equator physics?\n\nThe linear speed on a point at the equator on the surface of the Earth is going to be the radius of the Earth multiplied by this angular speed. So that’s 6.4 times 10 to the 6 meters—radius— times 2π radians over 86400 seconds which is 470 meters per second.\n\nWhat is the speed of someone on the equator?\n\nThus, the surface of the earth at the equator moves at a speed of 460 meters per second–or roughly 1,000 miles per hour.\n\nWhat is the linear velocity?\n\nWe define the rate of change in position over a time period as velocity. Linear velocity is simply an object’s velocity in a straight line, whereas Angular Velocity is how much an object spins, rotates, or turns.\n\n3800 m/s.\n\nWhat is the equation for linear speed?\n\nWe can use calculus to prove the formula for Linear Speed, which is v=rω. Consider a body moving with a uniform velocity v in a circular path of radius r.\n\nHow do you find linear velocity?\n\nThe linear velocity v of the point P is the distance it traveled divided by the time elapsed. That is, v=st.\n\nWhat is the angular velocity of a point at the equator of the earth?\n\nBased on the sidereal day, Earth’s true angular velocity, ωEarth, is equal to 15.04108°/mean solar hour (360°/23 hours 56 minutes 4 seconds). ωEarth can also be expressed in radians/second (rad/s) using the relationship ωEarth = 2*π /T, where T is Earth’s sidereal period (23 hours 56 minutes 4 seconds).\n\nWhat is the Earth’s angular speed the Earth’s radius is 6.37 106m it rotates once every 24 hours?\n\nv1 = 463.1 m/s\n\n– The speed of the point where θ = 18° from the equator v2 can be determined from the linear and rotational motion kinematic relation.\n\nWhat is the angular velocity of the Earth’s orbit around the sun?\n\n(a) The angular speed of the earth in its orbit about the sun is ω = 2π/year = 2π/(365*24*60*60 s) = 2*107/s.\n\nHow do you calculate the speed of the Earth at the equator?\n\nIf you estimate that a day is 24 hours long, you divide the circumference by the length of the day. This produces a speed at the equator of about 1,037 mph (1,670 km/h). You won’t be moving quite as fast at other latitudes, however.\n\nWhat is the latitude of any point on Earth’s equator?\n\nlatitude, angular distance of any point on the surface of the earth north or south of the equator. The equator is latitude 0°, and the North Pole and South Pole are latitudes 90°N and 90°S, respectively.\n\nWhere is the speed of rotation of the Earth highest?\n\nthe Equator\nThe speed of rotation is greatest at the Equator and gets smaller with increasing latitude. For example, at Columbus (Latitude 40-degrees North): Circumference of the Earth at 40-deg North = 30,600 kilometers. Time to complete one Rotation = 24 hours.\n\nIs linear velocity speed?\n\nLinear velocity is speed in a straight line (measured in m/s) while angular velocity is the change in angle over time (measured in rad/s, which can be converted into degrees as well).\n\nHow do you find the linear velocity of a rotating object?\n\nThe Formula for Linear Speed\n1. s = \\frac {d}{t} Where, …\n2. linear speed = angular speed \\times radius of the rotation.\n3. i.e. v = \\omega \\times r. v = linear speed (m per s)\n4. \\omega = angular speed (radians per s) Where, …\n5. Solution: First start to find the angular speed. …\n6. \\omega = 10.0 rev/s.\n7. r = \\frac{4}{2} = 2 m. …\n8. v = \\omega \\times r,\n\nWhat is example of linear velocity?\n\nLinear velocity is defined as distance over a period of time. For instance if a person ran 1 mile or approximately 1600 meters in 7 minutes, the they would have covered about 230 meters per minute.\n\nHow do you find the linear speed of a point on the Earth?\n\nThe linear velocity is expressed in terms of the angular velocity of the earth’s rotation and the radius of the horizontal circle. Formulas used: -The linear velocity of a rotating body is given by, $v = r\\omega$ where $r$ is the radius of the circle and $\\omega$ is the body’s angular velocity.\n\n720 m/s.\n\n6,371 km\n\nWhat is the variable for linear speed?\n\nAt a distance r from the center of the rotation, a point on the object has a linear speed equal to the angular speed multiplied by the distance r. The units of linear speed are meters per second, m/s.\n\nWhat is the linear speed of a point on the rim of the disk?\n\nanswer: 31.4 rad/s (correct) Part B: What is the linear speed of a point on the rim of the disk? answer: 1.40 m/s (correct) Part C: Does a point near the center of the disk have.\n\nHow do you find linear speed with radius and time?\n\nLinear Speed\n\nIf the angle were not exactly 1 radian, then the distance traveled by the point on the circle is the length of the arc s=rθ, or the radius length times the measure of the angle in radians. Substituting into the formula for linear speed gives v=rθt or v=r⋅θt.\n\nWhat is the initial linear velocity?\n\nv = initial linear velocity (m/s, ft/s) a = acceleration (m/s2, ft/s2) Linear distance can be expressed as (if acceleration is constant): s = v t + 1/2 a t2 (1c) Combining 1b and 1c to express the final velocity.\n\nv =ω ×r.\n\nWhat is the angular speed of someone standing on the equator?\n\nEarth angular speed is 7.27×105 rad /s\n\nSee also what is the total number of electrons shared in a double covalent bond\n\nEarth angular speed is 7.2921159 x 105 rad/s from: World Book Encyclopedia Vol 6.\n\nHow do you calculate angular velocity?\n\nWe can rewrite this expression to obtain the equation of angular velocity: ω = r × v / |r|² , where all of these variables are vectors, and |r| denotes the absolute value of the radius. Actually, the angular velocity is a pseudovector, the direction of which is perpendicular to the plane of the rotational movement.\n\nWhen calculating the angular velocity of the Earth as it completes a full rotation on its own axis (a solar day), this equation is represented as: ωavg = 2πrad/1day (86400 seconds), which works out to a moderate angular velocity of 7.2921159 × 105 radians/second.\n\nWhich factor does the torque on an object not depend on?\n\nWhich factor does the torque on an object not depend on? The angular velocity of the object to change.\n\nWhat is the angular speed and linear speed of Earth around sun?\n\nWe know the Earth goes round the Sun, all the way around is 2 radians (360 degrees). We also know that it takes a year (approx 365 days) which is therefore about 3.2×107 secs. Therefore = 2 / 3.2×107 = 2.0×107 rad/s.\n\nWhat is the angular speed of the Earth as it spins around its axis?\n\nIt takes the Earth approximately 23 hours, 56 minutes and 4.09 seconds to make one complete revolution (360 degrees). This length of time is known as a sidereal day. The Earth rotates at a moderate angular velocity of 7.2921159 × 105 radians/second.\n\nWhich way does angular velocity point for Earth?\n\nThe angular velocity is positive since the satellite travels eastward with the Earth’s rotation (counter-clockwise from above the north pole.)\nAngular velocity\nBehaviour under coord transformation pseudovector\nDerivations from other quantities ω = dθ / dt\nDimension\n\nSpeed at Equator The earth rotates about its axis once every\n\nRelated Searches\n\nwhat is the linear speed of a point at a latitude of 50.0 ∘ n, due to the earth’s rotation?\nwhat is the linear speed of a point on the arctic circle (latitude 66.5∘ n)?\nwhat is the linear speed of a point at a latitude of 16.0 ∘ n?"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.86190057,"math_prob":0.9966807,"size":9924,"snap":"2022-05-2022-21","text_gpt3_token_len":2529,"char_repetition_ratio":0.2702621,"word_repetition_ratio":0.33491063,"special_character_ratio":0.27055624,"punctuation_ratio":0.094321914,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9996904,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-22T19:58:43Z\",\"WARC-Record-ID\":\"<urn:uuid:1ca179b2-0377-4e76-96e7-541f924115da>\",\"Content-Length\":\"166653\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d2727655-6108-49bb-904d-bee877aca11c>\",\"WARC-Concurrent-To\":\"<urn:uuid:eeae29af-c7aa-48c0-8640-6aca7760f611>\",\"WARC-IP-Address\":\"172.67.132.36\",\"WARC-Target-URI\":\"https://lisbdnet.com/what-is-the-linear-speed-of-a-point-on-the-equator-due-to-the-earths-rotation/\",\"WARC-Payload-Digest\":\"sha1:DCIRYO45BUX6JYEH2D6L2TJ3M7WZOP25\",\"WARC-Block-Digest\":\"sha1:HTEAWAK545QSSJVKNWJTA7MNAB3UBOMG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320303884.44_warc_CC-MAIN-20220122194730-20220122224730-00152.warc.gz\"}"}
|
https://api.openml.org/d/35456
|
[
"Data\nQSAR-DATASET-FOR-DRUG-TARGET-CHEMBL4619\n\n# QSAR-DATASET-FOR-DRUG-TARGET-CHEMBL4619\n\nIssue #Downvotes for this reason By\n\nThis dataset contains QSAR data (from ChEMBL version 17) showing activity values (unit is pseudo-pCI50) of several compounds on drug target ChEMBL_ID: CHEMBL4619 (TID: 11176), and it has 54 rows and 43 features (not including molecule IDs and class feature: molecule_id and pXC50). The features represent Basic Molecular Descriptors which were generated from SMILES strings. Missing value imputation was applied to this dataset (By choosing the Median).\n\n### 45 features\n\n pXC50 (target) numeric 48 unique values 0 missing molecule_id (row identifier) nominal 54 unique values 0 missing AMW numeric 42 unique values 0 missing C. numeric 31 unique values 0 missing H. numeric 32 unique values 0 missing Me numeric 19 unique values 0 missing Mi numeric 23 unique values 0 missing Mp numeric 31 unique values 0 missing Mv numeric 31 unique values 0 missing MW numeric 44 unique values 0 missing N. numeric 29 unique values 0 missing nAB numeric 7 unique values 0 missing nAT numeric 23 unique values 0 missing nB numeric 1 unique values 0 missing nBM numeric 10 unique values 0 missing nBO numeric 14 unique values 0 missing nBR numeric 1 unique values 0 missing nBT numeric 24 unique values 0 missing nC numeric 10 unique values 0 missing nCL numeric 2 unique values 0 missing nCsp numeric 1 unique values 0 missing nCsp2 numeric 9 unique values 0 missing nCsp3 numeric 13 unique values 0 missing nDB numeric 3 unique values 0 missing nF numeric 3 unique values 0 missing nH numeric 17 unique values 0 missing nHet numeric 8 unique values 0 missing nHM numeric 2 unique values 0 missing nI numeric 1 unique values 0 missing nN numeric 5 unique values 0 missing nO numeric 4 unique values 0 missing nP numeric 1 unique values 0 missing nS numeric 1 unique values 0 missing nSK numeric 14 unique values 0 missing nTB numeric 1 unique values 0 missing nX numeric 3 unique values 0 missing O. numeric 26 unique values 0 missing RBF numeric 30 unique values 0 missing RBN numeric 10 unique values 0 missing SCBO numeric 24 unique values 0 missing Se numeric 44 unique values 0 missing Si numeric 44 unique values 0 missing Sp numeric 44 unique values 0 missing Sv numeric 44 unique values 0 missing X. numeric 7 unique values 0 missing\n\n### 62 properties\n\n54\nNumber of instances (rows) of the dataset.\n45\nNumber of attributes (columns) of the dataset.\n0\nNumber of distinct values of the target attribute (if it is nominal).\n0\nNumber of missing values in the dataset.\n0\nNumber of instances with at least one value missing.\n44\nNumber of numeric attributes.\n1\nNumber of nominal attributes.\nEntropy of the target attribute values.\nAn estimate of the amount of irrelevant information in the attributes regarding the class. Equals (MeanAttributeEntropy - MeanMutualInformation) divided by MeanMutualInformation.\nSecond quartile (Median) of entropy among attributes.\n0.83\nNumber of attributes divided by the number of instances.\nAverage number of distinct values among the attributes of the nominal type.\n1.75\nSecond quartile (Median) of kurtosis among attributes of the numeric type.\nNumber of attributes needed to optimally describe the class (under the assumption of independence among attributes). Equals ClassEntropy divided by MeanMutualInformation.\n0.52\nMean skewness among attributes of the numeric type.\n5.88\nSecond quartile (Median) of means among attributes of the numeric type.\nPercentage of instances belonging to the most frequent class.\n2.9\nMean standard deviation of attributes of the numeric type.\nSecond quartile (Median) of mutual information between the nominal attributes and the target attribute.\nNumber of instances belonging to the most frequent class.\nMinimal entropy among attributes.\n0.08\nSecond quartile (Median) of skewness among attributes of the numeric type.\nMaximum entropy among attributes.\n-1.12\nMinimum kurtosis among attributes of the numeric type.\n0\nPercentage of binary attributes.\n1.5\nSecond quartile (Median) of standard deviation of attributes of the numeric type.\n54\nMaximum kurtosis among attributes of the numeric type.\n0\nMinimum of means among attributes of the numeric type.\n0\nPercentage of instances having missing values.\nThird quartile of entropy among attributes.\n393.68\nMaximum of means among attributes of the numeric type.\nMinimal mutual information between the nominal attributes and the target attribute.\n0\nPercentage of missing values.\n2.68\nThird quartile of kurtosis among attributes of the numeric type.\nMaximum mutual information between the nominal attributes and the target attribute.\nThe minimal number of distinct values among attributes of the nominal type.\n97.78\nPercentage of numeric attributes.\n31.49\nThird quartile of means among attributes of the numeric type.\nThe maximum number of distinct values among attributes of the nominal type.\n-1.66\nMinimum skewness among attributes of the numeric type.\n2.22\nPercentage of nominal attributes.\nThird quartile of mutual information between the nominal attributes and the target attribute.\n7.35\nMaximum skewness among attributes of the numeric type.\n0\nMinimum standard deviation of attributes of the numeric type.\nFirst quartile of entropy among attributes.\n1.28\nThird quartile of skewness among attributes of the numeric type.\n42.9\nMaximum standard deviation of attributes of the numeric type.\nPercentage of instances belonging to the least frequent class.\n1.33\nFirst quartile of kurtosis among attributes of the numeric type.\n3.16\nThird quartile of standard deviation of attributes of the numeric type.\nAverage entropy of the attributes.\nNumber of instances belonging to the least frequent class.\n0.28\nFirst quartile of means among attributes of the numeric type.\nStandard deviation of the number of distinct values among attributes of the nominal type.\n5.02\nMean kurtosis among attributes of the numeric type.\n0\nNumber of binary attributes.\nFirst quartile of mutual information between the nominal attributes and the target attribute.\n23.34\nMean of means among attributes of the numeric type.\n-0.93\nFirst quartile of skewness among attributes of the numeric type.\n0.2\nAverage class difference between consecutive instances.\nAverage mutual information between the nominal attributes and the target attribute.\n0.02\nFirst quartile of standard deviation of attributes of the numeric type."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7573379,"math_prob":0.9455784,"size":4035,"snap":"2023-40-2023-50","text_gpt3_token_len":823,"char_repetition_ratio":0.282064,"word_repetition_ratio":0.34848484,"special_character_ratio":0.2,"punctuation_ratio":0.1251758,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9813448,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-29T17:04:37Z\",\"WARC-Record-ID\":\"<urn:uuid:e0bf38da-4cdf-4727-b3e0-2dce4cc3b506>\",\"Content-Length\":\"59271\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a550e526-85fc-4f66-ac6c-b3c2357ef471>\",\"WARC-Concurrent-To\":\"<urn:uuid:3d26903c-8f6f-4d44-a9a9-d5ff6bad7484>\",\"WARC-IP-Address\":\"131.155.11.11\",\"WARC-Target-URI\":\"https://api.openml.org/d/35456\",\"WARC-Payload-Digest\":\"sha1:NVTSUU72WZC7L2PKNFBKKVYJPVKJE5UZ\",\"WARC-Block-Digest\":\"sha1:NRTOOVMHTU43MU5NDBMCUJBIBVYWSG3O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510520.98_warc_CC-MAIN-20230929154432-20230929184432-00676.warc.gz\"}"}
|
https://www.perlmonks.org/index.pl?node_id=72600
|
[
"",
null,
"\"be consistent\" PerlMonks\n\n### Re: Rotisserie Baseball Section\n\nby Dominus (Parson)\n on Apr 14, 2001 at 22:20 UTC ( #72600=note: print w/replies, xml ) Need Help??\n\nin reply to Rotisserie Baseball Section\n\nGreat idea. Here's a program I wrote a few years back. The first time you run it, you get a table with the current statistics for all your players. After that, you run it daily and it shows you how the stats have changed since the previous run--- this effectively shows how the players performed on the previous day.\n\nIt also maintains a historical archive of each player's records and a daily summary for the entire team.\n\nI used to run this daily as a cron job, so every morning I would get a report about how my players were doing.\n\n```#!/usr/bin/perl\n\nuse HTTP::Request;\nuse HTTP::Response;\nuse LWP::UserAgent;\n\n\\$ua = LWP::UserAgent->new;\n\nsub fixup_stats (\\%);\n\n\\$ROOT = 'http://www.usatoday.com/sports/baseball/';\n\\$HOME = '/data/baseball/plover-1998';\n# \\$HOME = '/data/baseball/plover-1998/test';\n\n%WIDTH =\n(BB => 3, SG => 3, DB => 2, TP => 2, HR => 2, TB => 3,\nOB => 3, AB => 3, PA => 3,\nAVG => 4, OBA => 4, SLG => 4, SB => 2, CS => 2, SBG => 3,\nR => 3, RBI => 3,\n\nIP => 5, ER => 3, ERA => 5, W => 2, L => 2, S => 2, WLS => 3,\nH => 3, BB => 3, BRA => 5, K => 3, BB => 3, KBB => 5,\n);\n\n%LOCAL_STATS =\n(BAT => [qw(BB SG DB TP HR TB OB AB PA AVG OBA SLG SB CS SBG R RBI)]\n+,\nPIT => [qw(IP ER ERA W L S WLS H BB BRA K KBB)],\n);\n\n%REMOTE_STATS =\n(BAT => [qw(AVG SLG OBA G AB R H TB DB TP HR RBI BB SO SB CS E)],\nPIT => [qw(W L ERA AVG G GS CG GF SH S IP H R ER HR BB K)],\n);\n\n%P_TYPE =\n( '1B' => BAT, C => BAT, '2B' => BAT, '3B' => BAT,\nSS =>BAT, CF => BAT, OF => BAT, MI => BAT, IF => BAT,\n\nSP => PIT, RP => PIT,\n);\n\n%DS = ('C' => 0,\n'1B' => 1, '2B' => 2, 'SS' => 3, '3B' => 4,\n'MI' => 3.5, 'IF' => 4.5,\n'CF' => 5, 'OF' => 6,\n);\n\n%T_URL = (\nBAL => A1, BOS => A2, NYY => A10, TBR => A15, TOR => A14,\nCWS => A4, CLE => A5, DET => A6, KCR => A7, MIN => A9,\nANA => A3, OAK => A11, SEA => A12, TEX => A13, ATL => N1,\nFLA => N5, MON => N8, NYM => N9, PHI => N10, CHC => N3,\nCIN => N2, HOU => N6, MIL => N16, PIT => N11, STL => N14,\nARI => N15, COL => N4, LAD => N7, SDP => N12, SFG => N13,\n);\n\n%P_INFO =\n(\nSteinbach => [C, MIN, ACT],\nMcGwire => ['1B', STL, ACT],\nGraffanino => ['2B', ATL, RES],\nCaminiti => ['3B', SDP, ACT],\nVeras => ['2B', SDP, ACT],\nAnderson => [CF, BAL, ACT],\n'A. Jones' => [CF, ATL, ACT],\nSalmon => [OF, ANA, ACT],\nLoretta => [SS, MIL, ACT],\nHammonds => [CF, BAL, RES],\nKonerko => ['3B', CIN, RES],\nServais => [C, CHC, ACT],\n\nSantiago => [C, TOR, RES],\nBuhner => [OF, SEA, ACT],\nRivera => [OF, SDP, RES],\nYoung => ['1B', PIT, ACT],\nStrange => ['3B', PIT, RES],\nSpiers => ['3B', HOU, RES],\nPerez => ['1B', CIN, RES],\nAurilia => ['SS', SFG, ACT], # Signed in July draft\n\nAppier => [SP, KCR, RES],\nGlavine => [SP, ATL, ACT],\nRueter => [SP, SFG, ACT],\nSmoltz => [SP, ATL, ACT],\nMoyer => [SP, SEA, ACT],\nLima => [SP, HOU, ACT], # Signed in May draft\n\nJones => [RP, DET, ACT],\nWagner => [RP, HOU, ACT],\n\nBurkett => [SP, TEX, RES],\nBlair => [SP, ARI, RES],\nTaylor => [RP, OAK, RES],\n);\n\n################################################################\n\nforeach \\$player (keys %P_INFO) {\nmy (\\$pos, \\$team, \\$stat) = @{\\$P_INFO{\\$player}};\npush @{\\$players{\\$team}}, \\$player;\n}\n\n{\nmy (\\$sec, \\$min, \\$hour, \\$d, \\$m, \\$y) = localtime;\n\\$DATE = sprintf(\"%04d%02d%02d\", \\$y+1900, \\$m+1, \\$d);\n\\$DAILY = \"DAILY-\\$DATE\";\n\\$GAME = \"GAME-\\$DATE\";\nopen DP, \"> \\$HOME/\\$DAILY-P\"\nor die \"Couldn't open daily file \\$HOME/\\$DAILY-P: \\$!; aborting\";\nopen DB, \"> \\$HOME/\\$DAILY-B\"\nor die \"Couldn't open daily file \\$HOME/\\$DAILY-B: \\$!; aborting\";\nopen GP, \"> \\$HOME/\\$GAME-P\"\nor die \"Couldn't open game file \\$HOME/\\$GAME-P: \\$!; aborting\";\nopen GB, \"> \\$HOME/\\$GAME-B\"\nor die \"Couldn't open game file \\$HOME/\\$GAME-B: \\$!; aborting\";\n}\n\nmy @team_queue = keys %players;\nwhile (@team_queue) {\nmy \\$team = shift @team_queue;\nnext if \\$team eq XXX; # Players not on any team\nmy \\$url = team_url(\\$team);\nmy \\$request = HTTP::Request->new(GET => \\$url);\nmy \\$response = \\$ua->request(\\$request);\n\nunless (\\$response->is_success) {\nmy \\$error = \\$response->status_line;\nprint \"\\$team(\\$url): \\$error\\n\";\npush @team_queue, \\$team;\nnext;\n}\n\nmy @lines = split /\\r?\\n/, \\$response->content;\nforeach \\$player (@{\\$players{\\$team}}) {\nmy (\\$ppos, \\$pteam, \\$pstat) = @{\\$P_INFO{\\$player}};\nmy \\$ptype = \\$P_TYPE{\\$ppos};\nmy @loi = grep /^\\$player/, @lines;\nif (@loi == 0) {\nwarn \"Couldn't find information for player \\$player on team \\$team\n+.\\n\";\nnext;\n} elsif (@loi > 1) {\nwarn \"Found multiple information for player \\$player on team \\$tea\n+m.\\n\";\nnext;\n}\nmy %STATS = get_stats(\\$player, @loi);\nfixup_stats(%STATS);\nmy \\$pn = substr(\\$player . \" \", 0, 15);\nmy \\$fn = \"\\$HOME/:\\$player\";\n\\$fn =~ tr/ //d;\nmy \\$statline = put_stats(\\$player, %STATS);\nmy \\$yesterday = get_last_line(\\$fn);\nunless (open P, \">> \\$fn\") {\nwarn \"Couldn't append to file `\\$fn': \\$!; skipping \\$player.\\n\";\nnext;\n}\nprint P \\$DATE, \" \", \\$statline, \"\\n\";\n\nmy (%yesterday, \\$k);\n@yesterday{'DATE', @{\\$LOCAL_STATS{\\$ptype}}} = split /\\s+/, \\$yester\n+day;\nforeach \\$k (keys %STATS) {\nnext unless exists \\$yesterday{\\$k};\n\\$yesterday{\\$k} = int((\\$STATS{\\$k} - \\$yesterday{\\$k})*1000)/1000;\n\\$TOTAL{\\$k} += \\$yesterday;\n}\nmy \\$game_statline = put_stats(\\$player, %yesterday);\n\n\\$statline{\\$player} = \\$statline;\n\\$game_statline{\\$player} = \\$game_statline;\nprint STDERR \"Done with player \\$player.\\n\";\n}\n}\nclose P;\n\n@PLAYERS = keys %P_INFO;\n@PITCHERS = grep {\\$P_TYPE{\\$P_INFO{\\$_}} eq PIT} @PLAYERS;\n@BATTERS = grep {\\$P_TYPE{\\$P_INFO{\\$_}} eq BAT} @PLAYERS;\n\nif (open Q, \"< \\$HOME/BHEADER-D\") {\nwhile (<Q>) {\nprint DB;\nprint GB;\n}\nclose Q;\n} else {\n}\n\\$prevstat = 'ACT';\nforeach \\$player (sort {\\$P_INFO{\\$a} cmp \\$P_INFO{\\$b}\n||\n\\$DS{\\$P_INFO{\\$a}} <=> \\$DS{\\$P_INFO{\\$b}}\n||\n\\$a cmp \\$b\n}\n@BATTERS) {\nnext if \\$P_INFO{\\$player} eq XXX;\nif (\\$P_INFO{\\$player} eq RES && \\$prevstat eq ACT) {\nprint DB \"\\n\";\n\\$prevstat = RES;\n}\nmy \\$pn = substr(\"\\$player/\\$P_INFO{\\$player} \", 0, 13);\nprint DB \\$pn, \\$statline{\\$player}, \"\\n\";\nprint GB \\$pn, \\$game_statline{\\$player}, \"\\n\";\n}\nprint DB \"\\n\\n\";\nclose DB;\nprint GB \"\\n\\n\";\nclose GB;\n\nif (open Q, \"< \\$HOME/PHEADER-D\") {\nwhile (<Q>) {\nprint DP;\nprint GP;\n}\nclose Q;\n} else {\n}\n\\$prevstat = 'ACT';\nforeach \\$player (sort {\\$P_INFO{\\$a} cmp \\$P_INFO{\\$b}\n||\n\\$P_INFO{\\$b} cmp \\$P_INFO{\\$a}\n||\n\\$a cmp \\$b\n}\n@PITCHERS) {\nnext if \\$P_INFO{\\$player} eq XXX;\nif (\\$P_INFO{\\$player} eq RES && \\$prevstat eq ACT) {\nprint DP \"\\n\";\n\\$prevstat = RES;\n}\nmy \\$pn = substr(\"\\$player/\\$P_INFO{\\$player} \", 0, 13);\nprint DP \\$pn, \\$statline{\\$player}, \"\\n\";\nprint GP \\$pn, \\$game_statline{\\$player}, \"\\n\";\n}\nclose DP;\nclose GP;\n\nsystem qq{cat \\$HOME/\\$GAME-? | Mail -s 'Philadelphia Plovers Report' mj\n+d};\n\n################################################################\n\nsub team_url {\nmy \\$team = shift;\nmy (\\$l, \\$n) = (\\$T_URL{\\$team} =~ /^([AN])(\\d+)\\$/);\ndie \"Couldn't compute url for team \\$team; aborting\"\nunless defined \\$l;\n\\$n = sprintf(\"%02d\", \\$n);\n\\$l = lc \\$l;\n\\$ROOT . \"sb\\$l/sb\\$ {l}98\\$n.htm\";\n}\n\nsub get_stats {\nmy \\$player = shift;\nmy \\$line = shift;\n\\$line =~ s/^\\Q\\$player\\E\\s*//\nor warn \"Line of interest:\\n\\t\\$line\\ndoes not begin with player's\n+name `\\$player'.\\n\";\nmy @f = split /[\\s-]+/, \\$line;\n# shift @f while \\$f eq ''; # Discard leading null fields\nmy \\$bp = \\$P_TYPE{\\$P_INFO{\\$player}};\nmy %stats;\n@stats{@{\\$REMOTE_STATS{\\$bp}}} = @f;\n%stats;\n}\n\nsub put_stats {\nmy \\$player = shift;\nmy %stats = @_;\nmy \\$bp = \\$P_TYPE{\\$P_INFO{\\$player}};\nmy \\$statline = '';\nforeach \\$stat (@{\\$LOCAL_STATS{\\$bp}}) {\nmy \\$s = fill(\\$stats{\\$stat}, \\$WIDTH{\\$stat});\nif (! defined \\$s) {\nprint STDERR \"(\\$stat)\\n\";\nnext;\n}\n\\$statline .= \\$s . ' ';\n}\nchop \\$statline;\n\\$statline;\n}\n\nsub fill {\nmy \\$d = shift;\nmy \\$w = shift;\n\\$d =~ s/^0\\././;\n\\$d =~ s/^-0\\./-/;\n\\$d =~ s/0{5,}.*\\$//;\nif (length(\\$d) > \\$w) {\nprint STDERR \"Couldn't fill `\\$d' to width \\$w.\";\nreturn undef;\n}\n\\$d = (' ' x \\$w) . \\$d;\nsubstr(\\$d, -\\$w);\n}\n\nsub fixup_stats (\\%) {\nmy \\$s = shift;\n\n# Innings pitched 12.2 => 12.7\nif (exists \\$s->{IP}) {\nmy (\\$i, \\$f) = split /\\./, \\$s->{IP};\n\\$s->{IP} = sprintf(\"%2.1f\", \\$i + \\$f/3);\n}\n\nif (exists \\$s->{ERA}) {\n\\$s->{ERA} = sprintf(\"%.2f\", int(\\$s->{ERA} * 100)/100);\n}\n\nforeach \\$stat (qw(AVG OBA SLG)) {\nif (exists \\$s->{\\$stat}) {\n\\$s->{\\$stat} = sprintf(\".%03d\", int(\\$s->{\\$stat} * 1000));\n}\n}\n\nif (exists \\$s->{W}) { # Pitching\n\\$s->{WLS} = \\$s->{W} * 2 + \\$s->{S} - \\$s->{L};\neval {\\$s->{BRA} = sprintf(\"%4.2f\", 9 * (\\$s->{BB} + \\$s->{H}) / \\$s->\n+{IP})};\n\\$s->{BRA} = '----' if \\$@;\neval {\\$s->{KBB} = sprintf(\"%4.2f\", \\$s->{K} / \\$s->{BB})};\n\\$s->{KBB} = '---' if \\$@;\n} else { # Batting\n\\$s->{SG} = \\$s->{H} - \\$s->{DB} - \\$s->{TP} - \\$s->{HR};\n\\$s->{OB} = \\$s->{H} + \\$s->{BB};\n\\$s->{PA} = \\$s->{AB} + \\$s->{BB};\n\\$s->{SBG} = \\$s->{SB} - \\$s->{CS};\n}\n}\n\nsub get_last_line {\nmy \\$file = shift;\nmy \\$linelen = shift || 80;\nopen Q, \"< \\$file\" || die \"Couldn't open file `\\$file': \\$!; aborting\";\nseek Q, -\\$linelen, 2;\nmy \\$prev = undef;\nwhile (<Q>) {\n\\$prev = \\$_;\n}\nreturn \\$prev;\n}\n\nCreate A New User\nNode Status?\nnode history\nNode Type: note [id://72600]\nhelp\nChatterbox?\nand the web crawler heard nothing...\n\nHow do I use this? | Other CB clients\nOther Users?\nOthers avoiding work at the Monastery: (5)\nAs of 2020-10-30 07:13 GMT\nSections?\nInformation?\nFind Nodes?\nLeftovers?\nVoting Booth?\nMy favourite web site is:\n\nResults (278 votes). Check out past polls.\n\nNotices?"
] |
[
null,
"https://promote.pair.com/i/pair-banner-current.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.6828209,"math_prob":0.98699784,"size":8719,"snap":"2020-45-2020-50","text_gpt3_token_len":3247,"char_repetition_ratio":0.14216867,"word_repetition_ratio":0.06336634,"special_character_ratio":0.47104025,"punctuation_ratio":0.2514777,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9619114,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-30T07:15:21Z\",\"WARC-Record-ID\":\"<urn:uuid:f975807c-ad3d-479c-b8d1-6c2b92f21afa>\",\"Content-Length\":\"30761\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c3228a4a-b401-466a-9a0e-8d16e74e9b02>\",\"WARC-Concurrent-To\":\"<urn:uuid:abba01dc-5b0d-448e-8b31-865e1bf76e88>\",\"WARC-IP-Address\":\"66.39.54.27\",\"WARC-Target-URI\":\"https://www.perlmonks.org/index.pl?node_id=72600\",\"WARC-Payload-Digest\":\"sha1:V3HW5GBN7CLFDEXXQA24RQXXFFOD7AT2\",\"WARC-Block-Digest\":\"sha1:YGBMDXQJJHF776MT65VXCMA7JS26VAZD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107909746.93_warc_CC-MAIN-20201030063319-20201030093319-00458.warc.gz\"}"}
|
https://plainmath.net/83517/how-does-the-refractive-index-of-air-rel
|
[
"",
null,
"# How does the refractive index of air rely on the temperature? Is there a theoretical derivation of it?",
null,
"Deromediqm 2022-07-20 Answered\nHow does the refractive index of air rely on the temperature? Is there a theoretical derivation of it?\nYou can still ask an expert for help\n\n• Questions are typically answered in as fast as 30 minutes\n\nSolve your problem for the price of one coffee\n\n• Math expert for every subject\n• Pay only if we can solve it",
null,
"Killaninl2\nThe refractive index of air is easy, because air is a dilute gas with a very small refractive index, which is given by:\n$n=1-\\sum {n}_{i}{\\delta }_{i}\\left(k\\right)$\nfor small wavenumbers k. The ${n}_{i}$ are the number density for each species of molecule, and ${\\delta }_{i}$ is the contribution to the index from this molecular species. You can just use N2 and O2 to get a good enough fit, and include CO2 and H2O for a better fit.\nIn the ideal gas limit, which is nearly perfect for air, $n=\\frac{P}{kT}$. If you double the pressure, you double the deviation from 1. If you double the temperature, you halve the deviation from one, because all the components go with the same ideal gas law:\nSo the formula for the long-wavelength index of air is\n$\\overline{)n\\left(P,T\\right)=1+.000293×\\frac{P}{{P}_{0}}\\frac{{T}_{0}}{T}}$\nWhere ${P}_{0}$ is atmospheric pressure, and ${T}_{0}$ is the standard temperature of 300K. and this is essentially exact for all practical purposes, the corrections are negligible away from oxygen/nitrogen/water/CO2 resonances, and any deviation from the formula will be due to varying humidity.\nThe actual contributions ${\\delta }_{i}$ requires the forward scattering amplitude for light on a diatomic molecule. This is just beyond what you can do with pencil and paper, but it is within the reach of simulations."
] |
[
null,
"https://plainmath.net/build/images/search.png",
null,
"https://plainmath.net/build/images/avatar.jpeg",
null,
"https://plainmath.net/build/images/avatar.jpeg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9555935,"math_prob":0.98912126,"size":1552,"snap":"2022-27-2022-33","text_gpt3_token_len":319,"char_repetition_ratio":0.18992248,"word_repetition_ratio":0.007434944,"special_character_ratio":0.20296392,"punctuation_ratio":0.12944984,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9987791,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-12T08:18:09Z\",\"WARC-Record-ID\":\"<urn:uuid:0a18db2d-4f26-40c5-9078-49d86d983920>\",\"Content-Length\":\"63856\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:be88868f-3ad4-4295-b88d-84bb1ecf2556>\",\"WARC-Concurrent-To\":\"<urn:uuid:fedfa924-a949-4a4a-8fca-5da48681ed2e>\",\"WARC-IP-Address\":\"172.66.40.79\",\"WARC-Target-URI\":\"https://plainmath.net/83517/how-does-the-refractive-index-of-air-rel\",\"WARC-Payload-Digest\":\"sha1:6OCWDN44NRLF4JIBBF6ZFKRKNUIVV5FU\",\"WARC-Block-Digest\":\"sha1:NYEH6SI3RHHN344JZTKEBGKJMMPTOM6G\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571597.73_warc_CC-MAIN-20220812075544-20220812105544-00765.warc.gz\"}"}
|
http://deffufa.info/fast-facts-worksheets/addition-fast-facts-worksheets-the-best-image-collection/
|
[
"Addition Fast Facts Worksheets The Best Image Collection",
null,
"addition fast facts worksheets the best image collection.\n\nmultiplication and division fast facts worksheets times tables printable,multiplication worksheets facts to download them and try solve fast addition subtraction division,math multiplication fast facts worksheets basic times tables,addition fast facts worksheets the best image collection math multiplication and subtraction division,fast facts math worksheets basic addition and subtraction printable free grade multiplication worksheet,fast facts worksheets multiplication math worksheet printable,2nd grade fast facts worksheets print math multiplication addition and subtraction,grade multiplication table printable free for fast facts math 2nd worksheets division addition,multiplication facts worksheets to 7 a appear exactly once on 2nd grade fast math addition and subtraction,subtraction fast facts worksheets basic addition and common a math printable on multiplication division."
] |
[
null,
"http://deffufa.info/wp-content/uploads/2018/02/addition-fast-facts-worksheets-the-best-image-collection.jpg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7922389,"math_prob":0.8443829,"size":947,"snap":"2019-26-2019-30","text_gpt3_token_len":149,"char_repetition_ratio":0.22905621,"word_repetition_ratio":0.03539823,"special_character_ratio":0.13833158,"punctuation_ratio":0.08029197,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99845463,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-26T18:34:07Z\",\"WARC-Record-ID\":\"<urn:uuid:e9756947-1b29-4901-916f-62e1a546ce7f>\",\"Content-Length\":\"38945\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:28758f54-f6a4-46af-927f-71bfbe6a8698>\",\"WARC-Concurrent-To\":\"<urn:uuid:e6998170-9889-4adf-8b6d-390c0dc5359e>\",\"WARC-IP-Address\":\"104.27.131.87\",\"WARC-Target-URI\":\"http://deffufa.info/fast-facts-worksheets/addition-fast-facts-worksheets-the-best-image-collection/\",\"WARC-Payload-Digest\":\"sha1:RJXDXLPMHE7MCK2RLCZ5HFPZSWFZWNYY\",\"WARC-Block-Digest\":\"sha1:DF5TCDQLCF2QNTOLXX2WVGJWD6VT4N3X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560628000414.26_warc_CC-MAIN-20190626174622-20190626200622-00496.warc.gz\"}"}
|
https://www.elliottwaveforex.com/2016/09/gbpusd-15th-september-2016/
|
[
"Top\n[param_value val=source]\nvalue=\"\"\n[param_value val=medium]\nvalue=\"\"\n[param_value val=adnetwork]\nvalue=\"\"\n[param_value val=creative]\nvalue=\"\"\n[param_value val=keyword]\nvalue=\"\"\n[param_value val=matchtype]\nvalue=\"\"\n[param_value val=adposition]\nvalue=\"\"\n[param_value val=aceid]\nvalue=\"\"\n[param_value val=device]\nvalue=\"\"\n[param_value val=devicemodel]\nvalue=\"\"\n[param_value val=target]\nvalue=\"\"\n[param_value val=placement]\nvalue=\"\"\n[param_value val=permalink]\nvalue=\"gbpusd-15th-september-2016\"\n[param_value val=affid]\nvalue=\"\""
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9296865,"math_prob":0.99928445,"size":7057,"snap":"2019-13-2019-22","text_gpt3_token_len":1736,"char_repetition_ratio":0.18843046,"word_repetition_ratio":0.2513661,"special_character_ratio":0.25251523,"punctuation_ratio":0.09318498,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9985346,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-21T20:57:29Z\",\"WARC-Record-ID\":\"<urn:uuid:90353ff7-85bf-43ec-8721-f6b926abeff1>\",\"Content-Length\":\"61788\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e5b9fd09-2c06-4174-8761-985c7d6d8d9c>\",\"WARC-Concurrent-To\":\"<urn:uuid:fbc249f2-b032-4d3c-b0ce-bbb4dc037651>\",\"WARC-IP-Address\":\"178.128.5.163\",\"WARC-Target-URI\":\"https://www.elliottwaveforex.com/2016/09/gbpusd-15th-september-2016/\",\"WARC-Payload-Digest\":\"sha1:UMVTVC5P3UGKAYDNAYIMITQY4GUPNEXX\",\"WARC-Block-Digest\":\"sha1:PPFBVD4HVRFIXPCGHABHLO6OFRN4OWBM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232256571.66_warc_CC-MAIN-20190521202736-20190521224736-00512.warc.gz\"}"}
|
https://numbermatics.com/n/16677033/
|
[
"# 16677033\n\n## 16,677,033 is an odd composite number composed of three prime numbers multiplied together.\n\nWhat does the number 16677033 look like?\n\nThis visualization shows the relationship between its 3 prime factors (large circles) and 12 divisors.\n\n16677033 is an odd composite number. It is composed of three distinct prime numbers multiplied together. It has a total of twelve divisors.\n\n## Prime factorization of 16677033:\n\n### 3 × 532 × 1979\n\n(3 × 53 × 53 × 1979)\n\nSee below for interesting mathematical facts about the number 16677033 from the Numbermatics database.\n\n### Names of 16677033\n\n• Cardinal: 16677033 can be written as Sixteen million, six hundred seventy-seven thousand and thirty-three.\n\n### Scientific notation\n\n• Scientific notation: 1.6677033 × 107\n\n### Factors of 16677033\n\n• Number of distinct prime factors ω(n): 3\n• Total number of prime factors Ω(n): 4\n• Sum of prime factors: 2035\n\n### Divisors of 16677033\n\n• Number of divisors d(n): 12\n• Complete list of divisors:\n• Sum of all divisors σ(n): 22674960\n• Sum of proper divisors (its aliquot sum) s(n): 5997927\n• 16677033 is a deficient number, because the sum of its proper divisors (5997927) is less than itself. Its deficiency is 10679106\n\n### Bases of 16677033\n\n• Binary: 1111111001111000101010012\n• Base-36: 9XG2X\n\n### Squares and roots of 16677033\n\n• 16677033 squared (166770332) is 278123429683089\n• 16677033 cubed (166770333) is 4638273614898054794937\n• The square root of 16677033 is 4083.7523186403\n• The cube root of 16677033 is 255.4894252819\n\n### Scales and comparisons\n\nHow big is 16677033?\n• 16,677,033 seconds is equal to 27 weeks, 4 days, 30 minutes, 33 seconds.\n• To count from 1 to 16,677,033 would take you about forty-one weeks!\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 16677033 cubic inches would be around 21.3 feet tall.\n\n### Recreational maths with 16677033\n\n• 16677033 backwards is 33077661\n• The number of decimal digits it has is: 8\n• The sum of 16677033's digits is 33\n• More coming soon!"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.854993,"math_prob":0.9664133,"size":2879,"snap":"2020-24-2020-29","text_gpt3_token_len":774,"char_repetition_ratio":0.13913043,"word_repetition_ratio":0.038636364,"special_character_ratio":0.3463008,"punctuation_ratio":0.16635859,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9939464,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-06T11:36:01Z\",\"WARC-Record-ID\":\"<urn:uuid:47902545-0ac1-4ca4-8e33-fc1c99b83ca4>\",\"Content-Length\":\"17614\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:77c13e42-47a3-4bf0-8e0b-48065b688239>\",\"WARC-Concurrent-To\":\"<urn:uuid:f7014331-2f4e-4186-9da7-f4385ba9345a>\",\"WARC-IP-Address\":\"72.44.94.106\",\"WARC-Target-URI\":\"https://numbermatics.com/n/16677033/\",\"WARC-Payload-Digest\":\"sha1:OGWZVKGF2NDUXV72J5B4FL4XUKSQEKSV\",\"WARC-Block-Digest\":\"sha1:MKEDVDCEEKEI6LFTSEV3PXDGCFKB2EXC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655880616.1_warc_CC-MAIN-20200706104839-20200706134839-00205.warc.gz\"}"}
|
https://tex.stackexchange.com/questions/295317/beamer-custom-sidebar-with-navigation-within-subsubsections
|
[
"# Beamer custom sidebar with navigation within subsubsections\n\nI would like to add a left handed sidebar to my beamer presentation slides, however there are some specifics as to how I would like to do this:\n\n• The sidebar would only be present on specified pages (the majority of slides will not have the sidebar)\n• The side bar would not show navigation to any of the sections or subsections for the rest of the presentation, instead it would have links to a series of other slides that would all also have this sidebar.\n• This sidebar would be able to be called multiple times in the presentation where it would follow the same format, but each time called it would be in a different place, referencing slides in that location.\n• I don't want this to effect the top navigation bar at all\n• Ideally, I would be putting everything that the side bar would be referring to in its own subsubsection, but not all subsubsections would have this sidebar\n\nIt might help to know what this is for; I want to create a sidebar that will show steps of how to solve a math problem, where the content in the main part of the slide is the specifics for the particular problem.\n\nThis is some code to provide something to work with:\n\n\\documentclass[14pt]{beamer}\n\\usetheme{Frankfurt}\n\n\\begin{document}\n\\section{Section 1}\n\\subsection{Section 1.1}\n\\begin{frame}\n\\frametitle{1.1.1}\n\\end{frame}\n\\begin{frame}\n\\frametitle{1.1.2}\n\\end{frame}\n\\subsection{Section 1.2}\n\\begin{frame}\n\\frametitle{1.2.1}\n\\end{frame}\n\\begin{frame}\n\\frametitle{1.2.2}\n\\end{frame}\n\\subsection{Section 1.3}\n\\begin{frame}\n\\frametitle{1.3.1}\n\\end{frame}\n\\begin{frame}\n\\frametitle{1.3.2}\n\\end{frame}\n\n\\section{Section 2}\n\\subsection{Section 2.1}\n\\subsubsection{Section 2.1.1}\n\\begin{frame}\n\\frametitle{2.1.1 part A}\nThis would be the start to the problem\n\\end{frame}\n\\begin{frame}\n\\frametitle{2.1.1 part B}\nThis would start the solution\n\\end{frame}\n\\begin{frame}\n\\frametitle{2.1.1 part C}\nThis would have the next step\n\\end{frame}\n\\begin{frame}\n\\frametitle{2.1.1 part D}\nThis next step process would continue here (and to further slides if needed)\n\\end{frame}\n\n\\subsection{Section 2.2}\n\\begin{frame}\n\\frametitle{2.2.1}\n\\end{frame}\n\\begin{frame}\n\\frametitle{2.2.2}\n\\end{frame}\n\n\\end{document}\n\n\nWhere in this document I would like to have the sidebar be in the subsubsection part of this document. This would be a customized sidebar, but first would just like to focus on getting it there.\n\nIdeally, the sidebar in that subsubsection would have text that would link to the various slides in the subsubsection (but not necessarily all slides).\n\n• Please read the following SE question on how to write MWE for your questions: meta.tex.stackexchange.com/questions/228/… Most of the code you posted is completely unnecessary. – Benjamin Feb 22 '16 at 19:02\n• I wanted the complete header that I'm using in case it caused some potential problems with the solution, but your point is well taken. I will edit my post down to not include all of that code. – Jeremie Feb 22 '16 at 19:13\n\nYour problem sounds too specific to me, that a automated solution would be worth it. So why not just add the menu you need manually. You just have to add labels to the frames you want to link to. Then you can link to them from wherever you want – like a custom sidebar menu for example.\n\n\\documentclass{beamer}\n\n\\begin{document}\n\n\\section{Section 2}\n\\subsection{Section 2.1}\n\\subsubsection{Section 2.1.1}\n\\begin{frame}[label=problem]{2.1.1 part A}\n\\begin{minipage}{0.25\\linewidth}\n\\footnotesize\n\\begin{enumerate}\n\\end{enumerate}\n\\end{minipage}%\n\\begin{minipage}{0.75\\linewidth}\nThis would be the start to the problem\n\\end{minipage}\n\\end{frame}\n\n\\begin{frame}[label=solution]{2.1.1 part B}\n\\begin{minipage}{0.25\\linewidth}\n\\footnotesize\n\\begin{enumerate}\n\\end{enumerate}\n\\end{minipage}%\n\\begin{minipage}{0.75\\linewidth}\nThis would start the solution\n\\end{minipage}\n\\end{frame}\n\n\\begin{frame}[label=next]{2.1.1 part C}\n\\begin{minipage}{0.25\\linewidth}\n\\footnotesize\n\\begin{enumerate}\n\\end{enumerate}\n\\end{minipage}%\n\\begin{minipage}{0.75\\linewidth}\nThis would have the next step\n\\end{minipage}%\n\\end{frame}\n\\begin{frame}{2.1.1 part D}\nThis next step process would continue here (and to further slides if needed)\n\\end{frame}\n\n\\subsection{Section 2.2}\n\\begin{frame}{2.2.1}\n\\end{frame}\n\\begin{frame}{2.2.2}\n\\end{frame}\n\n\\end{document}\n\n• Thanks for taking a look at it. I'm wanting to have some of the customization possibilities that come with the sidebar rather than putting it as a minipage, but didn't see how to do that myself. Also, don't know if this happens for you, but when I click on the links to the slides as is coded above, it doesn't take me to that actual slide, but rather half way down that slide (where the text is). Also, I will likely have 20+ of these, rather than a few isolated instances, so automation would be helpful. – Jeremie Feb 22 '16 at 19:09"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8263486,"math_prob":0.8280266,"size":2517,"snap":"2020-45-2020-50","text_gpt3_token_len":706,"char_repetition_ratio":0.22443295,"word_repetition_ratio":0.0,"special_character_ratio":0.25069526,"punctuation_ratio":0.098790325,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9768992,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-21T19:29:20Z\",\"WARC-Record-ID\":\"<urn:uuid:79993fc0-9411-47eb-b1db-606ed15e07a3>\",\"Content-Length\":\"153036\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:75901fde-7998-4bd4-b633-8bf7eafd9f1c>\",\"WARC-Concurrent-To\":\"<urn:uuid:9de3c495-a52b-4a94-b62e-50303dcabee1>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://tex.stackexchange.com/questions/295317/beamer-custom-sidebar-with-navigation-within-subsubsections\",\"WARC-Payload-Digest\":\"sha1:BGRHUOI4W7K3JZJBMMVSAGHWRQRRZBSQ\",\"WARC-Block-Digest\":\"sha1:WAF4BIRKF54FE7MNAFEDYG7FM22VA3GT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107877420.17_warc_CC-MAIN-20201021180646-20201021210646-00488.warc.gz\"}"}
|
https://cm-to-inches.appspot.com/811-cm-to-inches.html
|
[
"Cm To Inches\n\n# 811 cm to in811 Centimeters to Inches\n\ncm\n=\nin\n\n## How to convert 811 centimeters to inches?\n\n 811 cm * 0.3937007874 in = 319.291338583 in 1 cm\nA common question is How many centimeter in 811 inch? And the answer is 2059.94 cm in 811 in. Likewise the question how many inch in 811 centimeter has the answer of 319.291338583 in in 811 cm.\n\n## How much are 811 centimeters in inches?\n\n811 centimeters equal 319.291338583 inches (811cm = 319.291338583in). Converting 811 cm to in is easy. Simply use our calculator above, or apply the formula to change the length 811 cm to in.\n\n## Convert 811 cm to common lengths\n\nUnitLength\nNanometer8110000000.0 nm\nMicrometer8110000.0 µm\nMillimeter8110.0 mm\nCentimeter811.0 cm\nInch319.291338583 in\nFoot26.6076115486 ft\nYard8.8692038495 yd\nMeter8.11 m\nKilometer0.00811 km\nMile0.0050393204 mi\nNautical mile0.0043790497 nmi\n\n## What is 811 centimeters in in?\n\nTo convert 811 cm to in multiply the length in centimeters by 0.3937007874. The 811 cm in in formula is [in] = 811 * 0.3937007874. Thus, for 811 centimeters in inch we get 319.291338583 in.\n\n## 811 Centimeter Conversion Table",
null,
"## Alternative spelling\n\n811 Centimeters to Inch, 811 Centimeters in Inch, 811 Centimeters to Inches, 811 Centimeters in Inches, 811 cm to Inches, 811 cm in Inches, 811 Centimeters to in, 811 Centimeters in in, 811 Centimeter to Inches, 811 Centimeter in Inches, 811 Centimeter to Inch, 811 Centimeter in Inch, 811 cm to in, 811 cm in in"
] |
[
null,
"https://cm-to-inches.appspot.com/image/811.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8257643,"math_prob":0.8636621,"size":1075,"snap":"2022-05-2022-21","text_gpt3_token_len":322,"char_repetition_ratio":0.26237163,"word_repetition_ratio":0.0,"special_character_ratio":0.4,"punctuation_ratio":0.15517241,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97961736,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-16T16:47:14Z\",\"WARC-Record-ID\":\"<urn:uuid:c3033f04-39df-4ccc-92c1-fa5327b90999>\",\"Content-Length\":\"28746\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0a31c8bd-29a6-4b0f-bb3c-665aac4239c1>\",\"WARC-Concurrent-To\":\"<urn:uuid:865adc30-817d-4143-8fce-f887fc8ea6ae>\",\"WARC-IP-Address\":\"172.253.63.153\",\"WARC-Target-URI\":\"https://cm-to-inches.appspot.com/811-cm-to-inches.html\",\"WARC-Payload-Digest\":\"sha1:WOAG7IPNAWM7Z3P3JCM2FP3WMLJG3IL6\",\"WARC-Block-Digest\":\"sha1:XRJT4NUYKQABROE5ZBQVE22NELCFPK7N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662510138.6_warc_CC-MAIN-20220516140911-20220516170911-00301.warc.gz\"}"}
|
https://schollz.com/blog/sampler/
|
[
"/blog",
null,
"Making a sample player in SuperCollider\n\nHow to make a versatile, feature-packed, cross-fading sampler engine in SuperCollider in just a seven steps.\n\nSuperCollider is a free platform for audio synthesis and algorithm composition. It really excels at real-time analysis, synthesis and processing and provides a framework for seamless combination of audio techniques like additive and subtractive synthesis (as explored in my previous tutorial on drones) or be used for sophisticated sampling+splicing, the focus of this tutorial.\n\nA sampler+splicer is useful when you have an audiofile and you want to cut it up into pieces and play it back in specific order. You can do this and change the tempo of a song by playing back snippets faster, or shuffle drum breaks to make new beats, or map specific sounds from a single audio file.\n\nBefore you begin\n\nBefore starting, make sure you have SuperCollider and plugins (if you want).\n\nIf you have these basic things installed, you are good to go. Feel free to do a SuperCollider tutorial if you want, but I’ll assume you don’t know how to use it.\n\nWith SuperCollider installed, you will need to run the program and then start the server using Ctl+B.\n\n1. Load a buffer with audio\n\nWe are going to start playing with a simple piano loop that I got from the radio:\n\nLet’s first load this into SuperCollider, by running the following lines:\n\n(\n)\n\n2. Use PlayBuf to play sample\n\nAnd now lets play it back using the simple PlayBuf “UGen”:\n\n(\nSynthDef(\"PlayBufPlayer\", {\narg out = 0, bufnum = 0;\nvar snd;\nsnd=PlayBuf.ar(2, bufnum, BufRateScale.kr(bufnum), doneAction: Done.freeSelf);\nOut.ar(out,snd)\n}).play(s, [\\out, 0, \\bufnum, b]);\n)\n\nWhen running that code you should immediately hear it play back!\n\nWhile this already works as a sampler (it plays back a sample), it actually won’t let us set the endpoints so we can splice the sample. Let’s do that next.\n\n3. Use BufRd + Phasor to precisely play sample\n\nIn order to precisely control the position of playback we must use something called a Phasor. A Phasor is basically a sawtooth-like signal that increments at a specific rate. It is really useful as a position index, to set the position of playback, because you can control its start and end poitns and the rate.\n\nHere is what a Phasor will look like:",
null,
"And instead of going from 0-100 we can change it to whatever we want while also changing the rate:",
null,
"We will introduce a lot of code to do this, but I’ll go through it piece by piece:\n\n(\nx=SynthDef(\"PlayBufPlayer\", {\narg out=0, bufnum=0, rate=1, start=0, end=1;\nvar snd,pos,frames;\n\nrate = rate*BufRateScale.kr(bufnum);\nframes = BufFrames.kr(bufnum);\n\npos=Phasor.ar(\nrate:rate,\nstart:start*frames,\nend:end*frames,\nresetPos:start*frames,\n);\n\nsnd=BufRd.ar(\nnumChannels:2,\nbufnum:bufnum,\nphase:pos,\nloop:0,\ninterpolation:4,\n);\nOut.ar(out,snd)\n}).play(s, [\\out, 0, \\bufnum, b]);\n)\n\nThe rate is now an argument and default is 1. However, it gets modulated by BufRateScale.kr(bufnum) where bufnum is a reference to the audio file. This modulation is a scale based on the sample rate of the audio file and the sample rate of the server. In the case the two sample rates don’t match, then you do need to change the speed you playback a sample to make sure it is exactly the same pitch when played at the other sample rate at a rate of 1.\n\nThe Phasor has start and end points and a rate and a resetPos which is the position it resets. The Phasor takes inputs in numbers of frames so we multiple the start and end points (which I am denoting to always be between 0 and 1) by the number of frames.\n\nThe BufRd is where the playback happens. We set the position of playback using the phase parameter. Notice we set loop to 0, but in actuality, because we are using a Phasor this will be ignored.\n\nWe can now change the start and end positions by running this command after running the SynthDef above:\n\nx.set(\\start,0.5,\\end,0.6);\n\nOne thing you might notice is that you cannot get this sample to reset if you run that command more than once. Resetting is a really useful thing, and we can fix this SynthDef to allow that.\n\n4. Use trigger to allow resetting sample\n\nThis fix is only one line, and adding a new argument, t_trig. This is a special argument and when it goes from 0 to 1 it can cause a change in a UGen. In this case we will use it to cause a change in Phasor, which will make it reset.\n\n(\nx=SynthDef(\"PlayBufPlayer\", {\narg out=0, bufnum=0, rate=1, start=0, end=1, t_trig=0; // NEW t_trig!\nvar snd,pos,frames;\n\nrate = rate*BufRateScale.kr(bufnum);\nframes = BufFrames.kr(bufnum);\n\npos=Phasor.ar(\ntrig:t_trig, // NEW!\nrate:rate,\nstart:start*frames,\nend:end*frames,\nresetPos:start*frames,\n);\n\nsnd=BufRd.ar(\nnumChannels:2,\nbufnum:bufnum,\nphase:pos,\nloop:0,\ninterpolation:4,\n);\nOut.ar(out,snd)\n}).play(s, [\\out, 0, \\bufnum, b]);\n)\n\nNow you can send various commands to this SynthDef which can cause it to reset to the new start position:\n\nx.set(\\t_trig,1,\\start,0,\\end,1)\nx.set(\\t_trig,1,\\start,0.5,\\end,1)\n\nYou can hear in that audio that I reset the position multiple times.\n\nOne problem that persists though is that, as mentioned earlier, we are using a Phasor which loops forever and overrides the loop parameter of the BufRd UGen. It would be better to have an option to set the loops to any number you want.\n\n5. Use an envelope, Env, to control looping\n\nIt turns out we can do a little trick to get a precise loop - we can use an envelope. An envelope is essentially a curve in time that we can multiple by the output amplitude. The function of the curve is to shape the amplitude, and in this case we will shape it so it turns on and then turns off after a certain amount of time.\n\nA basic envelope is generated like this:\n\n({\nEnvGen.ar(\nEnv.new(\nlevels: [0,1,1,0],\ntimes: [0,1,0],\n),\n)\n}.plot(2);)\n\nwhich generates an envelope that lasts 1 second and then goes to 0. It looks like this:",
null,
"There are all sorts of envelopes you can make. We can make this one fancier by having it fade in/out a little smoother by adding some time to the “attack” and “release” part of the envelope:\n\n(\n{ EnvGen.ar(\nEnv.new(\nlevels: [0,1,1,0],\ntimes: [0.2,1-0.4,0.2],\ncurve:\\sine,\n),\n)\n}.plot(2);\n)",
null,
"Great! Well all we need to do to preserve a loop is to calculate how long the duration of the envelope should be. This involves a little math, but it should be related to the number of frames, the rate (1/2 the rate = twice the time), the sample rate, and the number of loops:\n\nduration = frames*(end-start)/rate.abs/s.sampleRate*loops\n\nWe then just need to trigger the envelope when we trigger our sample and voila!\n\n(\nx=SynthDef(\"PlayBufPlayer\", {\narg out=0, bufnum=0, rate=1, start=0, end=1, t_trig=1,\nloops=1; // NEW\nvar snd,pos,frames,duration,env;\n\nrate = rate*BufRateScale.kr(bufnum);\nframes = BufFrames.kr(bufnum);\nduration = frames*(end-start)/rate/s.sampleRate*loops; // NEW\n\n// envelope to clamp looping\nenv=EnvGen.ar(\nEnv.new(\nlevels: [0,1,1,0],\ntimes: [0,duration-0.01,0.01],\ncurve:\\sine,\n),\ngate:t_trig,\n);\n\npos=Phasor.ar(\ntrig:t_trig,\nrate:rate,\nstart:start*frames,\nend:end*frames,\nresetPos:start*frames,\n);\n\nsnd=BufRd.ar(\nnumChannels:2,\nbufnum:bufnum,\nphase:pos,\ninterpolation:4,\n);\n\nsnd = snd * env;\n\nOut.ar(out,snd)\n}).play(s, [\\out, 0, \\bufnum, b]);\n)\n\nNow we can set the loop number, and reset the sample, and control the start and stop positions:\n\nx.set(\\t_trig,1,\\start,0.0,\\end,0.15,\\loops,1)\nx.set(\\t_trig,1,\\start,0.5,\\end,0.52,\\loops,6)\n\nThis sounds like the following:\n\nYou can see that loops stop and stay stopped! And you can make it loop as many times as you want.\n\nBut what happens if we reverse? If you change the rate to -1 it actually won’t play:\n\nx.set(\\t_trig,1,\\start,0.5,\\end,0.6,\\loops,3,\\rate,-1)\n\nIts because the start and end points need to swap. If we do that, then we can succesfully play in reverse:\n\nx.set(\\t_trig,1,\\start,0.6,\\end,0.5,\\loops,3,\\rate,-1)\n\nBut, lets alter the code above so that it works in reverse without having the start and end points switching around!\n\n6. Automatically swap start/end points when reversing\n\nTo swap the start/end points we need to check the rate and add some logic about whether the rate is positive or negative. You can’t really use if-statements in SuperCollider (well you can but its weird), but we can do this easily with math. For example, the start parameter of the Phasor can calculate a binary whether the rate is positive or negative and then make a sum based on it:\n\nstart:(((rate>0)*start)+((rate<0)*end))*frames\n\nIt looks complicated but its quite simple. If the rate>0 then the second part in the parentheses is 0 and its just start. If the rate<0 then the first part is 0 and then it just switches to end.\n\nThe final SynthDef looks like this:\n\n(\nx=SynthDef(\"PlayBufPlayer\", {\narg out=0, bufnum=0, rate=1, start=0, end=1, t_trig=1,\nloops=1;\nvar snd,pos,frames,duration,env;\n\nrate = rate*BufRateScale.kr(bufnum);\nframes = BufFrames.kr(bufnum);\nduration = frames*(end-start)/rate.abs/s.sampleRate*loops; // use rate.abs instead now\n\n// envelope to clamp looping\nenv=EnvGen.ar(\nEnv.new(\nlevels: [0,1,1,0],\ntimes: [0,duration,0],\n),\ngate:t_trig,\n);\n\npos=Phasor.ar(\ntrig:t_trig,\nrate:rate,\nstart:(((rate>0)*start)+((rate<0)*end))*frames,\nend:(((rate>0)*end)+((rate<0)*start))*frames,\nresetPos:(((rate>0)*start)+((rate<0)*end))*frames,\n);\n\nsnd=BufRd.ar(\nnumChannels:2,\nbufnum:bufnum,\nphase:pos,\ninterpolation:4,\n);\n\nsnd = snd * env;\n\nOut.ar(out,snd)\n}).play(s, [\\out, 0, \\bufnum, b]);\n)\n\nAnd when we use the problematic statement above, we can see that it just works:\n\nx.set(\\t_trig,1,\\start,0.5,\\end,0.6,\\loops,3,\\rate,-1)\n\nOkay, now one more thing. You may have noticed in playing around that there is an annoying “click” or “pop” when you reset the sample. For example, try to send the following a bunch of times really fast you’ll hear an audible noise artifact from the switching:\n\nx.set(\\t_trig,1,\\start,0.2,\\end,0.6,\\loops,1,\\rate,1)\n\nIt’s unpleasant right? Well we can make one more improvement to remove this type of thing.\n\n7. Preventing switching pops\n\nThe main problem of pops caused by switching is that there isn’t a smooth transition to the next position. The smooth transition we expect actually needs to come from the audio itself and not the position. To make a smooth transition then, we need to crossfade between the old loop and the new loop.\n\nDoing this is not nearly as hard as it seems at first. We already have one loop playing. We need to make another loop. Then we just need to make a new trigger, based on t_trig which we already use, that flips between triggering the two loops. We can use a special UGen for this called ToggleFF and then another UGen called Latch which will allow us to change only one of the loops at a time, alternating between the two.\n\nBelow is the new code. We still have the same arguments, but we have new variables for the two loops (startA+B, endA+B, crossfade, and aORB which is the new trigger). The crossfade is doing the major work here, we can create the audio crossfade by using something called Lag which will transition between the two values slowly.\n\nFor example, this is a 50 ms crossfade:\n\nThis is what the new code ends up being:\n\n(\nx=SynthDef(\"PlayBufPlayer\", {\narg out=0, bufnum=0, rate=1, start=0, end=1, t_trig=0,\nloops=1;\nvar snd,snd2,pos,pos2,frames,duration,env;\n\n// latch to change trigger between the two\naOrB=ToggleFF.kr(t_trig);\nstartA=Latch.kr(start,aOrB);\nendA=Latch.kr(end,aOrB);\nstartB=Latch.kr(start,1-aOrB);\nendB=Latch.kr(end,1-aOrB);\n\nrate = rate*BufRateScale.kr(bufnum);\nframes = BufFrames.kr(bufnum);\nduration = frames*(end-start)/rate.abs/s.sampleRate*loops;\n\n// envelope to clamp looping\nenv=EnvGen.ar(\nEnv.new(\nlevels: [0,1,1,0],\ntimes: [0,duration-0.05,0.05],\n),\ngate:t_trig,\n);\n\npos=Phasor.ar(\ntrig:aOrB,\nrate:rate,\nstart:(((rate>0)*startA)+((rate<0)*endA))*frames,\nend:(((rate>0)*endA)+((rate<0)*startA))*frames,\nresetPos:(((rate>0)*startA)+((rate<0)*endA))*frames,\n);\nsnd=BufRd.ar(\nnumChannels:2,\nbufnum:bufnum,\nphase:pos,\ninterpolation:4,\n);\n\npos2=Phasor.ar(\ntrig:(1-aOrB),\nrate:rate,\nstart:(((rate>0)*startB)+((rate<0)*endB))*frames,\nend:(((rate>0)*endB)+((rate<0)*startB))*frames,\nresetPos:(((rate>0)*startB)+((rate<0)*endB))*frames,\n);\nsnd2=BufRd.ar(\nnumChannels:2,\nbufnum:bufnum,\nphase:pos2,\ninterpolation:4,\n);\n\n}).play(s, [\\out, 0, \\bufnum, b]);\n)\n\nAnd we can try this out on the problematic loop from before:\n\nx.set(\\t_trig,1,\\start,0.2,\\end,0.6,\\loops,1,\\rate,1)\n\nEven though it is triggered a bunch of times, it sounds smooth! This is because, underneath it all, its switching back and forth between loops while crossfading them simultaneously.\n\n8. COOL, but now what?\n\nNow you can branch off with this SynthDef and do all sorts of things. You can add effects to it (maybe I can add more about this). One thing I like to do is that you can immediately do “onset detection”, gather splices, and pattern them!\n\nHere’s a synthdef I cobbled together to determine splicing from arbitrary samples:\n\n(\nSynthDef.removeAt(\"OnsetDetection\");\n\no = OSCFunc({ arg msg, time;\n[time, msg].postln;\nif (msg-~pos1.last>(0.15*s.sampleRate/b.numFrames),{\n},{});\n\nSynthDef(\"OnsetDetection\", {\narg bufnum, out, threshold;\nvar sig, chain, onsets, pips, pos, env, speedup=1;\n\nenv=EnvGen.ar(\nEnv.new(\nlevels: [0,1,1,0],\ntimes: [0,BufDur.kr(bufnum)/speedup,0],\ncurve:\\sine,\n),\ndoneAction: Done.freeSelf\n);\n\npos=Phasor.ar(0, BufRateScale.kr(bufnum)*speedup, 0, BufFrames.kr(bufnum),0);\nsig = BufRd.ar(2, bufnum, pos,0);\n\nchain = FFT(LocalBuf(512), sig+sig);\n\nonsets = Onsets.kr(chain, threshold, \\rcomplex,mingap:160);\n\n// You'll hear percussive \"ticks\" whenever an onset is detected\npips = WhiteNoise.ar(EnvGen.kr(Env.perc(0.001, 0.1, 0.2), onsets));\nSendTrig.kr(onsets,0,Clip.kr((pos-300)/BufFrames.kr(bufnum),0,1));\nOut.ar(out,Pan2.ar(sig, -0.75, 0.2) + Pan2.ar(pips, 0.75, 1));\n)\n\nOnce defined, you can run it with the following:\n\n(\n~pos1=List.new();\naction:{\nSynth(\"OnsetDetection\",[\\out,0,\\bufnum,b.bufnum,\\threshold,2.0]); // CHANGE THRESHOLD TO SOMETHING THAT WORKS\n});\n)\n\nMake sure you change the threshold (above its 2.0) to something where you hear a “click” on the appropriate onset. For example, using the piano from above:\n\nYou can hear it automatically detect onsets. And now you can playback individual splices:\n\nf = {arg i;x.set(\\t_trig,1,\\start,~pos1[i],\\end,~pos1[i+1]);}\nf.value(0); // plays splice \"0\"\nf.value(1); // plays splice \"1\"\n\nOr visualize them:\n\ng = {arg i; b.loadToFloatArray(~pos1[i]*b.numFrames,(~pos1[i+1]-~pos1[i])*b.numFrames,{arg array; a=array; {~temp=a.plot;~temp.setProperties(\\gridOnX,false,\\gridOnY,false)}.defer; })};\ng.value(0);\ng.value(1); // visualize it",
null,
"Or sequence them:\n\n(\n~player=[1,0,2,0,2,0,0,0,3,3,3,3,4,0,3,0];\ninf.do({ arg i;\nvar toPlay;\n0.125.wait;\ntoPlay = ~player[i%~player.size].postln;\nif (toPlay>0,{\ntoPlay.postln;\nx.set(\\t_trig,1,\\start,~pos1[toPlay-1],\\end,~pos1[toPlay],\\loops,1);\n},{});\n});\n}).play;\n)\n\nPlus much more…but you’ve had enough right?\n\nMade by Zack, filed in Blog. 2019."
] |
[
null,
"https://schollz.com/img/sc2/header.png",
null,
"https://schollz.com/img/sc2/phasor1.png",
null,
"https://schollz.com/img/sc2/phasor2.png",
null,
"https://schollz.com/img/sc2/env1.png",
null,
"https://schollz.com/img/sc2/env2.png",
null,
"https://schollz.com/img/sc2/82.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.80084586,"math_prob":0.9873308,"size":15514,"snap":"2022-05-2022-21","text_gpt3_token_len":4596,"char_repetition_ratio":0.10973565,"word_repetition_ratio":0.07702764,"special_character_ratio":0.28342143,"punctuation_ratio":0.23869753,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9757456,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-23T12:11:23Z\",\"WARC-Record-ID\":\"<urn:uuid:f43362dc-1601-4096-8600-422be29cbeed>\",\"Content-Length\":\"38578\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8fd66d91-bf77-4b5c-a9b0-9d00a2522a93>\",\"WARC-Concurrent-To\":\"<urn:uuid:64791242-5ea4-4049-bd9a-a4680774a9da>\",\"WARC-IP-Address\":\"142.93.177.120\",\"WARC-Target-URI\":\"https://schollz.com/blog/sampler/\",\"WARC-Payload-Digest\":\"sha1:QMDPO5FSXKHEOVGZOBLBWBJPIRD7FQW3\",\"WARC-Block-Digest\":\"sha1:UR7ZIBWJ6MZNN4GH4JL76BSZX3WX4KQ5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304261.85_warc_CC-MAIN-20220123111431-20220123141431-00379.warc.gz\"}"}
|
https://docs.splunk.com/Documentation/SplunkCloud/7.0.13/Search/Usethestatscommandandfunctions
|
[
"",
null,
"Download topic as PDF\n\n# Use the stats command and functions\n\nThis topic discusses how to use the statistical functions with the transforming commands `chart`, `timechart`, `stats`, `eventstats`, and `streamstats`.\n\n## About the stats commands and functions\n\nThe `stats`, `streamstats`, and `eventstats` commands each enable you to calculate summary statistics on the results of a search or the events retrieved from an index. The `stats` command works on the search results as a whole. The `streamstats` command calculates statistics for each event at the time the event is seen, in a streaming manner. The `eventstats` command calculates statistics on all search results and adds the aggregation inline to each event for which it is relevant. See more about the differences between these commands in the next section.\n\nThe `chart command` returns your results in a data structure that supports visualization as a chart (such as a column, line, area, and pie chart). You can decide what field is tracked on the x-axis of the chart. The `timechart command` returns your results formatted as a time-series chart, where your data is plotted against an x-axis that is always a time field. Read more about visualization features and options in the Visualization Reference of the Data Visualization Manual.\n\nThe `stats`, `chart`, and `timechart` commands (and their related commands `eventstats` and `streamstats`) are designed to work in conjunction with statistical functions. The list of statistical functions lets you count the occurrence of a field and calculate sums, averages, ranges, and so on, of the field values.\n\nFor the list of statistical functions and how they're used, see \"Statistical and charting functions\" in the Search Reference.\n\n## Stats, eventstats, and streamstats\n\nThe `eventstats` and `streamstats` commands are variations on the `stats` command.\n\nThe `stats` command works on the search results as a whole and returns only the fields that you specify. For example, the following search returns a table with two columns (and 10 rows).\n\n`sourcetype=access_* | head 10 | stats sum(bytes) as ASumOfBytes by clientip`\n\nThe `ASumOfBytes` and `clientip` fields are the only fields that exist after the stats command. For example, the following search returns empty cells in the `bytes` column because it is not a result field.\n\n`sourcetype=access_* | head 10 | stats sum(bytes) as ASumOfBytes by clientip | table bytes, ASumOfBytes, clientip`\n\nTo see more fields other than `ASumOfBytes` and `clientip` in the results, you need to include them in the stats command. Also, if you want to perform calculations on any of the original fields in your raw events, you need to do that before the stats command.\n\nThe `eventstats` command computes the same statistics as the `stats` command, but it also aggregates the results to the original raw data. When you run the following search, it returns an events list instead of a results table, because the eventstats command does not change the raw data.\n\n`sourcetype=access_* | head 10 | eventstats sum(bytes) as ASumOfBytes by clientip`\n\nYou can use the `table` command to format the results as a table that displays the fields you want. Now, you can also view the values of `bytes` (or any of the original fields in your raw events) in your results.\n\n`sourcetype=access_* | head 10 | eventstats sum(bytes) as ASumOfBytes by clientip | table bytes, ASumOfBytes, clientip`\n\nThe `streamstats` command also aggregates the calculated statistics to the original raw event, but it does this at the time the event is seen. To demonstrate this, include the `_time` field in the earlier search and use `streamstats`.\n\n`sourcetype=access_* | head 10 | sort _time | streamstats sum(bytes) as ASumOfBytes by clientip | table _time, clientip, bytes, ASumOfBytes`\n\nInstead of a total sum for each `clientip` (as returned by `stats` and `eventstats`), this search calculates a sum for each event based on the time that it is seen. The `streamstats` command is useful for reporting on events at a known time range.\n\n## Examples\n\n### Example 1\n\nThis example creates a chart of how many new users go online each hour of the day.\n\n`... | sort _time | streamstats dc(userid) as dcusers | delta dcusers as deltadcusers | timechart sum(deltadcusers)`\n\nThe `dc` (or `distinct_count`) function returns a count of the unique values of `userid` and renames the resulting field `dcusers`.\n\nIf you don't rename the function, for example \"dc(userid) as dcusers\", the resulting calculation is automatically saved to the function call, such as \"dc(userid)\".\n\nThe `delta` command is used to find the difference between the current and previous `dcusers` value. Then, the sum of this delta is charted over time.\n\n### Example 2\n\nThis example calculates the median for a field, then charts the count of events where the field has a value less than the median.\n\n`... | eventstats median(bytes) as medbytes | eval snap=if(bytes>=medbytes, bytes, \"smaller\") | timechart count by snap`\n\nEventstats is used to calculate the median for all the values of bytes from the previous search.\n\n### Example 3\n\nThis example calculates the standard deviation and variance of calculated fields.\n\n`sourcetype=log4j ERROR earliest=-7d@d latest=@d | eval warns=errorGroup+\"-\"+errorNum | stats count as Date_Warns_Count by date_mday,warns | stats stdev(Date_Warns_Count), var(Date_Warns_Count) by warns`\n\nThis search returns errors from the last 7 days and creates the new field, warns, from extracted fields errorGroup and errorNum. The stats command is used twice. First, it calculates the daily count of warns for each day. Then, it calculates the standard deviation and variance of that count per warns.\n\n### Example 4\n\nYou can use the calculated fields as filter parameters for your search.\n\n`sourcetype=access_* | eval URILen = len(useragent) | eventstats avg(URILen) as AvgURILen, stdev(URILen) as StdDevURILen| where URILen > AvgURILen+(2*StdDevURILen) | chart count by URILen span=10 cont=true`\n\nIn this example, eventstats is used to calculate the average and standard deviation of the URI lengths from `useragent`. Then, these numbers are used as filters for the retrieved events.\n\n PREVIOUS About calculating statistics NEXT Use stats with eval expressions and functions\n\nThis documentation applies to the following versions of Splunk Cloud: 7.0.11, 7.0.13, 7.1.3, 7.1.6, 7.2.4, 7.2.6, 7.2.7, 7.2.8, 7.2.9, 7.2.10, 8.0.2001, 8.0.2003, 8.0.2004, 8.0.2006"
] |
[
null,
"https://docs.splunk.com/skins/OxfordComma/images/acrobat-logo.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.823886,"math_prob":0.7984679,"size":6520,"snap":"2020-34-2020-40","text_gpt3_token_len":1567,"char_repetition_ratio":0.15699816,"word_repetition_ratio":0.088207096,"special_character_ratio":0.2184049,"punctuation_ratio":0.12510288,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97500443,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-14T12:06:05Z\",\"WARC-Record-ID\":\"<urn:uuid:c3ef87f2-3394-402e-bada-f5935294243c>\",\"Content-Length\":\"123380\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0e9936b7-248c-4743-a72f-32751e19051b>\",\"WARC-Concurrent-To\":\"<urn:uuid:a5ed080a-ca94-4ef5-be39-b7a317b8182c>\",\"WARC-IP-Address\":\"54.200.42.32\",\"WARC-Target-URI\":\"https://docs.splunk.com/Documentation/SplunkCloud/7.0.13/Search/Usethestatscommandandfunctions\",\"WARC-Payload-Digest\":\"sha1:JBN72HZXYB4IXB2ATKCVALPGVVOSTMFD\",\"WARC-Block-Digest\":\"sha1:CFMYVVL6PPEET7KOWCAD6BTLQ3D2IKV2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439739211.34_warc_CC-MAIN-20200814100602-20200814130602-00121.warc.gz\"}"}
|
https://ecstasyshots.wordpress.com/2017/02/26/legendre-differential-equation2-a-friendly-introduction/
|
[
"# Legendre Differential Equation(#2): A friendly introduction\n\nNow there is something about the Legendre differential equation that drove me crazy. What is up with the l(l+1) !!!",
null,
"$(1-x^2)y^{''} -2xy^{'} + l(l+1)y = 0$\n\nTo understand why let’s take this form of the LDE and arrive at the above:",
null,
"$(1-x^2)y^{''} -2xy^{'} + \\lambda y = 0$",
null,
"$y = \\sum\\limits_{n=0}^{\\infty} a_n x^n$\n\nIf we do a power series expansion and following the same steps as the previous post, we end up with the following recursion relation.",
null,
"$(n+2)(n+1)a_{n+2} = (\\lambda -n(n+1))a_n$\n\nor",
null,
"$a_{n+2} = a_n \\frac{\\lambda - n(n+1)}{(n+1)(n+2)}$\n\nHere’s the deal: We want a convergent solution for our differential solution. This means that as",
null,
"$n \\rightarrow l , a_{n+2} \\rightarrow 0$.\n\nHence we obtain that",
null,
"$\\lambda = l(l+1)$"
] |
[
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null,
"https://s0.wp.com/latex.php",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.91312534,"math_prob":0.9999757,"size":590,"snap":"2022-40-2023-06","text_gpt3_token_len":132,"char_repetition_ratio":0.102389075,"word_repetition_ratio":0.0,"special_character_ratio":0.21525423,"punctuation_ratio":0.10619469,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999938,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-07T15:25:55Z\",\"WARC-Record-ID\":\"<urn:uuid:cb31d6f7-7f77-491b-be42-00ec5739497a>\",\"Content-Length\":\"88100\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4477f88e-5024-4727-9e17-1cc5c7f52874>\",\"WARC-Concurrent-To\":\"<urn:uuid:8410fd1f-10db-41e1-b76f-8cade0afeb5c>\",\"WARC-IP-Address\":\"192.0.78.12\",\"WARC-Target-URI\":\"https://ecstasyshots.wordpress.com/2017/02/26/legendre-differential-equation2-a-friendly-introduction/\",\"WARC-Payload-Digest\":\"sha1:KXTOD5V5QBHBTBTIVO2YTYCF7IFYBIPM\",\"WARC-Block-Digest\":\"sha1:NEBNUAT5GSL4R24R7LUTTCU3AJVD3VIH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500619.96_warc_CC-MAIN-20230207134453-20230207164453-00436.warc.gz\"}"}
|
https://www.scribd.com/document/204564200/UKMT-Competition-2013
|
[
"You are on page 1of 2\n\n# A 40\n\nB 64\n\nC 108\n\nD 132\n\nE 16\n\n20. The ratio of two positive numbers equals the ratio of their sum to their difference. What is this ratio? A 21.\n\nUKMT\nUK SENIOR MATHEMATICAL CHALLENGE Thursday 7 November 2013 Organised by the United Kingdom Mathematics Trust and supported by\n\n(1+ 3):2\n\n2:1\n\n(1+ 5):2\n\n(2+ 2):1\n\n(1+ 2):1\n\nThe shaded design shown in the diagram is made by drawing eight circular arcs, all with the same radius. The centres of four arcs are the vertices of the square; the centres of the four touching arcs are the midpoints of the sides of the square. The diagonals of the square have length 1. What is the total length of the border of the shaded design? 5 7 A 2 B C 3 D E 4 2 2 22. Consider numbers of the form 10n + 1, where n is a positive integer. We shall call such a number grime if it cannot be expressed as the product of two smaller numbers, possibly equal, both of which are of the form 10k + 1, where k is a positive integer. How many grime numbers are there in the sequence 11, 21, 31, 41, ..., 981, 991? A 0 B 8 C 87 D 92 E 99\nP W T V S\nx 4 4 O 5 8 R 10\n\n23. PQRS is a square. The points T and U are the midpoints of QR and RS respectively. The line QS cuts PT and PU at W and V respectively. What fraction of the area of the square PQRS is the area of the pentagon RTWVU ? 1 2 3 5 4 B C D E 3 5 7 12 15 24. The diagram shows two straight lines PR and QS crossing P at O. What is the value of x? S A 7 2 B 2 29 C 14 2 D 7(1+ 13) E 9 2 A 25.\np q r s X t Y u\n\nR\nQ\n\nChallengeborough's underground train network consists of six lines, p, q, r , s, t , u, as shown. Wherever two lines meet there is a station which enables passengers to change lines. On each line, each train stops at every station. Jessica wants to travel from station X to station Y . She does not want to use any line more than once, nor return to station X after leaving it, nor leave station Y having reached it. How many different routes, satisfying these conditions, can she choose? A 9 B 36 C 41 D 81 E 720\n\nhttp://www.ukmt.org.uk\n\nMT UK\n\n19. The 16 small squares shown in the diagram each have a side length of 1 unit. How many pairs of vertices are there in the diagram whose distance apart is an integer number of units?\n\nUK MT\n\n1. Which of these is the largest number? A 2+0+1+3 B 20+1+3 C 2+01+3 D 2+0+13 E 2013 2. Little John claims he is 2m 8cm and 3mm tall. What is this height in metres? A 2.83m A 0 B 2.803m B 1 C 2.083m C 4 D 2.0803m D 5 E 2.0083m E 6\nT\n\n11. The diagram shows a circle with centre O and a triangle OPQ. Side PQ is a tangent to the circle. The area of the circle is equal to the area of the triangle. What is the ratio of the length of PQ to the P circumference of the circle? A 1:1 B 2:3 C 2: D 3:2\n\nO Q\n\nE :2\n\n3. What is the tens digit of 20132 2013? 4. A route on the 3 3 board shown consists of a number of steps. Each step is from one square to an adjacent square of a different colour. How many different routes are there from square S to square T which pass through every other square exactly once? A 0 B 1 C 2 D 3 E 4\n\n12. As a special treat, Sammy is allowed to eat five sweets from his very large jar which contains many sweets of each of three flavours Lemon, Orange and Strawberry. He wants to eat his five sweets in such a way that no two consecutive sweets have the same flavour. In how many ways can he do this? A 32 B 48 C 72 D 108 E 162 13. Two entrants in a school's sponsored run adopt different tactics. Angus walks for half the time and runs for the other half, whilst Bruce walks for half the distance and runs for the other half. Both competitors walk at 3mph and run at 6mph. Angus takes 40 minutes to complete the course. How many minutes does Bruce take? A 30 B 35 C 40 D 45 E 50\nQ P\n\n5. The numbers x and y satisfy the equations x (y + 2) = 100 and y (x + 2) = 60. What is the value of x y? A 60 B 50 C 40 D 30 E 20 6. Rebecca went swimming yesterday. After a while she had covered one fifth of her intended distance. After swimming six more lengths of the pool, she had covered one quarter of her intended distance. How many lengths of the pool did she intend to complete? A 40 B 72 C 80 D 100 E 120 7. In a ninety nine shop, all items cost a number of pounds and 99 pence. Susanna spent 65.76. How many items did she buy? A 23 B 24 C 65 D 66 E 76\nx 4x\n\n14. The diagram shows a rectangle PQRS in which PQ : QR = 1 : 2. The point T on PR is such that ST is perpendicular to PR. What is the ratio of the area of the triangle RST to the area of the rectangle PQRS? A 1:4 2 D 1 : 10 A 0 B 1 C 2 B 1:6 E 1 : 12 D 3 C 1:8\n\nT R S\n\n15. For how many positive integers n is 4n 1 a prime number? E infinitely many\n\n8. The right-angled triangle shown has a base which is 4 times its height. Four such triangles are placed so that their hypotenuses form the boundary of a large square as shown. What is the side-length of the shaded square in the diagram? A 2x B 2 2x C 3x D 2 3x E 15x\n\n16. Andrew states that every composite number of the form 8n + 3, where n is an integer, has a prime factor of the same form. Which of these numbers is an example showing that Andrew's statement is false? A 19 B 33 C 85 D 91 E 99\nP U S Q R T\n\n9. According to a headline, Glaciers in the French Alps have lost a quarter of their area in the past 40 years. What is the approximate percentage reduction in the length of the side of a square when it loses one quarter of its area, thereby becoming a smaller square? A 13% B 25% C 38% D 50% E 65% 10. Frank's teacher asks him to write down five integers such that the median is one more than the mean, and the mode is one greater than the median. Frank is also told that the median is 10. What is the smallest possible integer that he could include in his list? A 3 B 4 C 5 D 6 E 7\n\n17. The equilateral triangle PQR has side-length 1. The lines PT and PU trisect the angle RPQ, the lines RS and RT trisect the angle QRP and the lines QS and QU trisect the angle PQR. What is the side-length of the equilateral triangle STU ? cos 80 A B 1 C cos2 20 3 cos 20 cos 20 D 1 E cos20 cos80 6\n\n18. The numbers 2, 3, 12, 14, 15, 20, 21 may be divided into two sets so that the product of the numbers in each set is the same. What is this product? A 420 B 1260 C 2520 D 6720 E 6350400"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9332358,"math_prob":0.98874784,"size":7963,"snap":"2020-10-2020-16","text_gpt3_token_len":2289,"char_repetition_ratio":0.123005405,"word_repetition_ratio":0.024301337,"special_character_ratio":0.29687303,"punctuation_ratio":0.11499735,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.98960716,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-17T01:31:05Z\",\"WARC-Record-ID\":\"<urn:uuid:97d296ab-6d48-4ec6-845b-967738fa79ac>\",\"Content-Length\":\"308842\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:93fa607a-9fa3-45b5-9f70-37202f1a9dc6>\",\"WARC-Concurrent-To\":\"<urn:uuid:6f4a4425-38b2-409d-ab4b-0deb3f400a9f>\",\"WARC-IP-Address\":\"151.101.250.152\",\"WARC-Target-URI\":\"https://www.scribd.com/document/204564200/UKMT-Competition-2013\",\"WARC-Payload-Digest\":\"sha1:J2S522JJQAE4CX4QTKOGZQYPLYKCEECO\",\"WARC-Block-Digest\":\"sha1:WSYDBHFI2S227XF5F4GXP6ACVQTERQQP\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875141460.64_warc_CC-MAIN-20200217000519-20200217030519-00540.warc.gz\"}"}
|
https://www.coderanch.com/t/709426/engineering/Run-time-analysis-pseudo-Code
|
[
"Win a copy of JDBC Workbook this week in the JDBC and Relational Databases forum\nor A Day in Code in the A Day in Code forum!\nprogramming forums Java Mobile Certification Databases Caching Books Engineering Micro Controllers OS Languages Paradigms IDEs Build Tools Frameworks Application Servers Open Source This Site Careers Other all forums\nthis forum made possible by our volunteer staff, including ...\nMarshals:\n• Campbell Ritchie\n• Paul Clapham\n• Jeanne Boyarsky\n• Junilu Lacar\n• Henry Wong\nSheriffs:\n• Ron McLeod\n• Devaka Cooray\n• Tim Cooke\nSaloon Keepers:\n• Tim Moores\n• Stephan van Hulst\n• Frits Walraven\n• Tim Holloway\n• Carey Brown\nBartenders:\n• Piet Souris\n• salvin francis\n• fred rosenberger\n\n# Run-time analysis of pseudo Code\n\nGreenhorn\nPosts: 16\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"I'm not sure in which Forum to post this question so I put it in Java in General. Please tell me if you know a better fit for this question because I have the feeling I will post some of these in the following days ;)\nI'm looking for the return value as a functoin of n in big theta notation for the following pseudo code:\n\nThe first (repeat) loop goes (in principle) n/log_2(n) times only that the rest in the division doesn't matter. So I'm looking here for a mathematical way to display only positiv integer. Maybe with the modulo function?\nThe for loop runs exactly a times and therefore (imagine the result of the division is a positiv integer) has 2* n/log_2(n) calls.\nFor z I get the value z = n*(2j+1) because in the first step j=0 and z is n since z= 0 +0 +n = (j+1)*n.\nCan somebody confirm my results an help me out with the first loop?\n\nMarshal",
null,
"Posts: 69382\n276\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"Please explain what you are trying to find.",
null,
"Saloon Keeper",
null,
"Posts: 11995\n257\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"Hans Peterson wrote:I'm not sure in which Forum to post this question so I put it in Java in General.\n\nSince this is not a Java question, I'll move it to our Computing forum.\n\nThe first (repeat) loop goes (in principle) n/log_2(n) times only that the rest in the division doesn't matter.\n\nIt doesn't. The repeat loop iterates log₂(n) times, exactly as it says on line 8.\n\nWhat division are you talking about? Why doesn't the rest matter? What rest?\n\nSo I'm looking here for a mathematical way to display only positiv integer. Maybe with the modulo function?\n\nWhat positive integer? I thought you were looking for the Big Theta time complexity class.\n\nThe for loop runs exactly a times and therefore (imagine the result of the division is a positiv integer) has 2* n/log_2(n) calls.\n\nIt doesn't. a = 2^log₂(n) = n. Again, what division?\n\nFor z I get the value z = n*(2j+1) because in the first step j=0 and z is n since z= 0 +0 +n = (j+1)*n.\n\nJust because that's the answer in the first step doesn't make it the answer at the end of the loop.\n\nThe second loop runs n times. Every step you add j + n, where j increments with each step. That means that at the end of the loop,\n\nz = n² + 0 + 1 + ... + n-2 + n-1\n= n² + n/2(n-1)\n= 1½n² - ½n\n.\n\nNow, the first loop runs in Θ(log₂(n)) time and the second loop runs in Θ(n) time. Because the second loop has a larger time complexity class, that one determines the time complexity of the function.\n\nIf instead of using loops, you calculate z using the formula, the running time of the function will be in Θ(1).\n\nHans Peterson\nGreenhorn\nPosts: 16\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"It doesn't. a = 2^log₂(n)\n\nWhy is this so? Let n be 7. Then log_2(n) is approximately 2.8. Since the loop only repeats until i>2.8 it has 2 steps.\nFirst step: i = 2, a = 2\nSecond step: i = 3, a = 4\n\na will allways be a multiple of 2. Thats why I thought I'm not interested in the decimals when I calculate log_2(n).\n\nStephan van Hulst\nSaloon Keeper",
null,
"Posts: 11995\n257\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"So I guess in your first post by 'division' you meant 'logarithm' and by 'rest in the division' you meant 'decimal part of the logarithm'.\n\nHans Peterson wrote:a will allways be a multiple of 2.\n\nYou mean: a will always be a power of two.\n\nThats why I thought I'm not interested in the decimals when I calculate log_2(n).\n\nTrue, and my analysis was based on whole powers of two. a is the largest power of two that is less than or equal to n. Also, there is an edge case where n=1 -> a=2.\n\nThis however is of absolutely no consequence to the time complexity class of the function, which is still in Θ(n), because a is always between n/2 and n.\n\nStephan van Hulst\nSaloon Keeper",
null,
"Posts: 11995\n257\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"Here's a function that has the exact same results as your pseudo-code, except it performs in O(1).\n\nHans Peterson\nGreenhorn\nPosts: 16\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"Thank you I think I got the first part now.\n\nthe second loop runs in Θ(n)\n\nWhy isn't the loop running n^2 times? Still I don't quite understand why it runs n^2 times but I tested it until n = 5 and the result always was n^2 times:\nn=1 -> z =0+0+1 = 1\nn=2 -> z=1+1+2 = 4\nn=3 -> z=4+2+3 = 9\nn=4 -> z= 9+3+4 = 16\nn=5 -> z=16+4+5 = 25\n\nP.S: Is there a Latex mode or something so I can write down the maths a little bit more structured like you?\n\nCampbell Ritchie\nMarshal",
null,
"Posts: 69382\n276\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"Hans Peterson wrote:. . . Is there a Latex mode or something . . .\n\nNo, afraid not. I have never seen a LaTeX mode on any website. Stephan was using the code button.",
null,
"Stephan van Hulst\nSaloon Keeper",
null,
"Posts: 11995\n257\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"Those results aren't correct Hans.\n\nn = 1 -> z = 3\nn = 2 -> z = 5\nn = 3 -> z = 7\nn = 4 -> z = 22\nn = 5 -> z = 26\n\nThe reason you are getting your results is because you're performing f(n) = f(n-1) + n-1 + n, which is NOT what the second loop does.\n\nHans Peterson wrote:Why isn't the loop running n^2 times? Still I don't quite understand why it runs n^2 times but I tested it until n = 5 and the result always was n^2 times\n\nYou are conflating execution result and execution running time. z is the result of the function call. Θ(n) is a complexity class that describes the running time of the function. So while you are correct in saying that the function itself is in Θ(n²), the runtime of the function is in Θ(n), because the second loop never runs more than n times.\n\nI see now in your original post that you're \"looking for the return value as a functoin[sic] of n in big theta notation\", so you WERE actually asking for the function itself, and not the running time. Then yes, you're correct in saying that the function is in Θ(n²). This however is extremely confusing because complexity classes are usually used to characterize the running time or memory requirements of a function, not its result.\n\nBartender",
null,
"Posts: 3954\n154\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"At first I thought Stephan was wrong, but just before pressing the 'reply' button I realized that I myself was wrong. I read 'a = 2*a' as 'a = 2^a', and then making the second error of interpreting this as 'a = Math.pow(2, a)'. Silly me.\n\nBut nevertheless interesting by itself. What is the running time in this case? (and you don't need to express the result in BigO notation).\n\nHans Peterson\nGreenhorn\nPosts: 16\n•",
null,
"•",
null,
"•",
null,
"•",
null,
"Thanks for youre help folks. It's clear now",
null,
"Their achilles heel is the noogie! Give them noogies tiny ad! Devious Experiments for a Truly Passive Greenhouse! https://www.kickstarter.com/projects/paulwheaton/greenhouse-1\n•",
null,
""
] |
[
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/staff-star.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/i/b/Duke-8.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/staff-star.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/staff-star.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/staff-star.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/staff-star.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/i/b/Duke-8.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/staff-star.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/staff-star.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/plus-1-thumb.gif",
null,
"https://www.coderanch.com/templates/default/images/pie/give-pie-button.png",
null,
"https://www.coderanch.com/templates/default/betaview/images/quote_button.gif",
null,
"https://www.coderanch.com/templates/default/betaview/images/report_post.png",
null,
"https://www.coderanch.com/images/bunkhouse_smoke.gif",
null,
"https://coderanch.com/t/664156/i/170/nKhDm.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.887804,"math_prob":0.87022305,"size":1536,"snap":"2020-24-2020-29","text_gpt3_token_len":430,"char_repetition_ratio":0.11684073,"word_repetition_ratio":0.0068259384,"special_character_ratio":0.27799478,"punctuation_ratio":0.10882353,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9893683,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-02T15:48:23Z\",\"WARC-Record-ID\":\"<urn:uuid:b5c55a8d-a429-475e-a998-2da25412d0d7>\",\"Content-Length\":\"48313\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:13ec39a0-967c-4d5c-a676-2c1ffba18c3a>\",\"WARC-Concurrent-To\":\"<urn:uuid:222c07bf-6a03-4d25-9937-5305455e7940>\",\"WARC-IP-Address\":\"204.144.184.130\",\"WARC-Target-URI\":\"https://www.coderanch.com/t/709426/engineering/Run-time-analysis-pseudo-Code\",\"WARC-Payload-Digest\":\"sha1:CIBQWZNDBVMKP3WEOLF3VWFC4CPCD4MD\",\"WARC-Block-Digest\":\"sha1:VP5C55TJU5UYWRBBRZPJX4LDH5E6J7RB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655879532.0_warc_CC-MAIN-20200702142549-20200702172549-00565.warc.gz\"}"}
|
https://studylib.net/doc/7584815/finalwriteup---swarthmore-college
|
[
"# FinalWriteup - Swarthmore College",
null,
"```Introduction to\nOp-Amps\nSwarthmore College\nEngineering 72: Electronic Circuit Application\nLab # 1\nSeptember 14, 2004\nHeather Jones & David Luong\nProfessor Erik Cheever\nProcedure\nThe procedures can be found at the following web address:\nhttp://www.swarthmore.edu/NatSci/echeeve1/Class/e72/E72L2/Lab2(OpAmp).html\nAnalysis\n1. Op-Amp Circuits\na.\na. Inverting Amplifier\nSchematic 1\nThe internal resistances between the inputs (v+ and v-) and ground are infinite. Since v+is\nv\ngrounded, v - is also grounded. As a result, the current into the node at v – is simply in\nR2\nv\nby Ohm’s Law. The current across the R1 resistor is also in . By voltage division,\nR2\nv\nvout in R1 .\nR2\nSo the gain of the circuit is\nvout\nR\n 1 .\nvin\nR2\nFigure 1—Inverting Amplifier with R1 = 10kOhms\nFigure 2—Inverting Amplifier with R1 = 30kOhm\nb.\nNon-Inverting Amplifier\nSchematic 2\nThe node between R1 and R2 is vin since v+ = v-. Using a voltage divider,\nR1\nvin vout\nR1 R2\nRewriting,\nvout\nR\n 1 1 .\nvin\nR2\nA Multisim produced schematic and simulation are shown below.\nVCC\n12V\nXFG1\n7\n1\n5\nU1\n3\n6\nR1\n2\n1.00kOhm_1%\nLF411CH\n4\nV1\n12 V\nR2\n10.0kOhm_1%\nXSC1\nG\nT\nB\nSchematic 3\nFigure 3—Multisim Simulation\nA\nc. Ideal Integrator\nSchematic 4\nAssume that R1 has no effect on the circuit. Since this is essentially an inverting\namplifier,\nvout\nZ\n c ,\nvin\nR2\nwhere Z c is the impedance of the capacitor. It is equal to\n1\nvout\nsC\n1\n 1 \n.\nvin\nR2\nsC1 R2\n1\n. Rewriting,\nsC1\nFigure 4 –Ideal Integrator with R1 having infinite resistance\nFigure 5–Ideal Integrator with R1 = 1MOhm\n2. The resistor labeled R1 in the above diagram allows the integrator to deal with a DC\nsignal. When this resistor is removed, the gain of the circuit is Vo(s)/Vi(s) = -1/(RsC),\nwhich goes to infinity as s goes to zero, so any DC signal will cause the amplifier to\nsaturate.\n3. Our calculated peak-to-peak value was 500 mV. Referring to the vout/vin relationship\nof the integrator circuit, we have values for the capacitor and resistor. To determine vout,\nwe place vin on the right side of the equation, and replace it with its Laplace equivalent.\nKnowing that 1/s^2 is merely –ω^2, vout becomes 1/( ω^2*C1*R2). The time domain\nequivalent is vout(t) = 1/(C1*R2)*t. Noting that the input frequency is 1 kHz, it takes\nhalf that or .5 kHz to reach a peak. Substituting that and values for C1 and R2, vout(t) =\n500 mV. Our measured value was 660 mV. Below is a Multisim simulation of the\nintegrator circuit.\nFigure 6—Multisim Simulation\n4. We measured a slew rate of 11.69 V/s for the 411 op-amp, which is close to the rate\nof 10 V/s listed in the manufacturer’s specifications.\n5. An amplifier with a gain of one can be used as a buffer to transfer a voltage between\ncircuits where a direct connection would have allowed current to flow and changed the\nvoltage.\n6. In the comparator circuit, if the voltage at the inverting input terminal is greater than\nthe voltage at the non-inverting input terminal, there will be a closed switch inside the\ncomparator, connecting the output to ground. In this case, the resistor R3, which is\nconnected between Vcc and the output, prevents a short circuit between Vcc and ground.\nWhen the voltage at the non-inverting input terminal is greater than that at the inverting\nterminal, the switch is opened, and now no current can flow through R3, and the voltage\nat the output is pulled up to Vcc.\n7. Schmitt Trigger\nSchematic 5\na. The circuit looks at the inputs at v+ and v- and compares them. The circuit\ncreates two different thresholds, and checks the number of times the input\nsignal crosses the thresholds. Depending on the threshold that is crossed\n(either high or low), the output changes states—either high or low.\nSpecifically, when the input crosses the high threshold the output is low.\nWhen it crosses the low threshold, the output is high.\nb. When v- is greater than v+, the switch in the circuit, which is connected to\nground and the output, is closed. That makes vout = 0 volts, and by voltage\nR1 k \ndivision, v 5\n. [R1 is in parallel with R3]. For R1 = R2 =\nR1 R3 R2\nR3 =10 k , v =5/3 volts. When v- is less than v+, the switch is opened.\nR1\nBy voltage division, v 5\n=2.5 volts. Also vout is also 2.5 volts\nR1 R2\nbecause no current can flow through R3 as there is no place for it to go.\nc. From part b, the lower threshold output voltage is 0 volts, and the high is\n2.5 volts.\nd. See the printout below.\nFigure 7—Oscilloscope Output\n8. For the comparator and Schmitt trigger circuits, our output could range from 0-5V,\nwith threshold voltages at 2.5V or 1.67V. To get an input that was centered near this\nthreshold band, and would thus cross through it periodically, we had to add in a DC offset\nin the function generator. To see this offset on the oscilloscope, we had to turn on DC\ncoupling (AC coupling would have subtracted out the signal mean and shown the signal\ncentered around 0V).\n9. Relaxation Oscillator\nSchematic 6\nFigure 8-Oscilloscope Output\nWhen the output is high, that means that v+ is greater than v- and the switch is open.\nThis charges up the capacitor and thus increases v- until it becomes greater than v+. This\ncauses the switch to close, pulling the output to a lower voltage than v-, which in turn\ncauses the capacitor to discharge around the feedback loop until v+ is greater than vonce again. This condition causes the switch to open, and the process repeats, making the\ncircuit oscillate. The shape of the output is trivial—it is either high or low depending on\nthe relative magnitudes of the inverting and non-inverting inputs. V+ and v- increase and\ndecrease over time due to the oscillatory nature of the circuit as evidenced by the step\ntriangle waves. The measured frequency of oscillation is 115 kHz, and our calculated\none is 1/(R3*C) = 83 kHz.\nFigure 9-Multisim Simulation\n```"
] |
[
null,
"https://s3.studylib.net/store/data/007584815_2-7e3811a85d3925ab7e9d2165ca74b2b6.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9111055,"math_prob":0.9856794,"size":5779,"snap":"2020-34-2020-40","text_gpt3_token_len":1546,"char_repetition_ratio":0.12658009,"word_repetition_ratio":0.013539651,"special_character_ratio":0.2548884,"punctuation_ratio":0.11358025,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99347585,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-09T17:27:12Z\",\"WARC-Record-ID\":\"<urn:uuid:e9b74be6-40b4-4b19-a08b-6f90d52b4dbf>\",\"Content-Length\":\"69766\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:241c89e6-f389-4612-9b5a-24b254cfe5f0>\",\"WARC-Concurrent-To\":\"<urn:uuid:90061f39-6a63-4ab4-9cdb-14e655f4c3de>\",\"WARC-IP-Address\":\"172.67.175.240\",\"WARC-Target-URI\":\"https://studylib.net/doc/7584815/finalwriteup---swarthmore-college\",\"WARC-Payload-Digest\":\"sha1:TCWMB27S6JQFOECDC325BVNAAOK2QWN3\",\"WARC-Block-Digest\":\"sha1:IJQD7XX4AFEMFBKRKZLWC37PMIYHPAYO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738562.5_warc_CC-MAIN-20200809162458-20200809192458-00353.warc.gz\"}"}
|
https://www.bartleby.com/solution-answer/chapter-2-problem-12cq-college-physics-11th-edition/9781305952300/a-racing-car-starts-from-rest-and-reaches-a-final-speed-v-in-a-time-t-if-the-acceleration-of-the/3cb57c4a-98d8-11e8-ada4-0ee91056875a
|
[
"",
null,
"",
null,
"",
null,
"Chapter 2, Problem 12CQ\n\nChapter\nSection\nTextbook Problem\n\nA racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true? (a) The car travels a distance vt. (b) The average speed of the car is v/2. (c) The acceleration of the car is v/t. (d) The velocity of the car remains constant. (e) None of these.\n\nTo determine\nThe distance, velocity, and the acceleration of a car.\n\nExplanation\n\nThe car starts from its rest.\n\nThe constant acceleration is,\n\na=vut\n\nHere,\n\nv is the final velocity.\n\nu is the initial velocity.\n\na is the acceleration.\n\nt is the time.\n\nSubstitute 0 for u to find a .\n\na=v0t=vt\n\nThe average velocity of the car is,\n\nv¯=vu2\n\nHere,\n\nv¯ is the average velocity\n\nSubstitute 0 for u to find v¯ .\n\nv¯=v02=v2\n\nThe displacement of the car is,\n\ns=v¯t\n\nHere,\n\ns is displacement of the car.\n\nSubstitute v/2 for v¯ to find s\n\nStill sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\nThe Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\nGenerally speaking, vegetable and fish oils are rich in saturated fat. T F\n\nNutrition: Concepts and Controversies - Standalone book (MindTap Course List)\n\nThe smallest unit of any substance is the _____. a. atom b. molecule c. cell\n\nBiology: The Unity and Diversity of Life (MindTap Course List)\n\n24-32 What is the chemical nature of enkephalins?\n\nIntroduction to General, Organic and Biochemistry\n\nWhat is a life cycle?\n\nBiology: The Dynamic Science (MindTap Course List)",
null,
""
] |
[
null,
"https://www.bartleby.com/static/search-icon-white.svg",
null,
"https://www.bartleby.com/static/close-grey.svg",
null,
"https://www.bartleby.com/static/solution-list.svg",
null,
"https://www.bartleby.com/static/logo.svg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.74125427,"math_prob":0.8055477,"size":1921,"snap":"2019-43-2019-47","text_gpt3_token_len":435,"char_repetition_ratio":0.20292123,"word_repetition_ratio":0.04477612,"special_character_ratio":0.18011452,"punctuation_ratio":0.10197368,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9881931,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-20T01:01:26Z\",\"WARC-Record-ID\":\"<urn:uuid:2499bc9f-3e11-4910-931a-2f6cfa789d78>\",\"Content-Length\":\"448916\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88313654-74de-4bb2-aef6-4f865f4f2b49>\",\"WARC-Concurrent-To\":\"<urn:uuid:4041d147-d760-43de-860d-c536df6e5d56>\",\"WARC-IP-Address\":\"99.84.181.117\",\"WARC-Target-URI\":\"https://www.bartleby.com/solution-answer/chapter-2-problem-12cq-college-physics-11th-edition/9781305952300/a-racing-car-starts-from-rest-and-reaches-a-final-speed-v-in-a-time-t-if-the-acceleration-of-the/3cb57c4a-98d8-11e8-ada4-0ee91056875a\",\"WARC-Payload-Digest\":\"sha1:XVJAIYRNKYFDVWLR2GYWSQ5KTSVN5ZLX\",\"WARC-Block-Digest\":\"sha1:IPM7B2HSTAAU7MREZMCKTSZOTHICQTJQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986700560.62_warc_CC-MAIN-20191020001515-20191020025015-00085.warc.gz\"}"}
|
https://www.scienceforums.net/topic/53324-from-maximal-entropy-random-walk-to-quantum-thermodynamics/#comment-637463
|
[
"# From Maximal Entropy Random Walk to Quantum Thermodynamics\n\n## Recommended Posts\n\nBrownian motion requires relatively large 'walker', which is constantly being pushed in random directions (no memory) - it's derived as infinitesimal limit of Generic Random Walk (GRW) on a graph(lattice), in which each outgoing edge is equally probable.\n\nBut let's imagine we want to estimate probability density of positions of some entity which doesn't just constantly 'stop and make new independent decision', but make some concrete trajectory, which for example could depend on the past (by e.g. velocity) - in such situations the safer than taking statistical ensemble among single edges as in GRW/Brownian motion, should be using statistical ensemble among whole possible paths.\n\nThe simplest such model is Maximal Entropy Random Walk (MERW) on graph, it can be defined in a few ways:\n\n- stochastic process on given graph which maximizes average entropy production, or\n\n- assuming uniform probability distribution among possible paths on graph, or\n\n- for each two vertices, each path of given length between them is equally probable.\n\nObtained formulas are:\n\nP(a->b ) = $\\frac{M_{ab}}\\lambda \\frac {\\psi_b}{\\psi_a}$\n\nwhere M is graph's adjacency matrix ($M_{ij}\\in{0,1}$)\n\nlambda is its dominant eigenvalue with psi eigenvector (real, positive because of Frobenius-Perron theorem)\n\n$M \\psi=\\lambda \\psi$\n\nstationary probability distribution is:\n\nP(a) is proportional to $(\\psi_a)^2$\n\nThis stochastic process is Markovian - depends only on the last position, but to calculate these transition probabilities we just have to know the whole graph -\n\nwe should think about this probabilities not as that 'the walker' uses them directly, but that they are only used by us to propagate our knowledge while estimating probability density of his current position.\n\n(Minus adjacency matrix) occurs to correspond to discrete Hamiltonian, so while GRW/Brownian motion spreads probability density almost uniformly, MERW has very similar localization properties as quantum mechanics.\n\nWhile adding potential: changing statistical ensemble among paths into Boltzmann distribution and making infinitesimal limit of lattice constant, we get stationary probability density exactly as quantum mechanical ground state (similar to Feynman's euclidean path integrals).\n\nHere is PRL paper about MERW localization properties: http://prl.aps.org/abstract/PRL/v102/i16/e160602\n\nHere is my presentation with e.g. 2 intuitive derivations of MERW formulas and some connection to quantum chaos: http://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B7ppK4I%20yMhisYmI3YTAzNzYtMDkyNy00ZDAxLTg1NGEtOTg4NWNkYzU3M%20jQ1&hl=en\n\nHere is simulator which allows to compare conductance models using GRW and MERW: http://demonstrations.wolfram.com/preview.html?draft/93373/000008/ElectronConductanceModelUsingMaximalEntropyRandomWalk\n\nHere are more formal derivations: http://arxiv.org/abs/0710.3861\n\nHere is a trial to expand this similarity to quantum mechanics: http://arxiv.org/abs/0910.2724\n\nI'm currently working on my PhD thesis in physics on this subject and so I would really gladly discuss about it.\n\n##### Share on other sites\n\n• 11 months later...\n\nIf someone is interested, I have just finished large paper about MERW and its connections to quantum mechanics (e.g. to show these results on congress on emergent quantum mechanics this weekend) - a preliminary version of my current PhD:\n\n\"Surprisingly the looking natural random walk leading to Brownian occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a new philosophy of stochastic modeling was introduced, which by being mathematically similar to euclidean path integrals, finally fulfills these principles exactly. Its local behavior is usually similar, but may lead to drastically different global properties. In contrast to having practically no localization properties Brownian motion, this recent approach turns out in agreement with thermodynamical predictions of quantum mechanics, like thermalizing to the quantum ground state probability density: squares of coordinates of the lowest energy eigenvector of the Bose-Hubbard Hamiltonian for single particle in discrete case or of the standard Schrodinger operator while including potential and making infinitesimal limit. It also provides a natural intuition of the amplitudes' squares relating to probabilities. The present paper gathers and formalizes these results. There are also introduced and discussed some new expansions, like considering multiple particles with thermodynamical analogue of Pauli exclusion principle or time dependent cases, which allowed to introduce thermodynamical analogues of momentum operator, Ehrenfest equation and Heisenberg uncertainty principle.\"\n\nIt should appear on arxiv soon, now it can be download here:\n\nhttp://dl.dropbox.com/u/12405967/phd2.pdf\n\n## Create an account\n\nRegister a new account"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8883856,"math_prob":0.8888164,"size":3502,"snap":"2023-40-2023-50","text_gpt3_token_len":816,"char_repetition_ratio":0.08204688,"word_repetition_ratio":0.0,"special_character_ratio":0.21245003,"punctuation_ratio":0.104132235,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99090505,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-04T13:53:39Z\",\"WARC-Record-ID\":\"<urn:uuid:ba8f730a-ed12-4b18-b36b-5935f167a614>\",\"Content-Length\":\"90937\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9c9061a3-db28-4cc7-a812-ecee370bb185>\",\"WARC-Concurrent-To\":\"<urn:uuid:f2b45a1f-9e2d-4560-ac4c-1f0f1818908b>\",\"WARC-IP-Address\":\"94.229.79.58\",\"WARC-Target-URI\":\"https://www.scienceforums.net/topic/53324-from-maximal-entropy-random-walk-to-quantum-thermodynamics/#comment-637463\",\"WARC-Payload-Digest\":\"sha1:HEYMOZWWQCH6K2E3PCJKWY5DSCYFGRCW\",\"WARC-Block-Digest\":\"sha1:EW3PVWIUNSH5GOL7IN6OHPWWTCPYYI7H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511369.62_warc_CC-MAIN-20231004120203-20231004150203-00532.warc.gz\"}"}
|
http://bristolcrypto.blogspot.com/2013/05/
|
[
"## Friday, May 31, 2013\n\n### Eurocrypt 2013: Day Three, Secure Computation\n\nOn the third day of Eurocrypt, there were three presentations on secure computation. This post will cover two of them.\n\nTore Frederiksen from Aarhus University presented an efficiency improvement for active two party computation based on Yao's garbled circuits. The core component is an XOR-homomorphic commitment based on OT, which makes the approach compatible with garbled circuit optimizations like free-XOR. This was not the case for a previous work by the same group where they used Pedersen commitments. However, both use cut-and-choose at gate level as opposed to at circuit level to achieve active security.\n\nMost of the talk was devoted to the XOR-homomorphic commitment scheme based on OT and a linear error correcting code. The latter is required to have secret-sharing properties in order to achieve hiding. To produce a commitment, the input is encoded using the code and then input to a k-out-of-n random-OT. For the binding property, the receiver selects some bits of the encoded vector to check them against the output of the OT protocol.\n\nBy using OT extension, the usage of asymmetric cryptography can be reduced to depend only on the security parameter. Furthermore, all protocols are parallelizable, which leads to an overall constant number of rounds.\n\nAt the end of the session, Hoeteck Wee from George Washington University gave a pleasant talk about a result on secure computation with limited interaction. In the so-called one-pass model, the parties interact with a server once in a fixed order, after which the server announces the result. There is some inherent leakage: If the server colludes with the last k parties, they can evaluation the function with all possible inputs from those parties\n\nPrevious work in this model covered symmetric functions like sum and majority, and proved that pseudo-random functions are impossible to compute. The contribution presented at the conference extends the achievable functions to sparse multi-variate polynomials (e.g., variance) and read-once branching programs (e.g., string matching, finite automata, second-prize auctions), which allow branching once per player.\n\nThe protocol works as follows: The server encrypts all possible outputs under the keys of all parties and the server in order according to the branching in the program, that is, the outer-most encryption is under the key of the party associated with the last branching. The parties then interact with the server in the reverse order, that is, the party associated to the last branching comes first. Every party picks the possible ciphertexts according to his input, decrypts them and sends them to the server, who forwards them to the next party. At the end, the server decrypts the result.\n\nThe complexity of the protocol is determined by the width of the branching program. If the server is honest, secrecy is guaranteed by the encryption under the public key of the server. However, if the server colludes with the last k parties, the protocol inherently leaks information as described above, but not more. To achieve active security, non-interactive zero-knowledge arguments can be used. Finally, the biggest open question is the gap between the functions known how to compute in this model and the impossibility result.\n\n### Godel Prize goes to a \"Tripartite Pairing\" of Cryptographers\n\nThe 2013 Godel Prize winners have just been announced as being Antoine Joux, Dan Boneh and Matt Franklin; for their work in pairing based cryptography. The press release can be found here.\n\nIn the early 2000's the world of cryptography was revolutionized by two papers by these authors. A bit of background is probably needed to understand the revolution. In 1985 Victor Miller and Neal Koblitz introduced the idea of using elliptic curves as a means of building cryptographic systems; and since then elliptic curves have become deployed in a number of application domains such as on the web, in your mobile phone, or in your games console.\n\nHowever, quite early on it was realised that some elliptic curves are weaker than others; in particular those for which there exists an efficiently computable bilinear pairing (sometimes called a bilinear map). In its basic form this is a map from two groups G1 and G2 into a new group GT which is linear in the first two coordinates. In practice one instantiates these with G1 and G2 being subgroups of an elliptic curve and GT being a subgroup of a finite field. Only a small subset of elliptic curves have an efficiently computable pairing, and since the early 1990's these had been avoided in normal applications of elliptic curves in cryptography.\n\nHowever, in a paper in the ANTS conference in 2000 Antoine Joux showed how if we carefully chose the parameters of elliptic curves with a pairing then we could achieve a cryptographic functionality which we could not achieve with other techniques. This first application was to allowing three parties to agree a secret key using only one round of interaction; so called Tripartite Diffie-Hellman.\n\nThen in 2001 at the CRYPTO conference Boneh and Franklin showed how the same technique could be used to create an identity based encryption scheme. This is an encryption scheme in which the receivers key is simply their name. Again this is something which had not be possible before.\n\nOver the first decade of this century the number of papers on so-called Pairing Based Cryptography exploded. For example, according to Google Scholar, Joux's paper has been cited 886 times and the Boneh/Franklin paper has been cited 4527 times. The following work has ranged from algorithms to efficiently compute the various pairings needed (including the work in Bristol on the Ate-pairing algorithm) through to work on using pairings in advanced protocols such as group signatures, credentials, functional and attribute based encryption and our own work recent work on DAA protocols.\n\nWe have all just returned from Eurocrypt where the best paper award was given to some new ground breaking work which showed how one can construct pairings between more than two objects efficiently; so called multi-linear maps. We have discussed new work a lot in this blog in recent months; so I refer the reader to the previous posts on this topic. It can be expected that the development of multi-linear maps is going to have the same profound effect that the development of bilinear pairings had in the last decade.\n\n## Thursday, May 30, 2013\n\n### Eurocrypt 2013: Day Three, Session Two\n\nThe second talk in the 'Public Key Encryption' session of this year's Eurocrypt was given by Dennis Hofheinz, on his paper 'Circular Chosen-Ciphertext Security with Compact Ciphertexts'. The work gives the first KDM-CCA secure scheme with ciphertexts that have O(1) group elements, building on the past work of Boneh et al. who give a KDM-CPA secure scheme. For comparison the other CIRC-CCA secure scheme in the literature has ciphertexts with O(k) group elements. In the KDM-CCA security game, the adversary submits a (length-regular) function to the challenger and receives an encryption of either the function acting upon the secret keys in the system or an encryption of a zero message, and naturally the scheme is secure under this notion if all (efficient) adversaries cannot distinguish between these cases. Note that CIRC-CCA security (called clique security by Boneh et al.) is the scenario where the adversary is restricted to functions that on input take the secret keys in the system and output one of these secret keys. This is a special case of (and implied by) KDM-CCA security.\n\nThe KDM-CPA secure scheme of Boneh et al. relies on the possibility of constructing encryptions of secret keys (under their corresponding public keys) publicly, something that will clearly deem it KDM-CCA insecure. Consequently, something else is needed to realise a KDM-CCA scheme from this starting point. The main technical tool used to ramp up to KDM-CCA security is the 'Lossy Algebraic Filter', a family of functions indexed by a public key and a tag. A function LAF from this family takes as input a vector of elements Xi in Zp. For an injective tag, LAF will be injective. If the tag is lossy, then LAF only depends on a linear combination of the input elements. Crucially, different input vectors with the same linear combination (Σi=1n ωi Xi mod p) are mapped to the same value. The coefficients only depend on the public key of the filter, and not on the tag. Three properties are necessary for this definition to acheive its purpose. First of all, lossy and injective tags must be computationally indistinguishable; lossy tags can be generated using a special trapdoor; and finally that new lossy tags cannot be found efficiently without this trapdoor, even given polynomially many lossy tags before. The paper details how to construct LAFs based on the DLIN assumption with a suitable cryptographic pairing, and each tag corresponds to n DLIN-encrypted Waters signatures (if the signatures are valid then the tag is lossy).\n\nThe constructed CIRC-CCA secure PKE scheme adds an authentication tag (an encrypted image of the plaintext message under an LAF), and decryption queries are disallowed where the authentication tag is invalid. To prove security, all tags for key-dependent encryptions are made with respect to lossy filter tags, so little information about the secret key is released (information-theoretically speaking). But the fact that adversarial decryption queries must correspond to injective tags, the adversary needs to be able to guess the whole secret key to make any valid decryption query. The resulting scheme is secure under a combination of the DCR, DLIN and DDH assumptions (in appropriate groups).\n\n## Wednesday, May 29, 2013\n\n### Eurocrypt 2013: Homomorphic Cryptography session\n\nThe first afternoon session of day 2 was on homomorphic cryptography. There were three talks: the first was on fully homomorphic encryption, and the next two on the slightly lesser-known topics of homomorphic MACs and authenticated data structures. In this post I will talk about the first two talks, which captivated me the most.\n\nTancrède Lepoint gave the first talk, on integer-based fully homomorphic encryption, which was a merge of two papers. Much recent work on FHE has focussed on constructions based on ring-LWE, whilst Gentry's scheme and the integer-based DGHV variant are often ignored due to large parameter sizes. The talk aimed to bridge this gap and show that actually, the integer scheme can be competitive with ring-LWE. Following on from last year's Eurocrypt paper, which allowed for better 'noise control' using modulus switching, Tancrède described how batching techniques can be used to perform parallel homomorphic operations on ciphertexts. Batching allows multiple plaintexts to be 'packed' into a single ciphertext, so that when a homomorphic operation is performed on a ciphertext, it is applied to every plaintext element in parallel. These techniques were originally developed by Smart and Vercauteren, for plaintext spaces of polynomial rings, and it turns out that the CRT can similarly be used for the scheme over the integers. The use of batching makes a huge practical difference: previously a ciphertext of size 20 million bits could only encrypt a single bit; now the same-sized ciphertext can encrypt around 300 bits.\n\nIn addition to parallel operations, effective use of batching also requires the ability to permute plaintext elements within a single ciphertext. This is possible with ring-LWE based schemes because of their nice algebraic structure, however it seems more difficult over the integers. Instead, they take advantage of the bootstrapping step, which homomorphically decrypts a ciphertext, to perform a permutation. Using these techniques, they present an implementation of homomorphic AES that takes 12 minutes per block on average, compared with 5 minutes per block for the implementation from Crypto last year. This shows that integer-based FHE is still a viable option, although it is worth noting that the Crypto implementation did not use bootstrapping; it would be interesting to see if adding bootstrapping could put it much further ahead or not.\n\nThe second talk of the session was given by Dario Catalano, on homomorphic MACs for arithmetic circuits. In the scenario of delegating computation to a server, it is often important to be able to verify that the computation was carried out on the correct data, which was previously authenticated by the client. Using homomorphic MACs allows the client to verify the server's output, with respect to the function computed and the original, authenticated inputs. The key element is a mechanism whereby anyone can take a set of MAC'd messages and compute a MAC valid for the output of any function of the messages. Previous work in this area was only homomorphic for linear functions, or required the use of FHE, which is undesirable. Their construction allows homomorphism for polynomially sized circuits, is secure based only on the existence of PRFs, and is very efficient to compute the MACs. However, the complexity of verification grows with the degree of the circuit, which seems unfortunate, especially for the application of outsourced computation. Another open problem Dario mentioned was to construct a fully homomorphic MAC, for circuits of arbitrary size.\n\n## Tuesday, May 28, 2013\n\n### EuroCrypt 2013: Day one, part three\n\nThe first talk on Monday afternoon at EuroCrypt'13 was given by Nicolas Veyrat-Charvillon on \"Security Evaluations Beyond Computing Power - How to Analyze Side-Channel Attacks you Cannot Mount?\" (with B. Gérard and F.-X. Standaert as coauthors). The paper addresses an issue faced by certification labs that have to assess the security of a device against side channel attacks: In certification you know everything about the device that you are attacking, you know the key that you're attacking but if, after having made a certain effort, the side-channel attack doesn't yield the correct key you want to know how far away of the correct key you are.\n\nLet's look at the example of a side channel attack on AES: After the attack, you have for each 0<=i<16 word of the state a probability distribution Di that contains the probability of every possible value for this word. So you can compute for all of the possible 2128 keys their probability as returned by the attack. In particular, you can compute the probability of the most likely key and the probability of the correct key. (Of course, a real attacker wouldn't know the correct key; you know the correct key only because you're a certification lab staging an attack on something you already know.) The big question that remains is: How many other keys have a probability higher than the correct key? If the certification lab can answer that question with a good enough approximation, then they know how much additional effort is needed to complete the attack by brute force.\n\nThe stupid way to answer that question is to check the probabilities of all 2128 keys. But of course, if you were able to do that, you wouldn't need a side-channel attack in the first place, you could just brute force AES. The authors present in their paper the first feasible method to answer this question with a reasonably good approximation. Their primary idea is to arrange all the possible keys in a suitable hyper cube representation where they can make suitable time-memory trade-offs in the arrangement. This enables effective carving out of key candidate volumes that all have bigger or smaller probability. So they only have to keep track of the size of the carved out volumes and, when the remaining volume is small enough, they have their answer.\n\nObviously, being able to tell how much additional brute force effort is needed after a failed side-channel attack is important for certification labs to make a qualified judgement about the device's security. So the biggest remaining question for follow-up work in this direction is: Does the remaining brute-force effort relate to the additional number of traces that need to measured, stored & processed for a pure side-channel attack to be successful? Would the attacker be better of continuing with more measurements instead of brute-forcing at the end?\n\n## Monday, May 27, 2013\n\n### Eurocrypt 2013 : Number Theory Session\n\nThe number theory session consisted of three talks. One by Joux on the DLP, one by people from Microsoft Redmond on Genus 2 curves, and one by Bouillaguet and co-workers on breaking systems based on hidden quadratic equations. In this post I will mainly concentrate on the first one, and make a small comment on the second. The third talk was very interesting, and basically concluded that the systems considered in this work should not be considered secure.\n\nJoux presented his work on the medium prime case of DLP in a finite field. He first outlined the basis Function Field Sieve method of Joux and Lercier for solving such DLPs: If the finite field is of size p^k, for p of size Lp^k(1/3), then one selects two polynomials f1(x) and f2(x) of degree d1 and d2 respectively such that d1*d2>k and such that\nx-f1(f2(x))\nis divisible, modulo p, by an irreducible factor of degree exactly k.\n\nThe attacker then selects a smoothness basis of x-a and y-a, and sets y=f2(x), and x=f1(y). With this identification the bivariate linear polynomial\nx y + a y + b x + c\ncan be expressed either as a polynomial in x, or a polynomial in y. When both such polynomials split over the factor base one obtains a relation.\n\nThe basic idea of Joux's new method was to apply the technique used when the field can be expressed as a Kummer extension, to all extensions. Namely to fix on y=x^d1. Joux then showed that when one obtains a single relation one can amplify this to many relations using the substitution x = v X for some v. A similar trick working when we consider the other side of the relation. Thus relation finding becomes a task of taking known factorizations and matching them up. This produces a great improvement in the so-called sieving step; in fact eliminating the need for sieving entirely.\n\nJoux ended with discussing his recent work on charactereristic two discrete logarithms; which we have discussed elsewhere in this blog. He presented a new world record; announced in the last week of solving the DLP in a finite field of 6168 bits.\n\nIn the next talk Craig Costello presented some interesting performance improvement to arithmetic on genus two curves; obtaining some very impressive results. He presented two implementations; one based on general arithmetic using a four dimensional GLV style trick, and the second based on a Montgomery ladder technique based on the Kummer surface. He left with a tantalising open problem which was to apply GLV style methods to the Kummer surface. This looks very interesting, and a possible place to start this line of work would be to see what can be done in the simpler case of elliptic curves, where both GLV and the Kummer surface are easier to understand\n\n### Day one - part one - two\n\nThe third talk of Monday was given by Chris Peikert on ring-LWE. Lattice cryptography bases security mainly on SIS and LWE problemS. Whereas they enjoy worst-case security, this approach typically leads to constructions where key sizes and runtimes are big, roughly quadratic on the security parameter (Omega(n^2)). It turns out that their analogous on the ring setting are more efficient (Omega(n)), so it is important to understand until what extent, without compromising security, the ring counterpart can be employed.\n\nA key part in the security reduction of RLWE to lattices problems is that the underlying ring should have a particular algebraic structure. Namely, the class of rings considered are cyclotomic rings, defined as the quotient of polynomial rings with integers coefficents over cyclotomic polynomials, (the m-th cyclotomic polynomial is that with its roots being exactly all nth-primitive roots of unity). So unless one is able to provide a reduction for any number field, the question is, what cyclotomic rings and what representations of the ring elements are best suitable for efficiency purposes?\n\nMany applications require the degree to be a power of two. This work is on extending the setting to more general cyclotomic rings. From a practical point of view, the most obvious reason for doing so is that the security level of an application may not need to call to the next power of two in the ring dimension. Working with rings with tighter dimensions allows e.g. to have smaller keys. Also on the power of two case, improvements on efficiency like SIMD operations cannot be applied.\n\nUsing any cyclotomic field would not comprOmise security at all, but other difficulties arise if we do not restrict to some nicer structures. For example, reduction modulo general or irregular cyclotomic polynomials is ususally cumbersome because the polynomial can take any shape. The situation is different if the order is prime.\n\nIn the talk, three features were presented which in somehow also determine the ring structure; the canonical embedding, the tensorial decomposition, and the dual ring. A crucial quantity when trading security by efficiency is the expansion factor of the ring; it controls the noise growth after arithmetic operations. The size of this term can be given in different ways, for example one is tempted to consider the norm of the vector associated to the noise. This way, one is using the so-called coefficient embedding. Unfortunately this yields expansion factors depending on the cyclotomic polynomial, and they are usually quite loose, getting too large with high composite m. Another important caveat is that security decreases with the expansion factor. On the other hand we may use the canonical embedding. It maps the ring element (seen as a polynomial) to the vector of its evaluation at each primitive root, seated on the complex vectorial space. A nice property is that the expansion factor is very small and independent of the base ring. One might suspect that tensorial decomposition will allow SIMD operations. The decomposition is done via an old theorem that states that the m-th cyclotomic ring can be expressed as an multivariate quotient depending on the factorization of m. It turns out that this characterization with a basis of the ring called 'powerful basis' renders much efficient constructions, than if one uses the univariate version with the standard basis (sometimes called power basis). Lastly, under the canonical embedding the cylotomic ring is not self dual. In the formalization of the RLWE problem it was shown that the dual was necessary, and although it is possible to get rid of it DD12, it seems better to keep it since the error tolerance in decryption is larger when using the dual.\n\nThe take-home message of the talk was that mathematical objects (canonical embedding) and representations (tensorial bases) yields provable hardness, fast algorithms and tighter analysis.\n\n### EuroCrypt 2013: Day one, part one\n\nToday marks the start of Eurocrypt 2013 in Athens. The first session was on lattices and the first talk was on Candidate Multilinear Maps from Ideal Lattices, which received the best paper award. This paper was also discussed in an earlier blog post as part of a study group.\n\nThe second talk was on Lossy Codes and a New Variant of the Learning-With-Errors Problem, by Nico Döttling (who gave the talk) and Jörn Müller-Quade from KIT. In the Learning With Errors problem, you are given some noisy inner products (mod q) of a secret vector with random vectors and the goal is to retrieve the secret vector (search version) or distinguish these noisy inner products from random (decision version). In certain cases (depending on the modulus q and the noise distribution) it is possible to reduce the search to the decision problem. More importantly, if the noise is taken from an appropriate Gaussian distribution, it can be shown that the average-case instances are as hard as worst-case instances through a worst-case to average-case reduction.\n\nHowever, it is cumbersome to sample such Gaussian noise, and in this paper the authors examine whether it is possible to get a worst-case reduction for some non-Gaussian noise distribution. They give a new worst-case connection for LWE with uniformly distributed errors, but it comes with the drawback that the number of LWE samples that will be given out must be fixed in advance. As the paper title indicates, their proof relies on lossy codes, which is a proof-strategy that was used earlier by Peikert and Waters. Strictly speaking, they do not come with a new proof of the worst-case reduction, but use the proof for Gaussian noise in such a way that they do not require the Gaussians in the LWE instantiation.\n\nFor a fixed number of LWE samples, it is possible to write the problem in matrix form, where the matrix consists of the random vectors used in the inner products. In the original LWE variant this matrix consists of randomly drawn elements mod q. In the variant in this paper, this matrix is replaced by one from a distribution of lossy matrices, which are computationally indistinguishable from random matrices. If this lossy problem is somehow computationally easier than the standard LWE problem, this allows you to distinguish between the lossy matrices and random matrices. The main part of the paper is dedicated to showing that their specific LWE construction is actually lossy for their uniform noise distribution.\n\nThe end result is a reduction from worst-case GapSVP to the average case of their LWE variant. Compared to previous reductions, this one suffers from the loss of an additional factor m in the approximation factor for the lattice problem. It is an open problem to tighten this reduction.\n\n## Sunday, May 26, 2013\n\n### Workshop on Mathematics of Information-Theoretic Cryptography\n\nA workshop on Mathematics of Information-Theoretic Cryptography has been held this week in Leiden. The first morning started with a very interesting talk given by Amos Beimel on Multilinear Secret Sharing Schemes. He described a recent joint work with Aner Ben-Efraim, Carles Padro, and Ilya Tyomkin. Multilinear secret sharing schemes (MSSS) can be seen as a generalization of linear secret sharing schemes, in which the secret is composed by some field elements instead of just one, and they are based on multi-target monotone span program, a generalization of monotone span program. He showed, using representation of groups, that ideal multilinear p-schemes (in which the secret is composed of p field elements, for every prime p) are more powerful of ideal k-linear multilinear schemes for k<p.\n\nThe talk “Low Rank Parity Check Codes (LRPC) and their applications to cryptography”, by Gilles Zemor, was particularly appealing. These codes can be seen as the equivalent of LDPC codes (Low Density Parity Check codes) for the rank metric. More precisely, a LRPC code of rank d, length n and dimension k over Fq^m, is a code with parity check matrix H, that is an (n-k) x m matrix such that the subspace of Fq^m generated by its coefficients has dimension at most d. He described how these codes can be used to define a public key cryptosystem, with small keys and a poor structure, which is not based on the Gabidulin codes. Interestingly, as the more recent MDPC cryptosystem, this construction can be seen as a generalization of the NTRU cryptosystem, but with the rank metric.\nThe last talk of the day was given by Harald Niederreiter. He showed some applications of global function fields, i.e. algebraic function fields of one variable over a finite fields.\n\nFor me, the highlight of the third day was the talk given by Serge Fehr. He presented a joint work with Marco Tomamichel, Jedrzej Kaniewski, and Stephanie Wehner, that will be presented at Eurocrypt next week. During the talk he described a new quantum game (a monogamy-of-entangled-game) with various and important applications in cryptography. For example it is used to prove that standard BB84 QKD (Quantum Key Distribution) remains secure even when one party uses fully untrusted measurement devices.\n\n## Monday, May 20, 2013\n\n### Study Group: Non-Committing Encryption\n\nThe latest study group was presented by Arpita on the topic of non-committing encryption with material from the following papers:\n\nNon-committing encryption denotes semantically secure public-key encryption with the additional possibility of producing fake public keys and fake ciphertexts. Those should be computationally indistinguishable from real public keys and ciphertexts, respectively, but the fake ciphertexts can efficiently be opened to any message. A stronger notion is deniable encryption, where a real ciphertext can be opened to any message, and it is even possible to compute a secret key that decrypts a ciphertext to any message. Obviously, this would be helpful for individuals in jurisdictions that require key disclosure.\n\nThe main motivation for non-committing encryption (NCE) is adaptive security, that is, against an adversary that can corrupted parties in a protocol at any time in a protocol unlike a static adversary that has commit himself at the beginning. NCE can be used to achieve adaptive security in several circumstances such as secure channels, security against selective opening attacks (SOA), and oblivious transfer (implying multiparty computation). For selective opening attacks, the adversary is given a number of ciphertexts under the same public key, of which he can select some to learn the message and tge encryption randomness. A SOA-secure encryption scheme will guarantee that no information on the remaining ciphertexts can be deduced.\n\nNon-commiting encryption was introduced by Canetti et al. in 1996. Damgård and Nielsen proved that NCE can be constructed from simulatable public-key encryption and that ElGamal achieves this property. A simulatable cryptosystem allows to generate a public key and a ciphertext without generating a secret key and inputting message, respectively, and it is possible to extract adequate generation randomness from such a fake public key or ciphertext. The construction involves the sender and the receiver agreeing on a random bit to encrypt one bit as follows: The receiver generates a real and a fake public key and sends them in random order. The sender then encrypts one out two public messages using one of the keys at random, generates a fake ciphertext for the other key, and sends both ciphertexts. If the receiver can decrypt the ciphertext corresponding to the real key to the right public message, they have both chosen the same random bit, which can be used to encrypt one bit. Otherwise, they repeat the protocol.\n\nUnlike simple public-key encryption, this protocol requires interactivity. Nielsen proved in a paper at Crypto 2002 that non-interactive non-committing encryption implies that the secret key has to be as long as the message. However, Choi et al. introduced an NCE scheme that requires only expected two rounds, that is, it is non-interactive with high probability.\n\n## Sunday, May 19, 2013\n\n### School on Information-Theoretic Cryptography\n\nLast week the school on Mathematics of Information-Theoretic Cryptography was held at the Lorentz Center in Leiden, Netherlands. It was intended as a warm up for the workshop following next week at the same center, and that aims to bring together people working in the field, and present latest results on a variety of i-t topics.\n\nI quite enjoyed the school and found it very rewarding, as most of the lectures took special interest in giving careful presentations, on blackboard, with no hesitation on going into the details of what was being discussed. People in the audience feeling akin to take notes were able to do it without loosing track of what the lecturer was saying.\n\nThe school was opened by Jesper Buus Nielsen on Monday. He gave an intuitive presentation on Secure Multiparty Computation (MPC). He discussed aspects of passive security, the UC model, and the efficiency of MPC. Things like Shamir Secret Sharing, security of protocols via simulators and environments, dispute control technique, randomness extraction with Vandermonde matrices, SIMD operations and its relation to Benes networks, and more was dissected.\n\nTuesday and Wednesday were dedicated to a more in-deep range of mathematical topics. Peter Beelen gave a comprehensive introduction of function fields, which constitutes one of the building blocks of algebraic geometric secret sharing. Besides it can be hard to understand for someone with a no-so-wide knowledge in Algebra, he basically started from the scratch, giving examples and intuitions on why concepts are developed in a particular way. He also settled practice exercises that were later resolved on the board. He discussed objects like valuation rings, places, formal expressions known as differentials, the Riemann-Roch theorem, Ihara's constant, and recursively constructions of tower of function fields. I think it was a meticulous introduction, and surely papers dealing with AG secret sharing are much more understandable for anyone who attended this lecture. Chaoping Xing discussed aspects of Algebraic Curves. He was mainly concerned with three applications; algebraic geometric codes (comparison and improvements on bounds of the asymptotic behaviour, and generalization of\nReed-Solomon codes), field multiplication on extension fields (alternative to convolution product in polynomial rings, defined via two maps and the Schur product, and its connection to function fields), and lastly, perhaps a somewhat less crypto-related application, the Quasi-Monte Methods.\n\nCarles Padro gave explicit definitions of secret sharing schemes seen as random variables, realizations of SS for general access structures, and the relation to matroids and polymatroids. Also discussed on lower and upper bounds of the Information Rate. Thursday was devoted to arithmetic SS, and was driven by Ronald Cramer and Ignacio Cascudo. They explained the Codex Framework, which tries to embody together SS schemes that are multiplicative. Many of the aspects discussed the previous days crystalized in this framework. As an aside, Ronald also informally explained the research development on the topic in, roughly, the last twenty years.\n\nThe last day, Friday, Yuval Ishai also talked about MPC and Zero-Knowledge Proofs. He noted that historically i-t cryptography and honest majority MPC have made use of 2PC and ZKP, whereas the other direction seems less explored. He gave high level description on several topics regarding this connection, the one I enjoyed the most was the description of the \"MPC in the Head\" technique.\n\nAll the material is available at the school website.\n\n## Tuesday, May 7, 2013\n\n### Study Group: Multinlinear Maps (II) - Application\n\nFollowing on from last weeks study group on the construction of multilinear maps from ideal lattices (http://eprint.iacr.org/2012/610.pdf), this weeks study group, given by Essam and Gareth, was on applications of multilinear maps. One of the papers (appearing at Crypto later this year) this week can be found here: http://eprint.iacr.org/2013/128.pdf.\n\nThis paper, entitled \"Attribute Based Encryption for Circuits from Multi-linear Maps\", can be seen as something of a breakthrough for ABE, as previous results were significantly weaker. We note that there is another concurrent work due to S. Gorbunov, V. Vaikuntanathan and H. Weeto appearing at STOC which achieves a similar result basing security on the Learning With Errors assumption. At the time of writing this paper was unavailable.\n\nBefore going into details, let's talk about ABE. Introduced by Sahai and Waters in 05, ABE comes in two distinct flavours: key-policy and ciphertext-policy. In the former, secret keys are generated per boolean functions f from an allowable class of functions F. Ciphertexts encrypting messages are associated with an attribute (assignment of boolean values) x. Decryption of a ciphertext with a secret key sk_f is possible iff f(x) = 1. Ciphertext-policy is the just the same with the role of key and ciphertext reversed.\n\nOne of the main challenges has been to increase the depth of function f which can be evaluated. Previously this was only possible for log(n) depth circuits, where n is the max length of an attribute. The goal of this work is to realise ABE for any depth circuit. They construct a KP - ABE and CP-ABE for any polynomially bounded depth circuit, though it should be noted that this work is only a proof-of-concept and is not necessarily intended to be efficient in any way.\n\nThey identify the main problem in previous constructions (in paticular those based on bilinear maps) as \"backtracking\": lets say I decrypt a ciphertext with attribute x so I possess a secret key sk_f such that f(x) = 1. Now consider an OR gate (in f). When using pairings, a ciphertext which succesfully decrypts also allows us to learn information about a gate for which the ciphertext would not have succesfully decrypted since the pairing computation evaluates to the same thing on the OR gate. Now if the gate for which said attribute would not evalute to 1 on, had fan-out higher than 1, we can potentially use this information to decrypt a ciphertext for which f(x) should evaluate to 0, but the additional information is used such that it evaluates to 1.\n\nThe beauty of multi-linear maps is that we can replace the single bi-linear computation with maps from groups e:G_i X G_j -> G_{i+j} such that\ne(g_i^a,g_j^b) = g_{i+j}^{ab}\n\nUsing what they call \"move-forward-then-shift\" they can avoid the backtracking issue. Essentially, the difference lies in the fact we are now in a new group, whereas previously we applied the bilinear map once and the required value the adversary would need to cheat lied in the exponent coming from a bilinear map. Thus backtracking is no-longer possible.\n\n## Wednesday, May 1, 2013\n\n### Study Group: Multilinear Maps (I)\n\nThis week's student group (30 Apr) was given by Joop and Enrique. They discussed the paper \"Candidate Multilinear Maps from Ideal Lattices\" (PDF). The paper describes plausible lattice-based constructions with properties that approximate the soughtafter multilinear maps in hard-discrete-logarithm groups. The security of the constructions relies on seemingly hard assumption (which is a multilinear analog of DDH) in ideal lattices.\n\nDefinition. Cryptographic Multilinear Maps [BS03]:\nFor κ+1 cyclic groups G_1,...,G_κ ,G_T (written additively) of the same order p, a κ multilinear map e : G_1,...,G_κ→ G_T has the following properties:\n\n1. For elements {g_i G_i}_{i=1,...,κ}, index [κ] and integer αZ_pit holds that e(g_1,...,α· g_i,...,g _κ) = α· e(g_1,...,g _κ).\n\n2. The map e is non-degenerate in the following sense: if the elements {g_i G_i}_{i=1,...,κ}, are all generators of their respective groups, then e(g_1,...,g_κ ) is a generator of G_T .\n\nA cryptographic multilinear map scheme consists of efficient procedures for instance-generation, element-encoding validation, group-operation and negation, and multilinear map,\nMMP = (InstGenEncTestadd, neg, map). These procedures are as follows.\n• Instance Generation. A randomized algorithm InstGen that takes the security parameter λ and the multi-linearity parameter κ , and outputs (G_1,...,G_T,p,e,g_1,...,g_κ ). G_i's and G_T describe the groups, p Z is their order, G_1,...,G_κ→ G_T describes an κ -multilinear map as above, and g_i∈{0,1}^{*} for i = 1,..., κ encode generators in these groups. Denote params=(G_1,...,G_T,p,e).\n• Element Encoding. Given the instance params, an index i∈[κ ], and a string x ∈{0,1}^{*}, EncTest(params,i,x) decides if x encodes an element in G_i. Similarly EncTest(params, κ+1; x) efficiently recognizes description of elements in G_T .\n• Group Operation. Given x,yG_i, add(params,i,x,y) computes x+y G_i and neg(params,i,x) computes -x G_i. This implies also that for any α G_i we can e ciently compute α· G_i.\n• Multilinear Map.For {x_i G_i}_{i=1,...,κ}, map(params,x_1,...,x_κ) computes e(x_1,...,x_n)G_T.\n\nHardness Assumptions\n\nFor the multilinear map to be cryptographically useful, at least the discrete logarithm must be hard in the respective groups, and we usually also need the multilinear-DDH to be hard.\n\n1. Multilinear Discrete-log (MDL). The Multilinear Discrete-Log problem is hard for a scheme MMP, if for all κ > 1, all [κ] and all probabilistic polynomial time algorithms, the discrete logarithm advantage of A\n\nAdvDlog_{MMP,A,κ}(λ) = Pr[A(params,i,g_i, α· g_i) = α : (params,g_1,...,g_l) ← InstGen(1^λ,1^κ ), αZp],\nis negligible in λ.\n\n2. Multilinear DDH (MDDH). For a symmetric scheme MMP (with G_1 = G_2 = ), the Multilinear Decision-Di e-Hellman problem is hard for MMP if for any and every probabilistic polynomial time algorithms A, the advantage of A in distinguishing between the following two distributions is negligible in : (params, gα_{0}g, α_{1}g,...,α_{κ}g,( Prod_{i=0,..,κ} α_i)·e(g,..,g)) and (paramsgα_{0}g, α_{1}g,...,α_{κ}g, α·e(g,..,g)).\n\nGraded Encoding Scheme: Efficient Procedure, the Dream Version\nThe authors first describe a \"dream version\" of the efficient procedures which they do not know how to realize, then modify them to deal with technicalities that arise from their use of lattices in the realization.\n\nInstance Generation. The randomized InstGen(1 ^λ,1^κ ) takes as inputs the parameters λ, κ, and outputs (params, p_{zt}), where params is a description of a κ-Graded Encoding System, and p_{zt} is a zero-test parameter for level κ.\n\nRing Sampler. The randomized samp(params) outputs a level-zero encoding α S_{0}^( α) for a nearly uniform element α R.\n\nEncoding. The possibly randomized enc(paramsi, α) takes a level-zero encoding α S_{0}^( α) for some α ∈ R and index i ≦ κ , and outputs the level-i encoding u S_{i}^( α) for the same α .\n\nAddition and Negation. Given params and two encodings relative to the same index, u_{1 S_{i}^( α_1\nand u_{2 S_{i}^( α_2), we have add(params, i, u_1, u_2) = u_1 + u_2 S_{i}^( α_1+ α_2), and neg(params, i, u_1) = -u_1 S_{i}^(-α).\n\nMultiplication. For u_1 S_{i_1}^(α_1), u_2 S_{i_2}^(α_2) such that i_1+ i_2 ≦ κ , we have mul(params, i_1, u_1, i_2, u_2) = u_1 × u_2 S_{i_1 + i_2}^(α_1 · α_2) .\n\nZero-test. The procedure isZero(params, u) output 1 if u S_{κ}^(0) and 0 otherwise.\n\nExtraction. This procedure extracts a canonical and random representation of ring elements from their level-κ encoding. Namely ext(paramsp_{zt}, u) outputs s {0,1}^λ, such that:\n(a) For any α ∈ R and two u_1, u_2 S_{κ }^(α),\next(paramsp_{zt}, u_1) = ext(paramsp_{zt}, u_2),\n(b) The distribution {ext(paramsp_{zt}, u) : α ∈ R, u ∈ S_{κ }^(α)} is nearly uniform over {0,1}^λ.\n\nNew Encoding Scheme\nAn instance of the scheme relative to the parameters encodes elements of a quotient ring QR = / I, where I is a principal ideal I = <g> R, generated by a short vector g. Namely, the ring elements that are encoded in the scheme are cosets of the form e + I for some vector e. The short generator g itself is kept secret. In addition, the system depends on another secret element z, which is chosen at random in R_q. For higher-level encodings, a level-i encoding of the same coset is a vector of the form c/z^i R_q with c e + I short. Speci cally, for {0, 1, ..., κ} the set of all level-i encodings is S_i = {c/z_i R_q : ||c|| < q^{8/g}}, and the set of levle-i encodings of the plaintext element e + I is\nS_{i}^(e + I) = {c/z_i R_q : c ∈ e + I, ||c|| < q^{8/g}}.\n\nInstance Generation. The instance-generation procedure chooses at random the ideal-generator g and denominator z. The denominator z is chosen uniformly at random in R_q. The generator g R should be chosen so that both g and g^{-1} K = Q[X]/(X^n +1) are short. Once we have g, z, we choose and publish some other elements in R_q. Speci cally we have m + 1 elements rand_1,..., x_m, y that are used for encoding, and an element p_{zt} that is used as a zero-testing parameter. We also choose a random seed s for a strong randomness extractor. The instance-generation procedure outputs\nparams = (n, q, y, {x_i}_i, s) and p_{zt}.\n\nSampling level-zero encodings. To sample a level-zero encoding of a random coset, we just draw a random short element in R, d ← D_{Z_n, σ'} , where σ' = σ n (for σ that was used to sample g).\n\nEncodings at higher levels. To allow encoding of cosets at higher levels, we publish as part of our instance-generation a level-one encoding of 1 + I, namely an element y = [a/z]_q where a 1 + I is short. A simplistic method of doing that is drawing a ← D_{1+I, σ'} , then computing y from a.\n\nAdding and multiplying encodings. It is easy to see that the encoding as above is additively homomorphic, in the sense that adding encodings yields an encoding of the sum. This follows since if we have many short c_j 's then their sum is still short, || Prod_{j} c_j || ≦ q, and therefore the sum cProd_{j} c_j = [Prod_{j} c_j]_R_q belong to the coset Prod_{j} (c_j+I). Hence, if we denote u_j = c_j/z R_q then each u_j is an encoding of the coset c_j + I, and the sum [Prod_{j} u_j]_q is of the form c/z where c is still a short element in the sum of the cosets.\n\nZero-testingisZero(params, p_{zt}, u) = 1 if ||[p_{zt}_q ]||_∞ < q^{3/4}, or otherwise 0.\n\nExtraction. To extract a canonical and random representation of a coset from an encoding u = [c/z ^κ]_q, we just multiply by the zero-testing parameter p_{zt}, collect the (log q)/ most-signifi cant bits of each of the n coe fficients of the result, and apply a strong randomness extractor to the collected bits (using the seed from the public parameters). Namely ext(params, p_{zt}, u) = EXTRACT_s(msbs([u · p_{zt}]_q)) (msbs of coe fficient representation). This works because for any two encodings u, u' of the same coset we have ||p_{zt}u - p_{zt}u'|| = ||p_{zt}(u - u')|| < q^{3/4}.\n\nThe security of the graded encoding systems relies on new and at present it seems unlikely that they can be reduced to more established assumptions, such as learning-with-errors (LWE), or even the NTRU hardness assumption."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7722809,"math_prob":0.8824247,"size":7769,"snap":"2020-45-2020-50","text_gpt3_token_len":2379,"char_repetition_ratio":0.13728268,"word_repetition_ratio":0.010550113,"special_character_ratio":0.3199897,"punctuation_ratio":0.19475447,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97077453,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-30T05:14:41Z\",\"WARC-Record-ID\":\"<urn:uuid:919d1657-d553-4514-9f74-133260d31e36>\",\"Content-Length\":\"220104\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4c834288-03d4-48c6-b820-dc3d5c28d593>\",\"WARC-Concurrent-To\":\"<urn:uuid:22363ab3-883a-4b60-a12c-ce414d6b4daf>\",\"WARC-IP-Address\":\"172.217.12.225\",\"WARC-Target-URI\":\"http://bristolcrypto.blogspot.com/2013/05/\",\"WARC-Payload-Digest\":\"sha1:IRFRIAYGB4IMAJGOPU2QRUBKWK5RHSX6\",\"WARC-Block-Digest\":\"sha1:PFWLZZANHRCJQY67HPYQZ5DYLHG72G36\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107907213.64_warc_CC-MAIN-20201030033658-20201030063658-00492.warc.gz\"}"}
|
https://physics.stackexchange.com/questions/175274/is-it-possible-to-heat-plasma-to-the-point-where-there-is-no-electrical-resistan
|
[
"# Is it possible to heat plasma to the point where there is no electrical resistance?\n\nI was discussing Ohm's Law with my teacher and asked about what would happen if the resistance of a circuit was zero, to which he replied that the wire would melt. This got me wondering about plasma/ionised gas and whether or not it would have zero/negative resistance.\n\n• To be clear, a wire with zero resistance would not melt as resistance is required to produce heat. I am assuming the \"zero resistance\" comment was implying a short circuit (i.e., no resistance other than the intrinsic resistivity of the wire and power supply), in which case, yes the wire would have issues. It may not melt though, e.g., aluminum sublimes if super heated like this... – honeste_vivere Sep 23 '16 at 21:05\n\n• @mikuszefski: for a zero resistance wire and an ideal voltage source you get an infinite current, so the power dissipated in the wire in $\\infty^2\\times 0$ and this is undefined. However the power dissipated $\\rightarrow \\infty$ as $R \\rightarrow 0$, so the teacher is correct in this sense. Of course for a real voltage source you need to include the internal resistance of the PSU. In this case the power dissipated in the wire would go though through a maxium then go to zero as $R \\rightarrow 0$. Again, this is tangential to the OP's question. – John Rennie Apr 10 '15 at 10:42"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.935464,"math_prob":0.94963145,"size":3678,"snap":"2020-45-2020-50","text_gpt3_token_len":847,"char_repetition_ratio":0.11540555,"word_repetition_ratio":0.03733766,"special_character_ratio":0.225938,"punctuation_ratio":0.1002907,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9888114,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-22T07:07:06Z\",\"WARC-Record-ID\":\"<urn:uuid:25a95c04-6272-4aa0-885b-13ef937e8c0a>\",\"Content-Length\":\"152296\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5c159e18-7818-455e-abf8-c8a35465940c>\",\"WARC-Concurrent-To\":\"<urn:uuid:9f0e6ff9-3422-463e-8d67-6d1879dd09f0>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/175274/is-it-possible-to-heat-plasma-to-the-point-where-there-is-no-electrical-resistan\",\"WARC-Payload-Digest\":\"sha1:JLWZCHXIKMPSIGI5F4ODT4QM5MJVRKHR\",\"WARC-Block-Digest\":\"sha1:HMEFGGRVBWG4SZDXOVAFIRV7QCM4QD2J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107878921.41_warc_CC-MAIN-20201022053410-20201022083410-00577.warc.gz\"}"}
|
https://proceedings.spp-online.org/article/view/155
|
[
"# Analytic approximation to the energy eigenvalues of a 1D harmonic oscillator satisfying the minimal length generalized uncertainty principle\n\n## Authors\n\n• Kimver Louie Siu Nuñez National Institute of Physics, University of the Philippines Diliman\n• Jose Perico Esguerra National Institute of Physics, University of the Philippines Diliman\n\n## Abstract\n\nThe problem of solving for the energy eigenvalues in systems satisfying the minimal length generalized uncertainty principle has been previously treated using approximations to an infinite-order differential equation. Using the method of linear delta expansion, an analytic expression to the energy eigenvalues in a 1D harmonic oscillator satisfying the minimal length generalized uncertainty relation was derived starting with a second-order eigenvalue equation formulation. This approximation scheme was developed and applied to obtain the energy eigenvalues up to first order corrections. The result of which was found consistent with the exact result found in literature for small principal quantum number n.\n\nSPP-2017-PB-09\n\n## Section\n\nPoster Session B (Complex Systems, Simulations, and Theoretical Physics)\n\n2017-06-07\n\n## How to Cite\n\n\nKLS Nuñez and JP Esguerra, Analytic approximation to the energy eigenvalues of a 1D harmonic oscillator satisfying the minimal length generalized uncertainty principle, Proceedings of the Samahang Pisika ng Pilipinas 35, SPP-2017-PB-09 (2017). URL: https://proceedings.spp-online.org/article/view/155."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8869631,"math_prob":0.7255697,"size":862,"snap":"2023-14-2023-23","text_gpt3_token_len":139,"char_repetition_ratio":0.12587413,"word_repetition_ratio":0.13913043,"special_character_ratio":0.14733179,"punctuation_ratio":0.03968254,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95159805,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-05T06:17:25Z\",\"WARC-Record-ID\":\"<urn:uuid:c36643f7-9624-4f03-9634-bdbffdaa1e90>\",\"Content-Length\":\"21808\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cfab1d13-07c9-4d73-9ea7-23777610da3f>\",\"WARC-Concurrent-To\":\"<urn:uuid:b37033e2-e1a0-4e4d-b2f4-8949b1e40862>\",\"WARC-IP-Address\":\"34.128.107.180\",\"WARC-Target-URI\":\"https://proceedings.spp-online.org/article/view/155\",\"WARC-Payload-Digest\":\"sha1:5ZUEQNJEE3RZ34AIXIU3OUI2GWNSFAIG\",\"WARC-Block-Digest\":\"sha1:DATLWTW5JFHFTJX3U7FNEAKPG3FLGRRM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224651325.38_warc_CC-MAIN-20230605053432-20230605083432-00429.warc.gz\"}"}
|
https://www.analyticsvidhya.com/blog/2022/12/get-your-machine-learning-basics-right-to-crack-the-interviews/
|
[
"Akash Das — Published On December 1, 2022\n\nThis article was published as a part of the Data Science Blogathon.\n\n## Introduction to Machine Learning\n\nBy implementing cutting-edge technology like artificial intelligence (AI) and machine learning, businesses are attempting to increase the accessibility of information and services for consumers. These technologies are increasingly adopted in various business areas, including banking, finance, retail, manufacturing, and healthcare.\n\nSome in-demand organizational roles embracing AI are data scientists, artificial intelligence engineers, machine learning engineers, and data analysts. Knowing the types of machine learning interview questions that hiring managers could pose if you intend to apply for positions in this field is essential because an ML interview would demand rigorous preparation in terms of in-depth knowledge of ML concepts and algorithms, technical and programming skills, etc.\n\nTo help you streamline your efforts as you embrace this learning journey, I decided to start a series of the essential ML questions that one is expected to face during the interviews. Each part will consist of 10 questions to provide brief and focussed coverage of each topic. For the first part, I decided to deal with the question pertinent and meaningful to Machine Learning and Statistics. This should provide you with sufficient background and revision material before your following interview. Over the remaining sections, I would deal with questions specific to Deep Learning, Computer Vision, NLP, Time Series Analysis, etc.\n\n## 1. What are the Major Types of Machine Learning Algorithms?\n\nOn a broad category, ML algorithms can be sub-divided into three main categories:\n\nA. Supervised Learning: These algorithms give predictions based on inferring a function based on labeled training data, i.e., the target variables are present.\n\nIf the target variable is continuous, the usual choice of algorithms is the various regression models (linear, quadratic, polynomial)\n\nIf the target variable is categorical, preferred algorithms include Logistic Regression, Naive Bayes, KNN, SVM, Decision Tree, Boosting Algorithms, Random Forest, etc.\n\nB. Unsupervised Learning: These algorithms predict the target variable based on some patterns on the set of given data. The data for this purpose does not have any dependent variable or label to predict. Algorithms that fall into this category include Clustering Algorithms, Anomaly Detection, Latent Space Models, Singular Value Decomposition, Principal Component Analysis, etc.\n\nC. Reinforcement Learning: These algorithms use a trial-and-error-based approach, and learning occurs based on the rewards received from the previous action.\n\nSource: Experfy Insights\n\n## 2. How can you Determine the Critical Variables from the Dataset you are Working with?\n\nVarious means can be implemented to select essential variables from a dataset:\n\n1. Identify and discard the correlated values before finalizing the important variables\n\n2. Chose the variables based on the p” values obtained from hypothesis testing\n\n3. Forward, backward and stepwise selection\n\n4. Lasso Regression\n\n5. Use Random Forest and select variables based on the feature importance plots\n\n6. The top features can be selected based on the information gained from the available set of features\n\n## 3. Explain Covariance and Correlation.\n\nCovariance indicates the extent to which two random variables depend on each other. A higher number would denote a higher dependency. Their value lies in the range of -∞ and +∞. The problem with covariance is that they are hard to compute without performing normalization over the entire dataset, and a change of scale of the data would affect the covariance.\n\nCorrelation is a statistical measure that determines how strongly two variables are related. Its value would range from -1 to +1, which is scale-independent.\n\nSource: Experfy Insights\n\n## 4. What is the “P” Value?\n\nP – value is used to decide the hypothesis test. The P value denotes the minimum significant level at which we can reject the null hypothesis. A lower the P – value would mean that we are more likely to reject the null hypothesis.\n\n## 5. What are Parametric and Non-parametric Models?\n\nParametric models have limited parameters, and only knowledge about the model’s parameters is required to predict new data.\n\nNon-parametric models possess no limits to the number of input parameters allowing for more flexibility in predicting newer data. All we need to know to provide the predictions is the state of the data and the model parameters.\n\nTabular representation of the differences between Parametric and Non-parametric models\n\n## 6. What is the Difference between Sigmoid and Softmax functions?\n\nThe Sigmoid function is used for Binary Classification methods, where we have only two output classes, whereas the Softmax function is applied to Multiclass methods. Thus it is evident that the input and output of both parts would be slightly different.\n\nThe sigmoid function receives just one input and outputs a single number representing the probability of belonging to class 1 or 2.\n\nWhereas the softmax function is vectorized, i.e., it receives a vector with the same number of entries as the number of classes we have. The output vector contains the probabilities of belonging to that class.\n\nSchematic Representation of the Activation Functions, Source: Nomidl\n\n## 7. How can the Normality of a Dataset be Determined?\n\nThe easiest way to determine the normality is to plot the given data. However, a few of the normality tests also exist as below:\n\n• Shapiro-Wilk Test\n• Anderson-Darling Test\n• Kolmogorov-Smirnov Test\n• Martinez-Iglewicz Test\n• D’Agostino Skewness Test\n\n## 8. How can the K-value be Selected for the K-means Clustering Algorithm?\n\nThe K value can be selected in two different ways: Direct Method and Statistical Testing Method.\n\n1. Direct Method: It contains the elbow and silhouette methods\n\n2. Statistical Testing Method: It includes gap statistics\n\nThe silhouette method remains the most frequently used for determining the optimal K value.\n\n## 9. How can you Handle Outliers in a Dataset?\n\nOutliers are data points significantly different from the rest of the dataset. Approaches that can be used to discover the outliers include – Box Plot, Z-Score, Scatter Plot, etc.\n\nThe following strategies can typically handle outliers:\n\n1. The easiest way is to drop the outlier values\n\n2. They can be separately marked as outliers and used as a different feature vector\n\n3. The feature can alternatively be transformed to reduce the effect of the outlier\n\n## 10. Explain the Differences between Loss and Cost Function.\n\nThe term loss function can be used when dealing with a single data point, whereas when the sum of the error for multiple data is calculated, the term cost function can be used. As such, intuitively, both terms would mean the same, and no significant difference exists between them. Thus the loss function captures the difference between the actual and predicted values for a single data point, whereas the cost function sums the difference over the entire training data.\n\n## Conclusion on Machine Learning\n\nThus in this first part of the series, we brushed up on the fundamental question of Machine Learning that one is expected to face. Having these thorough who be a boost to your preparation. to summarize, the key takeaways from this article would:\n\n• The different categories of machine learning – how and on what basis they can be classified into supervised, unsupervised, and reinforcement learning.\n• Then we dealt with methods of determining the various essential features of the data, how to find correlation and covariance and how to extract critical, meaningful inferences from such data; we discussed p-value and lasso regression,\n• Then we discussed parametric and non-parametric models\n• Key differences between the sigmoid and softmax activation functions were dealt with next\n• Then an essential step of data normalization was discussed, and the various methods of carrying out the same.\n• Another critical factor affecting model performance – outliers was discussed next, and the various ways you can handle them were elaborated.\n• And finally, we finished with the differences between cost and loss function – two of the most common terms you might have used while developing your ML models;\n\nThese fundamental questions should be an excellent primer to build upon over the next few blogs to be followed. Stay tuned for the upcoming parts.\n\nIn part 2 of this series, I dealt with Deep Learning and the essential aspects of DL. Hope this read could add something valuable to your existing technical know-how of Machine Learning!",
null,
""
] |
[
null,
"https://www.analyticsvidhya.com/wp-content/themes/analytics-vidhya/images/default_avatar.svg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9024577,"math_prob":0.84053546,"size":9022,"snap":"2022-40-2023-06","text_gpt3_token_len":1746,"char_repetition_ratio":0.11199822,"word_repetition_ratio":0.004231312,"special_character_ratio":0.186544,"punctuation_ratio":0.109725684,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9798532,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-06T13:39:45Z\",\"WARC-Record-ID\":\"<urn:uuid:fdfb85b9-9828-4b63-be40-9637d671ddf5>\",\"Content-Length\":\"127346\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f86f4f97-c56a-4aff-8c56-f90e9cb53898>\",\"WARC-Concurrent-To\":\"<urn:uuid:8f821463-3233-4cb0-848a-16d61570f073>\",\"WARC-IP-Address\":\"172.67.74.218\",\"WARC-Target-URI\":\"https://www.analyticsvidhya.com/blog/2022/12/get-your-machine-learning-basics-right-to-crack-the-interviews/\",\"WARC-Payload-Digest\":\"sha1:7PQTDFLGNXTVC5UBWSVJ26F5SPIPEWDT\",\"WARC-Block-Digest\":\"sha1:UNZWVY7ZLASIY72H7CLXRE35GUSDQMHN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500339.37_warc_CC-MAIN-20230206113934-20230206143934-00547.warc.gz\"}"}
|
https://monkeymama.savingadvice.com/2015/04/07/march-savings-doings_196988/
|
[
"User Real IP - 54.227.97.219\n```Array\n(\n => Array\n(\n => 182.68.68.92\n)\n\n => Array\n(\n => 101.0.41.201\n)\n\n => Array\n(\n => 43.225.98.123\n)\n\n => Array\n(\n => 2.58.194.139\n)\n\n => Array\n(\n => 46.119.197.104\n)\n\n => Array\n(\n => 45.249.8.93\n)\n\n => Array\n(\n => 103.12.135.72\n)\n\n => Array\n(\n => 157.35.243.216\n)\n\n => Array\n(\n => 209.107.214.176\n)\n\n => Array\n(\n => 5.181.233.166\n)\n\n => Array\n(\n => 106.201.10.100\n)\n\n => Array\n(\n => 36.90.55.39\n)\n\n => Array\n(\n => 119.154.138.47\n)\n\n => Array\n(\n => 51.91.31.157\n)\n\n => Array\n(\n => 182.182.65.216\n)\n\n => Array\n(\n => 157.35.252.63\n)\n\n => Array\n(\n => 14.142.34.163\n)\n\n => Array\n(\n => 178.62.43.135\n)\n\n => Array\n(\n => 43.248.152.148\n)\n\n => Array\n(\n => 222.252.104.114\n)\n\n => Array\n(\n => 209.107.214.168\n)\n\n => Array\n(\n => 103.99.199.250\n)\n\n => Array\n(\n => 178.62.72.160\n)\n\n => Array\n(\n => 27.6.1.170\n)\n\n => Array\n(\n => 182.69.249.219\n)\n\n => Array\n(\n => 110.93.228.86\n)\n\n => Array\n(\n => 72.255.1.98\n)\n\n => Array\n(\n => 182.73.111.98\n)\n\n => Array\n(\n => 45.116.117.11\n)\n\n => Array\n(\n => 122.15.78.189\n)\n\n => Array\n(\n => 14.167.188.234\n)\n\n => Array\n(\n => 223.190.4.202\n)\n\n => Array\n(\n => 202.173.125.19\n)\n\n => Array\n(\n => 103.255.5.32\n)\n\n => Array\n(\n => 39.37.145.103\n)\n\n => Array\n(\n => 140.213.26.249\n)\n\n => Array\n(\n => 45.118.166.85\n)\n\n => Array\n(\n => 102.166.138.255\n)\n\n => Array\n(\n => 77.111.246.234\n)\n\n => Array\n(\n => 45.63.6.196\n)\n\n => Array\n(\n => 103.250.147.115\n)\n\n => Array\n(\n => 223.185.30.99\n)\n\n => Array\n(\n => 103.122.168.108\n)\n\n => Array\n(\n => 123.136.203.21\n)\n\n => Array\n(\n => 171.229.243.63\n)\n\n => Array\n(\n => 153.149.98.149\n)\n\n => Array\n(\n => 223.238.93.15\n)\n\n => Array\n(\n => 178.62.113.166\n)\n\n => Array\n(\n => 101.162.0.153\n)\n\n => Array\n(\n => 121.200.62.114\n)\n\n => Array\n(\n => 14.248.77.252\n)\n\n => Array\n(\n => 95.142.117.29\n)\n\n => Array\n(\n => 150.129.60.107\n)\n\n => Array\n(\n => 94.205.243.22\n)\n\n => Array\n(\n => 115.42.71.143\n)\n\n => Array\n(\n => 117.217.195.59\n)\n\n => Array\n(\n => 182.77.112.56\n)\n\n => Array\n(\n => 182.77.112.108\n)\n\n => Array\n(\n => 41.80.69.10\n)\n\n => Array\n(\n => 117.5.222.121\n)\n\n => Array\n(\n => 103.11.0.38\n)\n\n => Array\n(\n => 202.173.127.140\n)\n\n => Array\n(\n => 49.249.249.50\n)\n\n => Array\n(\n => 116.72.198.211\n)\n\n => Array\n(\n => 223.230.54.53\n)\n\n => Array\n(\n => 102.69.228.74\n)\n\n => Array\n(\n => 39.37.251.89\n)\n\n => Array\n(\n => 39.53.246.141\n)\n\n => Array\n(\n => 39.57.182.72\n)\n\n => Array\n(\n => 209.58.130.210\n)\n\n => Array\n(\n => 104.131.75.86\n)\n\n => Array\n(\n => 106.212.131.255\n)\n\n => Array\n(\n => 106.212.132.127\n)\n\n => Array\n(\n => 223.190.4.60\n)\n\n => Array\n(\n => 103.252.116.252\n)\n\n => Array\n(\n => 103.76.55.182\n)\n\n => Array\n(\n => 45.118.166.70\n)\n\n => Array\n(\n => 103.93.174.215\n)\n\n => Array\n(\n => 5.62.62.142\n)\n\n => Array\n(\n => 182.179.158.156\n)\n\n => Array\n(\n => 39.57.255.12\n)\n\n => Array\n(\n => 39.37.178.37\n)\n\n => Array\n(\n => 182.180.165.211\n)\n\n => Array\n(\n => 119.153.135.17\n)\n\n => Array\n(\n => 72.255.15.244\n)\n\n => Array\n(\n => 139.180.166.181\n)\n\n => Array\n(\n => 70.119.147.111\n)\n\n => Array\n(\n => 106.210.40.83\n)\n\n => Array\n(\n => 14.190.70.91\n)\n\n => Array\n(\n => 202.125.156.82\n)\n\n => Array\n(\n => 115.42.68.38\n)\n\n => Array\n(\n => 102.167.13.108\n)\n\n => Array\n(\n => 117.217.192.130\n)\n\n => Array\n(\n => 205.185.223.156\n)\n\n => Array\n(\n => 171.224.180.29\n)\n\n => Array\n(\n => 45.127.45.68\n)\n\n => Array\n(\n => 195.206.183.232\n)\n\n => Array\n(\n => 49.32.52.115\n)\n\n => Array\n(\n => 49.207.49.223\n)\n\n => Array\n(\n => 45.63.29.61\n)\n\n => Array\n(\n => 103.245.193.214\n)\n\n => Array\n(\n => 39.40.236.69\n)\n\n => Array\n(\n => 62.80.162.111\n)\n\n => Array\n(\n => 45.116.232.56\n)\n\n => Array\n(\n => 45.118.166.91\n)\n\n => Array\n(\n => 180.92.230.234\n)\n\n => Array\n(\n => 157.40.57.160\n)\n\n => Array\n(\n => 110.38.38.130\n)\n\n => Array\n(\n => 72.255.57.183\n)\n\n => Array\n(\n => 182.68.81.85\n)\n\n => Array\n(\n => 39.57.202.122\n)\n\n => Array\n(\n => 119.152.154.36\n)\n\n => Array\n(\n => 5.62.62.141\n)\n\n => Array\n(\n => 119.155.54.232\n)\n\n => Array\n(\n => 39.37.141.22\n)\n\n => Array\n(\n => 183.87.12.225\n)\n\n => Array\n(\n => 107.170.127.117\n)\n\n => Array\n(\n => 125.63.124.49\n)\n\n => Array\n(\n => 39.42.191.3\n)\n\n => Array\n(\n => 116.74.24.72\n)\n\n => Array\n(\n => 46.101.89.227\n)\n\n => Array\n(\n => 202.173.125.247\n)\n\n => Array\n(\n => 39.42.184.254\n)\n\n => Array\n(\n => 115.186.165.132\n)\n\n => Array\n(\n => 39.57.206.126\n)\n\n => Array\n(\n => 103.245.13.145\n)\n\n => Array\n(\n => 202.175.246.43\n)\n\n => Array\n(\n => 192.140.152.150\n)\n\n => Array\n(\n => 202.88.250.103\n)\n\n => Array\n(\n => 103.248.94.207\n)\n\n => Array\n(\n => 77.73.66.101\n)\n\n => Array\n(\n => 104.131.66.8\n)\n\n => Array\n(\n => 113.186.161.97\n)\n\n => Array\n(\n => 222.254.5.7\n)\n\n => Array\n(\n => 223.233.67.247\n)\n\n => Array\n(\n => 171.249.116.146\n)\n\n => Array\n(\n => 47.30.209.71\n)\n\n => Array\n(\n => 202.134.13.130\n)\n\n => Array\n(\n => 27.6.135.7\n)\n\n => Array\n(\n => 107.170.186.79\n)\n\n => Array\n(\n => 103.212.89.171\n)\n\n => Array\n(\n => 117.197.9.77\n)\n\n => Array\n(\n => 122.176.206.233\n)\n\n => Array\n(\n => 192.227.253.222\n)\n\n => Array\n(\n => 182.188.224.119\n)\n\n => Array\n(\n => 14.248.70.74\n)\n\n => Array\n(\n => 42.118.219.169\n)\n\n => Array\n(\n => 110.39.146.170\n)\n\n => Array\n(\n => 119.160.66.143\n)\n\n => Array\n(\n => 103.248.95.130\n)\n\n => Array\n(\n => 27.63.152.208\n)\n\n => Array\n(\n => 49.207.114.96\n)\n\n => Array\n(\n => 102.166.23.214\n)\n\n => Array\n(\n => 175.107.254.73\n)\n\n => Array\n(\n => 103.10.227.214\n)\n\n => Array\n(\n => 202.143.115.89\n)\n\n => Array\n(\n => 110.93.227.187\n)\n\n => Array\n(\n => 103.140.31.60\n)\n\n => Array\n(\n => 110.37.231.46\n)\n\n => Array\n(\n => 39.36.99.238\n)\n\n => Array\n(\n => 157.37.140.26\n)\n\n => Array\n(\n => 43.246.202.226\n)\n\n => Array\n(\n => 137.97.8.143\n)\n\n => Array\n(\n => 182.65.52.242\n)\n\n => Array\n(\n => 115.42.69.62\n)\n\n => Array\n(\n => 14.143.254.58\n)\n\n => Array\n(\n => 223.179.143.236\n)\n\n => Array\n(\n => 223.179.143.249\n)\n\n => Array\n(\n => 103.143.7.54\n)\n\n => Array\n(\n => 223.179.139.106\n)\n\n => Array\n(\n => 39.40.219.90\n)\n\n => Array\n(\n => 45.115.141.231\n)\n\n => Array\n(\n => 120.29.100.33\n)\n\n => Array\n(\n => 112.196.132.5\n)\n\n => Array\n(\n => 202.163.123.153\n)\n\n => Array\n(\n => 5.62.58.146\n)\n\n => Array\n(\n => 39.53.216.113\n)\n\n => Array\n(\n => 42.111.160.73\n)\n\n => Array\n(\n => 107.182.231.213\n)\n\n => Array\n(\n => 119.82.94.120\n)\n\n => Array\n(\n => 178.62.34.82\n)\n\n => Array\n(\n => 203.122.6.18\n)\n\n => Array\n(\n => 157.42.38.251\n)\n\n => Array\n(\n => 45.112.68.222\n)\n\n => Array\n(\n => 49.206.212.122\n)\n\n => Array\n(\n => 104.236.70.228\n)\n\n => Array\n(\n => 42.111.34.243\n)\n\n => Array\n(\n => 84.241.19.186\n)\n\n => Array\n(\n => 89.187.180.207\n)\n\n => Array\n(\n => 104.243.212.118\n)\n\n => Array\n(\n => 104.236.55.136\n)\n\n => Array\n(\n => 106.201.16.163\n)\n\n => Array\n(\n => 46.101.40.25\n)\n\n => Array\n(\n => 45.118.166.94\n)\n\n => Array\n(\n => 49.36.128.102\n)\n\n => Array\n(\n => 14.142.193.58\n)\n\n => Array\n(\n => 212.79.124.176\n)\n\n => Array\n(\n => 45.32.191.194\n)\n\n => Array\n(\n => 105.112.107.46\n)\n\n => Array\n(\n => 106.201.14.8\n)\n\n => Array\n(\n => 110.93.240.65\n)\n\n => Array\n(\n => 27.96.95.177\n)\n\n => Array\n(\n => 45.41.134.35\n)\n\n => Array\n(\n => 180.151.13.110\n)\n\n => Array\n(\n => 101.53.242.89\n)\n\n => Array\n(\n => 115.186.3.110\n)\n\n => Array\n(\n => 171.49.185.242\n)\n\n => Array\n(\n => 115.42.70.24\n)\n\n => Array\n(\n => 45.128.188.43\n)\n\n => Array\n(\n => 103.140.129.63\n)\n\n => Array\n(\n => 101.50.113.147\n)\n\n => Array\n(\n => 103.66.73.30\n)\n\n => Array\n(\n => 117.247.193.169\n)\n\n => Array\n(\n => 120.29.100.94\n)\n\n => Array\n(\n => 42.109.154.39\n)\n\n => Array\n(\n => 122.173.155.150\n)\n\n => Array\n(\n => 45.115.104.53\n)\n\n => Array\n(\n => 116.74.29.84\n)\n\n => Array\n(\n => 101.50.125.34\n)\n\n => Array\n(\n => 45.118.166.80\n)\n\n => Array\n(\n => 91.236.184.27\n)\n\n => Array\n(\n => 113.167.185.120\n)\n\n => Array\n(\n => 27.97.66.222\n)\n\n => Array\n(\n => 43.247.41.117\n)\n\n => Array\n(\n => 23.229.16.227\n)\n\n => Array\n(\n => 14.248.79.209\n)\n\n => Array\n(\n => 117.5.194.26\n)\n\n => Array\n(\n => 117.217.205.41\n)\n\n => Array\n(\n => 114.79.169.99\n)\n\n => Array\n(\n => 103.55.60.97\n)\n\n => Array\n(\n => 182.75.89.210\n)\n\n => Array\n(\n => 77.73.66.109\n)\n\n => Array\n(\n => 182.77.126.139\n)\n\n => Array\n(\n => 14.248.77.166\n)\n\n => Array\n(\n => 157.35.224.133\n)\n\n => Array\n(\n => 183.83.38.27\n)\n\n => Array\n(\n => 182.68.4.77\n)\n\n => Array\n(\n => 122.177.130.234\n)\n\n => Array\n(\n => 103.24.99.99\n)\n\n => Array\n(\n => 103.91.127.66\n)\n\n => Array\n(\n => 41.90.34.240\n)\n\n => Array\n(\n => 49.205.77.102\n)\n\n => Array\n(\n => 103.248.94.142\n)\n\n => Array\n(\n => 104.143.92.170\n)\n\n => Array\n(\n => 219.91.157.114\n)\n\n => Array\n(\n => 223.190.88.22\n)\n\n => Array\n(\n => 223.190.86.232\n)\n\n => Array\n(\n => 39.41.172.80\n)\n\n => Array\n(\n => 124.107.206.5\n)\n\n => Array\n(\n => 139.167.180.224\n)\n\n => Array\n(\n => 93.76.64.248\n)\n\n => Array\n(\n => 65.216.227.119\n)\n\n => Array\n(\n => 223.190.119.141\n)\n\n => Array\n(\n => 110.93.237.179\n)\n\n => Array\n(\n => 41.90.7.85\n)\n\n => Array\n(\n => 103.100.6.26\n)\n\n => Array\n(\n => 104.140.83.13\n)\n\n => Array\n(\n => 223.190.119.133\n)\n\n => Array\n(\n => 119.152.150.87\n)\n\n => Array\n(\n => 103.125.130.147\n)\n\n => Array\n(\n => 27.6.5.52\n)\n\n => Array\n(\n => 103.98.188.26\n)\n\n => Array\n(\n => 39.35.121.81\n)\n\n => Array\n(\n => 74.119.146.182\n)\n\n => Array\n(\n => 5.181.233.162\n)\n\n => Array\n(\n => 157.39.18.60\n)\n\n => Array\n(\n => 1.187.252.25\n)\n\n => Array\n(\n => 39.42.145.59\n)\n\n => Array\n(\n => 39.35.39.198\n)\n\n => Array\n(\n => 49.36.128.214\n)\n\n => Array\n(\n => 182.190.20.56\n)\n\n => Array\n(\n => 122.180.249.189\n)\n\n => Array\n(\n => 117.217.203.107\n)\n\n => Array\n(\n => 103.70.82.241\n)\n\n => Array\n(\n => 45.118.166.68\n)\n\n => Array\n(\n => 122.180.168.39\n)\n\n => Array\n(\n => 149.28.67.254\n)\n\n => Array\n(\n => 223.233.73.8\n)\n\n => Array\n(\n => 122.167.140.0\n)\n\n => Array\n(\n => 95.158.51.55\n)\n\n => Array\n(\n => 27.96.95.134\n)\n\n => Array\n(\n => 49.206.214.53\n)\n\n => Array\n(\n => 212.103.49.92\n)\n\n => Array\n(\n => 122.177.115.101\n)\n\n => Array\n(\n => 171.50.187.124\n)\n\n => Array\n(\n => 122.164.55.107\n)\n\n => Array\n(\n => 98.114.217.204\n)\n\n => Array\n(\n => 106.215.10.54\n)\n\n => Array\n(\n => 115.42.68.28\n)\n\n => Array\n(\n => 104.194.220.87\n)\n\n => Array\n(\n => 103.137.84.170\n)\n\n => Array\n(\n => 61.16.142.110\n)\n\n => Array\n(\n => 212.103.49.85\n)\n\n => Array\n(\n => 39.53.248.162\n)\n\n => Array\n(\n => 203.122.40.214\n)\n\n => Array\n(\n => 117.217.198.72\n)\n\n => Array\n(\n => 115.186.191.203\n)\n\n => Array\n(\n => 120.29.100.199\n)\n\n => Array\n(\n => 45.151.237.24\n)\n\n => Array\n(\n => 223.190.125.232\n)\n\n => Array\n(\n => 41.80.151.17\n)\n\n => Array\n(\n => 23.111.188.5\n)\n\n => Array\n(\n => 223.190.125.216\n)\n\n => Array\n(\n => 103.217.133.119\n)\n\n => Array\n(\n => 103.198.173.132\n)\n\n => Array\n(\n => 47.31.155.89\n)\n\n => Array\n(\n => 223.190.20.253\n)\n\n => Array\n(\n => 104.131.92.125\n)\n\n => Array\n(\n => 223.190.19.152\n)\n\n => Array\n(\n => 103.245.193.191\n)\n\n => Array\n(\n => 106.215.58.255\n)\n\n => Array\n(\n => 119.82.83.238\n)\n\n => Array\n(\n => 106.212.128.138\n)\n\n => Array\n(\n => 139.167.237.36\n)\n\n => Array\n(\n => 222.124.40.250\n)\n\n => Array\n(\n => 134.56.185.169\n)\n\n => Array\n(\n => 54.255.226.31\n)\n\n => Array\n(\n => 137.97.162.31\n)\n\n => Array\n(\n => 95.185.21.191\n)\n\n => Array\n(\n => 171.61.168.151\n)\n\n => Array\n(\n => 137.97.184.4\n)\n\n => Array\n(\n => 106.203.151.202\n)\n\n => Array\n(\n => 39.37.137.0\n)\n\n => Array\n(\n => 45.118.166.66\n)\n\n => Array\n(\n => 14.248.105.100\n)\n\n => Array\n(\n => 106.215.61.185\n)\n\n => Array\n(\n => 202.83.57.179\n)\n\n => Array\n(\n => 89.187.182.176\n)\n\n => Array\n(\n => 49.249.232.198\n)\n\n => Array\n(\n => 132.154.95.236\n)\n\n => Array\n(\n => 223.233.83.230\n)\n\n => Array\n(\n => 183.83.153.14\n)\n\n => Array\n(\n => 125.63.72.210\n)\n\n => Array\n(\n => 207.174.202.11\n)\n\n => Array\n(\n => 119.95.88.59\n)\n\n => Array\n(\n => 122.170.14.150\n)\n\n => Array\n(\n => 45.118.166.75\n)\n\n => Array\n(\n => 103.12.135.37\n)\n\n => Array\n(\n => 49.207.120.225\n)\n\n => Array\n(\n => 182.64.195.207\n)\n\n => Array\n(\n => 103.99.37.16\n)\n\n => Array\n(\n => 46.150.104.221\n)\n\n => Array\n(\n => 104.236.195.147\n)\n\n => Array\n(\n => 103.104.192.43\n)\n\n => Array\n(\n => 24.242.159.118\n)\n\n => Array\n(\n => 39.42.179.143\n)\n\n => Array\n(\n => 111.93.58.131\n)\n\n => Array\n(\n => 193.176.84.127\n)\n\n => Array\n(\n => 209.58.142.218\n)\n\n => Array\n(\n => 69.243.152.129\n)\n\n => Array\n(\n => 117.97.131.249\n)\n\n => Array\n(\n => 103.230.180.89\n)\n\n => Array\n(\n => 106.212.170.192\n)\n\n => Array\n(\n => 171.224.180.95\n)\n\n => Array\n(\n => 158.222.11.87\n)\n\n => Array\n(\n => 119.155.60.246\n)\n\n => Array\n(\n => 41.90.43.129\n)\n\n => Array\n(\n => 185.183.104.170\n)\n\n => Array\n(\n => 14.248.67.65\n)\n\n => Array\n(\n => 117.217.205.82\n)\n\n => Array\n(\n => 111.88.7.209\n)\n\n => Array\n(\n => 49.36.132.244\n)\n\n => Array\n(\n => 171.48.40.2\n)\n\n => Array\n(\n => 119.81.105.2\n)\n\n => Array\n(\n => 49.36.128.114\n)\n\n => Array\n(\n => 213.200.31.93\n)\n\n => Array\n(\n => 2.50.15.110\n)\n\n => Array\n(\n => 120.29.104.67\n)\n\n => Array\n(\n => 223.225.32.221\n)\n\n => Array\n(\n => 14.248.67.195\n)\n\n => Array\n(\n => 119.155.36.13\n)\n\n => Array\n(\n => 101.50.95.104\n)\n\n => Array\n(\n => 104.236.205.233\n)\n\n => Array\n(\n => 122.164.36.150\n)\n\n => Array\n(\n => 157.45.93.209\n)\n\n => Array\n(\n => 182.77.118.100\n)\n\n => Array\n(\n => 182.74.134.218\n)\n\n => Array\n(\n => 183.82.128.146\n)\n\n => Array\n(\n => 112.196.170.234\n)\n\n => Array\n(\n => 122.173.230.178\n)\n\n => Array\n(\n => 122.164.71.199\n)\n\n => Array\n(\n => 51.79.19.31\n)\n\n => Array\n(\n => 58.65.222.20\n)\n\n => Array\n(\n => 103.27.203.97\n)\n\n => Array\n(\n => 111.88.7.242\n)\n\n => Array\n(\n => 14.171.232.77\n)\n\n => Array\n(\n => 46.101.22.182\n)\n\n => Array\n(\n => 103.94.219.19\n)\n\n => Array\n(\n => 139.190.83.30\n)\n\n => Array\n(\n => 223.190.27.184\n)\n\n => Array\n(\n => 182.185.183.34\n)\n\n => Array\n(\n => 91.74.181.242\n)\n\n => Array\n(\n => 222.252.107.14\n)\n\n => Array\n(\n => 137.97.8.28\n)\n\n => Array\n(\n => 46.101.16.229\n)\n\n => Array\n(\n => 122.53.254.229\n)\n\n => Array\n(\n => 106.201.17.180\n)\n\n => Array\n(\n => 123.24.170.129\n)\n\n => Array\n(\n => 182.185.180.79\n)\n\n => Array\n(\n => 223.190.17.4\n)\n\n => Array\n(\n => 213.108.105.1\n)\n\n => Array\n(\n => 171.22.76.9\n)\n\n => Array\n(\n => 202.66.178.164\n)\n\n => Array\n(\n => 178.62.97.171\n)\n\n => Array\n(\n => 167.179.110.209\n)\n\n => Array\n(\n => 223.230.147.172\n)\n\n => Array\n(\n => 76.218.195.160\n)\n\n => Array\n(\n => 14.189.186.178\n)\n\n => Array\n(\n => 157.41.45.143\n)\n\n => Array\n(\n => 223.238.22.53\n)\n\n => Array\n(\n => 111.88.7.244\n)\n\n => Array\n(\n => 5.62.57.19\n)\n\n => Array\n(\n => 106.201.25.216\n)\n\n => Array\n(\n => 117.217.205.33\n)\n\n => Array\n(\n => 111.88.7.215\n)\n\n => Array\n(\n => 106.201.13.77\n)\n\n => Array\n(\n => 50.7.93.29\n)\n\n => Array\n(\n => 123.201.70.112\n)\n\n => Array\n(\n => 39.42.108.226\n)\n\n => Array\n(\n => 27.5.198.29\n)\n\n => Array\n(\n => 223.238.85.187\n)\n\n => Array\n(\n => 171.49.176.32\n)\n\n => Array\n(\n => 14.248.79.242\n)\n\n => Array\n(\n => 46.219.211.183\n)\n\n => Array\n(\n => 185.244.212.251\n)\n\n => Array\n(\n => 14.102.84.126\n)\n\n => Array\n(\n => 106.212.191.52\n)\n\n => Array\n(\n => 154.72.153.203\n)\n\n => Array\n(\n => 14.175.82.64\n)\n\n => Array\n(\n => 141.105.139.131\n)\n\n => Array\n(\n => 182.156.103.98\n)\n\n => Array\n(\n => 117.217.204.75\n)\n\n => Array\n(\n => 104.140.83.115\n)\n\n => Array\n(\n => 119.152.62.8\n)\n\n => Array\n(\n => 45.125.247.94\n)\n\n => Array\n(\n => 137.97.37.252\n)\n\n => Array\n(\n => 117.217.204.73\n)\n\n => Array\n(\n => 14.248.79.133\n)\n\n => Array\n(\n => 39.37.152.52\n)\n\n => Array\n(\n => 103.55.60.54\n)\n\n => Array\n(\n => 102.166.183.88\n)\n\n => Array\n(\n => 5.62.60.162\n)\n\n => Array\n(\n => 5.62.60.163\n)\n\n => Array\n(\n => 160.202.38.131\n)\n\n => Array\n(\n => 106.215.20.253\n)\n\n => Array\n(\n => 39.37.160.54\n)\n\n => Array\n(\n => 119.152.59.186\n)\n\n => Array\n(\n => 183.82.0.164\n)\n\n => Array\n(\n => 41.90.54.87\n)\n\n => Array\n(\n => 157.36.85.158\n)\n\n => Array\n(\n => 110.37.229.162\n)\n\n => Array\n(\n => 203.99.180.148\n)\n\n => Array\n(\n => 117.97.132.91\n)\n\n => Array\n(\n => 171.61.147.105\n)\n\n => Array\n(\n => 14.98.147.214\n)\n\n => Array\n(\n => 209.234.253.191\n)\n\n => Array\n(\n => 92.38.148.60\n)\n\n => Array\n(\n => 178.128.104.139\n)\n\n => Array\n(\n => 212.154.0.176\n)\n\n => Array\n(\n => 103.41.24.141\n)\n\n => Array\n(\n => 2.58.194.132\n)\n\n => Array\n(\n => 180.190.78.169\n)\n\n => Array\n(\n => 106.215.45.182\n)\n\n => Array\n(\n => 125.63.100.222\n)\n\n => Array\n(\n => 110.54.247.17\n)\n\n => Array\n(\n => 103.26.85.105\n)\n\n => Array\n(\n => 39.42.147.3\n)\n\n => Array\n(\n => 137.97.51.41\n)\n\n => Array\n(\n => 71.202.72.27\n)\n\n => Array\n(\n => 119.155.35.10\n)\n\n => Array\n(\n => 202.47.43.120\n)\n\n => Array\n(\n => 183.83.64.101\n)\n\n => Array\n(\n => 182.68.106.141\n)\n\n => Array\n(\n => 171.61.187.87\n)\n\n => Array\n(\n => 178.162.198.118\n)\n\n => Array\n(\n => 115.97.151.218\n)\n\n => Array\n(\n => 196.207.184.210\n)\n\n => Array\n(\n => 198.16.70.51\n)\n\n => Array\n(\n => 41.60.237.33\n)\n\n => Array\n(\n => 47.11.86.26\n)\n\n => Array\n(\n => 117.217.201.183\n)\n\n => Array\n(\n => 203.192.241.79\n)\n\n => Array\n(\n => 122.165.119.85\n)\n\n => Array\n(\n => 23.227.142.218\n)\n\n => Array\n(\n => 178.128.104.221\n)\n\n => Array\n(\n => 14.192.54.163\n)\n\n => Array\n(\n => 139.5.253.218\n)\n\n => Array\n(\n => 117.230.140.127\n)\n\n => Array\n(\n => 195.114.149.199\n)\n\n => Array\n(\n => 14.239.180.220\n)\n\n => Array\n(\n => 103.62.155.94\n)\n\n => Array\n(\n => 118.71.97.14\n)\n\n => Array\n(\n => 137.97.55.163\n)\n\n => Array\n(\n => 202.47.49.198\n)\n\n => Array\n(\n => 171.61.177.85\n)\n\n => Array\n(\n => 137.97.190.224\n)\n\n => Array\n(\n => 117.230.34.142\n)\n\n => Array\n(\n => 103.41.32.5\n)\n\n => Array\n(\n => 203.90.82.237\n)\n\n => Array\n(\n => 125.63.124.238\n)\n\n => Array\n(\n => 103.232.128.78\n)\n\n => Array\n(\n => 106.197.14.227\n)\n\n => Array\n(\n => 81.17.242.244\n)\n\n => Array\n(\n => 81.19.210.179\n)\n\n => Array\n(\n => 103.134.94.98\n)\n\n => Array\n(\n => 110.38.0.86\n)\n\n => Array\n(\n => 103.10.224.195\n)\n\n => Array\n(\n => 45.118.166.89\n)\n\n => Array\n(\n => 115.186.186.68\n)\n\n => Array\n(\n => 138.197.129.237\n)\n\n => Array\n(\n => 14.247.162.52\n)\n\n => Array\n(\n => 103.255.4.5\n)\n\n => Array\n(\n => 14.167.188.254\n)\n\n => Array\n(\n => 5.62.59.54\n)\n\n => Array\n(\n => 27.122.14.80\n)\n\n => Array\n(\n => 39.53.240.21\n)\n\n => Array\n(\n => 39.53.241.243\n)\n\n => Array\n(\n => 117.230.130.161\n)\n\n => Array\n(\n => 118.71.191.149\n)\n\n => Array\n(\n => 5.188.95.54\n)\n\n => Array\n(\n => 66.45.250.27\n)\n\n => Array\n(\n => 106.215.6.175\n)\n\n => Array\n(\n => 27.122.14.86\n)\n\n => Array\n(\n => 103.255.4.51\n)\n\n => Array\n(\n => 101.50.93.119\n)\n\n => Array\n(\n => 137.97.183.51\n)\n\n => Array\n(\n => 117.217.204.185\n)\n\n => Array\n(\n => 95.104.106.82\n)\n\n => Array\n(\n => 5.62.56.211\n)\n\n => Array\n(\n => 103.104.181.214\n)\n\n => Array\n(\n => 36.72.214.243\n)\n\n => Array\n(\n => 5.62.62.219\n)\n\n => Array\n(\n => 110.36.202.4\n)\n\n => Array\n(\n => 103.255.4.253\n)\n\n => Array\n(\n => 110.172.138.61\n)\n\n => Array\n(\n => 159.203.24.195\n)\n\n => Array\n(\n => 13.229.88.42\n)\n\n => Array\n(\n => 59.153.235.20\n)\n\n => Array\n(\n => 171.236.169.32\n)\n\n => Array\n(\n => 14.231.85.206\n)\n\n => Array\n(\n => 119.152.54.103\n)\n\n => Array\n(\n => 103.80.117.202\n)\n\n => Array\n(\n => 223.179.157.75\n)\n\n => Array\n(\n => 122.173.68.249\n)\n\n => Array\n(\n => 188.163.72.113\n)\n\n => Array\n(\n => 119.155.20.164\n)\n\n => Array\n(\n => 103.121.43.68\n)\n\n => Array\n(\n => 5.62.58.6\n)\n\n => Array\n(\n => 203.122.40.154\n)\n\n => Array\n(\n => 222.254.96.203\n)\n\n => Array\n(\n => 103.83.148.167\n)\n\n => Array\n(\n => 103.87.251.226\n)\n\n => Array\n(\n => 123.24.129.24\n)\n\n => Array\n(\n => 137.97.83.8\n)\n\n => Array\n(\n => 223.225.33.132\n)\n\n => Array\n(\n => 128.76.175.190\n)\n\n => Array\n(\n => 195.85.219.32\n)\n\n => Array\n(\n => 139.167.102.93\n)\n\n => Array\n(\n => 49.15.198.253\n)\n\n => Array\n(\n => 45.152.183.172\n)\n\n => Array\n(\n => 42.106.180.136\n)\n\n => Array\n(\n => 95.142.120.9\n)\n\n => Array\n(\n => 139.167.236.4\n)\n\n => Array\n(\n => 159.65.72.167\n)\n\n => Array\n(\n => 49.15.89.2\n)\n\n => Array\n(\n => 42.201.161.195\n)\n\n => Array\n(\n => 27.97.210.38\n)\n\n => Array\n(\n => 171.241.45.19\n)\n\n => Array\n(\n => 42.108.2.18\n)\n\n => Array\n(\n => 171.236.40.68\n)\n\n => Array\n(\n => 110.93.82.102\n)\n\n => Array\n(\n => 43.225.24.186\n)\n\n => Array\n(\n => 117.230.189.119\n)\n\n => Array\n(\n => 124.123.147.187\n)\n\n => Array\n(\n => 216.151.184.250\n)\n\n => Array\n(\n => 49.15.133.16\n)\n\n => Array\n(\n => 49.15.220.74\n)\n\n => Array\n(\n => 157.37.221.246\n)\n\n => Array\n(\n => 176.124.233.112\n)\n\n => Array\n(\n => 118.71.167.40\n)\n\n => Array\n(\n => 182.185.213.161\n)\n\n => Array\n(\n => 47.31.79.248\n)\n\n => Array\n(\n => 223.179.238.192\n)\n\n => Array\n(\n => 79.110.128.219\n)\n\n => Array\n(\n => 106.210.42.111\n)\n\n => Array\n(\n => 47.247.214.229\n)\n\n => Array\n(\n => 193.0.220.108\n)\n\n => Array\n(\n => 1.39.206.254\n)\n\n => Array\n(\n => 123.201.77.38\n)\n\n => Array\n(\n => 115.178.207.21\n)\n\n => Array\n(\n => 37.111.202.92\n)\n\n => Array\n(\n => 49.14.179.243\n)\n\n => Array\n(\n => 117.230.145.171\n)\n\n => Array\n(\n => 171.229.242.96\n)\n\n => Array\n(\n => 27.59.174.209\n)\n\n => Array\n(\n => 1.38.202.211\n)\n\n => Array\n(\n => 157.37.128.46\n)\n\n => Array\n(\n => 49.15.94.80\n)\n\n => Array\n(\n => 123.25.46.147\n)\n\n => Array\n(\n => 117.230.170.185\n)\n\n => Array\n(\n => 5.62.16.19\n)\n\n => Array\n(\n => 103.18.22.25\n)\n\n => Array\n(\n => 103.46.200.132\n)\n\n => Array\n(\n => 27.97.165.126\n)\n\n => Array\n(\n => 117.230.54.241\n)\n\n => Array\n(\n => 27.97.209.76\n)\n\n => Array\n(\n => 47.31.182.109\n)\n\n => Array\n(\n => 47.30.223.221\n)\n\n => Array\n(\n => 103.31.94.82\n)\n\n => Array\n(\n => 103.211.14.45\n)\n\n => Array\n(\n => 171.49.233.58\n)\n\n => Array\n(\n => 65.49.126.95\n)\n\n => Array\n(\n => 69.255.101.170\n)\n\n => Array\n(\n => 27.56.224.67\n)\n\n => Array\n(\n => 117.230.146.86\n)\n\n => Array\n(\n => 27.59.154.52\n)\n\n => Array\n(\n => 132.154.114.10\n)\n\n => Array\n(\n => 182.186.77.60\n)\n\n => Array\n(\n => 117.230.136.74\n)\n\n => Array\n(\n => 43.251.94.253\n)\n\n => Array\n(\n => 103.79.168.225\n)\n\n => Array\n(\n => 117.230.56.51\n)\n\n => Array\n(\n => 27.97.187.45\n)\n\n => Array\n(\n => 137.97.190.61\n)\n\n => Array\n(\n => 193.0.220.26\n)\n\n => Array\n(\n => 49.36.137.62\n)\n\n => Array\n(\n => 47.30.189.248\n)\n\n => Array\n(\n => 109.169.23.84\n)\n\n => Array\n(\n => 111.119.185.46\n)\n\n => Array\n(\n => 103.83.148.246\n)\n\n => Array\n(\n => 157.32.119.138\n)\n\n => Array\n(\n => 5.62.41.53\n)\n\n => Array\n(\n => 47.8.243.236\n)\n\n => Array\n(\n => 112.79.158.69\n)\n\n => Array\n(\n => 180.92.148.218\n)\n\n => Array\n(\n => 157.36.162.154\n)\n\n => Array\n(\n => 39.46.114.47\n)\n\n => Array\n(\n => 117.230.173.250\n)\n\n => Array\n(\n => 117.230.155.188\n)\n\n => Array\n(\n => 193.0.220.17\n)\n\n => Array\n(\n => 117.230.171.166\n)\n\n => Array\n(\n => 49.34.59.228\n)\n\n => Array\n(\n => 111.88.197.247\n)\n\n => Array\n(\n => 47.31.156.112\n)\n\n => Array\n(\n => 137.97.64.180\n)\n\n => Array\n(\n => 14.244.227.18\n)\n\n => Array\n(\n => 113.167.158.8\n)\n\n => Array\n(\n => 39.37.175.189\n)\n\n => Array\n(\n => 139.167.211.8\n)\n\n => Array\n(\n => 73.120.85.235\n)\n\n => Array\n(\n => 104.236.195.72\n)\n\n => Array\n(\n => 27.97.190.71\n)\n\n => Array\n(\n => 79.46.170.222\n)\n\n => Array\n(\n => 102.185.244.207\n)\n\n => Array\n(\n => 37.111.136.30\n)\n\n => Array\n(\n => 50.7.93.28\n)\n\n => Array\n(\n => 110.54.251.43\n)\n\n => Array\n(\n => 49.36.143.40\n)\n\n => Array\n(\n => 103.130.112.185\n)\n\n => Array\n(\n => 37.111.139.202\n)\n\n => Array\n(\n => 49.36.139.108\n)\n\n => Array\n(\n => 37.111.136.179\n)\n\n => Array\n(\n => 123.17.165.77\n)\n\n => Array\n(\n => 49.207.143.206\n)\n\n => Array\n(\n => 39.53.80.149\n)\n\n => Array\n(\n => 223.188.71.214\n)\n\n => Array\n(\n => 1.39.222.233\n)\n\n => Array\n(\n => 117.230.9.85\n)\n\n => Array\n(\n => 103.251.245.216\n)\n\n => Array\n(\n => 122.169.133.145\n)\n\n => Array\n(\n => 43.250.165.57\n)\n\n => Array\n(\n => 39.44.13.235\n)\n\n => Array\n(\n => 157.47.181.2\n)\n\n => Array\n(\n => 27.56.203.50\n)\n\n => Array\n(\n => 191.96.97.58\n)\n\n => Array\n(\n => 111.88.107.172\n)\n\n => Array\n(\n => 113.193.198.136\n)\n\n => Array\n(\n => 117.230.172.175\n)\n\n => Array\n(\n => 191.96.182.239\n)\n\n => Array\n(\n => 2.58.46.28\n)\n\n => Array\n(\n => 183.83.253.87\n)\n\n => Array\n(\n => 49.15.139.242\n)\n\n => Array\n(\n => 42.107.220.236\n)\n\n => Array\n(\n => 14.192.53.196\n)\n\n => Array\n(\n => 42.119.212.202\n)\n\n => Array\n(\n => 192.158.234.45\n)\n\n => Array\n(\n => 49.149.102.192\n)\n\n => Array\n(\n => 47.8.170.17\n)\n\n => Array\n(\n => 117.197.13.247\n)\n\n => Array\n(\n => 116.74.34.44\n)\n\n => Array\n(\n => 103.79.249.163\n)\n\n => Array\n(\n => 182.189.95.70\n)\n\n => Array\n(\n => 137.59.218.118\n)\n\n => Array\n(\n => 103.79.170.243\n)\n\n => Array\n(\n => 39.40.54.25\n)\n\n => Array\n(\n => 119.155.40.170\n)\n\n => Array\n(\n => 1.39.212.157\n)\n\n => Array\n(\n => 70.127.59.89\n)\n\n => Array\n(\n => 14.171.22.58\n)\n\n => Array\n(\n => 194.44.167.141\n)\n\n => Array\n(\n => 111.88.179.154\n)\n\n => Array\n(\n => 117.230.140.232\n)\n\n => Array\n(\n => 137.97.96.128\n)\n\n => Array\n(\n => 198.16.66.123\n)\n\n => Array\n(\n => 106.198.44.193\n)\n\n => Array\n(\n => 119.153.45.75\n)\n\n => Array\n(\n => 49.15.242.208\n)\n\n => Array\n(\n => 119.155.241.20\n)\n\n => Array\n(\n => 106.223.109.155\n)\n\n => Array\n(\n => 119.160.119.245\n)\n\n => Array\n(\n => 106.215.81.160\n)\n\n => Array\n(\n => 1.39.192.211\n)\n\n => Array\n(\n => 223.230.35.208\n)\n\n => Array\n(\n => 39.59.4.158\n)\n\n => Array\n(\n => 43.231.57.234\n)\n\n => Array\n(\n => 60.254.78.193\n)\n\n => Array\n(\n => 122.170.224.87\n)\n\n => Array\n(\n => 117.230.22.141\n)\n\n => Array\n(\n => 119.152.107.211\n)\n\n => Array\n(\n => 103.87.192.206\n)\n\n => Array\n(\n => 39.45.244.47\n)\n\n => Array\n(\n => 50.72.141.94\n)\n\n => Array\n(\n => 39.40.6.128\n)\n\n => Array\n(\n => 39.45.180.186\n)\n\n => Array\n(\n => 49.207.131.233\n)\n\n => Array\n(\n => 139.59.69.142\n)\n\n => Array\n(\n => 111.119.187.29\n)\n\n => Array\n(\n => 119.153.40.69\n)\n\n => Array\n(\n => 49.36.133.64\n)\n\n => Array\n(\n => 103.255.4.249\n)\n\n => Array\n(\n => 198.144.154.15\n)\n\n => Array\n(\n => 1.22.46.172\n)\n\n => Array\n(\n => 103.255.5.46\n)\n\n => Array\n(\n => 27.56.195.188\n)\n\n => Array\n(\n => 203.101.167.53\n)\n\n => Array\n(\n => 117.230.62.195\n)\n\n => Array\n(\n => 103.240.194.186\n)\n\n => Array\n(\n => 107.170.166.118\n)\n\n => Array\n(\n => 101.53.245.80\n)\n\n => Array\n(\n => 157.43.13.208\n)\n\n => Array\n(\n => 137.97.100.77\n)\n\n => Array\n(\n => 47.31.150.208\n)\n\n => Array\n(\n => 137.59.222.65\n)\n\n => Array\n(\n => 103.85.127.250\n)\n\n => Array\n(\n => 103.214.119.32\n)\n\n => Array\n(\n => 182.255.49.52\n)\n\n => Array\n(\n => 103.75.247.72\n)\n\n => Array\n(\n => 103.85.125.250\n)\n\n => Array\n(\n => 183.83.253.167\n)\n\n => Array\n(\n => 1.39.222.111\n)\n\n => Array\n(\n => 111.119.185.9\n)\n\n => Array\n(\n => 111.119.187.10\n)\n\n => Array\n(\n => 39.37.147.144\n)\n\n => Array\n(\n => 103.200.198.183\n)\n\n => Array\n(\n => 1.39.222.18\n)\n\n => Array\n(\n => 198.8.80.103\n)\n\n => Array\n(\n => 42.108.1.243\n)\n\n => Array\n(\n => 111.119.187.16\n)\n\n => Array\n(\n => 39.40.241.8\n)\n\n => Array\n(\n => 122.169.150.158\n)\n\n => Array\n(\n => 39.40.215.119\n)\n\n => Array\n(\n => 103.255.5.77\n)\n\n => Array\n(\n => 157.38.108.196\n)\n\n => Array\n(\n => 103.255.4.67\n)\n\n => Array\n(\n => 5.62.60.62\n)\n\n => Array\n(\n => 39.37.146.202\n)\n\n => Array\n(\n => 110.138.6.221\n)\n\n => Array\n(\n => 49.36.143.88\n)\n\n => Array\n(\n => 37.1.215.39\n)\n\n => Array\n(\n => 27.106.59.190\n)\n\n => Array\n(\n => 139.167.139.41\n)\n\n => Array\n(\n => 114.142.166.179\n)\n\n => Array\n(\n => 223.225.240.112\n)\n\n => Array\n(\n => 103.255.5.36\n)\n\n => Array\n(\n => 175.136.1.48\n)\n\n => Array\n(\n => 103.82.80.166\n)\n\n => Array\n(\n => 182.185.196.126\n)\n\n => Array\n(\n => 157.43.45.76\n)\n\n => Array\n(\n => 119.152.132.49\n)\n\n => Array\n(\n => 5.62.62.162\n)\n\n => Array\n(\n => 103.255.4.39\n)\n\n => Array\n(\n => 202.5.144.153\n)\n\n => Array\n(\n => 1.39.223.210\n)\n\n => Array\n(\n => 92.38.176.154\n)\n\n => Array\n(\n => 117.230.186.142\n)\n\n => Array\n(\n => 183.83.39.123\n)\n\n => Array\n(\n => 182.185.156.76\n)\n\n => Array\n(\n => 104.236.74.212\n)\n\n => Array\n(\n => 107.170.145.187\n)\n\n => Array\n(\n => 117.102.7.98\n)\n\n => Array\n(\n => 137.59.220.0\n)\n\n => Array\n(\n => 157.47.222.14\n)\n\n => Array\n(\n => 47.15.206.82\n)\n\n => Array\n(\n => 117.230.159.99\n)\n\n => Array\n(\n => 117.230.175.151\n)\n\n => Array\n(\n => 157.50.97.18\n)\n\n => Array\n(\n => 117.230.47.164\n)\n\n => Array\n(\n => 77.111.244.34\n)\n\n => Array\n(\n => 139.167.189.131\n)\n\n => Array\n(\n => 1.39.204.103\n)\n\n => Array\n(\n => 117.230.58.0\n)\n\n => Array\n(\n => 182.185.226.66\n)\n\n => Array\n(\n => 115.42.70.119\n)\n\n => Array\n(\n => 171.48.114.134\n)\n\n => Array\n(\n => 144.34.218.75\n)\n\n => Array\n(\n => 199.58.164.135\n)\n\n => Array\n(\n => 101.53.228.151\n)\n\n => Array\n(\n => 117.230.50.57\n)\n\n => Array\n(\n => 223.225.138.84\n)\n\n => Array\n(\n => 110.225.67.65\n)\n\n => Array\n(\n => 47.15.200.39\n)\n\n => Array\n(\n => 39.42.20.127\n)\n\n => Array\n(\n => 117.97.241.81\n)\n\n => Array\n(\n => 111.119.185.11\n)\n\n => Array\n(\n => 103.100.5.94\n)\n\n => Array\n(\n => 103.25.137.69\n)\n\n => Array\n(\n => 47.15.197.159\n)\n\n => Array\n(\n => 223.188.176.122\n)\n\n => Array\n(\n => 27.4.175.80\n)\n\n => Array\n(\n => 181.215.43.82\n)\n\n => Array\n(\n => 27.56.228.157\n)\n\n => Array\n(\n => 117.230.19.19\n)\n\n => Array\n(\n => 47.15.208.71\n)\n\n => Array\n(\n => 119.155.21.176\n)\n\n => Array\n(\n => 47.15.234.202\n)\n\n => Array\n(\n => 117.230.144.135\n)\n\n => Array\n(\n => 112.79.139.199\n)\n\n => Array\n(\n => 116.75.246.41\n)\n\n => Array\n(\n => 117.230.177.126\n)\n\n => Array\n(\n => 212.103.48.134\n)\n\n => Array\n(\n => 102.69.228.78\n)\n\n => Array\n(\n => 117.230.37.118\n)\n\n => Array\n(\n => 175.143.61.75\n)\n\n => Array\n(\n => 139.167.56.138\n)\n\n => Array\n(\n => 58.145.189.250\n)\n\n => Array\n(\n => 103.255.5.65\n)\n\n => Array\n(\n => 39.37.153.182\n)\n\n => Array\n(\n => 157.43.85.106\n)\n\n => Array\n(\n => 185.209.178.77\n)\n\n => Array\n(\n => 1.39.212.45\n)\n\n => Array\n(\n => 103.72.7.16\n)\n\n => Array\n(\n => 117.97.185.244\n)\n\n => Array\n(\n => 117.230.59.106\n)\n\n => Array\n(\n => 137.97.121.103\n)\n\n => Array\n(\n => 103.82.123.215\n)\n\n => Array\n(\n => 103.68.217.248\n)\n\n => Array\n(\n => 157.39.27.175\n)\n\n => Array\n(\n => 47.31.100.249\n)\n\n => Array\n(\n => 14.171.232.139\n)\n\n => Array\n(\n => 103.31.93.208\n)\n\n => Array\n(\n => 117.230.56.77\n)\n\n => Array\n(\n => 124.182.25.124\n)\n\n => Array\n(\n => 106.66.191.242\n)\n\n => Array\n(\n => 175.107.237.25\n)\n\n => Array\n(\n => 119.155.1.27\n)\n\n => Array\n(\n => 72.255.6.24\n)\n\n => Array\n(\n => 192.140.152.223\n)\n\n => Array\n(\n => 212.103.48.136\n)\n\n => Array\n(\n => 39.45.134.56\n)\n\n => Array\n(\n => 139.167.173.30\n)\n\n => Array\n(\n => 117.230.63.87\n)\n\n => Array\n(\n => 182.189.95.203\n)\n\n => Array\n(\n => 49.204.183.248\n)\n\n => Array\n(\n => 47.31.125.188\n)\n\n => Array\n(\n => 103.252.171.13\n)\n\n => Array\n(\n => 112.198.74.36\n)\n\n => Array\n(\n => 27.109.113.152\n)\n\n => Array\n(\n => 42.112.233.44\n)\n\n => Array\n(\n => 47.31.68.193\n)\n\n => Array\n(\n => 103.252.171.134\n)\n\n => Array\n(\n => 77.123.32.114\n)\n\n => Array\n(\n => 1.38.189.66\n)\n\n => Array\n(\n => 39.37.181.108\n)\n\n => Array\n(\n => 42.106.44.61\n)\n\n => Array\n(\n => 157.36.8.39\n)\n\n => Array\n(\n => 223.238.41.53\n)\n\n => Array\n(\n => 202.89.77.10\n)\n\n => Array\n(\n => 117.230.150.68\n)\n\n => Array\n(\n => 175.176.87.60\n)\n\n => Array\n(\n => 137.97.117.87\n)\n\n => Array\n(\n => 132.154.123.11\n)\n\n => Array\n(\n => 45.113.124.141\n)\n\n => Array\n(\n => 103.87.56.203\n)\n\n => Array\n(\n => 159.89.171.156\n)\n\n => Array\n(\n => 119.155.53.88\n)\n\n => Array\n(\n => 222.252.107.215\n)\n\n => Array\n(\n => 132.154.75.238\n)\n\n => Array\n(\n => 122.183.41.168\n)\n\n => Array\n(\n => 42.106.254.158\n)\n\n => Array\n(\n => 103.252.171.37\n)\n\n => Array\n(\n => 202.59.13.180\n)\n\n => Array\n(\n => 37.111.139.137\n)\n\n => Array\n(\n => 39.42.93.25\n)\n\n => Array\n(\n => 118.70.177.156\n)\n\n => Array\n(\n => 117.230.148.64\n)\n\n => Array\n(\n => 39.42.15.194\n)\n\n => Array\n(\n => 137.97.176.86\n)\n\n => Array\n(\n => 106.210.102.113\n)\n\n => Array\n(\n => 39.59.84.236\n)\n\n => Array\n(\n => 49.206.187.177\n)\n\n => Array\n(\n => 117.230.133.11\n)\n\n => Array\n(\n => 42.106.253.173\n)\n\n => Array\n(\n => 178.62.102.23\n)\n\n => Array\n(\n => 111.92.76.175\n)\n\n => Array\n(\n => 132.154.86.45\n)\n\n => Array\n(\n => 117.230.128.39\n)\n\n => Array\n(\n => 117.230.53.165\n)\n\n => Array\n(\n => 49.37.200.171\n)\n\n => Array\n(\n => 104.236.213.230\n)\n\n => Array\n(\n => 103.140.30.81\n)\n\n => Array\n(\n => 59.103.104.117\n)\n\n => Array\n(\n => 65.49.126.79\n)\n\n => Array\n(\n => 202.59.12.251\n)\n\n => Array\n(\n => 37.111.136.17\n)\n\n => Array\n(\n => 163.53.85.67\n)\n\n => Array\n(\n => 123.16.240.73\n)\n\n => Array\n(\n => 103.211.14.183\n)\n\n => Array\n(\n => 103.248.93.211\n)\n\n => Array\n(\n => 116.74.59.127\n)\n\n => Array\n(\n => 137.97.169.254\n)\n\n => Array\n(\n => 113.177.79.100\n)\n\n => Array\n(\n => 74.82.60.187\n)\n\n => Array\n(\n => 117.230.157.66\n)\n\n => Array\n(\n => 169.149.194.241\n)\n\n => Array\n(\n => 117.230.156.11\n)\n\n => Array\n(\n => 202.59.12.157\n)\n\n => Array\n(\n => 42.106.181.25\n)\n\n => Array\n(\n => 202.59.13.78\n)\n\n => Array\n(\n => 39.37.153.32\n)\n\n => Array\n(\n => 177.188.216.175\n)\n\n => Array\n(\n => 222.252.53.165\n)\n\n => Array\n(\n => 37.139.23.89\n)\n\n => Array\n(\n => 117.230.139.150\n)\n\n => Array\n(\n => 104.131.176.234\n)\n\n => Array\n(\n => 42.106.181.117\n)\n\n => Array\n(\n => 117.230.180.94\n)\n\n => Array\n(\n => 180.190.171.5\n)\n\n => Array\n(\n => 150.129.165.185\n)\n\n => Array\n(\n => 51.15.0.150\n)\n\n => Array\n(\n => 42.111.4.84\n)\n\n => Array\n(\n => 74.82.60.116\n)\n\n => Array\n(\n => 137.97.121.165\n)\n\n => Array\n(\n => 64.62.187.194\n)\n\n => Array\n(\n => 137.97.106.162\n)\n\n => Array\n(\n => 137.97.92.46\n)\n\n => Array\n(\n => 137.97.170.25\n)\n\n => Array\n(\n => 103.104.192.100\n)\n\n => Array\n(\n => 185.246.211.34\n)\n\n => Array\n(\n => 119.160.96.78\n)\n\n => Array\n(\n => 212.103.48.152\n)\n\n => Array\n(\n => 183.83.153.90\n)\n\n => Array\n(\n => 117.248.150.41\n)\n\n => Array\n(\n => 185.240.246.180\n)\n\n => Array\n(\n => 162.253.131.125\n)\n\n => Array\n(\n => 117.230.153.217\n)\n\n => Array\n(\n => 117.230.169.1\n)\n\n => Array\n(\n => 49.15.138.247\n)\n\n => Array\n(\n => 117.230.37.110\n)\n\n => Array\n(\n => 14.167.188.75\n)\n\n => Array\n(\n => 169.149.239.93\n)\n\n => Array\n(\n => 103.216.176.91\n)\n\n => Array\n(\n => 117.230.12.126\n)\n\n => Array\n(\n => 184.75.209.110\n)\n\n => Array\n(\n => 117.230.6.60\n)\n\n => Array\n(\n => 117.230.135.132\n)\n\n => Array\n(\n => 31.179.29.109\n)\n\n => Array\n(\n => 74.121.188.186\n)\n\n => Array\n(\n => 117.230.35.5\n)\n\n => Array\n(\n => 111.92.74.239\n)\n\n => Array\n(\n => 104.245.144.236\n)\n\n => Array\n(\n => 39.50.22.100\n)\n\n => Array\n(\n => 47.31.190.23\n)\n\n => Array\n(\n => 157.44.73.187\n)\n\n => Array\n(\n => 117.230.8.91\n)\n\n => Array\n(\n => 157.32.18.2\n)\n\n => Array\n(\n => 111.119.187.43\n)\n\n => Array\n(\n => 203.101.185.246\n)\n\n => Array\n(\n => 5.62.34.22\n)\n\n => Array\n(\n => 122.8.143.76\n)\n\n => Array\n(\n => 115.186.2.187\n)\n\n => Array\n(\n => 202.142.110.89\n)\n\n => Array\n(\n => 157.50.61.254\n)\n\n => Array\n(\n => 223.182.211.185\n)\n\n => Array\n(\n => 103.85.125.210\n)\n\n => Array\n(\n => 103.217.133.147\n)\n\n => Array\n(\n => 103.60.196.217\n)\n\n => Array\n(\n => 157.44.238.6\n)\n\n => Array\n(\n => 117.196.225.68\n)\n\n => Array\n(\n => 104.254.92.52\n)\n\n => Array\n(\n => 39.42.46.72\n)\n\n => Array\n(\n => 221.132.119.36\n)\n\n => Array\n(\n => 111.92.77.47\n)\n\n => Array\n(\n => 223.225.19.152\n)\n\n => Array\n(\n => 159.89.121.217\n)\n\n => Array\n(\n => 39.53.221.205\n)\n\n => Array\n(\n => 193.34.217.28\n)\n\n => Array\n(\n => 139.167.206.36\n)\n\n => Array\n(\n => 96.40.10.7\n)\n\n => Array\n(\n => 124.29.198.123\n)\n\n => Array\n(\n => 117.196.226.1\n)\n\n => Array\n(\n => 106.200.85.135\n)\n\n => Array\n(\n => 106.223.180.28\n)\n\n => Array\n(\n => 103.49.232.110\n)\n\n => Array\n(\n => 139.167.208.50\n)\n\n => Array\n(\n => 139.167.201.102\n)\n\n => Array\n(\n => 14.244.224.237\n)\n\n => Array\n(\n => 103.140.31.187\n)\n\n => Array\n(\n => 49.36.134.136\n)\n\n => Array\n(\n => 160.16.61.75\n)\n\n => Array\n(\n => 103.18.22.228\n)\n\n => Array\n(\n => 47.9.74.121\n)\n\n => Array\n(\n => 47.30.216.159\n)\n\n => Array\n(\n => 117.248.150.78\n)\n\n => Array\n(\n => 5.62.34.17\n)\n\n => Array\n(\n => 139.167.247.181\n)\n\n => Array\n(\n => 193.176.84.29\n)\n\n => Array\n(\n => 103.195.201.121\n)\n\n => Array\n(\n => 89.187.175.115\n)\n\n => Array\n(\n => 137.97.81.251\n)\n\n => Array\n(\n => 157.51.147.62\n)\n\n => Array\n(\n => 103.104.192.42\n)\n\n => Array\n(\n => 14.171.235.26\n)\n\n => Array\n(\n => 178.62.89.121\n)\n\n => Array\n(\n => 119.155.4.164\n)\n\n => Array\n(\n => 43.250.241.89\n)\n\n => Array\n(\n => 103.31.100.80\n)\n\n => Array\n(\n => 119.155.7.44\n)\n\n => Array\n(\n => 106.200.73.114\n)\n\n => Array\n(\n => 77.111.246.18\n)\n\n => Array\n(\n => 157.39.99.247\n)\n\n => Array\n(\n => 103.77.42.132\n)\n\n => Array\n(\n => 74.115.214.133\n)\n\n => Array\n(\n => 117.230.49.224\n)\n\n => Array\n(\n => 39.50.108.238\n)\n\n => Array\n(\n => 47.30.221.45\n)\n\n => Array\n(\n => 95.133.164.235\n)\n\n => Array\n(\n => 212.103.48.141\n)\n\n => Array\n(\n => 104.194.218.147\n)\n\n => Array\n(\n => 106.200.88.241\n)\n\n => Array\n(\n => 182.189.212.211\n)\n\n => Array\n(\n => 39.50.142.129\n)\n\n => Array\n(\n => 77.234.43.133\n)\n\n => Array\n(\n => 49.15.192.58\n)\n\n => Array\n(\n => 119.153.37.55\n)\n\n => Array\n(\n => 27.56.156.128\n)\n\n => Array\n(\n => 168.211.4.33\n)\n\n => Array\n(\n => 203.81.236.239\n)\n\n => Array\n(\n => 157.51.149.61\n)\n\n => Array\n(\n => 117.230.45.255\n)\n\n => Array\n(\n => 39.42.106.169\n)\n\n => Array\n(\n => 27.71.89.76\n)\n\n => Array\n(\n => 123.27.109.167\n)\n\n => Array\n(\n => 106.202.21.91\n)\n\n => Array\n(\n => 103.85.125.206\n)\n\n => Array\n(\n => 122.173.250.229\n)\n\n => Array\n(\n => 106.210.102.77\n)\n\n => Array\n(\n => 134.209.47.156\n)\n\n => Array\n(\n => 45.127.232.12\n)\n\n => Array\n(\n => 45.134.224.11\n)\n\n => Array\n(\n => 27.71.89.122\n)\n\n => Array\n(\n => 157.38.105.117\n)\n\n => Array\n(\n => 191.96.73.215\n)\n\n => Array\n(\n => 171.241.92.31\n)\n\n => Array\n(\n => 49.149.104.235\n)\n\n => Array\n(\n => 104.229.247.252\n)\n\n => Array\n(\n => 111.92.78.42\n)\n\n => Array\n(\n => 47.31.88.183\n)\n\n => Array\n(\n => 171.61.203.234\n)\n\n => Array\n(\n => 183.83.226.192\n)\n\n => Array\n(\n => 119.157.107.45\n)\n\n => Array\n(\n => 91.202.163.205\n)\n\n => Array\n(\n => 157.43.62.108\n)\n\n => Array\n(\n => 182.68.248.92\n)\n\n => Array\n(\n => 157.32.251.234\n)\n\n => Array\n(\n => 110.225.196.188\n)\n\n => Array\n(\n => 27.71.89.98\n)\n\n => Array\n(\n => 175.176.87.3\n)\n\n => Array\n(\n => 103.55.90.208\n)\n\n => Array\n(\n => 47.31.41.163\n)\n\n => Array\n(\n => 223.182.195.5\n)\n\n => Array\n(\n => 122.52.101.166\n)\n\n => Array\n(\n => 103.207.82.154\n)\n\n => Array\n(\n => 171.224.178.84\n)\n\n => Array\n(\n => 110.225.235.187\n)\n\n => Array\n(\n => 119.160.97.248\n)\n\n => Array\n(\n => 116.90.101.121\n)\n\n => Array\n(\n => 182.255.48.154\n)\n\n => Array\n(\n => 180.149.221.140\n)\n\n => Array\n(\n => 194.44.79.13\n)\n\n => Array\n(\n => 47.247.18.3\n)\n\n => Array\n(\n => 27.56.242.95\n)\n\n => Array\n(\n => 41.60.236.83\n)\n\n => Array\n(\n => 122.164.162.7\n)\n\n => Array\n(\n => 71.136.154.5\n)\n\n => Array\n(\n => 132.154.119.122\n)\n\n => Array\n(\n => 110.225.80.135\n)\n\n => Array\n(\n => 84.17.61.143\n)\n\n => Array\n(\n => 119.160.102.244\n)\n\n => Array\n(\n => 47.31.27.44\n)\n\n => Array\n(\n => 27.71.89.160\n)\n\n => Array\n(\n => 107.175.38.101\n)\n\n => Array\n(\n => 195.211.150.152\n)\n\n => Array\n(\n => 157.35.250.255\n)\n\n => Array\n(\n => 111.119.187.53\n)\n\n => Array\n(\n => 119.152.97.213\n)\n\n => Array\n(\n => 180.92.143.145\n)\n\n => Array\n(\n => 72.255.61.46\n)\n\n => Array\n(\n => 47.8.183.6\n)\n\n => Array\n(\n => 92.38.148.53\n)\n\n => Array\n(\n => 122.173.194.72\n)\n\n => Array\n(\n => 183.83.226.97\n)\n\n => Array\n(\n => 122.173.73.231\n)\n\n => Array\n(\n => 119.160.101.101\n)\n\n => Array\n(\n => 93.177.75.174\n)\n\n => Array\n(\n => 115.97.196.70\n)\n\n => Array\n(\n => 111.119.187.35\n)\n\n => Array\n(\n => 103.226.226.154\n)\n\n => Array\n(\n => 103.244.172.73\n)\n\n => Array\n(\n => 119.155.61.222\n)\n\n => Array\n(\n => 157.37.184.92\n)\n\n => Array\n(\n => 119.160.103.204\n)\n\n => Array\n(\n => 175.176.87.21\n)\n\n => Array\n(\n => 185.51.228.246\n)\n\n => Array\n(\n => 103.250.164.255\n)\n\n => Array\n(\n => 122.181.194.16\n)\n\n => Array\n(\n => 157.37.230.232\n)\n\n => Array\n(\n => 103.105.236.6\n)\n\n => Array\n(\n => 111.88.128.174\n)\n\n => Array\n(\n => 37.111.139.82\n)\n\n => Array\n(\n => 39.34.133.52\n)\n\n => Array\n(\n => 113.177.79.80\n)\n\n => Array\n(\n => 180.183.71.184\n)\n\n => Array\n(\n => 116.72.218.255\n)\n\n => Array\n(\n => 119.160.117.26\n)\n\n => Array\n(\n => 158.222.0.252\n)\n\n => Array\n(\n => 23.227.142.146\n)\n\n => Array\n(\n => 122.162.152.152\n)\n\n => Array\n(\n => 103.255.149.106\n)\n\n => Array\n(\n => 104.236.53.155\n)\n\n => Array\n(\n => 119.160.119.155\n)\n\n => Array\n(\n => 175.107.214.244\n)\n\n => Array\n(\n => 102.7.116.7\n)\n\n => Array\n(\n => 111.88.91.132\n)\n\n => Array\n(\n => 119.157.248.108\n)\n\n => Array\n(\n => 222.252.36.107\n)\n\n => Array\n(\n => 157.46.209.227\n)\n\n => Array\n(\n => 39.40.54.1\n)\n\n => Array\n(\n => 223.225.19.254\n)\n\n => Array\n(\n => 154.72.150.8\n)\n\n => Array\n(\n => 107.181.177.130\n)\n\n => Array\n(\n => 101.50.75.31\n)\n\n => Array\n(\n => 84.17.58.69\n)\n\n => Array\n(\n => 178.62.5.157\n)\n\n => Array\n(\n => 112.206.175.147\n)\n\n => Array\n(\n => 137.97.113.137\n)\n\n => Array\n(\n => 103.53.44.154\n)\n\n => Array\n(\n => 180.92.143.129\n)\n\n => Array\n(\n => 14.231.223.7\n)\n\n => Array\n(\n => 167.88.63.201\n)\n\n => Array\n(\n => 103.140.204.8\n)\n\n => Array\n(\n => 221.121.135.108\n)\n\n => Array\n(\n => 119.160.97.129\n)\n\n => Array\n(\n => 27.5.168.249\n)\n\n => Array\n(\n => 119.160.102.191\n)\n\n => Array\n(\n => 122.162.219.12\n)\n\n => Array\n(\n => 157.50.141.122\n)\n\n => Array\n(\n => 43.245.8.17\n)\n\n => Array\n(\n => 113.181.198.179\n)\n\n => Array\n(\n => 47.30.221.59\n)\n\n => Array\n(\n => 110.38.29.246\n)\n\n => Array\n(\n => 14.192.140.199\n)\n\n => Array\n(\n => 24.68.10.106\n)\n\n => Array\n(\n => 47.30.209.179\n)\n\n => Array\n(\n => 106.223.123.21\n)\n\n => Array\n(\n => 103.224.48.30\n)\n\n => Array\n(\n => 104.131.19.173\n)\n\n => Array\n(\n => 119.157.100.206\n)\n\n => Array\n(\n => 103.10.226.73\n)\n\n => Array\n(\n => 162.208.51.163\n)\n\n => Array\n(\n => 47.30.221.227\n)\n\n => Array\n(\n => 119.160.116.210\n)\n\n => Array\n(\n => 198.16.78.43\n)\n\n => Array\n(\n => 39.44.201.151\n)\n\n => Array\n(\n => 71.63.181.84\n)\n\n => Array\n(\n => 14.142.192.218\n)\n\n => Array\n(\n => 39.34.147.178\n)\n\n => Array\n(\n => 111.92.75.25\n)\n\n => Array\n(\n => 45.135.239.58\n)\n\n => Array\n(\n => 14.232.235.1\n)\n\n => Array\n(\n => 49.144.100.155\n)\n\n => Array\n(\n => 62.182.99.33\n)\n\n => Array\n(\n => 104.243.212.187\n)\n\n => Array\n(\n => 59.97.132.214\n)\n\n => Array\n(\n => 47.9.15.179\n)\n\n => Array\n(\n => 39.44.103.186\n)\n\n => Array\n(\n => 183.83.241.132\n)\n\n => Array\n(\n => 103.41.24.180\n)\n\n => Array\n(\n => 104.238.46.39\n)\n\n => Array\n(\n => 103.79.170.78\n)\n\n => Array\n(\n => 59.103.138.81\n)\n\n => Array\n(\n => 106.198.191.146\n)\n\n => Array\n(\n => 106.198.255.122\n)\n\n => Array\n(\n => 47.31.46.37\n)\n\n => Array\n(\n => 109.169.23.76\n)\n\n => Array\n(\n => 103.143.7.55\n)\n\n => Array\n(\n => 49.207.114.52\n)\n\n => Array\n(\n => 198.54.106.250\n)\n\n => Array\n(\n => 39.50.64.18\n)\n\n => Array\n(\n => 222.252.48.132\n)\n\n => Array\n(\n => 42.201.186.53\n)\n\n => Array\n(\n => 115.97.198.95\n)\n\n => Array\n(\n => 93.76.134.244\n)\n\n => Array\n(\n => 122.173.15.189\n)\n\n => Array\n(\n => 39.62.38.29\n)\n\n => Array\n(\n => 103.201.145.254\n)\n\n => Array\n(\n => 111.119.187.23\n)\n\n => Array\n(\n => 157.50.66.33\n)\n\n => Array\n(\n => 157.49.68.163\n)\n\n => Array\n(\n => 103.85.125.215\n)\n\n => Array\n(\n => 103.255.4.16\n)\n\n => Array\n(\n => 223.181.246.206\n)\n\n => Array\n(\n => 39.40.109.226\n)\n\n => Array\n(\n => 43.225.70.157\n)\n\n => Array\n(\n => 103.211.18.168\n)\n\n => Array\n(\n => 137.59.221.60\n)\n\n => Array\n(\n => 103.81.214.63\n)\n\n => Array\n(\n => 39.35.163.2\n)\n\n => Array\n(\n => 106.205.124.39\n)\n\n => Array\n(\n => 209.99.165.216\n)\n\n => Array\n(\n => 103.75.247.187\n)\n\n => Array\n(\n => 157.46.217.41\n)\n\n => Array\n(\n => 75.186.73.80\n)\n\n => Array\n(\n => 212.103.48.153\n)\n\n => Array\n(\n => 47.31.61.167\n)\n\n => Array\n(\n => 119.152.145.131\n)\n\n => Array\n(\n => 171.76.177.244\n)\n\n => Array\n(\n => 103.135.78.50\n)\n\n => Array\n(\n => 103.79.170.75\n)\n\n => Array\n(\n => 105.160.22.74\n)\n\n => Array\n(\n => 47.31.20.153\n)\n\n => Array\n(\n => 42.107.204.65\n)\n\n => Array\n(\n => 49.207.131.35\n)\n\n => Array\n(\n => 92.38.148.61\n)\n\n => Array\n(\n => 183.83.255.206\n)\n\n => Array\n(\n => 107.181.177.131\n)\n\n => Array\n(\n => 39.40.220.157\n)\n\n => Array\n(\n => 39.41.133.176\n)\n\n => Array\n(\n => 103.81.214.61\n)\n\n => Array\n(\n => 223.235.108.46\n)\n\n => Array\n(\n => 171.241.52.118\n)\n\n => Array\n(\n => 39.57.138.47\n)\n\n => Array\n(\n => 106.204.196.172\n)\n\n => Array\n(\n => 39.53.228.40\n)\n\n => Array\n(\n => 185.242.5.99\n)\n\n => Array\n(\n => 103.255.5.96\n)\n\n => Array\n(\n => 157.46.212.120\n)\n\n => Array\n(\n => 107.181.177.138\n)\n\n => Array\n(\n => 47.30.193.65\n)\n\n => Array\n(\n => 39.37.178.33\n)\n\n => Array\n(\n => 157.46.173.29\n)\n\n => Array\n(\n => 39.57.238.211\n)\n\n => Array\n(\n => 157.37.245.113\n)\n\n => Array\n(\n => 47.30.201.138\n)\n\n => Array\n(\n => 106.204.193.108\n)\n\n => Array\n(\n => 212.103.50.212\n)\n\n => Array\n(\n => 58.65.221.187\n)\n\n => Array\n(\n => 178.62.92.29\n)\n\n => Array\n(\n => 111.92.77.166\n)\n\n => Array\n(\n => 47.30.223.158\n)\n\n => Array\n(\n => 103.224.54.83\n)\n\n => Array\n(\n => 119.153.43.22\n)\n\n => Array\n(\n => 223.181.126.251\n)\n\n => Array\n(\n => 39.42.175.202\n)\n\n => Array\n(\n => 103.224.54.190\n)\n\n => Array\n(\n => 49.36.141.210\n)\n\n => Array\n(\n => 5.62.63.218\n)\n\n => Array\n(\n => 39.59.9.18\n)\n\n => Array\n(\n => 111.88.86.45\n)\n\n => Array\n(\n => 178.54.139.5\n)\n\n => Array\n(\n => 116.68.105.241\n)\n\n => Array\n(\n => 119.160.96.187\n)\n\n => Array\n(\n => 182.189.192.103\n)\n\n => Array\n(\n => 119.160.96.143\n)\n\n => Array\n(\n => 110.225.89.98\n)\n\n => Array\n(\n => 169.149.195.134\n)\n\n => Array\n(\n => 103.238.104.54\n)\n\n => Array\n(\n => 47.30.208.142\n)\n\n => Array\n(\n => 157.46.179.209\n)\n\n => Array\n(\n => 223.235.38.119\n)\n\n => Array\n(\n => 42.106.180.165\n)\n\n => Array\n(\n => 154.122.240.239\n)\n\n => Array\n(\n => 106.223.104.191\n)\n\n => Array\n(\n => 111.93.110.218\n)\n\n => Array\n(\n => 182.183.161.171\n)\n\n => Array\n(\n => 157.44.184.211\n)\n\n => Array\n(\n => 157.50.185.193\n)\n\n => Array\n(\n => 117.230.19.194\n)\n\n => Array\n(\n => 162.243.246.160\n)\n\n => Array\n(\n => 106.223.143.53\n)\n\n => Array\n(\n => 39.59.41.15\n)\n\n => Array\n(\n => 106.210.65.42\n)\n\n => Array\n(\n => 180.243.144.208\n)\n\n => Array\n(\n => 116.68.105.22\n)\n\n => Array\n(\n => 115.42.70.46\n)\n\n => Array\n(\n => 99.72.192.148\n)\n\n => Array\n(\n => 182.183.182.48\n)\n\n => Array\n(\n => 171.48.58.97\n)\n\n => Array\n(\n => 37.120.131.188\n)\n\n => Array\n(\n => 117.99.167.177\n)\n\n => Array\n(\n => 111.92.76.210\n)\n\n => Array\n(\n => 14.192.144.245\n)\n\n => Array\n(\n => 169.149.242.87\n)\n\n => Array\n(\n => 47.30.198.149\n)\n\n => Array\n(\n => 59.103.57.140\n)\n\n => Array\n(\n => 117.230.161.168\n)\n\n => Array\n(\n => 110.225.88.173\n)\n\n => Array\n(\n => 169.149.246.95\n)\n\n => Array\n(\n => 42.106.180.52\n)\n\n => Array\n(\n => 14.231.160.157\n)\n\n => Array\n(\n => 123.27.109.47\n)\n\n => Array\n(\n => 157.46.130.54\n)\n\n => Array\n(\n => 39.42.73.194\n)\n\n => Array\n(\n => 117.230.18.147\n)\n\n => Array\n(\n => 27.59.231.98\n)\n\n => Array\n(\n => 125.209.78.227\n)\n\n => Array\n(\n => 157.34.80.145\n)\n\n => Array\n(\n => 42.201.251.86\n)\n\n => Array\n(\n => 117.230.129.158\n)\n\n => Array\n(\n => 103.82.80.103\n)\n\n => Array\n(\n => 47.9.171.228\n)\n\n => Array\n(\n => 117.230.24.92\n)\n\n => Array\n(\n => 103.129.143.119\n)\n\n => Array\n(\n => 39.40.213.45\n)\n\n => Array\n(\n => 178.92.188.214\n)\n\n => Array\n(\n => 110.235.232.191\n)\n\n => Array\n(\n => 5.62.34.18\n)\n\n => Array\n(\n => 47.30.212.134\n)\n\n => Array\n(\n => 157.42.34.196\n)\n\n => Array\n(\n => 157.32.169.9\n)\n\n => Array\n(\n => 103.255.4.11\n)\n\n => Array\n(\n => 117.230.13.69\n)\n\n => Array\n(\n => 117.230.58.97\n)\n\n => Array\n(\n => 92.52.138.39\n)\n\n => Array\n(\n => 221.132.119.63\n)\n\n => Array\n(\n => 117.97.167.188\n)\n\n => Array\n(\n => 119.153.56.58\n)\n\n => Array\n(\n => 105.50.22.150\n)\n\n => Array\n(\n => 115.42.68.126\n)\n\n => Array\n(\n => 182.189.223.159\n)\n\n => Array\n(\n => 39.59.36.90\n)\n\n => Array\n(\n => 111.92.76.114\n)\n\n => Array\n(\n => 157.47.226.163\n)\n\n => Array\n(\n => 202.47.44.37\n)\n\n => Array\n(\n => 106.51.234.172\n)\n\n => Array\n(\n => 103.101.88.166\n)\n\n => Array\n(\n => 27.6.246.146\n)\n\n => Array\n(\n => 103.255.5.83\n)\n\n => Array\n(\n => 103.98.210.185\n)\n\n => Array\n(\n => 122.173.114.134\n)\n\n => Array\n(\n => 122.173.77.248\n)\n\n => Array\n(\n => 5.62.41.172\n)\n\n => Array\n(\n => 180.178.181.17\n)\n\n => Array\n(\n => 37.120.133.224\n)\n\n => Array\n(\n => 45.131.5.156\n)\n\n => Array\n(\n => 110.39.100.110\n)\n\n => Array\n(\n => 176.110.38.185\n)\n\n => Array\n(\n => 36.255.41.64\n)\n\n => Array\n(\n => 103.104.192.15\n)\n\n => Array\n(\n => 43.245.131.195\n)\n\n => Array\n(\n => 14.248.111.185\n)\n\n => Array\n(\n => 122.173.217.133\n)\n\n => Array\n(\n => 106.223.90.245\n)\n\n => Array\n(\n => 119.153.56.80\n)\n\n => Array\n(\n => 103.7.60.172\n)\n\n => Array\n(\n => 157.46.184.233\n)\n\n => Array\n(\n => 182.190.31.95\n)\n\n => Array\n(\n => 109.87.189.122\n)\n\n => Array\n(\n => 91.74.25.100\n)\n\n => Array\n(\n => 182.185.224.144\n)\n\n => Array\n(\n => 106.223.91.221\n)\n\n => Array\n(\n => 182.190.223.40\n)\n\n => Array\n(\n => 2.58.194.134\n)\n\n => Array\n(\n => 196.246.225.236\n)\n\n => Array\n(\n => 106.223.90.173\n)\n\n => Array\n(\n => 23.239.16.54\n)\n\n => Array\n(\n => 157.46.65.225\n)\n\n => Array\n(\n => 115.186.130.14\n)\n\n => Array\n(\n => 103.85.125.157\n)\n\n => Array\n(\n => 14.248.103.6\n)\n\n => Array\n(\n => 123.24.169.247\n)\n\n => Array\n(\n => 103.130.108.153\n)\n\n => Array\n(\n => 115.42.67.21\n)\n\n => Array\n(\n => 202.166.171.190\n)\n\n => Array\n(\n => 39.37.169.104\n)\n\n => Array\n(\n => 103.82.80.59\n)\n\n => Array\n(\n => 175.107.208.58\n)\n\n => Array\n(\n => 203.192.238.247\n)\n\n => Array\n(\n => 103.217.178.150\n)\n\n => Array\n(\n => 103.66.214.173\n)\n\n => Array\n(\n => 110.93.236.174\n)\n\n => Array\n(\n => 143.189.242.64\n)\n\n => Array\n(\n => 77.111.245.12\n)\n\n => Array\n(\n => 145.239.2.231\n)\n\n => Array\n(\n => 115.186.190.38\n)\n\n => Array\n(\n => 109.169.23.67\n)\n\n => Array\n(\n => 198.16.70.29\n)\n\n => Array\n(\n => 111.92.76.186\n)\n\n => Array\n(\n => 115.42.69.34\n)\n\n => Array\n(\n => 73.61.100.95\n)\n\n => Array\n(\n => 103.129.142.31\n)\n\n => Array\n(\n => 103.255.5.53\n)\n\n => Array\n(\n => 103.76.55.2\n)\n\n => Array\n(\n => 47.9.141.138\n)\n\n => Array\n(\n => 103.55.89.234\n)\n\n => Array\n(\n => 103.223.13.53\n)\n\n => Array\n(\n => 175.158.50.203\n)\n\n => Array\n(\n => 103.255.5.90\n)\n\n => Array\n(\n => 106.223.100.138\n)\n\n => Array\n(\n => 39.37.143.193\n)\n\n => Array\n(\n => 206.189.133.131\n)\n\n => Array\n(\n => 43.224.0.233\n)\n\n => Array\n(\n => 115.186.132.106\n)\n\n => Array\n(\n => 31.43.21.159\n)\n\n => Array\n(\n => 119.155.56.131\n)\n\n => Array\n(\n => 103.82.80.138\n)\n\n => Array\n(\n => 24.87.128.119\n)\n\n => Array\n(\n => 106.210.103.163\n)\n\n => Array\n(\n => 103.82.80.90\n)\n\n => Array\n(\n => 157.46.186.45\n)\n\n => Array\n(\n => 157.44.155.238\n)\n\n => Array\n(\n => 103.119.199.2\n)\n\n => Array\n(\n => 27.97.169.205\n)\n\n => Array\n(\n => 157.46.174.89\n)\n\n => Array\n(\n => 43.250.58.220\n)\n\n => Array\n(\n => 76.189.186.64\n)\n\n => Array\n(\n => 103.255.5.57\n)\n\n => Array\n(\n => 171.61.196.136\n)\n\n => Array\n(\n => 202.47.40.88\n)\n\n => Array\n(\n => 97.118.94.116\n)\n\n => Array\n(\n => 157.44.124.157\n)\n\n => Array\n(\n => 95.142.120.13\n)\n\n => Array\n(\n => 42.201.229.151\n)\n\n => Array\n(\n => 157.46.178.95\n)\n\n => Array\n(\n => 169.149.215.192\n)\n\n => Array\n(\n => 42.111.19.48\n)\n\n => Array\n(\n => 1.38.52.18\n)\n\n => Array\n(\n => 145.239.91.241\n)\n\n => Array\n(\n => 47.31.78.191\n)\n\n => Array\n(\n => 103.77.42.60\n)\n\n => Array\n(\n => 157.46.107.144\n)\n\n => Array\n(\n => 157.46.125.124\n)\n\n => Array\n(\n => 110.225.218.108\n)\n\n => Array\n(\n => 106.51.77.185\n)\n\n => Array\n(\n => 123.24.161.207\n)\n\n => Array\n(\n => 106.210.108.22\n)\n\n => Array\n(\n => 42.111.10.14\n)\n\n => Array\n(\n => 223.29.231.175\n)\n\n => Array\n(\n => 27.56.152.132\n)\n\n => Array\n(\n => 119.155.31.100\n)\n\n => Array\n(\n => 122.173.172.127\n)\n\n => Array\n(\n => 103.77.42.64\n)\n\n => Array\n(\n => 157.44.164.106\n)\n\n => Array\n(\n => 14.181.53.38\n)\n\n => Array\n(\n => 115.42.67.64\n)\n\n => Array\n(\n => 47.31.33.140\n)\n\n => Array\n(\n => 103.15.60.234\n)\n\n => Array\n(\n => 182.64.219.181\n)\n\n => Array\n(\n => 103.44.51.6\n)\n\n => Array\n(\n => 116.74.25.157\n)\n\n => Array\n(\n => 116.71.2.128\n)\n\n => Array\n(\n => 157.32.185.239\n)\n\n => Array\n(\n => 47.31.25.79\n)\n\n => Array\n(\n => 178.62.85.75\n)\n\n => Array\n(\n => 180.178.190.39\n)\n\n => Array\n(\n => 39.48.52.179\n)\n\n => Array\n(\n => 106.193.11.240\n)\n\n => Array\n(\n => 103.82.80.226\n)\n\n => Array\n(\n => 49.206.126.30\n)\n\n => Array\n(\n => 157.245.191.173\n)\n\n => Array\n(\n => 49.205.84.237\n)\n\n => Array\n(\n => 47.8.181.232\n)\n\n => Array\n(\n => 182.66.2.92\n)\n\n => Array\n(\n => 49.34.137.220\n)\n\n => Array\n(\n => 209.205.217.125\n)\n\n => Array\n(\n => 192.64.5.73\n)\n\n => Array\n(\n => 27.63.166.108\n)\n\n => Array\n(\n => 120.29.96.211\n)\n\n => Array\n(\n => 182.186.112.135\n)\n\n => Array\n(\n => 45.118.165.151\n)\n\n => Array\n(\n => 47.8.228.12\n)\n\n => Array\n(\n => 106.215.3.162\n)\n\n => Array\n(\n => 111.92.72.66\n)\n\n => Array\n(\n => 169.145.2.9\n)\n\n => Array\n(\n => 106.207.205.100\n)\n\n => Array\n(\n => 223.181.8.12\n)\n\n => Array\n(\n => 157.48.149.78\n)\n\n => Array\n(\n => 103.206.138.116\n)\n\n => Array\n(\n => 39.53.119.22\n)\n\n => Array\n(\n => 157.33.232.106\n)\n\n => Array\n(\n => 49.37.205.139\n)\n\n => Array\n(\n => 115.42.68.3\n)\n\n => Array\n(\n => 93.72.182.251\n)\n\n => Array\n(\n => 202.142.166.22\n)\n\n => Array\n(\n => 157.119.81.111\n)\n\n => Array\n(\n => 182.186.116.155\n)\n\n => Array\n(\n => 157.37.171.37\n)\n\n => Array\n(\n => 117.206.164.48\n)\n\n => Array\n(\n => 49.36.52.63\n)\n\n => Array\n(\n => 203.175.72.112\n)\n\n => Array\n(\n => 171.61.132.193\n)\n\n => Array\n(\n => 111.119.187.44\n)\n\n => Array\n(\n => 39.37.165.216\n)\n\n => Array\n(\n => 103.86.109.58\n)\n\n => Array\n(\n => 39.59.2.86\n)\n\n => Array\n(\n => 111.119.187.28\n)\n\n => Array\n(\n => 106.201.9.10\n)\n\n => Array\n(\n => 49.35.25.106\n)\n\n => Array\n(\n => 157.49.239.103\n)\n\n => Array\n(\n => 157.49.237.198\n)\n\n => Array\n(\n => 14.248.64.121\n)\n\n => Array\n(\n => 117.102.7.214\n)\n\n => Array\n(\n => 120.29.91.246\n)\n\n => Array\n(\n => 103.7.79.41\n)\n\n => Array\n(\n => 132.154.99.209\n)\n\n => Array\n(\n => 212.36.27.245\n)\n\n => Array\n(\n => 157.44.154.9\n)\n\n => Array\n(\n => 47.31.56.44\n)\n\n => Array\n(\n => 192.142.199.136\n)\n\n => Array\n(\n => 171.61.159.49\n)\n\n => Array\n(\n => 119.160.116.151\n)\n\n => Array\n(\n => 103.98.63.39\n)\n\n => Array\n(\n => 41.60.233.216\n)\n\n => Array\n(\n => 49.36.75.212\n)\n\n => Array\n(\n => 223.188.60.20\n)\n\n => Array\n(\n => 103.98.63.50\n)\n\n => Array\n(\n => 178.162.198.21\n)\n\n => Array\n(\n => 157.46.209.35\n)\n\n => Array\n(\n => 119.155.32.151\n)\n\n => Array\n(\n => 102.185.58.161\n)\n\n => Array\n(\n => 59.96.89.231\n)\n\n => Array\n(\n => 119.155.255.198\n)\n\n => Array\n(\n => 42.107.204.57\n)\n\n => Array\n(\n => 42.106.181.74\n)\n\n => Array\n(\n => 157.46.219.186\n)\n\n => Array\n(\n => 115.42.71.49\n)\n\n => Array\n(\n => 157.46.209.131\n)\n\n => Array\n(\n => 220.81.15.94\n)\n\n => Array\n(\n => 111.119.187.24\n)\n\n => Array\n(\n => 49.37.195.185\n)\n\n => Array\n(\n => 42.106.181.85\n)\n\n => Array\n(\n => 43.249.225.134\n)\n\n => Array\n(\n => 117.206.165.151\n)\n\n => Array\n(\n => 119.153.48.250\n)\n\n => Array\n(\n => 27.4.172.162\n)\n\n => Array\n(\n => 117.20.29.51\n)\n\n => Array\n(\n => 103.98.63.135\n)\n\n => Array\n(\n => 117.7.218.229\n)\n\n => Array\n(\n => 157.49.233.105\n)\n\n => Array\n(\n => 39.53.151.199\n)\n\n => Array\n(\n => 101.255.118.33\n)\n\n => Array\n(\n => 41.141.246.9\n)\n\n => Array\n(\n => 221.132.113.78\n)\n\n => Array\n(\n => 119.160.116.202\n)\n\n => Array\n(\n => 117.237.193.244\n)\n\n => Array\n(\n => 157.41.110.145\n)\n\n => Array\n(\n => 103.98.63.5\n)\n\n => Array\n(\n => 103.125.129.58\n)\n\n => Array\n(\n => 183.83.254.66\n)\n\n => Array\n(\n => 45.135.236.160\n)\n\n => Array\n(\n => 198.199.87.124\n)\n\n => Array\n(\n => 193.176.86.41\n)\n\n => Array\n(\n => 115.97.142.98\n)\n\n => Array\n(\n => 222.252.38.198\n)\n\n => Array\n(\n => 110.93.237.49\n)\n\n => Array\n(\n => 103.224.48.122\n)\n\n => Array\n(\n => 110.38.28.130\n)\n\n => Array\n(\n => 106.211.238.154\n)\n\n => Array\n(\n => 111.88.41.73\n)\n\n => Array\n(\n => 119.155.13.143\n)\n\n => Array\n(\n => 103.213.111.60\n)\n\n => Array\n(\n => 202.0.103.42\n)\n\n => Array\n(\n => 157.48.144.33\n)\n\n => Array\n(\n => 111.119.187.62\n)\n\n => Array\n(\n => 103.87.212.71\n)\n\n => Array\n(\n => 157.37.177.20\n)\n\n => Array\n(\n => 223.233.71.92\n)\n\n => Array\n(\n => 116.213.32.107\n)\n\n => Array\n(\n => 104.248.173.151\n)\n\n => Array\n(\n => 14.181.102.222\n)\n\n => Array\n(\n => 103.10.224.252\n)\n\n => Array\n(\n => 175.158.50.57\n)\n\n => Array\n(\n => 165.22.122.199\n)\n\n => Array\n(\n => 23.106.56.12\n)\n\n => Array\n(\n => 203.122.10.146\n)\n\n => Array\n(\n => 37.111.136.138\n)\n\n => Array\n(\n => 103.87.193.66\n)\n\n => Array\n(\n => 39.59.122.246\n)\n\n => Array\n(\n => 111.119.183.63\n)\n\n => Array\n(\n => 157.46.72.102\n)\n\n => Array\n(\n => 185.132.133.82\n)\n\n => Array\n(\n => 118.103.230.148\n)\n\n => Array\n(\n => 5.62.39.45\n)\n\n => Array\n(\n => 119.152.144.134\n)\n\n => Array\n(\n => 172.105.117.102\n)\n\n => Array\n(\n => 122.254.70.212\n)\n\n => Array\n(\n => 102.185.128.97\n)\n\n => Array\n(\n => 182.69.249.11\n)\n\n => Array\n(\n => 105.163.134.167\n)\n\n => Array\n(\n => 111.119.187.38\n)\n\n => Array\n(\n => 103.46.195.93\n)\n\n => Array\n(\n => 106.204.161.156\n)\n\n => Array\n(\n => 122.176.2.175\n)\n\n => Array\n(\n => 117.99.162.31\n)\n\n => Array\n(\n => 106.212.241.242\n)\n\n => Array\n(\n => 42.107.196.149\n)\n\n => Array\n(\n => 212.90.60.57\n)\n\n => Array\n(\n => 175.107.237.12\n)\n\n => Array\n(\n => 157.46.119.152\n)\n\n => Array\n(\n => 157.34.81.12\n)\n\n => Array\n(\n => 162.243.1.22\n)\n\n => Array\n(\n => 110.37.222.178\n)\n\n => Array\n(\n => 103.46.195.68\n)\n\n => Array\n(\n => 119.160.116.81\n)\n\n => Array\n(\n => 138.197.131.28\n)\n\n => Array\n(\n => 103.88.218.124\n)\n\n => Array\n(\n => 192.241.172.113\n)\n\n => Array\n(\n => 110.39.174.106\n)\n\n => Array\n(\n => 111.88.48.17\n)\n\n => Array\n(\n => 42.108.160.218\n)\n\n => Array\n(\n => 117.102.0.16\n)\n\n => Array\n(\n => 157.46.125.235\n)\n\n => Array\n(\n => 14.190.242.251\n)\n\n => Array\n(\n => 47.31.184.64\n)\n\n => Array\n(\n => 49.205.84.157\n)\n\n => Array\n(\n => 122.162.115.247\n)\n\n => Array\n(\n => 41.202.219.74\n)\n\n => Array\n(\n => 106.215.9.67\n)\n\n => Array\n(\n => 103.87.56.208\n)\n\n => Array\n(\n => 103.46.194.147\n)\n\n => Array\n(\n => 116.90.98.81\n)\n\n => Array\n(\n => 115.42.71.213\n)\n\n => Array\n(\n => 39.49.35.192\n)\n\n => Array\n(\n => 41.202.219.65\n)\n\n => Array\n(\n => 131.212.249.93\n)\n\n => Array\n(\n => 49.205.16.251\n)\n\n => Array\n(\n => 39.34.147.250\n)\n\n => Array\n(\n => 183.83.210.185\n)\n\n => Array\n(\n => 49.37.194.215\n)\n\n => Array\n(\n => 103.46.194.108\n)\n\n => Array\n(\n => 89.36.219.233\n)\n\n => Array\n(\n => 119.152.105.178\n)\n\n => Array\n(\n => 202.47.45.125\n)\n\n => Array\n(\n => 156.146.59.27\n)\n\n => Array\n(\n => 132.154.21.156\n)\n\n => Array\n(\n => 157.44.35.31\n)\n\n => Array\n(\n => 41.80.118.124\n)\n\n => Array\n(\n => 47.31.159.198\n)\n\n => Array\n(\n => 103.209.223.140\n)\n\n => Array\n(\n => 157.46.130.138\n)\n\n => Array\n(\n => 49.37.199.246\n)\n\n => Array\n(\n => 111.88.242.10\n)\n\n => Array\n(\n => 43.241.145.110\n)\n\n => Array\n(\n => 124.153.16.30\n)\n\n => Array\n(\n => 27.5.22.173\n)\n\n => Array\n(\n => 111.88.191.173\n)\n\n => Array\n(\n => 41.60.236.200\n)\n\n => Array\n(\n => 115.42.67.146\n)\n\n => Array\n(\n => 150.242.173.7\n)\n\n => Array\n(\n => 14.248.71.23\n)\n\n => Array\n(\n => 111.119.187.4\n)\n\n => Array\n(\n => 124.29.212.118\n)\n\n => Array\n(\n => 51.68.205.163\n)\n\n => Array\n(\n => 182.184.107.63\n)\n\n => Array\n(\n => 106.211.253.87\n)\n\n => Array\n(\n => 223.190.89.5\n)\n\n => Array\n(\n => 183.83.212.63\n)\n\n => Array\n(\n => 129.205.113.227\n)\n\n => Array\n(\n => 106.210.40.141\n)\n\n => Array\n(\n => 91.202.163.169\n)\n\n => Array\n(\n => 76.105.191.89\n)\n\n => Array\n(\n => 171.51.244.160\n)\n\n => Array\n(\n => 37.139.188.92\n)\n\n => Array\n(\n => 23.106.56.37\n)\n\n => Array\n(\n => 157.44.175.180\n)\n\n => Array\n(\n => 122.2.122.97\n)\n\n => Array\n(\n => 103.87.192.194\n)\n\n => Array\n(\n => 192.154.253.6\n)\n\n => Array\n(\n => 77.243.191.19\n)\n\n => Array\n(\n => 122.254.70.46\n)\n\n => Array\n(\n => 154.76.233.73\n)\n\n => Array\n(\n => 195.181.167.150\n)\n\n => Array\n(\n => 209.209.228.5\n)\n\n => Array\n(\n => 203.192.212.115\n)\n\n => Array\n(\n => 221.132.118.179\n)\n\n => Array\n(\n => 117.208.210.204\n)\n\n => Array\n(\n => 120.29.90.126\n)\n\n => Array\n(\n => 36.77.239.190\n)\n\n => Array\n(\n => 157.37.137.127\n)\n\n => Array\n(\n => 39.40.243.6\n)\n\n => Array\n(\n => 182.182.41.201\n)\n\n => Array\n(\n => 39.59.32.46\n)\n\n => Array\n(\n => 111.119.183.36\n)\n\n => Array\n(\n => 103.83.147.61\n)\n\n => Array\n(\n => 103.82.80.85\n)\n\n => Array\n(\n => 103.46.194.161\n)\n\n => Array\n(\n => 101.50.105.38\n)\n\n => Array\n(\n => 111.119.183.58\n)\n\n => Array\n(\n => 47.9.234.51\n)\n\n => Array\n(\n => 120.29.86.157\n)\n\n => Array\n(\n => 175.158.50.70\n)\n\n => Array\n(\n => 112.196.163.235\n)\n\n => Array\n(\n => 139.167.161.85\n)\n\n => Array\n(\n => 106.207.39.181\n)\n\n => Array\n(\n => 103.77.42.159\n)\n\n => Array\n(\n => 185.56.138.220\n)\n\n => Array\n(\n => 119.155.33.205\n)\n\n => Array\n(\n => 157.42.117.124\n)\n\n => Array\n(\n => 103.117.202.202\n)\n\n => Array\n(\n => 220.253.101.109\n)\n\n => Array\n(\n => 49.37.7.247\n)\n\n => Array\n(\n => 119.160.65.27\n)\n\n => Array\n(\n => 114.122.21.151\n)\n\n => Array\n(\n => 157.44.141.83\n)\n\n => Array\n(\n => 103.131.9.7\n)\n\n => Array\n(\n => 125.99.222.21\n)\n\n => Array\n(\n => 103.238.104.206\n)\n\n => Array\n(\n => 110.93.227.100\n)\n\n => Array\n(\n => 49.14.119.114\n)\n\n => Array\n(\n => 115.186.189.82\n)\n\n => Array\n(\n => 106.201.194.2\n)\n\n => Array\n(\n => 106.204.227.28\n)\n\n => Array\n(\n => 47.31.206.13\n)\n\n => Array\n(\n => 39.42.144.109\n)\n\n => Array\n(\n => 14.253.254.90\n)\n\n => Array\n(\n => 157.44.142.118\n)\n\n => Array\n(\n => 192.142.176.21\n)\n\n => Array\n(\n => 103.217.178.225\n)\n\n => Array\n(\n => 106.78.78.16\n)\n\n => Array\n(\n => 167.71.63.184\n)\n\n => Array\n(\n => 207.244.71.82\n)\n\n => Array\n(\n => 71.105.25.145\n)\n\n => Array\n(\n => 39.51.250.30\n)\n\n => Array\n(\n => 157.41.120.160\n)\n\n => Array\n(\n => 39.37.137.81\n)\n\n => Array\n(\n => 41.80.237.27\n)\n\n => Array\n(\n => 111.119.187.50\n)\n\n => Array\n(\n => 49.145.224.252\n)\n\n => Array\n(\n => 106.197.28.106\n)\n\n => Array\n(\n => 103.217.178.240\n)\n\n => Array\n(\n => 27.97.182.237\n)\n\n => Array\n(\n => 106.211.253.72\n)\n\n => Array\n(\n => 119.152.154.172\n)\n\n => Array\n(\n => 103.255.151.148\n)\n\n => Array\n(\n => 154.157.80.12\n)\n\n => Array\n(\n => 156.146.59.28\n)\n\n => Array\n(\n => 171.61.211.64\n)\n\n => Array\n(\n => 27.76.59.22\n)\n\n => Array\n(\n => 167.99.92.124\n)\n\n => Array\n(\n => 132.154.94.51\n)\n\n => Array\n(\n => 111.119.183.38\n)\n\n => Array\n(\n => 115.42.70.169\n)\n\n => Array\n(\n => 109.169.23.83\n)\n\n => Array\n(\n => 157.46.213.64\n)\n\n => Array\n(\n => 39.37.179.171\n)\n\n => Array\n(\n => 14.232.233.32\n)\n\n => Array\n(\n => 157.49.226.13\n)\n\n => Array\n(\n => 185.209.178.78\n)\n\n => Array\n(\n => 222.252.46.230\n)\n\n => Array\n(\n => 139.5.255.168\n)\n\n => Array\n(\n => 202.8.118.12\n)\n\n => Array\n(\n => 39.53.205.63\n)\n\n => Array\n(\n => 157.37.167.227\n)\n\n => Array\n(\n => 157.49.237.121\n)\n\n => Array\n(\n => 208.89.99.6\n)\n\n => Array\n(\n => 111.119.187.33\n)\n\n => Array\n(\n => 39.37.132.101\n)\n\n => Array\n(\n => 72.255.61.15\n)\n\n => Array\n(\n => 157.41.69.126\n)\n\n => Array\n(\n => 27.6.193.15\n)\n\n => Array\n(\n => 157.41.104.8\n)\n\n => Array\n(\n => 157.41.97.162\n)\n\n => Array\n(\n => 95.136.91.67\n)\n\n => Array\n(\n => 110.93.209.138\n)\n\n => Array\n(\n => 119.152.154.82\n)\n\n => Array\n(\n => 111.88.239.223\n)\n\n => Array\n(\n => 157.230.62.100\n)\n\n => Array\n(\n => 37.111.136.167\n)\n\n => Array\n(\n => 139.167.162.65\n)\n\n => Array\n(\n => 120.29.72.72\n)\n\n => Array\n(\n => 39.42.169.69\n)\n\n => Array\n(\n => 157.49.247.12\n)\n\n => Array\n(\n => 43.231.58.221\n)\n\n => Array\n(\n => 111.88.229.18\n)\n\n => Array\n(\n => 171.79.185.198\n)\n\n => Array\n(\n => 169.149.193.102\n)\n\n => Array\n(\n => 207.244.89.162\n)\n\n => Array\n(\n => 27.4.217.129\n)\n\n => Array\n(\n => 91.236.184.12\n)\n\n => Array\n(\n => 14.192.154.150\n)\n\n => Array\n(\n => 167.172.55.253\n)\n\n => Array\n(\n => 103.77.42.192\n)\n\n => Array\n(\n => 39.59.122.140\n)\n\n => Array\n(\n => 41.80.84.46\n)\n\n => Array\n(\n => 202.47.52.115\n)\n\n => Array\n(\n => 222.252.43.47\n)\n\n => Array\n(\n => 119.155.37.250\n)\n\n => Array\n(\n => 157.41.18.88\n)\n\n => Array\n(\n => 39.42.8.59\n)\n\n => Array\n(\n => 39.45.162.110\n)\n\n => Array\n(\n => 111.88.237.25\n)\n\n => Array\n(\n => 103.76.211.168\n)\n\n => Array\n(\n => 178.137.114.165\n)\n\n => Array\n(\n => 43.225.74.146\n)\n\n => Array\n(\n => 157.42.25.26\n)\n\n => Array\n(\n => 137.59.146.63\n)\n\n => Array\n(\n => 119.160.117.190\n)\n\n => Array\n(\n => 1.186.181.133\n)\n\n => Array\n(\n => 39.42.145.94\n)\n\n => Array\n(\n => 203.175.73.96\n)\n\n => Array\n(\n => 39.37.160.14\n)\n\n => Array\n(\n => 157.39.123.250\n)\n\n => Array\n(\n => 95.135.57.82\n)\n\n => Array\n(\n => 162.210.194.35\n)\n\n => Array\n(\n => 39.42.153.135\n)\n\n => Array\n(\n => 118.103.230.106\n)\n\n => Array\n(\n => 108.61.39.115\n)\n\n => Array\n(\n => 102.7.108.45\n)\n\n => Array\n(\n => 183.83.138.134\n)\n\n => Array\n(\n => 115.186.70.223\n)\n\n => Array\n(\n => 157.34.17.139\n)\n\n => Array\n(\n => 122.166.158.231\n)\n\n => Array\n(\n => 43.227.135.90\n)\n\n => Array\n(\n => 182.68.46.180\n)\n\n => Array\n(\n => 223.225.28.138\n)\n\n => Array\n(\n => 103.77.42.220\n)\n\n => Array\n(\n => 192.241.219.13\n)\n\n => Array\n(\n => 103.82.80.113\n)\n\n => Array\n(\n => 42.111.243.151\n)\n\n => Array\n(\n => 171.79.189.247\n)\n\n => Array\n(\n => 157.32.132.102\n)\n\n => Array\n(\n => 103.130.105.243\n)\n\n => Array\n(\n => 117.223.98.120\n)\n\n => Array\n(\n => 106.215.197.187\n)\n\n => Array\n(\n => 182.190.194.179\n)\n\n => Array\n(\n => 223.225.29.42\n)\n\n => Array\n(\n => 117.222.94.151\n)\n\n => Array\n(\n => 182.185.199.104\n)\n\n => Array\n(\n => 49.36.145.77\n)\n\n => Array\n(\n => 103.82.80.73\n)\n\n => Array\n(\n => 103.77.16.13\n)\n\n => Array\n(\n => 221.132.118.86\n)\n\n => Array\n(\n => 202.47.45.77\n)\n\n => Array\n(\n => 202.8.118.116\n)\n\n => Array\n(\n => 42.106.180.185\n)\n\n => Array\n(\n => 203.122.8.234\n)\n\n => Array\n(\n => 88.230.104.245\n)\n\n => Array\n(\n => 103.131.9.33\n)\n\n => Array\n(\n => 117.207.209.60\n)\n\n => Array\n(\n => 42.111.253.227\n)\n\n => Array\n(\n => 23.106.56.54\n)\n\n => Array\n(\n => 122.178.143.181\n)\n\n => Array\n(\n => 111.88.180.5\n)\n\n => Array\n(\n => 174.55.224.161\n)\n\n => Array\n(\n => 49.205.87.100\n)\n\n => Array\n(\n => 49.34.183.118\n)\n\n => Array\n(\n => 124.155.255.154\n)\n\n => Array\n(\n => 106.212.135.200\n)\n\n => Array\n(\n => 139.99.159.11\n)\n\n => Array\n(\n => 45.135.229.8\n)\n\n => Array\n(\n => 88.230.106.85\n)\n\n => Array\n(\n => 91.153.145.221\n)\n\n => Array\n(\n => 103.95.83.33\n)\n\n => Array\n(\n => 122.178.116.76\n)\n\n => Array\n(\n => 103.135.78.14\n)\n\n => Array\n(\n => 111.88.233.206\n)\n\n => Array\n(\n => 192.140.153.210\n)\n\n => Array\n(\n => 202.8.118.69\n)\n\n => Array\n(\n => 103.83.130.81\n)\n\n => Array\n(\n => 182.190.213.143\n)\n\n => Array\n(\n => 198.16.74.204\n)\n\n => Array\n(\n => 101.128.117.248\n)\n\n => Array\n(\n => 103.108.5.147\n)\n\n => Array\n(\n => 157.32.130.158\n)\n\n => Array\n(\n => 103.244.172.93\n)\n\n => Array\n(\n => 47.30.140.126\n)\n\n => Array\n(\n => 223.188.40.124\n)\n\n => Array\n(\n => 157.44.191.102\n)\n\n => Array\n(\n => 41.60.237.62\n)\n\n => Array\n(\n => 47.31.228.161\n)\n\n => Array\n(\n => 137.59.217.188\n)\n\n => Array\n(\n => 39.53.220.237\n)\n\n => Array\n(\n => 45.127.45.199\n)\n\n => Array\n(\n => 14.190.71.19\n)\n\n => Array\n(\n => 47.18.205.54\n)\n\n => Array\n(\n => 110.93.240.11\n)\n\n => Array\n(\n => 134.209.29.111\n)\n\n => Array\n(\n => 49.36.175.104\n)\n\n => Array\n(\n => 203.192.230.61\n)\n\n => Array\n(\n => 176.10.125.115\n)\n\n => Array\n(\n => 182.18.206.17\n)\n\n => Array\n(\n => 103.87.194.102\n)\n\n => Array\n(\n => 171.79.123.106\n)\n\n => Array\n(\n => 45.116.233.35\n)\n\n => Array\n(\n => 223.190.57.225\n)\n\n => Array\n(\n => 114.125.6.158\n)\n\n => Array\n(\n => 223.179.138.176\n)\n\n => Array\n(\n => 111.119.183.61\n)\n\n => Array\n(\n => 202.8.118.43\n)\n\n => Array\n(\n => 157.51.175.216\n)\n\n => Array\n(\n => 41.60.238.100\n)\n\n => Array\n(\n => 117.207.210.199\n)\n\n => Array\n(\n => 111.119.183.26\n)\n\n => Array\n(\n => 103.252.226.12\n)\n\n => Array\n(\n => 103.221.208.82\n)\n\n => Array\n(\n => 103.82.80.228\n)\n\n => Array\n(\n => 111.119.187.39\n)\n\n => Array\n(\n => 157.51.161.199\n)\n\n => Array\n(\n => 59.96.88.246\n)\n\n => Array\n(\n => 27.4.181.183\n)\n\n => Array\n(\n => 43.225.98.124\n)\n\n => Array\n(\n => 157.51.113.74\n)\n\n => Array\n(\n => 207.244.89.161\n)\n\n => Array\n(\n => 49.37.184.82\n)\n\n => Array\n(\n => 111.119.183.4\n)\n\n => Array\n(\n => 39.42.130.147\n)\n\n => Array\n(\n => 103.152.101.2\n)\n\n => Array\n(\n => 111.119.183.2\n)\n\n => Array\n(\n => 157.51.171.149\n)\n\n => Array\n(\n => 103.82.80.245\n)\n\n => Array\n(\n => 175.107.207.133\n)\n\n => Array\n(\n => 103.204.169.158\n)\n\n => Array\n(\n => 157.51.181.12\n)\n\n => Array\n(\n => 195.158.193.212\n)\n\n => Array\n(\n => 204.14.73.85\n)\n\n => Array\n(\n => 39.59.59.31\n)\n\n => Array\n(\n => 45.148.11.82\n)\n\n => Array\n(\n => 157.46.117.250\n)\n\n => Array\n(\n => 157.46.127.170\n)\n\n => Array\n(\n => 77.247.181.165\n)\n\n => Array\n(\n => 111.119.183.54\n)\n\n => Array\n(\n => 41.60.232.183\n)\n\n => Array\n(\n => 157.42.206.174\n)\n\n => Array\n(\n => 196.53.10.246\n)\n\n => Array\n(\n => 27.97.186.131\n)\n\n => Array\n(\n => 103.73.101.134\n)\n\n => Array\n(\n => 111.119.183.35\n)\n\n => Array\n(\n => 202.8.118.111\n)\n\n => Array\n(\n => 103.75.246.207\n)\n\n => Array\n(\n => 47.8.94.225\n)\n\n => Array\n(\n => 106.202.40.83\n)\n\n => Array\n(\n => 117.102.2.0\n)\n\n => Array\n(\n => 156.146.59.11\n)\n\n => Array\n(\n => 223.190.115.125\n)\n\n => Array\n(\n => 169.149.212.232\n)\n\n => Array\n(\n => 39.45.150.127\n)\n\n => Array\n(\n => 45.63.10.204\n)\n\n => Array\n(\n => 27.57.86.46\n)\n\n => Array\n(\n => 103.127.20.138\n)\n\n => Array\n(\n => 223.190.27.26\n)\n\n => Array\n(\n => 49.15.248.78\n)\n\n => Array\n(\n => 130.105.135.103\n)\n\n => Array\n(\n => 47.31.3.239\n)\n\n => Array\n(\n => 185.66.71.8\n)\n\n => Array\n(\n => 103.226.226.198\n)\n\n => Array\n(\n => 39.34.134.16\n)\n\n => Array\n(\n => 95.158.53.120\n)\n\n => Array\n(\n => 45.9.249.246\n)\n\n => Array\n(\n => 223.235.162.157\n)\n\n => Array\n(\n => 37.111.139.23\n)\n\n => Array\n(\n => 49.37.153.47\n)\n\n => Array\n(\n => 103.242.60.205\n)\n\n => Array\n(\n => 185.66.68.18\n)\n\n => Array\n(\n => 162.221.202.138\n)\n\n => Array\n(\n => 202.63.195.29\n)\n\n => Array\n(\n => 112.198.75.226\n)\n\n => Array\n(\n => 46.200.69.233\n)\n\n => Array\n(\n => 103.135.78.30\n)\n\n => Array\n(\n => 119.152.226.9\n)\n\n => Array\n(\n => 167.172.242.50\n)\n\n => Array\n(\n => 49.36.151.31\n)\n\n => Array\n(\n => 111.88.237.156\n)\n\n => Array\n(\n => 103.215.168.1\n)\n\n => Array\n(\n => 107.181.177.137\n)\n\n => Array\n(\n => 157.119.186.202\n)\n\n => Array\n(\n => 37.111.139.106\n)\n\n => Array\n(\n => 182.180.152.198\n)\n\n => Array\n(\n => 43.248.153.72\n)\n\n => Array\n(\n => 64.188.20.84\n)\n\n => Array\n(\n => 103.92.214.11\n)\n\n => Array\n(\n => 182.182.14.148\n)\n\n => Array\n(\n => 116.75.154.119\n)\n\n => Array\n(\n => 37.228.235.94\n)\n\n => Array\n(\n => 197.210.55.43\n)\n\n => Array\n(\n => 45.118.165.153\n)\n\n => Array\n(\n => 122.176.32.27\n)\n\n => Array\n(\n => 106.215.161.20\n)\n\n => Array\n(\n => 152.32.113.58\n)\n\n => Array\n(\n => 111.125.106.132\n)\n\n => Array\n(\n => 212.102.40.72\n)\n\n => Array\n(\n => 2.58.194.140\n)\n\n => Array\n(\n => 122.174.68.115\n)\n\n => Array\n(\n => 117.241.66.56\n)\n\n => Array\n(\n => 71.94.172.140\n)\n\n => Array\n(\n => 103.209.228.139\n)\n\n => Array\n(\n => 43.242.177.140\n)\n\n => Array\n(\n => 38.91.101.66\n)\n\n => Array\n(\n => 103.82.80.67\n)\n\n => Array\n(\n => 117.248.62.138\n)\n\n => Array\n(\n => 103.81.215.51\n)\n\n => Array\n(\n => 103.253.174.4\n)\n\n => Array\n(\n => 202.142.110.111\n)\n\n => Array\n(\n => 162.216.142.1\n)\n\n => Array\n(\n => 58.186.7.252\n)\n\n => Array\n(\n => 113.203.247.66\n)\n\n => Array\n(\n => 111.88.50.63\n)\n\n => Array\n(\n => 182.182.94.227\n)\n\n => Array\n(\n => 49.15.232.50\n)\n\n => Array\n(\n => 182.189.76.225\n)\n\n => Array\n(\n => 139.99.159.14\n)\n\n => Array\n(\n => 163.172.159.235\n)\n\n => Array\n(\n => 157.36.235.241\n)\n\n => Array\n(\n => 111.119.187.3\n)\n\n => Array\n(\n => 103.100.4.61\n)\n\n => Array\n(\n => 192.142.130.88\n)\n\n => Array\n(\n => 43.242.176.114\n)\n\n => Array\n(\n => 180.178.156.165\n)\n\n => Array\n(\n => 182.189.236.77\n)\n\n => Array\n(\n => 49.34.197.239\n)\n\n => Array\n(\n => 157.36.107.107\n)\n\n => Array\n(\n => 103.209.85.175\n)\n\n => Array\n(\n => 203.139.63.83\n)\n\n => Array\n(\n => 43.242.177.161\n)\n\n => Array\n(\n => 182.182.77.138\n)\n\n => Array\n(\n => 114.124.168.117\n)\n\n => Array\n(\n => 124.253.79.191\n)\n\n => Array\n(\n => 192.142.168.235\n)\n\n => Array\n(\n => 14.232.235.111\n)\n\n => Array\n(\n => 152.57.124.214\n)\n\n => Array\n(\n => 123.24.172.48\n)\n\n => Array\n(\n => 43.242.176.87\n)\n\n => Array\n(\n => 43.242.176.101\n)\n\n => Array\n(\n => 49.156.84.110\n)\n\n => Array\n(\n => 58.65.222.6\n)\n\n => Array\n(\n => 157.32.189.112\n)\n\n => Array\n(\n => 47.31.155.87\n)\n\n => Array\n(\n => 39.53.244.182\n)\n\n => Array\n(\n => 39.33.221.76\n)\n\n => Array\n(\n => 161.35.130.245\n)\n\n => Array\n(\n => 152.32.113.137\n)\n\n => Array\n(\n => 192.142.187.220\n)\n\n => Array\n(\n => 185.54.228.123\n)\n\n => Array\n(\n => 103.233.87.221\n)\n\n => Array\n(\n => 223.236.200.224\n)\n\n => Array\n(\n => 27.97.189.170\n)\n\n => Array\n(\n => 103.82.80.212\n)\n\n => Array\n(\n => 43.242.176.37\n)\n\n => Array\n(\n => 49.36.144.94\n)\n\n => Array\n(\n => 180.251.62.185\n)\n\n => Array\n(\n => 39.50.243.227\n)\n\n => Array\n(\n => 124.253.20.21\n)\n\n => Array\n(\n => 41.60.233.31\n)\n\n => Array\n(\n => 103.81.215.57\n)\n\n => Array\n(\n => 185.91.120.16\n)\n\n => Array\n(\n => 182.190.107.163\n)\n\n => Array\n(\n => 222.252.61.68\n)\n\n => Array\n(\n => 109.169.23.78\n)\n\n => Array\n(\n => 39.50.151.222\n)\n\n => Array\n(\n => 43.242.176.86\n)\n\n => Array\n(\n => 178.162.222.161\n)\n\n => Array\n(\n => 37.111.139.158\n)\n\n => Array\n(\n => 39.57.224.97\n)\n\n => Array\n(\n => 39.57.157.194\n)\n\n => Array\n(\n => 111.119.183.48\n)\n\n => Array\n(\n => 180.190.171.129\n)\n\n => Array\n(\n => 39.52.174.177\n)\n\n => Array\n(\n => 43.242.176.103\n)\n\n => Array\n(\n => 124.253.83.14\n)\n\n => Array\n(\n => 182.189.116.245\n)\n\n => Array\n(\n => 157.36.178.213\n)\n\n => Array\n(\n => 45.250.65.119\n)\n\n => Array\n(\n => 103.209.86.6\n)\n\n => Array\n(\n => 43.242.176.80\n)\n\n => Array\n(\n => 137.59.147.2\n)\n\n => Array\n(\n => 117.222.95.23\n)\n\n => Array\n(\n => 124.253.81.10\n)\n\n => Array\n(\n => 43.242.177.21\n)\n\n => Array\n(\n => 182.189.224.186\n)\n\n => Array\n(\n => 39.52.178.142\n)\n\n => Array\n(\n => 106.214.29.176\n)\n\n => Array\n(\n => 111.88.145.107\n)\n\n => Array\n(\n => 49.36.142.67\n)\n\n => Array\n(\n => 202.142.65.50\n)\n\n => Array\n(\n => 1.22.186.76\n)\n\n => Array\n(\n => 103.131.8.225\n)\n\n => Array\n(\n => 39.53.212.111\n)\n\n => Array\n(\n => 103.82.80.149\n)\n\n => Array\n(\n => 43.242.176.12\n)\n\n => Array\n(\n => 103.109.13.189\n)\n\n => Array\n(\n => 124.253.206.202\n)\n\n => Array\n(\n => 117.195.115.85\n)\n\n => Array\n(\n => 49.36.245.229\n)\n\n => Array\n(\n => 42.118.8.100\n)\n\n => Array\n(\n => 1.22.73.17\n)\n\n => Array\n(\n => 157.36.166.131\n)\n\n => Array\n(\n => 182.182.38.223\n)\n\n => Array\n(\n => 49.14.150.21\n)\n\n => Array\n(\n => 43.242.176.89\n)\n\n => Array\n(\n => 157.46.185.69\n)\n\n => Array\n(\n => 103.31.92.150\n)\n\n => Array\n(\n => 59.96.90.94\n)\n\n => Array\n(\n => 49.156.111.64\n)\n\n => Array\n(\n => 103.75.244.16\n)\n\n => Array\n(\n => 54.37.18.139\n)\n\n => Array\n(\n => 27.255.173.50\n)\n\n => Array\n(\n => 84.202.161.120\n)\n\n => Array\n(\n => 27.3.224.180\n)\n\n => Array\n(\n => 39.44.14.192\n)\n\n => Array\n(\n => 37.120.133.201\n)\n\n => Array\n(\n => 109.251.143.236\n)\n\n => Array\n(\n => 23.80.97.111\n)\n\n => Array\n(\n => 43.242.176.9\n)\n\n => Array\n(\n => 14.248.107.50\n)\n\n => Array\n(\n => 182.189.221.114\n)\n\n => Array\n(\n => 103.253.173.74\n)\n\n => Array\n(\n => 27.97.177.45\n)\n\n => Array\n(\n => 49.14.98.9\n)\n\n => Array\n(\n => 163.53.85.169\n)\n\n => Array\n(\n => 39.59.90.168\n)\n\n => Array\n(\n => 111.88.202.253\n)\n\n => Array\n(\n => 111.119.178.155\n)\n\n => Array\n(\n => 171.76.163.75\n)\n\n => Array\n(\n => 202.5.154.23\n)\n\n => Array\n(\n => 119.160.65.164\n)\n\n => Array\n(\n => 14.253.253.190\n)\n\n => Array\n(\n => 117.206.167.25\n)\n\n => Array\n(\n => 61.2.183.186\n)\n\n => Array\n(\n => 103.100.4.83\n)\n\n => Array\n(\n => 124.253.71.126\n)\n\n => Array\n(\n => 182.189.49.217\n)\n\n => Array\n(\n => 103.196.160.41\n)\n\n => Array\n(\n => 23.106.56.35\n)\n\n => Array\n(\n => 110.38.12.70\n)\n\n => Array\n(\n => 154.157.199.239\n)\n\n => Array\n(\n => 14.231.163.113\n)\n\n => Array\n(\n => 103.69.27.232\n)\n\n => Array\n(\n => 175.107.220.192\n)\n\n => Array\n(\n => 43.231.58.173\n)\n\n => Array\n(\n => 138.128.91.215\n)\n\n => Array\n(\n => 103.233.86.1\n)\n\n => Array\n(\n => 182.187.67.111\n)\n\n => Array\n(\n => 49.156.71.31\n)\n\n => Array\n(\n => 27.255.174.125\n)\n\n => Array\n(\n => 195.24.220.35\n)\n\n => Array\n(\n => 120.29.98.28\n)\n\n => Array\n(\n => 41.202.219.255\n)\n\n => Array\n(\n => 103.88.3.243\n)\n\n => Array\n(\n => 111.125.106.75\n)\n\n => Array\n(\n => 106.76.71.74\n)\n\n => Array\n(\n => 112.201.138.85\n)\n\n => Array\n(\n => 110.137.101.229\n)\n\n => Array\n(\n => 43.242.177.96\n)\n\n => Array\n(\n => 39.36.198.196\n)\n\n => Array\n(\n => 27.255.181.140\n)\n\n => Array\n(\n => 194.99.104.58\n)\n\n => Array\n(\n => 78.129.139.109\n)\n\n => Array\n(\n => 47.247.185.67\n)\n\n => Array\n(\n => 27.63.37.90\n)\n\n => Array\n(\n => 103.211.54.1\n)\n\n => Array\n(\n => 94.202.167.139\n)\n\n => Array\n(\n => 111.119.183.3\n)\n\n => Array\n(\n => 124.253.194.1\n)\n\n => Array\n(\n => 192.142.188.115\n)\n\n => Array\n(\n => 39.44.137.107\n)\n\n => Array\n(\n => 43.251.191.25\n)\n\n => Array\n(\n => 103.140.30.114\n)\n\n => Array\n(\n => 117.5.194.159\n)\n\n => Array\n(\n => 109.169.23.79\n)\n\n => Array\n(\n => 122.178.127.170\n)\n\n => Array\n(\n => 45.118.165.156\n)\n\n => Array\n(\n => 39.48.199.148\n)\n\n => Array\n(\n => 182.64.138.32\n)\n\n => Array\n(\n => 37.73.129.186\n)\n\n => Array\n(\n => 182.186.110.35\n)\n\n => Array\n(\n => 43.242.177.24\n)\n\n => Array\n(\n => 119.155.23.112\n)\n\n => Array\n(\n => 84.16.238.119\n)\n\n => Array\n(\n => 41.202.219.252\n)\n\n => Array\n(\n => 43.242.176.119\n)\n\n => Array\n(\n => 111.119.187.6\n)\n\n => Array\n(\n => 95.12.200.188\n)\n\n => Array\n(\n => 139.28.219.138\n)\n\n => Array\n(\n => 89.163.247.130\n)\n\n => Array\n(\n => 122.173.103.88\n)\n\n => Array\n(\n => 103.248.87.10\n)\n\n => Array\n(\n => 23.106.249.36\n)\n\n => Array\n(\n => 124.253.94.125\n)\n\n => Array\n(\n => 39.53.244.147\n)\n\n => Array\n(\n => 193.109.85.11\n)\n\n => Array\n(\n => 43.242.176.71\n)\n\n => Array\n(\n => 43.242.177.58\n)\n\n => Array\n(\n => 47.31.6.139\n)\n\n => Array\n(\n => 39.59.34.67\n)\n\n => Array\n(\n => 43.242.176.58\n)\n\n => Array\n(\n => 103.107.198.198\n)\n\n => Array\n(\n => 147.135.11.113\n)\n\n => Array\n(\n => 27.7.212.112\n)\n\n => Array\n(\n => 43.242.177.1\n)\n\n => Array\n(\n => 175.107.227.27\n)\n\n => Array\n(\n => 103.103.43.254\n)\n\n => Array\n(\n => 49.15.221.10\n)\n\n => Array\n(\n => 43.242.177.43\n)\n\n => Array\n(\n => 36.85.59.11\n)\n\n => Array\n(\n => 124.253.204.50\n)\n\n => Array\n(\n => 5.181.233.54\n)\n\n => Array\n(\n => 43.242.177.154\n)\n\n => Array\n(\n => 103.84.37.169\n)\n\n => Array\n(\n => 222.252.54.108\n)\n\n => Array\n(\n => 14.162.160.254\n)\n\n => Array\n(\n => 178.151.218.45\n)\n\n => Array\n(\n => 110.137.101.93\n)\n\n => Array\n(\n => 122.162.212.59\n)\n\n => Array\n(\n => 81.12.118.162\n)\n\n => Array\n(\n => 171.76.186.148\n)\n\n => Array\n(\n => 182.69.253.77\n)\n\n => Array\n(\n => 111.119.183.43\n)\n\n => Array\n(\n => 49.149.74.226\n)\n\n => Array\n(\n => 43.242.177.63\n)\n\n => Array\n(\n => 14.99.243.54\n)\n\n => Array\n(\n => 110.137.100.25\n)\n\n => Array\n(\n => 116.107.25.163\n)\n\n => Array\n(\n => 49.36.71.141\n)\n\n => Array\n(\n => 182.180.117.219\n)\n\n => Array\n(\n => 150.242.172.194\n)\n\n => Array\n(\n => 49.156.111.40\n)\n\n => Array\n(\n => 49.15.208.115\n)\n\n => Array\n(\n => 103.209.87.219\n)\n\n => Array\n(\n => 43.242.176.56\n)\n\n => Array\n(\n => 103.132.187.100\n)\n\n => Array\n(\n => 49.156.96.120\n)\n\n => Array\n(\n => 192.142.176.171\n)\n\n => Array\n(\n => 51.91.18.131\n)\n\n => Array\n(\n => 103.83.144.121\n)\n\n => Array\n(\n => 1.39.75.72\n)\n\n => Array\n(\n => 14.231.172.177\n)\n\n => Array\n(\n => 94.232.213.159\n)\n\n => Array\n(\n => 103.228.158.38\n)\n\n => Array\n(\n => 43.242.177.100\n)\n\n => Array\n(\n => 171.76.149.130\n)\n\n => Array\n(\n => 113.183.26.59\n)\n\n => Array\n(\n => 182.74.232.166\n)\n\n => Array\n(\n => 47.31.205.211\n)\n\n => Array\n(\n => 106.211.253.70\n)\n\n => Array\n(\n => 39.51.233.214\n)\n\n => Array\n(\n => 182.70.249.161\n)\n\n => Array\n(\n => 222.252.40.196\n)\n\n => Array\n(\n => 49.37.6.29\n)\n\n => Array\n(\n => 119.155.33.170\n)\n\n => Array\n(\n => 43.242.177.79\n)\n\n => Array\n(\n => 111.119.183.62\n)\n\n => Array\n(\n => 137.59.226.97\n)\n\n => Array\n(\n => 42.111.18.121\n)\n\n => Array\n(\n => 223.190.46.91\n)\n\n => Array\n(\n => 45.118.165.159\n)\n\n => Array\n(\n => 110.136.60.44\n)\n\n => Array\n(\n => 43.242.176.57\n)\n\n => Array\n(\n => 117.212.58.0\n)\n\n => Array\n(\n => 49.37.7.66\n)\n\n => Array\n(\n => 39.52.174.33\n)\n\n => Array\n(\n => 150.242.172.55\n)\n\n => Array\n(\n => 103.94.111.236\n)\n\n => Array\n(\n => 106.215.239.184\n)\n\n => Array\n(\n => 101.128.117.75\n)\n\n => Array\n(\n => 162.210.194.10\n)\n\n => Array\n(\n => 136.158.31.132\n)\n\n => Array\n(\n => 39.51.245.69\n)\n\n => Array\n(\n => 39.42.149.159\n)\n\n => Array\n(\n => 51.77.108.159\n)\n\n => Array\n(\n => 45.127.247.250\n)\n\n => Array\n(\n => 122.172.78.22\n)\n\n => Array\n(\n => 117.220.208.38\n)\n\n => Array\n(\n => 112.201.138.95\n)\n\n => Array\n(\n => 49.145.105.113\n)\n\n => Array\n(\n => 110.93.247.12\n)\n\n => Array\n(\n => 39.52.150.32\n)\n\n => Array\n(\n => 122.161.89.41\n)\n\n => Array\n(\n => 39.52.176.49\n)\n\n => Array\n(\n => 157.33.12.154\n)\n\n => Array\n(\n => 73.111.248.162\n)\n\n => Array\n(\n => 112.204.167.67\n)\n\n => Array\n(\n => 107.150.30.182\n)\n\n => Array\n(\n => 115.99.222.229\n)\n\n => Array\n(\n => 180.190.195.96\n)\n\n => Array\n(\n => 157.44.57.255\n)\n\n => Array\n(\n => 39.37.9.167\n)\n\n => Array\n(\n => 39.49.48.33\n)\n\n => Array\n(\n => 157.44.218.118\n)\n\n => Array\n(\n => 103.211.54.253\n)\n\n => Array\n(\n => 43.242.177.81\n)\n\n => Array\n(\n => 103.111.224.227\n)\n\n => Array\n(\n => 223.176.48.237\n)\n\n => Array\n(\n => 124.253.87.117\n)\n\n => Array\n(\n => 124.29.247.14\n)\n\n => Array\n(\n => 182.189.232.32\n)\n\n => Array\n(\n => 111.68.97.206\n)\n\n => Array\n(\n => 103.117.15.70\n)\n\n => Array\n(\n => 182.18.236.101\n)\n\n => Array\n(\n => 43.242.177.60\n)\n\n => Array\n(\n => 180.190.7.178\n)\n\n => Array\n(\n => 112.201.142.95\n)\n\n => Array\n(\n => 122.178.255.123\n)\n\n => Array\n(\n => 49.36.240.103\n)\n\n => Array\n(\n => 210.56.16.13\n)\n\n => Array\n(\n => 103.91.123.219\n)\n\n => Array\n(\n => 39.52.155.252\n)\n\n => Array\n(\n => 192.142.207.230\n)\n\n => Array\n(\n => 188.163.82.179\n)\n\n => Array\n(\n => 182.189.9.196\n)\n\n => Array\n(\n => 175.107.221.51\n)\n\n => Array\n(\n => 39.53.221.200\n)\n\n => Array\n(\n => 27.255.190.59\n)\n\n => Array\n(\n => 183.83.212.118\n)\n\n => Array\n(\n => 45.118.165.143\n)\n\n => Array\n(\n => 182.189.124.35\n)\n\n => Array\n(\n => 203.101.186.1\n)\n\n => Array\n(\n => 49.36.246.25\n)\n\n => Array\n(\n => 39.42.186.234\n)\n\n => Array\n(\n => 103.82.80.14\n)\n\n => Array\n(\n => 210.18.182.42\n)\n\n => Array\n(\n => 42.111.13.81\n)\n\n => Array\n(\n => 46.200.69.240\n)\n\n => Array\n(\n => 103.209.87.213\n)\n\n => Array\n(\n => 103.31.95.95\n)\n\n => Array\n(\n => 180.190.174.25\n)\n\n => Array\n(\n => 103.77.0.128\n)\n\n => Array\n(\n => 49.34.103.82\n)\n\n => Array\n(\n => 39.48.196.22\n)\n\n => Array\n(\n => 192.142.166.20\n)\n\n => Array\n(\n => 202.142.110.186\n)\n\n => Array\n(\n => 122.163.135.95\n)\n\n => Array\n(\n => 183.83.255.225\n)\n\n => Array\n(\n => 157.45.46.10\n)\n\n => Array\n(\n => 182.189.4.77\n)\n\n => Array\n(\n => 49.145.104.71\n)\n\n => Array\n(\n => 103.143.7.34\n)\n\n => Array\n(\n => 61.2.180.15\n)\n\n => Array\n(\n => 103.81.215.61\n)\n\n => Array\n(\n => 115.42.71.122\n)\n\n => Array\n(\n => 124.253.73.20\n)\n\n => Array\n(\n => 49.33.210.169\n)\n\n => Array\n(\n => 78.159.101.115\n)\n\n => Array\n(\n => 42.111.17.221\n)\n\n => Array\n(\n => 43.242.178.67\n)\n\n => Array\n(\n => 36.68.138.36\n)\n\n => Array\n(\n => 103.195.201.51\n)\n\n => Array\n(\n => 79.141.162.81\n)\n\n => Array\n(\n => 202.8.118.239\n)\n\n => Array\n(\n => 103.139.128.161\n)\n\n => Array\n(\n => 207.244.71.84\n)\n\n => Array\n(\n => 124.253.184.45\n)\n\n => Array\n(\n => 111.125.106.124\n)\n\n => Array\n(\n => 111.125.105.139\n)\n\n => Array\n(\n => 39.59.94.233\n)\n\n => Array\n(\n => 112.211.60.168\n)\n\n => Array\n(\n => 103.117.14.72\n)\n\n => Array\n(\n => 111.119.183.56\n)\n\n => Array\n(\n => 47.31.53.228\n)\n\n => Array\n(\n => 124.253.186.8\n)\n\n => Array\n(\n => 183.83.213.214\n)\n\n => Array\n(\n => 103.106.239.70\n)\n\n => Array\n(\n => 182.182.92.81\n)\n\n => Array\n(\n => 14.162.167.98\n)\n\n => Array\n(\n => 112.211.11.107\n)\n\n => Array\n(\n => 77.111.246.20\n)\n\n => Array\n(\n => 49.156.86.182\n)\n\n => Array\n(\n => 47.29.122.112\n)\n\n => Array\n(\n => 125.99.74.42\n)\n\n => Array\n(\n => 124.123.169.24\n)\n\n => Array\n(\n => 106.202.105.128\n)\n\n => Array\n(\n => 103.244.173.14\n)\n\n => Array\n(\n => 103.98.63.104\n)\n\n => Array\n(\n => 180.245.6.60\n)\n\n => Array\n(\n => 49.149.96.14\n)\n\n => Array\n(\n => 14.177.120.169\n)\n\n => Array\n(\n => 192.135.90.145\n)\n\n => Array\n(\n => 223.190.18.218\n)\n\n => Array\n(\n => 171.61.190.2\n)\n\n => Array\n(\n => 58.65.220.219\n)\n\n => Array\n(\n => 122.177.29.87\n)\n\n => Array\n(\n => 223.236.175.203\n)\n\n => Array\n(\n => 39.53.237.106\n)\n\n => Array\n(\n => 1.186.114.83\n)\n\n => Array\n(\n => 43.230.66.153\n)\n\n => Array\n(\n => 27.96.94.247\n)\n\n => Array\n(\n => 39.52.176.185\n)\n\n => Array\n(\n => 59.94.147.62\n)\n\n => Array\n(\n => 119.160.117.10\n)\n\n => Array\n(\n => 43.241.146.105\n)\n\n => Array\n(\n => 39.59.87.75\n)\n\n => Array\n(\n => 119.160.118.203\n)\n\n => Array\n(\n => 39.52.161.76\n)\n\n => Array\n(\n => 202.168.84.189\n)\n\n => Array\n(\n => 103.215.168.2\n)\n\n => Array\n(\n => 39.42.146.160\n)\n\n => Array\n(\n => 182.182.30.246\n)\n\n => Array\n(\n => 122.173.212.133\n)\n\n => Array\n(\n => 39.51.238.44\n)\n\n => Array\n(\n => 183.83.252.51\n)\n\n => Array\n(\n => 202.142.168.86\n)\n\n => Array\n(\n => 39.40.198.209\n)\n\n => Array\n(\n => 192.135.90.151\n)\n\n => Array\n(\n => 72.255.41.174\n)\n\n => Array\n(\n => 137.97.92.124\n)\n\n => Array\n(\n => 182.185.159.155\n)\n\n => Array\n(\n => 157.44.133.131\n)\n\n => Array\n(\n => 39.51.230.253\n)\n\n => Array\n(\n => 103.70.87.200\n)\n\n => Array\n(\n => 103.117.15.82\n)\n\n => Array\n(\n => 103.217.244.69\n)\n\n => Array\n(\n => 157.34.76.185\n)\n\n => Array\n(\n => 39.52.130.163\n)\n\n => Array\n(\n => 182.181.41.39\n)\n\n => Array\n(\n => 49.37.212.226\n)\n\n => Array\n(\n => 119.160.117.100\n)\n\n => Array\n(\n => 103.209.87.43\n)\n\n => Array\n(\n => 180.190.195.45\n)\n\n => Array\n(\n => 122.160.57.230\n)\n\n => Array\n(\n => 203.192.213.81\n)\n\n => Array\n(\n => 182.181.63.91\n)\n\n => Array\n(\n => 157.44.184.5\n)\n\n => Array\n(\n => 27.97.213.128\n)\n\n => Array\n(\n => 122.55.252.145\n)\n\n => Array\n(\n => 103.117.15.92\n)\n\n => Array\n(\n => 42.201.251.179\n)\n\n => Array\n(\n => 122.186.84.53\n)\n\n => Array\n(\n => 119.157.75.242\n)\n\n => Array\n(\n => 39.42.163.6\n)\n\n => Array\n(\n => 14.99.246.78\n)\n\n => Array\n(\n => 103.209.87.227\n)\n\n => Array\n(\n => 182.68.215.31\n)\n\n => Array\n(\n => 45.118.165.140\n)\n\n => Array\n(\n => 207.244.71.81\n)\n\n => Array\n(\n => 27.97.162.57\n)\n\n => Array\n(\n => 103.113.106.98\n)\n\n => Array\n(\n => 95.135.44.103\n)\n\n => Array\n(\n => 125.209.114.238\n)\n\n => Array\n(\n => 77.123.14.176\n)\n\n => Array\n(\n => 110.36.202.169\n)\n\n => Array\n(\n => 124.253.205.230\n)\n\n => Array\n(\n => 106.215.72.117\n)\n\n => Array\n(\n => 116.72.226.35\n)\n\n => Array\n(\n => 137.97.103.141\n)\n\n => Array\n(\n => 112.79.212.161\n)\n\n => Array\n(\n => 103.209.85.150\n)\n\n => Array\n(\n => 103.159.127.6\n)\n\n => Array\n(\n => 43.239.205.66\n)\n\n => Array\n(\n => 143.244.51.152\n)\n\n => Array\n(\n => 182.64.15.3\n)\n\n => Array\n(\n => 182.185.207.146\n)\n\n => Array\n(\n => 45.118.165.155\n)\n\n => Array\n(\n => 115.160.241.214\n)\n\n => Array\n(\n => 47.31.230.68\n)\n\n => Array\n(\n => 49.15.84.145\n)\n\n => Array\n(\n => 39.51.239.206\n)\n\n => Array\n(\n => 103.149.154.212\n)\n\n => Array\n(\n => 43.239.207.155\n)\n\n => Array\n(\n => 182.182.30.181\n)\n\n => Array\n(\n => 157.37.198.16\n)\n\n => Array\n(\n => 162.239.24.60\n)\n\n => Array\n(\n => 106.212.101.97\n)\n\n => Array\n(\n => 124.253.97.44\n)\n\n => Array\n(\n => 106.214.95.176\n)\n\n => Array\n(\n => 102.69.228.114\n)\n\n => Array\n(\n => 116.74.58.221\n)\n\n => Array\n(\n => 162.210.194.38\n)\n\n => Array\n(\n => 39.52.162.121\n)\n\n => Array\n(\n => 103.216.143.255\n)\n\n => Array\n(\n => 103.49.155.134\n)\n\n => Array\n(\n => 182.191.119.236\n)\n\n => Array\n(\n => 111.88.213.172\n)\n\n => Array\n(\n => 43.239.207.207\n)\n\n => Array\n(\n => 140.213.35.143\n)\n\n => Array\n(\n => 154.72.153.215\n)\n\n => Array\n(\n => 122.170.47.36\n)\n\n => Array\n(\n => 51.158.111.163\n)\n\n => Array\n(\n => 203.122.10.150\n)\n\n => Array\n(\n => 47.31.176.111\n)\n\n => Array\n(\n => 103.75.246.34\n)\n\n => Array\n(\n => 103.244.178.45\n)\n\n => Array\n(\n => 182.185.138.0\n)\n\n => Array\n(\n => 183.83.254.224\n)\n\n => Array\n(\n => 49.36.246.145\n)\n\n => Array\n(\n => 202.47.60.85\n)\n\n => Array\n(\n => 180.190.163.160\n)\n\n => Array\n(\n => 27.255.187.221\n)\n\n => Array\n(\n => 14.248.94.2\n)\n\n => Array\n(\n => 185.233.17.187\n)\n\n => Array\n(\n => 139.5.254.227\n)\n\n => Array\n(\n => 103.149.160.66\n)\n\n => Array\n(\n => 122.168.235.47\n)\n\n => Array\n(\n => 45.113.248.224\n)\n\n => Array\n(\n => 110.54.170.142\n)\n\n => Array\n(\n => 223.235.226.55\n)\n\n => Array\n(\n => 157.32.19.235\n)\n\n => Array\n(\n => 49.15.221.114\n)\n\n => Array\n(\n => 27.97.166.163\n)\n\n => Array\n(\n => 223.233.99.5\n)\n\n => Array\n(\n => 49.33.203.53\n)\n\n => Array\n(\n => 27.56.214.41\n)\n\n => Array\n(\n => 103.138.51.3\n)\n\n => Array\n(\n => 111.119.183.21\n)\n\n => Array\n(\n => 47.15.138.233\n)\n\n => Array\n(\n => 202.63.213.184\n)\n\n => Array\n(\n => 49.36.158.94\n)\n\n => Array\n(\n => 27.97.186.179\n)\n\n => Array\n(\n => 27.97.214.69\n)\n\n => Array\n(\n => 203.128.18.163\n)\n\n => Array\n(\n => 106.207.235.63\n)\n\n => Array\n(\n => 116.107.220.231\n)\n\n => Array\n(\n => 223.226.169.249\n)\n\n => Array\n(\n => 106.201.24.6\n)\n\n => Array\n(\n => 49.15.89.7\n)\n\n => Array\n(\n => 49.15.142.20\n)\n\n => Array\n(\n => 223.177.24.85\n)\n\n => Array\n(\n => 37.156.17.37\n)\n\n => Array\n(\n => 102.129.224.2\n)\n\n => Array\n(\n => 49.15.85.221\n)\n\n => Array\n(\n => 106.76.208.153\n)\n\n => Array\n(\n => 61.2.47.71\n)\n\n => Array\n(\n => 27.97.178.79\n)\n\n => Array\n(\n => 39.34.143.196\n)\n\n => Array\n(\n => 103.10.227.158\n)\n\n => Array\n(\n => 117.220.210.159\n)\n\n => Array\n(\n => 182.189.28.11\n)\n\n => Array\n(\n => 122.185.38.170\n)\n\n => Array\n(\n => 112.196.132.115\n)\n\n => Array\n(\n => 187.156.137.83\n)\n\n => Array\n(\n => 203.122.3.88\n)\n\n => Array\n(\n => 51.68.142.45\n)\n\n => Array\n(\n => 124.253.217.55\n)\n\n => Array\n(\n => 103.152.41.2\n)\n\n => Array\n(\n => 157.37.154.219\n)\n\n => Array\n(\n => 39.45.32.77\n)\n\n => Array\n(\n => 182.182.22.221\n)\n\n => Array\n(\n => 157.43.205.117\n)\n\n => Array\n(\n => 202.142.123.58\n)\n\n => Array\n(\n => 43.239.207.121\n)\n\n => Array\n(\n => 49.206.122.113\n)\n\n => Array\n(\n => 106.193.199.203\n)\n\n => Array\n(\n => 103.67.157.251\n)\n\n => Array\n(\n => 49.34.97.81\n)\n\n => Array\n(\n => 49.156.92.130\n)\n\n => Array\n(\n => 203.160.179.210\n)\n\n => Array\n(\n => 106.215.33.244\n)\n\n => Array\n(\n => 191.101.148.41\n)\n\n => Array\n(\n => 203.90.94.94\n)\n\n => Array\n(\n => 105.129.205.134\n)\n\n => Array\n(\n => 106.215.45.165\n)\n\n => Array\n(\n => 112.196.132.15\n)\n\n => Array\n(\n => 39.59.64.174\n)\n\n => Array\n(\n => 124.253.155.116\n)\n\n => Array\n(\n => 94.179.192.204\n)\n\n => Array\n(\n => 110.38.29.245\n)\n\n => Array\n(\n => 124.29.209.78\n)\n\n => Array\n(\n => 103.75.245.240\n)\n\n => Array\n(\n => 49.36.159.170\n)\n\n => Array\n(\n => 223.190.18.160\n)\n\n => Array\n(\n => 124.253.113.226\n)\n\n => Array\n(\n => 14.180.77.240\n)\n\n => Array\n(\n => 106.215.76.24\n)\n\n => Array\n(\n => 106.210.155.153\n)\n\n => Array\n(\n => 111.119.187.42\n)\n\n => Array\n(\n => 146.196.32.106\n)\n\n => Array\n(\n => 122.162.22.27\n)\n\n => Array\n(\n => 49.145.59.252\n)\n\n => Array\n(\n => 95.47.247.92\n)\n\n => Array\n(\n => 103.99.218.50\n)\n\n => Array\n(\n => 157.37.192.88\n)\n\n => Array\n(\n => 82.102.31.242\n)\n\n => Array\n(\n => 157.46.220.64\n)\n\n => Array\n(\n => 180.151.107.52\n)\n\n => Array\n(\n => 203.81.240.75\n)\n\n => Array\n(\n => 122.167.213.130\n)\n\n => Array\n(\n => 103.227.70.164\n)\n\n => Array\n(\n => 106.215.81.169\n)\n\n => Array\n(\n => 157.46.214.170\n)\n\n => Array\n(\n => 103.69.27.163\n)\n\n => Array\n(\n => 124.253.23.213\n)\n\n => Array\n(\n => 157.37.167.174\n)\n\n => Array\n(\n => 1.39.204.67\n)\n\n => Array\n(\n => 112.196.132.51\n)\n\n => Array\n(\n => 119.152.61.222\n)\n\n => Array\n(\n => 47.31.36.174\n)\n\n => Array\n(\n => 47.31.152.174\n)\n\n => Array\n(\n => 49.34.18.105\n)\n\n => Array\n(\n => 157.37.170.101\n)\n\n => Array\n(\n => 118.209.241.234\n)\n\n => Array\n(\n => 103.67.19.9\n)\n\n => Array\n(\n => 182.189.14.154\n)\n\n => Array\n(\n => 45.127.233.232\n)\n\n => Array\n(\n => 27.96.94.91\n)\n\n => Array\n(\n => 183.83.214.250\n)\n\n => Array\n(\n => 47.31.27.140\n)\n\n => Array\n(\n => 47.31.129.199\n)\n\n => Array\n(\n => 157.44.156.111\n)\n\n => Array\n(\n => 42.110.163.2\n)\n\n => Array\n(\n => 124.253.64.210\n)\n\n => Array\n(\n => 49.36.167.54\n)\n\n => Array\n(\n => 27.63.135.145\n)\n\n => Array\n(\n => 157.35.254.63\n)\n\n => Array\n(\n => 39.45.18.182\n)\n\n => Array\n(\n => 197.210.85.102\n)\n\n => Array\n(\n => 112.196.132.90\n)\n\n => Array\n(\n => 59.152.97.84\n)\n\n => Array\n(\n => 43.242.178.7\n)\n\n => Array\n(\n => 47.31.40.70\n)\n\n => Array\n(\n => 202.134.10.136\n)\n\n => Array\n(\n => 132.154.241.43\n)\n\n => Array\n(\n => 185.209.179.240\n)\n\n => Array\n(\n => 202.47.50.28\n)\n\n => Array\n(\n => 182.186.1.29\n)\n\n => Array\n(\n => 124.253.114.229\n)\n\n => Array\n(\n => 49.32.210.126\n)\n\n => Array\n(\n => 43.242.178.122\n)\n\n => Array\n(\n => 42.111.28.52\n)\n\n => Array\n(\n => 23.227.141.44\n)\n\n => Array\n(\n => 23.227.141.156\n)\n\n => Array\n(\n => 103.253.173.79\n)\n\n => Array\n(\n => 116.75.231.74\n)\n\n => Array\n(\n => 106.76.78.196\n)\n\n => Array\n(\n => 116.75.197.68\n)\n\n => Array\n(\n => 42.108.172.131\n)\n\n => Array\n(\n => 157.38.27.199\n)\n\n => Array\n(\n => 103.70.86.205\n)\n\n => Array\n(\n => 119.152.63.239\n)\n\n => Array\n(\n => 103.233.116.94\n)\n\n => Array\n(\n => 111.119.188.17\n)\n\n => Array\n(\n => 103.196.160.156\n)\n\n => Array\n(\n => 27.97.208.40\n)\n\n => Array\n(\n => 188.163.7.136\n)\n\n => Array\n(\n => 49.15.202.205\n)\n\n => Array\n(\n => 124.253.201.111\n)\n\n => Array\n(\n => 182.190.213.246\n)\n\n => Array\n(\n => 5.154.174.10\n)\n\n => Array\n(\n => 103.21.185.16\n)\n\n => Array\n(\n => 112.196.132.67\n)\n\n => Array\n(\n => 49.15.194.230\n)\n\n => Array\n(\n => 103.118.34.103\n)\n\n => Array\n(\n => 49.15.201.92\n)\n\n => Array\n(\n => 42.111.13.238\n)\n\n => Array\n(\n => 203.192.213.137\n)\n\n => Array\n(\n => 45.115.190.82\n)\n\n => Array\n(\n => 78.26.130.102\n)\n\n => Array\n(\n => 49.15.85.202\n)\n\n => Array\n(\n => 106.76.193.33\n)\n\n => Array\n(\n => 103.70.41.30\n)\n\n => Array\n(\n => 103.82.78.254\n)\n\n => Array\n(\n => 110.38.35.90\n)\n\n => Array\n(\n => 181.214.107.27\n)\n\n => Array\n(\n => 27.110.183.162\n)\n\n => Array\n(\n => 94.225.230.215\n)\n\n => Array\n(\n => 27.97.185.58\n)\n\n => Array\n(\n => 49.146.196.124\n)\n\n => Array\n(\n => 119.157.76.144\n)\n\n => Array\n(\n => 103.99.218.34\n)\n\n => Array\n(\n => 185.32.221.247\n)\n\n => Array\n(\n => 27.97.161.12\n)\n\n => Array\n(\n => 27.62.144.214\n)\n\n => Array\n(\n => 124.253.90.151\n)\n\n => Array\n(\n => 49.36.135.69\n)\n\n => Array\n(\n => 39.40.217.106\n)\n\n => Array\n(\n => 119.152.235.136\n)\n\n => Array\n(\n => 103.91.103.226\n)\n\n => Array\n(\n => 117.222.226.93\n)\n\n => Array\n(\n => 182.190.24.126\n)\n\n => Array\n(\n => 27.97.223.179\n)\n\n => Array\n(\n => 202.137.115.11\n)\n\n => Array\n(\n => 43.242.178.130\n)\n\n => Array\n(\n => 182.189.125.232\n)\n\n => Array\n(\n => 182.190.202.87\n)\n\n => Array\n(\n => 124.253.102.193\n)\n\n => Array\n(\n => 103.75.247.73\n)\n\n => Array\n(\n => 122.177.100.97\n)\n\n => Array\n(\n => 47.31.192.254\n)\n\n => Array\n(\n => 49.149.73.185\n)\n\n => Array\n(\n => 39.57.147.197\n)\n\n => Array\n(\n => 103.110.147.52\n)\n\n => Array\n(\n => 124.253.106.255\n)\n\n => Array\n(\n => 152.57.116.136\n)\n\n => Array\n(\n => 110.38.35.102\n)\n\n => Array\n(\n => 182.18.206.127\n)\n\n => Array\n(\n => 103.133.59.246\n)\n\n => Array\n(\n => 27.97.189.139\n)\n\n => Array\n(\n => 179.61.245.54\n)\n\n => Array\n(\n => 103.240.233.176\n)\n\n => Array\n(\n => 111.88.124.196\n)\n\n => Array\n(\n => 49.146.215.3\n)\n\n => Array\n(\n => 110.39.10.246\n)\n\n => Array\n(\n => 27.5.42.135\n)\n\n => Array\n(\n => 27.97.177.251\n)\n\n => Array\n(\n => 93.177.75.254\n)\n\n => Array\n(\n => 43.242.177.3\n)\n\n => Array\n(\n => 112.196.132.97\n)\n\n => Array\n(\n => 116.75.242.188\n)\n\n => Array\n(\n => 202.8.118.101\n)\n\n => Array\n(\n => 49.36.65.43\n)\n\n => Array\n(\n => 157.37.146.220\n)\n\n => Array\n(\n => 157.37.143.235\n)\n\n => Array\n(\n => 157.38.94.34\n)\n\n => Array\n(\n => 49.36.131.1\n)\n\n => Array\n(\n => 132.154.92.97\n)\n\n => Array\n(\n => 132.154.123.115\n)\n\n => Array\n(\n => 49.15.197.222\n)\n\n => Array\n(\n => 124.253.198.72\n)\n\n => Array\n(\n => 27.97.217.95\n)\n\n => Array\n(\n => 47.31.194.65\n)\n\n => Array\n(\n => 197.156.190.156\n)\n\n => Array\n(\n => 197.156.190.230\n)\n\n => Array\n(\n => 103.62.152.250\n)\n\n => Array\n(\n => 103.152.212.126\n)\n\n => Array\n(\n => 185.233.18.177\n)\n\n => Array\n(\n => 116.75.63.83\n)\n\n => Array\n(\n => 157.38.56.125\n)\n\n => Array\n(\n => 119.157.107.195\n)\n\n => Array\n(\n => 103.87.50.73\n)\n\n => Array\n(\n => 95.142.120.141\n)\n\n => Array\n(\n => 154.13.1.221\n)\n\n => Array\n(\n => 103.147.87.79\n)\n\n => Array\n(\n => 39.53.173.186\n)\n\n => Array\n(\n => 195.114.145.107\n)\n\n => Array\n(\n => 157.33.201.185\n)\n\n => Array\n(\n => 195.85.219.36\n)\n\n => Array\n(\n => 105.161.67.127\n)\n\n => Array\n(\n => 110.225.87.77\n)\n\n => Array\n(\n => 103.95.167.236\n)\n\n => Array\n(\n => 89.187.162.213\n)\n\n => Array\n(\n => 27.255.189.50\n)\n\n => Array\n(\n => 115.96.77.54\n)\n\n => Array\n(\n => 223.182.220.223\n)\n\n => Array\n(\n => 157.47.206.192\n)\n\n => Array\n(\n => 182.186.110.226\n)\n\n => Array\n(\n => 39.53.243.237\n)\n\n => Array\n(\n => 39.40.228.58\n)\n\n => Array\n(\n => 157.38.60.9\n)\n\n => Array\n(\n => 106.198.244.189\n)\n\n => Array\n(\n => 124.253.51.164\n)\n\n => Array\n(\n => 49.147.113.58\n)\n\n => Array\n(\n => 14.231.196.229\n)\n\n => Array\n(\n => 103.81.214.152\n)\n\n => Array\n(\n => 117.222.220.60\n)\n\n => Array\n(\n => 83.142.111.213\n)\n\n => Array\n(\n => 14.224.77.147\n)\n\n => Array\n(\n => 110.235.236.95\n)\n\n => Array\n(\n => 103.26.83.30\n)\n\n => Array\n(\n => 106.206.191.82\n)\n\n => Array\n(\n => 103.49.117.135\n)\n\n => Array\n(\n => 202.47.39.9\n)\n\n => Array\n(\n => 180.178.145.205\n)\n\n => Array\n(\n => 43.251.93.119\n)\n\n => Array\n(\n => 27.6.212.182\n)\n\n => Array\n(\n => 39.42.156.20\n)\n\n => Array\n(\n => 47.31.141.195\n)\n\n => Array\n(\n => 157.37.146.73\n)\n\n => Array\n(\n => 49.15.93.155\n)\n\n => Array\n(\n => 162.210.194.37\n)\n\n => Array\n(\n => 223.188.160.236\n)\n\n => Array\n(\n => 47.9.90.158\n)\n\n => Array\n(\n => 49.15.85.224\n)\n\n => Array\n(\n => 49.15.93.134\n)\n\n => Array\n(\n => 107.179.244.94\n)\n\n => Array\n(\n => 182.190.203.90\n)\n\n => Array\n(\n => 185.192.69.203\n)\n\n => Array\n(\n => 185.17.27.99\n)\n\n => Array\n(\n => 119.160.116.182\n)\n\n => Array\n(\n => 203.99.177.25\n)\n\n => Array\n(\n => 162.228.207.248\n)\n\n => Array\n(\n => 47.31.245.69\n)\n\n => Array\n(\n => 49.15.210.159\n)\n\n => Array\n(\n => 42.111.2.112\n)\n\n => Array\n(\n => 223.186.116.79\n)\n\n => Array\n(\n => 103.225.176.143\n)\n\n => Array\n(\n => 45.115.190.49\n)\n\n => Array\n(\n => 115.42.71.105\n)\n\n => Array\n(\n => 157.51.11.157\n)\n\n => Array\n(\n => 14.175.56.186\n)\n\n => Array\n(\n => 59.153.16.7\n)\n\n => Array\n(\n => 106.202.84.144\n)\n\n => Array\n(\n => 27.6.242.91\n)\n\n => Array\n(\n => 47.11.112.107\n)\n\n => Array\n(\n => 106.207.54.187\n)\n\n => Array\n(\n => 124.253.196.121\n)\n\n => Array\n(\n => 51.79.161.244\n)\n\n => Array\n(\n => 103.41.24.100\n)\n\n => Array\n(\n => 195.66.79.32\n)\n\n => Array\n(\n => 117.196.127.42\n)\n\n => Array\n(\n => 103.75.247.197\n)\n\n => Array\n(\n => 89.187.162.107\n)\n\n => Array\n(\n => 223.238.154.49\n)\n\n => Array\n(\n => 117.223.99.139\n)\n\n => Array\n(\n => 103.87.59.134\n)\n\n => Array\n(\n => 124.253.212.30\n)\n\n => Array\n(\n => 202.47.62.55\n)\n\n => Array\n(\n => 47.31.219.128\n)\n\n => Array\n(\n => 49.14.121.72\n)\n\n => Array\n(\n => 124.253.212.189\n)\n\n => Array\n(\n => 103.244.179.24\n)\n\n => Array\n(\n => 182.190.213.92\n)\n\n => Array\n(\n => 43.242.178.51\n)\n\n => Array\n(\n => 180.92.138.54\n)\n\n => Array\n(\n => 111.119.187.26\n)\n\n => Array\n(\n => 49.156.111.31\n)\n\n => Array\n(\n => 27.63.108.183\n)\n\n => Array\n(\n => 27.58.184.79\n)\n\n => Array\n(\n => 39.40.225.130\n)\n\n => Array\n(\n => 157.38.5.178\n)\n\n => Array\n(\n => 103.112.55.44\n)\n\n => Array\n(\n => 119.160.100.247\n)\n\n => Array\n(\n => 39.53.101.15\n)\n\n => Array\n(\n => 47.31.207.117\n)\n\n => Array\n(\n => 112.196.158.155\n)\n\n => Array\n(\n => 94.204.247.123\n)\n\n => Array\n(\n => 103.118.76.38\n)\n\n => Array\n(\n => 124.29.212.208\n)\n\n => Array\n(\n => 124.253.196.250\n)\n\n => Array\n(\n => 118.70.182.242\n)\n\n => Array\n(\n => 157.38.78.67\n)\n\n => Array\n(\n => 103.99.218.33\n)\n\n => Array\n(\n => 137.59.220.191\n)\n\n => Array\n(\n => 47.31.139.182\n)\n\n => Array\n(\n => 182.179.136.36\n)\n\n => Array\n(\n => 106.203.73.130\n)\n\n => Array\n(\n => 193.29.107.188\n)\n\n => Array\n(\n => 81.96.92.111\n)\n\n => Array\n(\n => 110.93.203.185\n)\n\n => Array\n(\n => 103.163.248.128\n)\n\n => Array\n(\n => 43.229.166.135\n)\n\n => Array\n(\n => 43.230.106.175\n)\n\n => Array\n(\n => 202.47.62.54\n)\n\n => Array\n(\n => 39.37.181.46\n)\n\n => Array\n(\n => 49.15.204.204\n)\n\n => Array\n(\n => 122.163.237.110\n)\n\n => Array\n(\n => 45.249.8.92\n)\n\n => Array\n(\n => 27.34.50.159\n)\n\n => Array\n(\n => 39.42.171.27\n)\n\n => Array\n(\n => 124.253.101.195\n)\n\n => Array\n(\n => 188.166.145.20\n)\n\n => Array\n(\n => 103.83.145.220\n)\n\n => Array\n(\n => 39.40.96.137\n)\n\n => Array\n(\n => 157.37.185.196\n)\n\n => Array\n(\n => 103.115.124.32\n)\n\n => Array\n(\n => 72.255.48.85\n)\n\n => Array\n(\n => 124.253.74.46\n)\n\n => Array\n(\n => 60.243.225.5\n)\n\n => Array\n(\n => 103.58.152.194\n)\n\n => Array\n(\n => 14.248.71.63\n)\n\n => Array\n(\n => 152.57.214.137\n)\n\n => Array\n(\n => 103.166.58.14\n)\n\n => Array\n(\n => 14.248.71.103\n)\n\n => Array\n(\n => 49.156.103.124\n)\n\n => Array\n(\n => 103.99.218.56\n)\n\n => Array\n(\n => 27.97.177.246\n)\n\n => Array\n(\n => 152.57.94.84\n)\n\n => Array\n(\n => 111.119.187.60\n)\n\n => Array\n(\n => 119.160.99.11\n)\n\n => Array\n(\n => 117.203.11.220\n)\n\n => Array\n(\n => 114.31.131.67\n)\n\n => Array\n(\n => 47.31.253.95\n)\n\n => Array\n(\n => 83.139.184.178\n)\n\n => Array\n(\n => 125.57.9.72\n)\n\n => Array\n(\n => 185.233.16.53\n)\n\n => Array\n(\n => 49.36.180.197\n)\n\n => Array\n(\n => 95.142.119.27\n)\n\n => Array\n(\n => 223.225.70.77\n)\n\n => Array\n(\n => 47.15.222.200\n)\n\n => Array\n(\n => 47.15.218.231\n)\n\n => Array\n(\n => 111.119.187.34\n)\n\n => Array\n(\n => 157.37.198.81\n)\n\n => Array\n(\n => 43.242.177.92\n)\n\n => Array\n(\n => 122.161.68.214\n)\n\n => Array\n(\n => 47.31.145.92\n)\n\n => Array\n(\n => 27.7.196.201\n)\n\n => Array\n(\n => 39.42.172.183\n)\n\n => Array\n(\n => 49.15.129.162\n)\n\n => Array\n(\n => 49.15.206.110\n)\n\n => Array\n(\n => 39.57.141.45\n)\n\n => Array\n(\n => 171.229.175.90\n)\n\n => Array\n(\n => 119.160.68.200\n)\n\n => Array\n(\n => 193.176.84.214\n)\n\n => Array\n(\n => 43.242.177.77\n)\n\n => Array\n(\n => 137.59.220.95\n)\n\n => Array\n(\n => 122.177.118.209\n)\n\n => Array\n(\n => 103.92.214.27\n)\n\n => Array\n(\n => 178.62.10.228\n)\n\n => Array\n(\n => 103.81.214.91\n)\n\n => Array\n(\n => 156.146.33.68\n)\n\n => Array\n(\n => 42.118.116.60\n)\n\n => Array\n(\n => 183.87.122.190\n)\n\n => Array\n(\n => 157.37.159.162\n)\n\n => Array\n(\n => 59.153.16.9\n)\n\n => Array\n(\n => 223.185.43.241\n)\n\n => Array\n(\n => 103.81.214.153\n)\n\n => Array\n(\n => 47.31.143.169\n)\n\n => Array\n(\n => 112.196.158.250\n)\n\n => Array\n(\n => 156.146.36.110\n)\n\n => Array\n(\n => 27.255.34.80\n)\n\n => Array\n(\n => 49.205.77.19\n)\n\n => Array\n(\n => 95.142.120.20\n)\n\n => Array\n(\n => 171.49.195.53\n)\n\n => Array\n(\n => 39.37.152.132\n)\n\n => Array\n(\n => 103.121.204.237\n)\n\n => Array\n(\n => 43.242.176.153\n)\n\n => Array\n(\n => 43.242.176.120\n)\n\n => Array\n(\n => 122.161.66.120\n)\n\n => Array\n(\n => 182.70.140.223\n)\n\n => Array\n(\n => 103.201.135.226\n)\n\n => Array\n(\n => 202.47.44.135\n)\n\n => Array\n(\n => 182.179.172.27\n)\n\n => Array\n(\n => 185.22.173.86\n)\n\n => Array\n(\n => 67.205.148.219\n)\n\n => Array\n(\n => 27.58.183.140\n)\n\n => Array\n(\n => 39.42.118.163\n)\n\n => Array\n(\n => 117.5.204.59\n)\n\n => Array\n(\n => 223.182.193.163\n)\n\n => Array\n(\n => 157.37.184.33\n)\n\n => Array\n(\n => 110.37.218.92\n)\n\n => Array\n(\n => 106.215.8.67\n)\n\n => Array\n(\n => 39.42.94.179\n)\n\n => Array\n(\n => 106.51.25.124\n)\n\n => Array\n(\n => 157.42.25.212\n)\n\n => Array\n(\n => 43.247.40.170\n)\n\n => Array\n(\n => 101.50.108.111\n)\n\n => Array\n(\n => 117.102.48.152\n)\n\n => Array\n(\n => 95.142.120.48\n)\n\n => Array\n(\n => 183.81.121.160\n)\n\n => Array\n(\n => 42.111.21.195\n)\n\n => Array\n(\n => 50.7.142.180\n)\n\n => Array\n(\n => 223.130.28.33\n)\n\n => Array\n(\n => 107.161.86.141\n)\n\n => Array\n(\n => 117.203.249.159\n)\n\n => Array\n(\n => 110.225.192.64\n)\n\n => Array\n(\n => 157.37.152.168\n)\n\n => Array\n(\n => 110.39.2.202\n)\n\n => Array\n(\n => 23.106.56.52\n)\n\n => Array\n(\n => 59.150.87.85\n)\n\n => Array\n(\n => 122.162.175.128\n)\n\n => Array\n(\n => 39.40.63.182\n)\n\n => Array\n(\n => 182.190.108.76\n)\n\n => Array\n(\n => 49.36.44.216\n)\n\n => Array\n(\n => 73.105.5.185\n)\n\n => Array\n(\n => 157.33.67.204\n)\n\n => Array\n(\n => 157.37.164.171\n)\n\n => Array\n(\n => 192.119.160.21\n)\n\n => Array\n(\n => 156.146.59.29\n)\n\n => Array\n(\n => 182.190.97.213\n)\n\n => Array\n(\n => 39.53.196.168\n)\n\n => Array\n(\n => 112.196.132.93\n)\n\n => Array\n(\n => 182.189.7.18\n)\n\n => Array\n(\n => 101.53.232.117\n)\n\n => Array\n(\n => 43.242.178.105\n)\n\n => Array\n(\n => 49.145.233.44\n)\n\n => Array\n(\n => 5.107.214.18\n)\n\n => Array\n(\n => 139.5.242.124\n)\n\n => Array\n(\n => 47.29.244.80\n)\n\n => Array\n(\n => 43.242.178.180\n)\n\n => Array\n(\n => 194.110.84.171\n)\n\n => Array\n(\n => 103.68.217.99\n)\n\n => Array\n(\n => 182.182.27.59\n)\n\n => Array\n(\n => 119.152.139.146\n)\n\n => Array\n(\n => 39.37.131.1\n)\n\n => Array\n(\n => 106.210.99.47\n)\n\n => Array\n(\n => 103.225.176.68\n)\n\n => Array\n(\n => 42.111.23.67\n)\n\n => Array\n(\n => 223.225.37.57\n)\n\n => Array\n(\n => 114.79.1.247\n)\n\n => Array\n(\n => 157.42.28.39\n)\n\n => Array\n(\n => 47.15.13.68\n)\n\n => Array\n(\n => 223.230.151.59\n)\n\n => Array\n(\n => 115.186.7.112\n)\n\n => Array\n(\n => 111.92.78.33\n)\n\n => Array\n(\n => 119.160.117.249\n)\n\n => Array\n(\n => 103.150.209.45\n)\n\n => Array\n(\n => 182.189.22.170\n)\n\n => Array\n(\n => 49.144.108.82\n)\n\n => Array\n(\n => 39.49.75.65\n)\n\n => Array\n(\n => 39.52.205.223\n)\n\n => Array\n(\n => 49.48.247.53\n)\n\n => Array\n(\n => 5.149.250.222\n)\n\n => Array\n(\n => 47.15.187.153\n)\n\n => Array\n(\n => 103.70.86.101\n)\n\n => Array\n(\n => 112.196.158.138\n)\n\n => Array\n(\n => 156.241.242.139\n)\n\n => Array\n(\n => 157.33.205.213\n)\n\n => Array\n(\n => 39.53.206.247\n)\n\n => Array\n(\n => 157.45.83.132\n)\n\n => Array\n(\n => 49.36.220.138\n)\n\n => Array\n(\n => 202.47.47.118\n)\n\n => Array\n(\n => 182.185.233.224\n)\n\n => Array\n(\n => 182.189.30.99\n)\n\n => Array\n(\n => 223.233.68.178\n)\n\n => Array\n(\n => 161.35.139.87\n)\n\n => Array\n(\n => 121.46.65.124\n)\n\n => Array\n(\n => 5.195.154.87\n)\n\n => Array\n(\n => 103.46.236.71\n)\n\n => Array\n(\n => 195.114.147.119\n)\n\n => Array\n(\n => 195.85.219.35\n)\n\n => Array\n(\n => 111.119.183.34\n)\n\n => Array\n(\n => 39.34.158.41\n)\n\n => Array\n(\n => 180.178.148.13\n)\n\n => Array\n(\n => 122.161.66.166\n)\n\n => Array\n(\n => 185.233.18.1\n)\n\n => Array\n(\n => 146.196.34.119\n)\n\n => Array\n(\n => 27.6.253.159\n)\n\n => Array\n(\n => 198.8.92.156\n)\n\n => Array\n(\n => 106.206.179.160\n)\n\n => Array\n(\n => 202.164.133.53\n)\n\n => Array\n(\n => 112.196.141.214\n)\n\n => Array\n(\n => 95.135.15.148\n)\n\n => Array\n(\n => 111.92.119.165\n)\n\n => Array\n(\n => 84.17.34.18\n)\n\n => Array\n(\n => 49.36.232.117\n)\n\n => Array\n(\n => 122.180.235.92\n)\n\n => Array\n(\n => 89.187.163.177\n)\n\n => Array\n(\n => 103.217.238.38\n)\n\n => Array\n(\n => 103.163.248.115\n)\n\n => Array\n(\n => 156.146.59.10\n)\n\n => Array\n(\n => 223.233.68.183\n)\n\n => Array\n(\n => 103.12.198.92\n)\n\n => Array\n(\n => 42.111.9.221\n)\n\n => Array\n(\n => 111.92.77.242\n)\n\n => Array\n(\n => 192.142.128.26\n)\n\n => Array\n(\n => 182.69.195.139\n)\n\n => Array\n(\n => 103.209.83.110\n)\n\n => Array\n(\n => 207.244.71.80\n)\n\n => Array\n(\n => 41.140.106.29\n)\n\n => Array\n(\n => 45.118.167.65\n)\n\n => Array\n(\n => 45.118.167.70\n)\n\n => Array\n(\n => 157.37.159.180\n)\n\n => Array\n(\n => 103.217.178.194\n)\n\n => Array\n(\n => 27.255.165.94\n)\n\n => Array\n(\n => 45.133.7.42\n)\n\n => Array\n(\n => 43.230.65.168\n)\n\n => Array\n(\n => 39.53.196.221\n)\n\n => Array\n(\n => 42.111.17.83\n)\n\n => Array\n(\n => 110.39.12.34\n)\n\n => Array\n(\n => 45.118.158.169\n)\n\n => Array\n(\n => 202.142.110.165\n)\n\n => Array\n(\n => 106.201.13.212\n)\n\n => Array\n(\n => 103.211.14.94\n)\n\n => Array\n(\n => 160.202.37.105\n)\n\n => Array\n(\n => 103.99.199.34\n)\n\n => Array\n(\n => 183.83.45.104\n)\n\n => Array\n(\n => 49.36.233.107\n)\n\n => Array\n(\n => 182.68.21.51\n)\n\n => Array\n(\n => 110.227.93.182\n)\n\n => Array\n(\n => 180.178.144.251\n)\n\n => Array\n(\n => 129.0.102.0\n)\n\n => Array\n(\n => 124.253.105.176\n)\n\n => Array\n(\n => 105.156.139.225\n)\n\n => Array\n(\n => 208.117.87.154\n)\n\n => Array\n(\n => 138.68.185.17\n)\n\n => Array\n(\n => 43.247.41.207\n)\n\n => Array\n(\n => 49.156.106.105\n)\n\n => Array\n(\n => 223.238.197.124\n)\n\n => Array\n(\n => 202.47.39.96\n)\n\n => Array\n(\n => 223.226.131.80\n)\n\n => Array\n(\n => 122.161.48.139\n)\n\n => Array\n(\n => 106.201.144.12\n)\n\n => Array\n(\n => 122.178.223.244\n)\n\n => Array\n(\n => 195.181.164.65\n)\n\n => Array\n(\n => 106.195.12.187\n)\n\n => Array\n(\n => 124.253.48.48\n)\n\n => Array\n(\n => 103.140.30.214\n)\n\n => Array\n(\n => 180.178.147.132\n)\n\n => Array\n(\n => 138.197.139.130\n)\n\n => Array\n(\n => 5.254.2.138\n)\n\n => Array\n(\n => 183.81.93.25\n)\n\n => Array\n(\n => 182.70.39.254\n)\n\n => Array\n(\n => 106.223.87.131\n)\n\n => Array\n(\n => 106.203.91.114\n)\n\n => Array\n(\n => 196.70.137.128\n)\n\n => Array\n(\n => 150.242.62.167\n)\n\n => Array\n(\n => 184.170.243.198\n)\n\n => Array\n(\n => 59.89.30.66\n)\n\n => Array\n(\n => 49.156.112.201\n)\n\n => Array\n(\n => 124.29.212.168\n)\n\n => Array\n(\n => 103.204.170.238\n)\n\n => Array\n(\n => 124.253.116.81\n)\n\n => Array\n(\n => 41.248.102.107\n)\n\n => Array\n(\n => 119.160.100.51\n)\n\n => Array\n(\n => 5.254.40.91\n)\n\n => Array\n(\n => 103.149.154.25\n)\n\n => Array\n(\n => 103.70.41.28\n)\n\n => Array\n(\n => 103.151.234.42\n)\n\n => Array\n(\n => 39.37.142.107\n)\n\n => Array\n(\n => 27.255.186.115\n)\n\n => Array\n(\n => 49.15.193.151\n)\n\n => Array\n(\n => 103.201.146.115\n)\n\n => Array\n(\n => 223.228.177.70\n)\n\n => Array\n(\n => 182.179.141.37\n)\n\n => Array\n(\n => 110.172.131.126\n)\n\n => Array\n(\n => 45.116.232.0\n)\n\n => Array\n(\n => 193.37.32.206\n)\n\n => Array\n(\n => 119.152.62.246\n)\n\n => Array\n(\n => 180.178.148.228\n)\n\n => Array\n(\n => 195.114.145.120\n)\n\n => Array\n(\n => 122.160.49.194\n)\n\n => Array\n(\n => 103.240.237.17\n)\n\n => Array\n(\n => 103.75.245.238\n)\n\n => Array\n(\n => 124.253.215.148\n)\n\n => Array\n(\n => 45.118.165.146\n)\n\n => Array\n(\n => 103.75.244.111\n)\n\n => Array\n(\n => 223.185.7.42\n)\n\n => Array\n(\n => 139.5.240.165\n)\n\n => Array\n(\n => 45.251.117.204\n)\n\n => Array\n(\n => 132.154.71.227\n)\n\n => Array\n(\n => 178.92.100.97\n)\n\n => Array\n(\n => 49.48.248.42\n)\n\n => Array\n(\n => 182.190.109.252\n)\n\n => Array\n(\n => 43.231.57.209\n)\n\n => Array\n(\n => 39.37.185.133\n)\n\n => Array\n(\n => 123.17.79.174\n)\n\n => Array\n(\n => 180.178.146.215\n)\n\n => Array\n(\n => 41.248.83.40\n)\n\n => Array\n(\n => 103.255.4.79\n)\n\n => Array\n(\n => 103.39.119.233\n)\n\n => Array\n(\n => 85.203.44.24\n)\n\n => Array\n(\n => 93.74.18.246\n)\n\n => Array\n(\n => 95.142.120.51\n)\n\n => Array\n(\n => 202.47.42.57\n)\n\n => Array\n(\n => 41.202.219.253\n)\n\n => Array\n(\n => 154.28.188.182\n)\n\n => Array\n(\n => 14.163.178.106\n)\n\n => Array\n(\n => 118.185.57.226\n)\n\n => Array\n(\n => 49.15.141.102\n)\n\n => Array\n(\n => 182.189.86.47\n)\n\n => Array\n(\n => 111.88.68.79\n)\n\n => Array\n(\n => 156.146.59.8\n)\n\n => Array\n(\n => 119.152.62.82\n)\n\n => Array\n(\n => 49.207.128.103\n)\n\n => Array\n(\n => 203.212.30.234\n)\n\n => Array\n(\n => 41.202.219.254\n)\n\n => Array\n(\n => 103.46.203.10\n)\n\n => Array\n(\n => 112.79.141.15\n)\n\n => Array\n(\n => 103.68.218.75\n)\n\n => Array\n(\n => 49.35.130.14\n)\n\n => Array\n(\n => 172.247.129.90\n)\n\n => Array\n(\n => 116.90.74.214\n)\n\n => Array\n(\n => 180.178.142.242\n)\n\n => Array\n(\n => 111.119.183.59\n)\n\n => Array\n(\n => 117.5.103.189\n)\n\n => Array\n(\n => 203.110.93.146\n)\n\n => Array\n(\n => 188.163.97.86\n)\n\n => Array\n(\n => 124.253.90.47\n)\n\n => Array\n(\n => 139.167.249.160\n)\n\n => Array\n(\n => 103.226.206.55\n)\n\n => Array\n(\n => 154.28.188.191\n)\n\n => Array\n(\n => 182.190.197.205\n)\n\n => Array\n(\n => 111.119.183.33\n)\n\n => Array\n(\n => 14.253.254.64\n)\n\n => Array\n(\n => 117.237.197.246\n)\n\n => Array\n(\n => 172.105.53.82\n)\n\n => Array\n(\n => 124.253.207.164\n)\n\n => Array\n(\n => 103.255.4.33\n)\n\n => Array\n(\n => 27.63.131.206\n)\n\n => Array\n(\n => 103.118.170.99\n)\n\n => Array\n(\n => 111.119.183.55\n)\n\n => Array\n(\n => 14.182.101.109\n)\n\n => Array\n(\n => 175.107.223.199\n)\n\n => Array\n(\n => 39.57.168.94\n)\n\n => Array\n(\n => 122.182.213.139\n)\n\n => Array\n(\n => 112.79.214.237\n)\n\n => Array\n(\n => 27.6.252.22\n)\n\n => Array\n(\n => 89.163.212.83\n)\n\n => Array\n(\n => 182.189.23.1\n)\n\n => Array\n(\n => 49.15.222.253\n)\n\n => Array\n(\n => 125.63.97.110\n)\n\n => Array\n(\n => 223.233.65.159\n)\n\n => Array\n(\n => 139.99.159.18\n)\n\n => Array\n(\n => 45.118.165.137\n)\n\n => Array\n(\n => 39.52.2.167\n)\n\n => Array\n(\n => 39.57.141.24\n)\n\n => Array\n(\n => 27.5.32.145\n)\n\n => Array\n(\n => 49.36.212.33\n)\n\n => Array\n(\n => 157.33.218.32\n)\n\n => Array\n(\n => 116.71.4.122\n)\n\n => Array\n(\n => 110.93.244.176\n)\n\n => Array\n(\n => 154.73.203.156\n)\n\n => Array\n(\n => 136.158.30.235\n)\n\n => Array\n(\n => 122.161.53.72\n)\n\n => Array\n(\n => 106.203.203.156\n)\n\n => Array\n(\n => 45.133.7.22\n)\n\n => Array\n(\n => 27.255.180.69\n)\n\n => Array\n(\n => 94.46.244.3\n)\n\n => Array\n(\n => 43.242.178.157\n)\n\n => Array\n(\n => 171.79.189.215\n)\n\n => Array\n(\n => 37.117.141.89\n)\n\n => Array\n(\n => 196.92.32.64\n)\n\n => Array\n(\n => 154.73.203.157\n)\n\n => Array\n(\n => 183.83.176.14\n)\n\n => Array\n(\n => 106.215.84.145\n)\n\n => Array\n(\n => 95.142.120.12\n)\n\n => Array\n(\n => 190.232.110.94\n)\n\n => Array\n(\n => 179.6.194.47\n)\n\n => Array\n(\n => 103.62.155.172\n)\n\n => Array\n(\n => 39.34.156.177\n)\n\n => Array\n(\n => 122.161.49.120\n)\n\n => Array\n(\n => 103.58.155.253\n)\n\n => Array\n(\n => 175.107.226.20\n)\n\n => Array\n(\n => 206.81.28.165\n)\n\n => Array\n(\n => 49.36.216.36\n)\n\n => Array\n(\n => 104.223.95.178\n)\n\n => Array\n(\n => 122.177.69.35\n)\n\n => Array\n(\n => 39.57.163.107\n)\n\n => Array\n(\n => 122.161.53.35\n)\n\n => Array\n(\n => 182.190.102.13\n)\n\n => Array\n(\n => 122.161.68.95\n)\n\n => Array\n(\n => 154.73.203.147\n)\n\n => Array\n(\n => 122.173.125.2\n)\n\n => Array\n(\n => 117.96.140.189\n)\n\n => Array\n(\n => 106.200.244.10\n)\n\n => Array\n(\n => 110.36.202.5\n)\n\n => Array\n(\n => 124.253.51.144\n)\n\n => Array\n(\n => 176.100.1.145\n)\n\n => Array\n(\n => 156.146.59.20\n)\n\n => Array\n(\n => 122.176.100.151\n)\n\n => Array\n(\n => 185.217.117.237\n)\n\n => Array\n(\n => 49.37.223.97\n)\n\n => Array\n(\n => 101.50.108.80\n)\n\n => Array\n(\n => 124.253.155.88\n)\n\n => Array\n(\n => 39.40.208.96\n)\n\n => Array\n(\n => 122.167.151.154\n)\n\n => Array\n(\n => 172.98.89.13\n)\n\n => Array\n(\n => 103.91.52.6\n)\n\n => Array\n(\n => 106.203.84.5\n)\n\n => Array\n(\n => 117.216.221.34\n)\n\n => Array\n(\n => 154.73.203.131\n)\n\n => Array\n(\n => 223.182.210.117\n)\n\n => Array\n(\n => 49.36.185.208\n)\n\n => Array\n(\n => 111.119.183.30\n)\n\n => Array\n(\n => 39.42.107.13\n)\n\n => Array\n(\n => 39.40.15.174\n)\n\n => Array\n(\n => 1.38.244.65\n)\n\n => Array\n(\n => 49.156.75.252\n)\n\n => Array\n(\n => 122.161.51.99\n)\n\n => Array\n(\n => 27.73.78.57\n)\n\n => Array\n(\n => 49.48.228.70\n)\n\n => Array\n(\n => 111.119.183.18\n)\n\n => Array\n(\n => 116.204.252.218\n)\n\n => Array\n(\n => 73.173.40.248\n)\n\n => Array\n(\n => 223.130.28.81\n)\n\n => Array\n(\n => 202.83.58.81\n)\n\n => Array\n(\n => 45.116.233.31\n)\n\n => Array\n(\n => 111.119.183.1\n)\n\n => Array\n(\n => 45.133.7.66\n)\n\n => Array\n(\n => 39.48.204.174\n)\n\n => Array\n(\n => 37.19.213.30\n)\n\n => Array\n(\n => 111.119.183.22\n)\n\n => Array\n(\n => 122.177.74.19\n)\n\n => Array\n(\n => 124.253.80.59\n)\n\n => Array\n(\n => 111.119.183.60\n)\n\n => Array\n(\n => 157.39.106.191\n)\n\n => Array\n(\n => 157.47.86.121\n)\n\n => Array\n(\n => 47.31.159.100\n)\n\n => Array\n(\n => 106.214.85.144\n)\n\n => Array\n(\n => 182.189.22.197\n)\n\n => Array\n(\n => 111.119.183.51\n)\n\n => Array\n(\n => 202.47.35.57\n)\n\n => Array\n(\n => 42.108.33.220\n)\n\n => Array\n(\n => 180.178.146.158\n)\n\n => Array\n(\n => 124.253.184.239\n)\n\n => Array\n(\n => 103.165.20.8\n)\n\n => Array\n(\n => 94.178.239.156\n)\n\n => Array\n(\n => 72.255.41.142\n)\n\n => Array\n(\n => 116.90.107.102\n)\n\n => Array\n(\n => 39.36.164.250\n)\n\n => Array\n(\n => 124.253.195.172\n)\n\n => Array\n(\n => 203.142.218.149\n)\n\n => Array\n(\n => 157.43.165.180\n)\n\n => Array\n(\n => 39.40.242.57\n)\n\n => Array\n(\n => 103.92.43.150\n)\n\n => Array\n(\n => 39.42.133.202\n)\n\n => Array\n(\n => 119.160.66.11\n)\n\n => Array\n(\n => 138.68.3.7\n)\n\n => Array\n(\n => 210.56.125.226\n)\n\n => Array\n(\n => 157.50.4.249\n)\n\n => Array\n(\n => 124.253.81.162\n)\n\n => Array\n(\n => 103.240.235.141\n)\n\n => Array\n(\n => 132.154.128.20\n)\n\n => Array\n(\n => 49.156.115.37\n)\n\n => Array\n(\n => 45.133.7.48\n)\n\n => Array\n(\n => 122.161.49.137\n)\n\n => Array\n(\n => 202.47.46.31\n)\n\n => Array\n(\n => 192.140.145.148\n)\n\n => Array\n(\n => 202.14.123.10\n)\n\n => Array\n(\n => 122.161.53.98\n)\n\n => Array\n(\n => 124.253.114.113\n)\n\n => Array\n(\n => 103.227.70.34\n)\n\n => Array\n(\n => 223.228.175.227\n)\n\n => Array\n(\n => 157.39.119.110\n)\n\n => Array\n(\n => 180.188.224.231\n)\n\n => Array\n(\n => 132.154.188.85\n)\n\n => Array\n(\n => 197.210.227.207\n)\n\n => Array\n(\n => 103.217.123.177\n)\n\n => Array\n(\n => 124.253.85.31\n)\n\n => Array\n(\n => 123.201.105.97\n)\n\n => Array\n(\n => 39.57.190.37\n)\n\n => Array\n(\n => 202.63.205.248\n)\n\n => Array\n(\n => 122.161.51.100\n)\n\n => Array\n(\n => 39.37.163.97\n)\n\n => Array\n(\n => 43.231.57.173\n)\n\n => Array\n(\n => 223.225.135.169\n)\n\n => Array\n(\n => 119.160.71.136\n)\n\n => Array\n(\n => 122.165.114.93\n)\n\n => Array\n(\n => 47.11.77.102\n)\n\n => Array\n(\n => 49.149.107.198\n)\n\n => Array\n(\n => 192.111.134.206\n)\n\n => Array\n(\n => 182.64.102.43\n)\n\n => Array\n(\n => 124.253.184.111\n)\n\n => Array\n(\n => 171.237.97.228\n)\n\n => Array\n(\n => 117.237.237.101\n)\n\n => Array\n(\n => 49.36.33.19\n)\n\n => Array\n(\n => 103.31.101.241\n)\n\n => Array\n(\n => 129.0.207.203\n)\n\n => Array\n(\n => 157.39.122.155\n)\n\n => Array\n(\n => 197.210.85.120\n)\n\n => Array\n(\n => 124.253.219.201\n)\n\n => Array\n(\n => 152.57.75.92\n)\n\n => Array\n(\n => 169.149.195.121\n)\n\n => Array\n(\n => 198.16.76.27\n)\n\n => Array\n(\n => 157.43.192.188\n)\n\n => Array\n(\n => 119.155.244.221\n)\n\n => Array\n(\n => 39.51.242.216\n)\n\n => Array\n(\n => 39.57.180.158\n)\n\n => Array\n(\n => 134.202.32.5\n)\n\n => Array\n(\n => 122.176.139.205\n)\n\n => Array\n(\n => 151.243.50.9\n)\n\n => Array\n(\n => 39.52.99.161\n)\n\n => Array\n(\n => 136.144.33.95\n)\n\n => Array\n(\n => 157.37.205.216\n)\n\n => Array\n(\n => 217.138.220.134\n)\n\n => Array\n(\n => 41.140.106.65\n)\n\n => Array\n(\n => 39.37.253.126\n)\n\n => Array\n(\n => 103.243.44.240\n)\n\n => Array\n(\n => 157.46.169.29\n)\n\n => Array\n(\n => 92.119.177.122\n)\n\n => Array\n(\n => 196.240.60.21\n)\n\n => Array\n(\n => 122.161.6.246\n)\n\n => Array\n(\n => 117.202.162.46\n)\n\n => Array\n(\n => 205.164.137.120\n)\n\n => Array\n(\n => 171.237.79.241\n)\n\n => Array\n(\n => 198.16.76.28\n)\n\n => Array\n(\n => 103.100.4.151\n)\n\n => Array\n(\n => 178.239.162.236\n)\n\n => Array\n(\n => 106.197.31.240\n)\n\n => Array\n(\n => 122.168.179.251\n)\n\n => Array\n(\n => 39.37.167.126\n)\n\n => Array\n(\n => 171.48.8.115\n)\n\n => Array\n(\n => 157.44.152.14\n)\n\n => Array\n(\n => 103.77.43.219\n)\n\n => Array\n(\n => 122.161.49.38\n)\n\n => Array\n(\n => 122.161.52.83\n)\n\n => Array\n(\n => 122.173.108.210\n)\n\n => Array\n(\n => 60.254.109.92\n)\n\n => Array\n(\n => 103.57.85.75\n)\n\n => Array\n(\n => 106.0.58.36\n)\n\n => Array\n(\n => 122.161.49.212\n)\n\n => Array\n(\n => 27.255.182.159\n)\n\n => Array\n(\n => 116.75.230.159\n)\n\n => Array\n(\n => 122.173.152.133\n)\n\n => Array\n(\n => 129.0.79.247\n)\n\n => Array\n(\n => 223.228.163.44\n)\n\n => Array\n(\n => 103.168.78.82\n)\n\n => Array\n(\n => 39.59.67.124\n)\n\n => Array\n(\n => 182.69.19.120\n)\n\n => Array\n(\n => 196.202.236.195\n)\n\n => Array\n(\n => 137.59.225.206\n)\n\n => Array\n(\n => 143.110.209.194\n)\n\n => Array\n(\n => 117.201.233.91\n)\n\n => Array\n(\n => 37.120.150.107\n)\n\n => Array\n(\n => 58.65.222.10\n)\n\n => Array\n(\n => 202.47.43.86\n)\n\n => Array\n(\n => 106.206.223.234\n)\n\n => Array\n(\n => 5.195.153.158\n)\n\n => Array\n(\n => 223.227.127.243\n)\n\n => Array\n(\n => 103.165.12.222\n)\n\n => Array\n(\n => 49.36.185.189\n)\n\n => Array\n(\n => 59.96.92.57\n)\n\n => Array\n(\n => 203.194.104.235\n)\n\n => Array\n(\n => 122.177.72.33\n)\n\n => Array\n(\n => 106.213.126.40\n)\n\n => Array\n(\n => 45.127.232.69\n)\n\n => Array\n(\n => 156.146.59.39\n)\n\n => Array\n(\n => 103.21.184.11\n)\n\n => Array\n(\n => 106.212.47.59\n)\n\n => Array\n(\n => 182.179.137.235\n)\n\n => Array\n(\n => 49.36.178.154\n)\n\n => Array\n(\n => 171.48.7.128\n)\n\n => Array\n(\n => 119.160.57.96\n)\n\n => Array\n(\n => 197.210.79.92\n)\n\n => Array\n(\n => 36.255.45.87\n)\n\n => Array\n(\n => 47.31.219.47\n)\n\n => Array\n(\n => 122.161.51.160\n)\n\n => Array\n(\n => 103.217.123.129\n)\n\n => Array\n(\n => 59.153.16.12\n)\n\n => Array\n(\n => 103.92.43.226\n)\n\n => Array\n(\n => 47.31.139.139\n)\n\n => Array\n(\n => 210.2.140.18\n)\n\n => Array\n(\n => 106.210.33.219\n)\n\n => Array\n(\n => 175.107.203.34\n)\n\n => Array\n(\n => 146.196.32.144\n)\n\n => Array\n(\n => 103.12.133.121\n)\n\n => Array\n(\n => 103.59.208.182\n)\n\n => Array\n(\n => 157.37.190.232\n)\n\n => Array\n(\n => 106.195.35.201\n)\n\n => Array\n(\n => 27.122.14.83\n)\n\n => Array\n(\n => 194.193.44.5\n)\n\n => Array\n(\n => 5.62.43.245\n)\n\n => Array\n(\n => 103.53.80.50\n)\n\n => Array\n(\n => 47.29.142.233\n)\n\n => Array\n(\n => 154.6.20.63\n)\n\n => Array\n(\n => 173.245.203.128\n)\n\n => Array\n(\n => 103.77.43.231\n)\n\n => Array\n(\n => 5.107.166.235\n)\n\n => Array\n(\n => 106.212.44.123\n)\n\n => Array\n(\n => 157.41.60.93\n)\n\n => Array\n(\n => 27.58.179.79\n)\n\n => Array\n(\n => 157.37.167.144\n)\n\n => Array\n(\n => 119.160.57.115\n)\n\n => Array\n(\n => 122.161.53.224\n)\n\n => Array\n(\n => 49.36.233.51\n)\n\n => Array\n(\n => 101.0.32.8\n)\n\n => Array\n(\n => 119.160.103.158\n)\n\n => Array\n(\n => 122.177.79.115\n)\n\n => Array\n(\n => 107.181.166.27\n)\n\n => Array\n(\n => 183.6.0.125\n)\n\n => Array\n(\n => 49.36.186.0\n)\n\n => Array\n(\n => 202.181.5.4\n)\n\n => Array\n(\n => 45.118.165.144\n)\n\n => Array\n(\n => 171.96.157.133\n)\n\n => Array\n(\n => 222.252.51.163\n)\n\n => Array\n(\n => 103.81.215.162\n)\n\n => Array\n(\n => 110.225.93.208\n)\n\n => Array\n(\n => 122.161.48.200\n)\n\n => Array\n(\n => 119.63.138.173\n)\n\n => Array\n(\n => 202.83.58.208\n)\n\n => Array\n(\n => 122.161.53.101\n)\n\n => Array\n(\n => 137.97.95.21\n)\n\n => Array\n(\n => 112.204.167.123\n)\n\n => Array\n(\n => 122.180.21.151\n)\n\n => Array\n(\n => 103.120.44.108\n)\n\n => Array\n(\n => 49.37.220.174\n)\n\n => Array\n(\n => 1.55.255.124\n)\n\n => Array\n(\n => 23.227.140.173\n)\n\n => Array\n(\n => 43.248.153.110\n)\n\n => Array\n(\n => 106.214.93.101\n)\n\n => Array\n(\n => 103.83.149.36\n)\n\n => Array\n(\n => 103.217.123.57\n)\n\n => Array\n(\n => 193.9.113.119\n)\n\n => Array\n(\n => 14.182.57.204\n)\n\n => Array\n(\n => 117.201.231.0\n)\n\n => Array\n(\n => 14.99.198.186\n)\n\n => Array\n(\n => 36.255.44.204\n)\n\n => Array\n(\n => 103.160.236.42\n)\n\n => Array\n(\n => 31.202.16.116\n)\n\n => Array\n(\n => 223.239.49.201\n)\n\n => Array\n(\n => 122.161.102.149\n)\n\n => Array\n(\n => 117.196.123.184\n)\n\n => Array\n(\n => 49.205.112.105\n)\n\n => Array\n(\n => 103.244.176.201\n)\n\n => Array\n(\n => 95.216.15.219\n)\n\n => Array\n(\n => 103.107.196.174\n)\n\n => Array\n(\n => 203.190.34.65\n)\n\n => Array\n(\n => 23.227.140.182\n)\n\n => Array\n(\n => 171.79.74.74\n)\n\n => Array\n(\n => 106.206.223.244\n)\n\n => Array\n(\n => 180.151.28.140\n)\n\n => Array\n(\n => 165.225.124.114\n)\n\n => Array\n(\n => 106.206.223.252\n)\n\n => Array\n(\n => 39.62.23.38\n)\n\n => Array\n(\n => 112.211.252.33\n)\n\n => Array\n(\n => 146.70.66.242\n)\n\n => Array\n(\n => 222.252.51.38\n)\n\n => Array\n(\n => 122.162.151.223\n)\n\n => Array\n(\n => 180.178.154.100\n)\n\n => Array\n(\n => 180.94.33.94\n)\n\n => Array\n(\n => 205.164.130.82\n)\n\n => Array\n(\n => 117.196.114.167\n)\n\n => Array\n(\n => 43.224.0.189\n)\n\n => Array\n(\n => 154.6.20.59\n)\n\n => Array\n(\n => 122.161.131.67\n)\n\n => Array\n(\n => 70.68.68.159\n)\n\n => Array\n(\n => 103.125.130.200\n)\n\n => Array\n(\n => 43.242.176.147\n)\n\n => Array\n(\n => 129.0.102.29\n)\n\n => Array\n(\n => 182.64.180.32\n)\n\n => Array\n(\n => 110.93.250.196\n)\n\n => Array\n(\n => 139.135.57.197\n)\n\n => Array\n(\n => 157.33.219.2\n)\n\n => Array\n(\n => 205.253.123.239\n)\n\n => Array\n(\n => 122.177.66.119\n)\n\n => Array\n(\n => 182.64.105.252\n)\n\n => Array\n(\n => 14.97.111.154\n)\n\n => Array\n(\n => 146.196.35.35\n)\n\n => Array\n(\n => 103.167.162.205\n)\n\n => Array\n(\n => 37.111.130.245\n)\n\n => Array\n(\n => 49.228.51.196\n)\n\n => Array\n(\n => 157.39.148.205\n)\n\n => Array\n(\n => 129.0.102.28\n)\n\n => Array\n(\n => 103.82.191.229\n)\n\n => Array\n(\n => 194.104.23.140\n)\n\n => Array\n(\n => 49.205.193.252\n)\n\n => Array\n(\n => 222.252.33.119\n)\n\n => Array\n(\n => 173.255.132.114\n)\n\n => Array\n(\n => 182.64.148.162\n)\n\n => Array\n(\n => 175.176.87.8\n)\n\n => Array\n(\n => 5.62.57.6\n)\n\n => Array\n(\n => 119.160.96.229\n)\n\n => Array\n(\n => 49.205.180.226\n)\n\n => Array\n(\n => 95.142.120.59\n)\n\n => Array\n(\n => 183.82.116.204\n)\n\n => Array\n(\n => 202.89.69.186\n)\n\n => Array\n(\n => 39.48.165.36\n)\n\n => Array\n(\n => 192.140.149.81\n)\n\n => Array\n(\n => 198.16.70.28\n)\n\n => Array\n(\n => 103.25.250.236\n)\n\n => Array\n(\n => 106.76.202.244\n)\n\n => Array\n(\n => 47.8.8.165\n)\n\n => Array\n(\n => 202.5.145.213\n)\n\n => Array\n(\n => 106.212.188.243\n)\n\n => Array\n(\n => 106.215.89.2\n)\n\n => Array\n(\n => 119.82.83.148\n)\n\n => Array\n(\n => 123.24.164.245\n)\n\n => Array\n(\n => 187.67.51.106\n)\n\n => Array\n(\n => 117.196.119.95\n)\n\n => Array\n(\n => 95.142.120.66\n)\n\n => Array\n(\n => 156.146.59.35\n)\n\n => Array\n(\n => 49.205.213.148\n)\n\n => Array\n(\n => 111.223.27.206\n)\n\n => Array\n(\n => 49.205.212.86\n)\n\n => Array\n(\n => 103.77.42.103\n)\n\n => Array\n(\n => 110.227.62.25\n)\n\n => Array\n(\n => 122.179.54.140\n)\n\n => Array\n(\n => 157.39.239.81\n)\n\n => Array\n(\n => 138.128.27.234\n)\n\n => Array\n(\n => 103.244.176.194\n)\n\n => Array\n(\n => 130.105.10.127\n)\n\n => Array\n(\n => 103.116.250.191\n)\n\n => Array\n(\n => 122.180.186.6\n)\n\n => Array\n(\n => 101.53.228.52\n)\n\n => Array\n(\n => 39.57.138.90\n)\n\n => Array\n(\n => 197.156.137.165\n)\n\n => Array\n(\n => 49.37.155.78\n)\n\n => Array\n(\n => 39.59.81.32\n)\n\n => Array\n(\n => 45.127.44.78\n)\n\n => Array\n(\n => 103.58.155.83\n)\n\n => Array\n(\n => 175.107.220.20\n)\n\n => Array\n(\n => 14.255.9.197\n)\n\n => Array\n(\n => 103.55.63.146\n)\n\n => Array\n(\n => 49.205.138.81\n)\n\n => Array\n(\n => 45.35.222.243\n)\n\n => Array\n(\n => 203.190.34.57\n)\n\n => Array\n(\n => 205.253.121.11\n)\n\n => Array\n(\n => 154.72.171.177\n)\n\n => Array\n(\n => 39.52.203.37\n)\n\n => Array\n(\n => 122.161.52.2\n)\n\n => Array\n(\n => 82.145.41.170\n)\n\n => Array\n(\n => 103.217.123.33\n)\n\n => Array\n(\n => 103.150.238.100\n)\n\n => Array\n(\n => 125.99.11.182\n)\n\n => Array\n(\n => 103.217.178.70\n)\n\n => Array\n(\n => 197.210.227.95\n)\n\n => Array\n(\n => 116.75.212.153\n)\n\n => Array\n(\n => 212.102.42.202\n)\n\n => Array\n(\n => 49.34.177.147\n)\n\n => Array\n(\n => 173.242.123.110\n)\n\n => Array\n(\n => 49.36.35.254\n)\n\n => Array\n(\n => 202.47.59.82\n)\n\n => Array\n(\n => 157.42.197.119\n)\n\n => Array\n(\n => 103.99.196.250\n)\n\n => Array\n(\n => 119.155.228.244\n)\n\n => Array\n(\n => 130.105.160.170\n)\n\n => Array\n(\n => 78.132.235.189\n)\n\n => Array\n(\n => 202.142.186.114\n)\n\n => Array\n(\n => 115.99.156.136\n)\n\n => Array\n(\n => 14.162.166.254\n)\n\n => Array\n(\n => 157.39.133.205\n)\n\n => Array\n(\n => 103.196.139.157\n)\n\n => Array\n(\n => 139.99.159.20\n)\n\n => Array\n(\n => 175.176.87.42\n)\n\n => Array\n(\n => 103.46.202.244\n)\n\n => Array\n(\n => 175.176.87.16\n)\n\n => Array\n(\n => 49.156.85.55\n)\n\n => Array\n(\n => 157.39.101.65\n)\n\n => Array\n(\n => 124.253.195.93\n)\n\n => Array\n(\n => 110.227.59.8\n)\n\n => Array\n(\n => 157.50.50.6\n)\n\n => Array\n(\n => 95.142.120.25\n)\n\n => Array\n(\n => 49.36.186.141\n)\n\n => Array\n(\n => 110.227.54.161\n)\n\n => Array\n(\n => 88.117.62.180\n)\n\n => Array\n(\n => 110.227.57.8\n)\n\n => Array\n(\n => 106.200.36.21\n)\n\n => Array\n(\n => 202.131.143.247\n)\n\n => Array\n(\n => 103.46.202.4\n)\n\n => Array\n(\n => 122.177.78.217\n)\n\n => Array\n(\n => 124.253.195.201\n)\n\n => Array\n(\n => 27.58.17.91\n)\n\n => Array\n(\n => 223.228.143.162\n)\n\n => Array\n(\n => 119.160.96.233\n)\n\n => Array\n(\n => 49.156.69.213\n)\n\n => Array\n(\n => 41.80.97.54\n)\n\n => Array\n(\n => 122.176.207.193\n)\n\n)\n```\nMarch Savings & Doings: Monkey Mama*s Monkey Money Blog\n Layout: Blue and Brown (Default) Author's Creation\n Home > March Savings & Doings\n\n# March Savings & Doings\n\nApril 7th, 2015 at 03:12 am\n\nReceived \\$45 bank interest for the month of March.\n\nRedeemed \\$50 credit card rewards (cash back) from our gas/grocery card. Deposited this snowflake into investments.\n\nRedeemed \\$42 cash back on Citi card. Deposited this snowflake into investments.\n\nSavings (From paycheck):\n\n+\\$200 to investments\n+\\$300 to cash**\n+\\$900 to IRAs\n\n**I did pull out \\$1,100 cash for Japan airfare.\n\nShort-Term Savings (for non-monthly expenses within the year):\n\n+\\$1,300 to cash\n-\\$500 for life insurance\n\nShort-term savings is robust right now (you might have noticed way more + than - in recent months) but that is mostly because we prepaid property taxes in December. Which leaves an extra \\$2,500 cash buffer or so since we've already saved up the next property tax installment (which isn't due until December).\n\n---------------------------------------------------\n\nDoings:\n\n**Life has been busy. Mostly work.\n\n**I did finally sign up for that credit card reward. \\$200 cash back + free prime for one year. Should get the rewards soon.\n\n**Mid-month I get my OT check for the year. I will also have to sort out overseas trip expenses with my dad. OT should be way more than expenses. So I am mostly just looking forward to sorting all that out. Then we can see where we are at financially and look ahead.\n\n**The funny thing about \"more money\" is more choices and stress. That's the mode I am in right now. A lot of stuff is popping up on the horizon now that we have some extra money. I think it's just a matter of time -we need to think through and prioritize. But for the moment I am feeling very overwhelmed. Some of it I haven't talked over with dh yet and I know it will be better once we sit down and talk it all out. (Who knows - he may outright veto me. That would make it easy).\n\nOur \"year of splurge\" is definitely over when it comes to the frivolous, but there is still a lot of less frivolous stuff to sort out. Home improvements and medical stuff.\n\nWith the extreme drought situation here we may have the opportunity to redo our front yard landscaping. (Both city and HOA approval, perhaps. Both have been very picky with the unnatural lush green lawns). We can do the back whenever but it's been more of a dream more than a priority. Talking about being able to do the front yard too and having some extra money is suddenly bumping that up to the top of our priorities. Maybe the theme for us this year is \"conservation\". I really want to dump the gas guzzler too.\n\n(We've wanted a more appropriate yard, for our climate, for ages. It's just not something we really thought through before we bought our house. We didn't really know the local climate either. Since living here for a time, it's always bothered me what a water wasting city this is compared to our last city. & we met a few people who had more appropriate landscaping so kind of put it in the back of our heads that is what we really wanted. It was just I had never heard of the idea before, I guess. When we did start seeing other kinds of yards we had no money).\n\nAnyway, I went for a walk in parents' way more water conservative (though less dry) city over the weekend and saw a lot of ripped out lawns. I am going to broach the subject with dh. At the least let's kill the backyard lawn. Why have we not done that yet??? That part is a frugal (free) step. The problem is that I perused the websites/portfolios of a few recommended landscapers. So now I am dreaming of a fancy hardscape kind of backyard.",
null,
"I am sure everything I was drooling over was expensive.\n\nOf course, maybe I should dream away. We are probably at a point where we could be rid of our gardeners. I'd love to keep them on but the most of what they do is mowing lawns. I don't know that they'd still help us with our meager yard work if we have no lawns. It is something to consider though. If we go REALLY low maintenance we would save \\$1,000 per year on help. Maybe this is sounding more sensible. Well, if I have to talk to dh about it and get some quotes. Our neighbors are kind of ritzy so I don't think I was looking at reasonable landscapers. (Neighborhood recommendations). It will be a little more work to seek out a deal. But, we won't know until we start getting quotes and doing more homework.\n\nI think that is a lot of my being overwhelmed. I personally tend to estimate things high and plan for the worst. Which is good financially but maybe unnecessary stress at times. Right now I just have a lot of question marks.\n\n### 5 Responses to “March Savings & Doings”\n\n1. Kiki Says:\n\nThat is one of the things I want to do as well. I've been looking at websites and trying to figure out what to do with a large portion of this back yard that is on the north side. I'd like to keep the two small rose bushes but everything else go and make it much more in line with the sacramento weather and area. The south side I'd keep a small section of grass (10' by 10') right next to patio and everything else low maintenance and more natural. The bushes in the yard seem to need a lot of water and I am not interested in that, nor do I like them.\n\n2. VS_ozgirl Says:\n\nIn Australia, drought can be a big problem at times. Where we are, not at the moment. But water-saving (aka drought-tolerant) gardens are very popular. As are water tanks and grey water from washing machines. We have both and it's great. We use the rain-water tanks to water the garden and have a pipe connected to the washing machine so that when the lawn looks dry we can use the washing machine water (grey water) to water the lawn. I highly recommend changing your garden to use less water, it's a good feeling.\n\n3. MonkeyMama Says:\n\n@Kiki - Tell me if you hire a good landscaper!",
null,
"4. FrugalTexan75 Says:\n\nSo you're thinking about xeriscaping your front and back yards? A lot of homes in New Mexico do that, also due to water restrictions. It seems to make a lot of sense to do, especially in more arid climates.\n\n5. MonkeyMama Says:\n\nYes FT. We mostly have drought resistant landscaping but we want to do something with our lawns. Those are the water wasters. That said, I'd maybe rather replace with concrete than much else. Cacti and rocks sound good to me too. Will see what we come up with.\n\n(Note: If you were logged in, we could automatically fill in these fields for you.)\n Name: * Email: Will not be published. Subscribe: Notify me of additional comments to this entry. URL: Verification: * Please spell out the number 4. [ Why? ]\n\nvB Code: You can use these tags: [b] [i] [u] [url] [email]"
] |
[
null,
"https://www.savingadvice.com/forums/core/images/smilies/biggrin.png",
null,
"https://www.savingadvice.com/forums/core/images/smilies/biggrin.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.97368014,"math_prob":0.999214,"size":4707,"snap":"2021-43-2021-49","text_gpt3_token_len":1131,"char_repetition_ratio":0.08994259,"word_repetition_ratio":0.016260162,"special_character_ratio":0.26195028,"punctuation_ratio":0.099071205,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9996173,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-01T16:14:44Z\",\"WARC-Record-ID\":\"<urn:uuid:2cebd1ec-1876-4410-8371-0052f870e767>\",\"Content-Length\":\"381719\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ab7975ca-a525-4eec-a0d1-7f0396c642d9>\",\"WARC-Concurrent-To\":\"<urn:uuid:ab61940d-d3b5-470d-9554-caba5780f783>\",\"WARC-IP-Address\":\"173.231.200.26\",\"WARC-Target-URI\":\"https://monkeymama.savingadvice.com/2015/04/07/march-savings-doings_196988/\",\"WARC-Payload-Digest\":\"sha1:YDROOWNH3KTPKDEWVA6VPXXWEDVGZ665\",\"WARC-Block-Digest\":\"sha1:G5Q37AKULGAA7HGAGJQSZQAC7N2HPUZO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964360803.6_warc_CC-MAIN-20211201143545-20211201173545-00610.warc.gz\"}"}
|
http://www.54manong.com/?id=13
|
[
"",
null,
"# 数据结构经典面试题：在字符串中找到出现频率大于50%的那个字符\n\n###### 1415 人参与 2018年08月18日 09:01 分类 : 数据结构精品文章 评论",
null,
"# 代码如下：\n\n```//在字符串中找到出现频率大于50%的那个字符\nchar get_char(char *ch)\n{\nchar str;\nint times = 0;\nwhile(*ch)\n{\nif(times == 0)\nstr= *ch, times = 1;\nelse\n{\nif(str== *ch)\ntimes++;\nelse\ntimes--;\n}\nch++;\n}\nreturn str;\n}```\n\n某个字符str如果出现频率大于一半，比如出现频率为55%，那么其他字符出现频率的总和为（1-55%）=45%，字符str出现频率比其他字符出现频率的总和大（55%-45%）=10%,按照上述我们的程序思路，在最坏的情况下，每次抵消的两个字符中都有一个str，那么最终还能剩10%的字符str。该算法的时间复杂度为O（n）。\n\n在一个int型数组中，某三个数字出现频率分别大于25%，请找出这三个数字。\n\n和原问题大同小异，只要降低规模即可，每次抵消四个不相同的数字，不断重复，最后剩下的三个数字就是答案。\n\n# 代码如下：\n\n```int candiA = 0, candiB = 0, candiC = 0;\nvoid get_three_num(int num[])\n{\nint countA = 0, countB = 0, countC = 0;\nfor (int i = 0; i < num.Length; i++)\n{\nif (countA == 0 || countB == 0 || countC == 0 )\n{\nif (countA == 0)\n{\nif (countB != 0 && num[i] == candiB)\ncountB++;\nelse if (countC != 0 && num[i] == candiC)\ncountC++;\nelse\n{\ncandiA = num[i];\ncountA++;\n}\n}\nelse if (countB == 0)\n{\nif (countA != 0 && num[i] == candiA)\ncountA++;\nelse if (countC != 0 && num[i] == candiC)\ncountC++;\nelse\n{\ncandiB = num[i];\ncountB++;\n}\n}\nelse if (countC == 0)\n{\nif (countA != 0 && num[i] == candiA)\ncountA++;\nelse if (countB != 0 && num[i] == candiB)\ncountB++;\nelse\n{\ncandiC = num[i];\ncountC++;\n}\n}\n}\nelse\n{\nif (num[i] == candiA)\ncountA++;\nelse if (num[i] == candiB)\ncountB++;\nelse if (num[i] == candiC)\ncountC++;\nelse\n{\ncountA--;\ncountB--;\ncountC--;\n}\n}\n}\n}```\n\n<< 上一篇 下一篇 >>"
] |
[
null,
"http://54manong.com/images/grgzh.jpg",
null,
"http://www.54manong.com/zb_users/upload/2018/08/201808181534595499194695.png",
null
] |
{"ft_lang_label":"__label__zh","ft_lang_prob":0.62181014,"math_prob":0.99631155,"size":1952,"snap":"2020-45-2020-50","text_gpt3_token_len":1211,"char_repetition_ratio":0.19353183,"word_repetition_ratio":0.23318386,"special_character_ratio":0.36065573,"punctuation_ratio":0.14838709,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9851785,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-24T03:16:51Z\",\"WARC-Record-ID\":\"<urn:uuid:d1174248-526e-4cdf-a540-9ccb483848b9>\",\"Content-Length\":\"29629\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:59c5acaf-f21e-4b58-8e70-6823519a13f6>\",\"WARC-Concurrent-To\":\"<urn:uuid:a5a12760-c4a9-45d0-a239-2c5beeeacdad>\",\"WARC-IP-Address\":\"123.57.88.168\",\"WARC-Target-URI\":\"http://www.54manong.com/?id=13\",\"WARC-Payload-Digest\":\"sha1:Q3EAIGVQAYH45OSGYDMZG77YRA3R4YWL\",\"WARC-Block-Digest\":\"sha1:D3FJIQS6NF25MLZRBPXHOM7VOS6MKSUG\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141171077.4_warc_CC-MAIN-20201124025131-20201124055131-00492.warc.gz\"}"}
|
https://nl.mathworks.com/matlabcentral/cody/problems/1295-bit-reversal/solutions/874848
|
[
"Cody\n\n# Problem 1295. Bit Reversal\n\nSolution 874848\n\nSubmitted on 15 Apr 2016 by Marco Castelli\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Pass\nassert(bit_reverse(1,1) == 1)\n\ny = 1\n\n2 Pass\nassert(bit_reverse(4,3) == 1)\n\ny = 1\n\n3 Pass\nassert(bit_reverse(2,3) == 2)\n\ny = 2\n\n4 Pass\nassert(bit_reverse(6,3) == 3)\n\ny = 3\n\n5 Pass\nassert(bit_reverse(5,3) == 5)\n\ny = 5\n\n6 Pass\nassert(bit_reverse(7,3) == 7)\n\ny = 7"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.5690288,"math_prob":0.92201215,"size":451,"snap":"2020-10-2020-16","text_gpt3_token_len":175,"char_repetition_ratio":0.2147651,"word_repetition_ratio":0.05,"special_character_ratio":0.46341464,"punctuation_ratio":0.08695652,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9967143,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-01T21:50:42Z\",\"WARC-Record-ID\":\"<urn:uuid:fd4504c9-1f46-497d-8dca-cbcf1c2b74f2>\",\"Content-Length\":\"74838\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2ffd0966-bd53-4373-a445-19398a4d8b27>\",\"WARC-Concurrent-To\":\"<urn:uuid:59b2d1e8-d4a1-4c76-81a4-079a6a579c89>\",\"WARC-IP-Address\":\"104.117.0.182\",\"WARC-Target-URI\":\"https://nl.mathworks.com/matlabcentral/cody/problems/1295-bit-reversal/solutions/874848\",\"WARC-Payload-Digest\":\"sha1:ZSRGOW7QNRW53GH2A5VAJ6FPUMJTDH2R\",\"WARC-Block-Digest\":\"sha1:GPMXYRUXFY6ZGVG22DKBMVEGN5KFJX5T\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370506121.24_warc_CC-MAIN-20200401192839-20200401222839-00083.warc.gz\"}"}
|
https://electronics-tutorial.net/finite-state-machines/Metastability/
|
[
"Home > finite state machines > Metastability\n\n# Metastability\n\nMetastability is a type of failure which occurs when digital circuits attempt to synchronize asynchronous digital data. As shown in Figure, when a clocked flip-flop synchronizes an asynchronous input there is a small probability that the output exhibits an unpredictable response. This phenomenon occures when the input transition changes the the setup and hold time specification. This occurs within the small timing window where the flip-flop accepts the inputs. Thus, under this kind of circumstances the flip-flop enters in an unstable intermediate state which is called as called metastable state. In this case a slight deviation leads to the outputs to revert to one of the two stable states. However, the settling time depends not only on the gain bandwidth product of the circuit, but also on the original balance and the noise level of the circuit. As shown in Figure, a critical trigger window tW is defined. If a flip-flop timing constraint is changed during the time window tW, the output Q is still unresolved within a decision time td. Referenced to the beginning of the trigger event which is the positive clock edge for the sample circuit in Figure, td thus includes the normal propagation delay tCO and extra delay due to metastability tM. The relation tW = f(td) is used for defining the metastable behavior of flipflops.The exponential function is asymptotically valid for the relation as follows, tW = f(td) = a*exp(b*td) • The probability density function for actual setup time E(tsu) is unity for one clock period tCLK . The probability for one data event to hit the critical window tW is equivalent to the indicated area tW/tCLK. With given tW(td) the reliability mean time between failures, (MTBF) of a synchronizer is calculated as follows, MTBF(td) = 1/(tW(td)*fCLK*fDATA)\n\nThis expression can also be rewritten in exponential form as, MTBF = exp(td/k2)/(k1 *fCLK*fDATA) Where k1 and k2 are constants which will get from exponential results to calculate MTBF with relative td, clock frequency fCLK and data frequency fDATA.",
null,
""
] |
[
null,
"https://electronics-tutorial.net/finite-state-machines/Metastability/Fig1-Metastability.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.89579296,"math_prob":0.97463,"size":2050,"snap":"2022-40-2023-06","text_gpt3_token_len":441,"char_repetition_ratio":0.100195505,"word_repetition_ratio":0.0,"special_character_ratio":0.19707318,"punctuation_ratio":0.06970509,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9924576,"pos_list":[0,1,2],"im_url_duplicate_count":[null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T15:10:20Z\",\"WARC-Record-ID\":\"<urn:uuid:3d848e8f-81a3-4f94-bb12-995ddd882fd2>\",\"Content-Length\":\"111026\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a98d0c01-108a-4c6e-ae35-d028c0488661>\",\"WARC-Concurrent-To\":\"<urn:uuid:cfc383a9-6086-4e0f-9e49-5a442fd0fb3d>\",\"WARC-IP-Address\":\"172.67.183.252\",\"WARC-Target-URI\":\"https://electronics-tutorial.net/finite-state-machines/Metastability/\",\"WARC-Payload-Digest\":\"sha1:QVASZ3WISQTRUHPFXDJHBBXHGEXLEL6Z\",\"WARC-Block-Digest\":\"sha1:AF6Q6W6QUHGZMPAA24F2FIJQX736VFSB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337421.33_warc_CC-MAIN-20221003133425-20221003163425-00336.warc.gz\"}"}
|
http://www4.geometry.net/detail/theorems_and_conjectures/chinese_remainder_theorem.html
|
[
"",
null,
"Home - Theorems_And_Conjectures - Chinese Remainder Theorem\ne99.com Bookstore\n Images Newsgroups\n Page 1 1-20 of 75 1 | 2 | 3 | 4 | Next 20\n\nChinese Remainder Theorem: more detail\n1. OSU-CS-TR by Kim Sin Lee, 1994\n2. Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography by C. Ding, D. Pei, et all 1999-06",
null,
"1. Chinese Remainder Theorem\nchinese remainder theorem. This is an engin to solve a kind of Chinese Remainder problem by using the method described in Page 137, Elementary Number Theory and its Applications ( Third Edition 1993)\nhttp://www.linguistlist.org/~zheng/courseware/remainder.html\n##### Chinese Remainder Theorem\nThis is an engin to solve a kind of Chinese Remainder problem by using the method described in Page 137, Elementary Number Theory and its Applications (Third Edition,1993) by Kenneth H. Rosen. Please fill the necessary values in the form,then click OK button. x ( mod\nx ( mod\nx ( mod\nx ( mod\nx ( mod\n\nclick to get the solution. Return to CGI Coursewares for Number Theory Page.\n\n2. Chinese Remainder Theorem\nDefinition of chinese remainder theorem, possibly with links to more information and implementations. chinese remainder theorem. ( algorithm) Definition An integer n can be solved uniquely mod\n##### Chinese remainder theorem\n(algorithm) Definition: An integer n can be solved uniquely mod LCM(A(i)) Note: For example, knowing the remainder of n when it's divided by 3 and the remainder when it's divided by 5 allows you to determine the remainder of n when it's divided by LCM(3,5) = 15. After LK. Author: PEB Go to the Dictionary of Algorithms and Data Structures home page. If you have suggestions, corrections, or comments, please get in touch with Paul E. Black ([email protected]). Entry modified Wed Dec 3 11:51:02 2003.\n\n 3. The Prime Glossary: Chinese Remainder Theorem related to prime numbers. This pages contains the entry titled Chineseremainder theorem. Come explore a new prime term today!http://primes.utm.edu/glossary/page.php?sort=ChineseRemainderTheorem\n\n4. Chinese Remainder Theorem\nchinese remainder theorem. Proof. We first construct a solution. Let and, for each i, . Note that for every i. Thus, has a solution . Define. Since. we see that. To see the uniqueness, Let x' be another solution. Then for each i.\nhttp://www.math.swt.edu/~haz/prob_sets/notes/node25.html\nNext: Exercises Up: Congruences Previous: Exercises\n##### Chinese Remainder Theorem\nProof. We first construct a solution. Let and, for each i . Note that for every i . Thus, has a solution . Define Since we see that To see the uniqueness, Let x ' be another solution. Then for each i . Noting that all 's are pairwise relatively prime, we have that , i.e., the solution x is unique.\nDonald Hazlewood and Carol Hazlewood\nWed Jun 5 14:35:14 CDT 1996\n\n5. Math 5410 Chinese Remainder Theorem\nchinese remainder theorem. Theorem Suppose that m1, m2, , mr are pairwise relatively prime positive integers prime in pairs, the chinese remainder theorem tells us that there is\nhttp://www-math.cudenver.edu/~wcherowi/courses/m5410/ctccrt.html\n##### Chinese Remainder Theorem\nTheorem : Suppose that m , m , ..., m r are pairwise relatively prime positive integers, and let a , a , ..., a r be integers. Then the system of congruences, x = a i (mod m i x m x ... x m r , which is given by:\nx = a M y + a M y + ... + a r M r y r (mod M), where M i = M/m i and y i = (M i (mod m i Pf : Notice that gcd(M i , m i i all exist (and can be determined easily from the extended Euclidean Algorithm). Now, notice that since M i y i = 1 (mod m i ), we have a i M i y i = a i (mod m i i M i y i = (mod m j ) if j is not i (since m j i in this case). Thus, we see that x = a i (mod m i If there were two solutions, say x , and x , then we would have x - x = (mod m i ) for all i, so x - x = (mod M), i.e., they are the same modulo M.\n##### Example\nFind the smallest multiple of 10 which has remainder 2 when divided by 3, and remainder 3 when divided by 7. We are looking for a number which satisfies the congruences, x = 2 mod 3, x = 3 mod 7, x = mod 2 and x = mod 5. Since, 2, 3, 5 and 7 are all relatively prime in pairs, the Chinese Remainder Theorem tells us that there is a unique solution modulo 210 ( = 2x3x5x7). We calculate the M i 's and y i 's as follows:\nM = 210/2 = 105; y\n\n6. Math_class: Number Theory 101 (Chinese Remainder Theorem)\nmath_class Number Theory 101 (chinese remainder theorem) Disclaimers and Apologies. I said, in the last lesson, that we would get into factoring during this lesson. the time, that I wanted to hit on the chinese remainder theorem. So, factoring will have to wait until next class\nhttp://www.csh.rit.edu/~pat/math/series/nt/20020926\n##### : Number Theory 101 (Chinese Remainder Theorem)\nI said, in the last lesson, that we would get into factoring during this lesson. I had forgotten, at the time, that I wanted to hit on the Chinese Remainder Theorem. So, factoring will have to wait until next class. In other news, I entirely blew creating a class for two weeks ago. And, last week, I was sick to the point of inertness for 80% of the week. My apologies for blowing the class two weeks ago. I hope the content is interesting enough to bring y'all back after this unscheduled hiatus.\n##### Greatest Common Divisor (Continued)\nOne more interesting thing to note about the Greatest Common Divisor of two numbers (at least one of which is non-zero). The Greatest Common Divisor of two numbers is the smallest positive number which can be written as a linear combination of the two numbers. It shouldn't come as a surprise to you that the proof of this takes advantage of the Well-Ordering Principle. Just about any mathematical statement containing \"smallest number\" requires the Well-Ordering Principle. The proof creates a set of all positive numbers a * u + b * v where u and v are integers. It shows that the set is non-empty (one way to do this is to let\n\n7. Chinese Remainder Theorem\nchinese remainder theorem. Problems of this kind are all examples ofwhat universally became known as the chinese remainder theorem.\nhttp://www.cut-the-knot.org/blue/chinese.shtml\nCTK Exchange Front Page\nMovie shortcuts\n\nPersonal info\n...\nRecommend this site\n##### Chinese Remainder Theorem\nAccording to D.Wells, the following problem was posed by Sun Tsu Suan-Ching (4th century AD): There are certain things whose number is unknown. Repeatedly divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2. What will be the number? Oystein Ore mentions another puzzle with a dramatic element from Brahma-Sphuta-Siddhanta (Brahma's Correct System) by Brahmagupta (born 598 AD): An old woman goes to market and a horse steps on her basket and crashes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had? Problems of this kind are all examples of what universally became known as the Chinese Remainder Theorem . In mathematical parlance the problems can be stated as finding n, given its remainders of division by several numbers m\n\n8. Chinese Remainder Theorem\nchinese remainder theorem. Application of Modular Arithmetic. chinese remainder theorem. According to D.Wells, the following problem was posed by Sun Tsu universally became known as the chinese remainder theorem. In mathematical parlance the\nhttp://www.cut-the-knot.com/blue/chinese.html\nCTK Exchange Front Page\nMovie shortcuts\n\nPersonal info\n...\nRecommend this site\n##### Chinese Remainder Theorem\nAccording to D.Wells, the following problem was posed by Sun Tsu Suan-Ching (4th century AD): There are certain things whose number is unknown. Repeatedly divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2. What will be the number? Oystein Ore mentions another puzzle with a dramatic element from Brahma-Sphuta-Siddhanta (Brahma's Correct System) by Brahmagupta (born 598 AD): An old woman goes to market and a horse steps on her basket and crashes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had? Problems of this kind are all examples of what universally became known as the Chinese Remainder Theorem . In mathematical parlance the problems can be stated as finding n, given its remainders of division by several numbers m\n\n9. CTK Exchange\nSubject Re chinese remainder theorem Date Tue, 2 Sep 1997 0000590400 From Alex Bogomolny Dear Tan Yours is an example of\nhttp://www.cut-the-knot.org/exchange/chinese2.shtml\n CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Subject: Re: Chinese remainder theorem Date: Tue, 2 Sep 1997 00:00:59 -0400 From: Alex Bogomolny Dear Tan: Yours is an example of problems solved in general case by what's known as the Chinese Remainder Theorem. You can look it up in O.Ore, \"Number Theory and Its History\", or H.Davenport, \"The Higher Arithmetic\" Both available through my bookstore. In your particular case, you are looking for a number X such that X = 1 (mod 2,3,4) and X = (mod 5) which means that divided by 2,3,4 X has the remainder 1 while divided by 5 the remainder is 0. The first three condition say that (X - 1) is divided by 2,3 and 4, i.e., by their least common multiple which is 12. Therefore, X - 1 = 12t for some integer t. From X = (mod 5) it follows that X - 1 = 4 (mod 5). Or 12t = 4(mod 5), 3t = 1 (mod 5). As you can check then, t = 5k + 2 for an integer k. Combining this with X = 12t + 1 we get X = 60k + 25. There are three numbers below 200 in this form: 25, 85 and 145. Best regards\n\n10. Chinese Remainder Theorem -- From MathWorld\nchinese remainder theorem.\nhttp://mathworld.wolfram.com/ChineseRemainderTheorem.html\n INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Number Theory Congruences Chinese Remainder Theorem Let r and s be positive integers which are relatively prime and let a and b be any two integers . Then there is an integer N such that and Moreover, N is uniquely determined modulo rs . An equivalent statement is that if then every pair of residue classes modulo r and s corresponds to a simple residue class modulo rs The Chinese remainder theorem is implemented as ChineseRemainder a a m m Mathematica add-on package NumberTheoryNumberTheoryFunctions (which can be loaded with the command ). The Chinese remainder theorem is also implemented indirectly using Reduce in Mathematica version 5.0 in with a domain specification of Integers The theorem can also be generalized as follows. Given a set of simultaneous congruences for i r and for which the are pairwise relatively prime , the solution of the set of congruences is where and the are determined from Congruence Congruence Equation Linear Congruence Equation search Flannery, S. and Flannery, D.\n\n 11. Chinese Remainder Theorem From MathWorld chinese remainder theorem from MathWorld Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N\\equiv a\\ \\lefthttp://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/ChineseRemainderTh\n\n12. Chinese Remainder Problem\nUnfortunately, Problem 26 is the only problem that illustrates thechinese remainder theorem in the Sun Tzu Suan Ching. As such, we\nhttp://www.math.sfu.ca/histmath/China/3rdCenturyBC/CRP1.html\n##### What is it?\nThese particular kinds of mathematical problem falls in the category of indeterminate analysis. Usually, it appears in the form as such (in modern notation):\nN = m1x + r1 N = m2y + r2 N = m3z + r3\nOr in modern number theory notation:\nN r1 (mod m1) N r2 (mod m2) N r3 (mod m3)\nAside: Writing N r1 (mod m1) [this means N is congruent to r1 modulo m1] means that N divided by m1 leaves r1 as the remainder. The goal here is to find the smallest positive integer satisfying the congruences states above.\n##### Origins.\nNow that you know what a Chinese Remainder Problem is, you must be wondering why or what has this particular kind of problem to do with Chinese Mathematical History. The reason why it is called the Chinese Remainder Problem is because the earliest versions of these congruence problems occured in early Chinese mathematical works. The earliest of such works that contains the Chinese Remainder Problem is the Sun Tzu Suan Ching (also known as Sunzi suanjing) written in approximately late third century by Sun Zi . Problem 26 (also known as the problem of Master Sun) in the third volume of the Sun Tzu Suan Ching offers the earliest recorded Chinese Remainder Problem. Problem 26 is as stated below:\n\"We have a number of things, but we do not know exactly how many. If we count them by threes we have two left over. If we count them by fives we have three left over. If we count them by sevens we have two left over. How many things are there?\" (Quoted from Sun Tze Suan Ching).\n\n 13. CHINESE REMAINDER THEOREM E. L. Lady chinese remainder theoremE. L. LadyThe chinese remainder theorem involves a situation like the following we are asked tohttp://www.math.hawaii.edu/~lee/courses/Chinese.pdf\n\n14. Chinese Remainder Theorem - Wikipedia, The Free Encyclopedia\nchinese remainder theorem. The chinese remainder theorem is any of anumber of related results in abstract algebra and number theory.\nhttp://en.wikipedia.org/wiki/Chinese_remainder_theorem\n##### Chinese remainder theorem\nThe Chinese remainder theorem is any of a number of related results in abstract algebra and number theory Table of contents 1 Simultaneous congruences of integers\n2 Statement for principal ideal domains\n\n3 Statement for general rings\n\n...\nedit\n##### Simultaneous congruences of integers\nThe original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Qin_Jiushao.html published in , is a statement about simultaneous congruences (see modular arithmetic ). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences\nx a i mod n i i k\nFurthermore, all solutions x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set\n\n15. Chinese Remainder Theorem - Wikipedia, The Free Encyclopedia\nchinese remainder theorem. (Redirected from chinese remainder theorem).The Chinese I k ) ). External links. chinese remainder theorem.\nhttp://en.wikipedia.org/wiki/Chinese_Remainder_Theorem\n##### Chinese remainder theorem\n(Redirected from Chinese Remainder Theorem The Chinese remainder theorem is any of a number of related results in abstract algebra and number theory Table of contents 1 Simultaneous congruences of integers 2 Statement for principal ideal domains 3 Statement for general rings 4 External links ... edit\n##### Simultaneous congruences of integers\nThe original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Qin_Jiushao.html published in , is a statement about simultaneous congruences (see modular arithmetic ). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences\nx a i mod n i i k\nFurthermore, all solutions x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set\n\n16. Chinese Remainder Theorem - Wikipedia, The Free Encyclopedia\nhttp://en2.wikipedia.org/wiki/Chinese_remainder_theorem\n##### Chinese remainder theorem\nThe Chinese remainder theorem is any of a number of related results in abstract algebra and number theory Table of contents 1 Simultaneous congruences of integers\n2 Statement for principal ideal domains\n\n3 Statement for general rings\n\n...\nedit\n##### Simultaneous congruences of integers\nThe original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Qin_Jiushao.html published in , is a statement about simultaneous congruences (see modular arithmetic ). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences\nx a i mod n i i k\nFurthermore, all solutions x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set\n\n17. CHINESE REMAINDER THEOREM\nchinese remainder theorem Applications in Computing, Coding, Cryptography by CDing (Turku Centre for Computer Science, Finland), D Pei (Chinese Academy of\nhttp://www.worldscientific.com/books/compsci/3254.html\n\n18. The Chinese Remainder Theorem\nThe chinese remainder theorem. Last updated August 7th, 1995 The ChineseRemainder Theorem (CRT) gives the answer to the problem\nhttp://www.apfloat.org/crt.html\n##### The Chinese Remainder Theorem\nLast updated: August 7th, 1995 The Chinese Remainder Theorem (CRT) gives the answer to the problem: Find the number x, that satisfies all the n equations simultaneously:\n• x = r1 (mod p1)\n• x = r2 (mod p2)\n• x = rk (mod pk)\n• x = rn (mod pn)\nWe will assume here (for practical purposes) that the moduli pk are primes. Then there exists a unique solution x modulo p1*p2*...*pn. The solution can be found with the following algorithm: Let P=p1*p2*...*pn Let the numbers T1...Tn be defined so that for each Tk (k=1...n) (P/pk)*Tk=1 (mod pk) that is, Tk is the inverse of P/pk (mod pk). The inverse of a (mod p) can be found for example by calculating a^(p-2) (mod p). Note that a*a^(p-2)=a^(p-1)=1 (mod p). Then the solution is x = (P/p1)*r1*T1 + (P/p2)*r2*T2 + ... + (P/pn)*rn*Tn (mod P) The good thing is, that you can calculate the factors (P/pk)*Tk beforehand, and then to get x for different rk, you only need to do simple multiplications and additions (supposing that the primes pk remain the same). When using the CRT in a number theoretic transform, the algorithm can be implemented very efficiently using only single-precision arithmetic when rk\n\n19. Chinese Remainder Theorem\nchinese remainder theorem. The chinese remainder theorem is the name appliedto a number of related results in abstract algebra and number theory.\nhttp://www.fact-index.com/c/ch/chinese_remainder_theorem.html\nMain Page See live article Alphabetical index\n##### Chinese remainder theorem\nThe Chinese remainder theorem is the name applied to a number of related results in abstract algebra and number theory Table of contents 1 Simultaneous congruences of integers\n2 Statement for principal ideal domains\n\n3 Statement for general rings\n##### Simultaneous congruences of integers\nThe original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao published in , is a statement about simultaneous congruences (see modular arithmetic ). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences\nx a i mod n i ) for i k\nFurthermore, all solutions x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set e i s n n i , then we have\ne i mod n i ) and e i mod n j ) for j i\nThe number x i k a i e i then solves the given system of simultaneous congruences.\n\n20. The Chinese Remainder Theorem\nThe chinese remainder theorem. We prove the chinese remainder theorem andThue s Theorem as well as several useful number theory propositions.\nhttp://mizar.uwb.edu.pl/JFM/Vol9/wsierp_1.html\nJournal of Formalized Mathematics\nVolume 9, 1997\n\nUniversity of Bialystok\n\nAssociation of Mizar Users\n##### The Chinese Remainder Theorem\nAndrzej Kondracki\nAMS Management Systems Poland, Warsaw\n##### MML Identifier:\nThe terminology and notation used in this paper have been introduced in the following articles [ Contents (PDF format)\n##### Bibliography\n1] Grzegorz Bancerek. The fundamental properties of natural numbers Journal of Formalized Mathematics\n2] Grzegorz Bancerek. The ordinal numbers Journal of Formalized Mathematics\n3] Grzegorz Bancerek. Joining of decorated trees Journal of Formalized Mathematics\n4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences Journal of Formalized Mathematics\n5] Czeslaw Bylinski. Functions and their basic properties Journal of Formalized Mathematics\n6] Czeslaw Bylinski. The sum and product of finite sequences of real numbers Journal of Formalized Mathematics\n7] Katarzyna Jankowska. Transpose matrices and groups of permutations Journal of Formalized Mathematics\n8] Andrzej Kondracki. Basic properties of rational numbers Journal of Formalized Mathematics\n9] Jaroslaw Kotowicz and Yatsuka Nakamura.\n\n Page 1 1-20 of 75 1 | 2 | 3 | 4 | Next 20"
] |
[
null,
"http://www4.geometry.net/gnet_logo.gif",
null,
"http://ecx.images-amazon.com/images/I/21BMQ58651L.jpg",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.78015006,"math_prob":0.9517309,"size":5375,"snap":"2023-14-2023-23","text_gpt3_token_len":1344,"char_repetition_ratio":0.29528952,"word_repetition_ratio":0.12721893,"special_character_ratio":0.21897675,"punctuation_ratio":0.18981019,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.998471,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-05-30T21:54:57Z\",\"WARC-Record-ID\":\"<urn:uuid:4f292804-a7f4-459a-bdb0-7739325c5bfb>\",\"Content-Length\":\"55390\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2497cb1d-a5c5-40c2-93b9-48b1f97bd55c>\",\"WARC-Concurrent-To\":\"<urn:uuid:a402916e-cc7d-40f0-a40c-35b278f42bd3>\",\"WARC-IP-Address\":\"169.60.163.244\",\"WARC-Target-URI\":\"http://www4.geometry.net/detail/theorems_and_conjectures/chinese_remainder_theorem.html\",\"WARC-Payload-Digest\":\"sha1:UEPTVOYYWR4KK63VZLMJGW27HNZH2XE5\",\"WARC-Block-Digest\":\"sha1:EGRJ64ATQBCWCFYMDFIOIALYEB7NJ7DF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224646144.69_warc_CC-MAIN-20230530194919-20230530224919-00575.warc.gz\"}"}
|
https://studyres.com/doc/8530431/chapter-3
|
[
"• Study Resource\n• Explore\n\nSurvey\n\n* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project\n\nDocument related concepts\n\nHistory of statistics wikipedia, lookup\n\nStudent's t-test wikipedia, lookup\n\nTaylor's law wikipedia, lookup\n\nBootstrapping (statistics) wikipedia, lookup\n\nResampling (statistics) wikipedia, lookup\n\nMisuse of statistics wikipedia, lookup\n\nDegrees of freedom (statistics) wikipedia, lookup\n\nAnalysis of variance wikipedia, lookup\n\nTranscript\n```Comparison of groups\nThe purpose of analysis is to compare\ntwo or more population means by\nanalyzing sample means and variances.\nOne-way analysis is used with data\ncategorized with one treatment (or\nfactor), which is a characteristic that\nallows us to distinguish the different\npopulations from one another.\nExample:\nA headline in USA Today proclaimed that “Men,\nwomen are equal talkers.” That headline\nreferred to a study of the numbers of words\nthat samples of men and women spoke in a\nday. Given below are the results from the\nstudy. Does there appear to be a difference?\nExample:\nWeights of college students in September and\nApril of their freshman year were measured.\nThe following table lists a small portion of\nthose sample values. (Here we use only a\nsmall portion of the available data so that we\ncan better illustrate the problem.) Can you\nclaim some change in weight from September\nto April?\nIndependence assumption\nTwo or more samples are independent if the\nsample values selected from one group are\nnot related to or somehow paired or\nmatched with the sample values from the\nother groups.\nTwo groups can be dependent if the sample\nvalues are paired. (That is, each pair of\nsample values consists of two\nmeasurements from the same subject (such\nas before/after data), or each pair of sample\nvalues consists of matched pairs (such as\nhusband/wife data), where the matching is\nbased on some inherent relationship.)\nIdentifying Means That Are Different\nInformal methods for comparing means\n1. Use the same scale for constructing\nboxplots of the data sets to see if one or\nmore of the data sets are very different from\nthe others.\n2. Calculate the mean for each group, then\ncompare those means to see if one or more\nof them are significantly different from the\nothers.\nAnalysis of Variance\nFundamental Concepts\nEstimate the common value of :\n2\n1. The variance between groups (also called\nvariation due to treatment) is an estimate of the\n2\ncommon population variance that is based\non the variability among the sample means.\n2. The variance within groups (also called\nvariation due to error) is an estimate of the\n2\ncommon population variance based on the\nsample variances.\nAnalysis of Variance\nRequirements\n1. The populations have approximately normal\ndistributions.\n2. The populations have the same variance \n(or standard deviation ).\n2\n3. The samples are independent of each other.\n4. The different samples are from populations\nthat are categorized in only one way.\nKey Components of\nAnalysis of Variance\nSS(total), or total sum of squares, is a\nmeasure of the total variation (around x) in\nall the sample data combined.\n\nS\nS\nt\no\nt\na\nl\n\nx\n\nx\n\n2\nKey Components of\nAnalysis of Variance\nSS(treatment), also referred to as Sum of\nSquares between groups, is a measure of\nthe variation between the sample means.\nS\nS\nt\nr\ne\na\nt\nm\ne\nn\nt\n\n\n\nn\n\nx\nn\n\nx\nn\n\nx\nx\n\nx\n\nx\n\n1\n1\n2\n2\nk\nk\n2\n2\n\nn\nx\nx\n\n\ni\ni\n2\n2\nKey Components of\nAnalysis of Variance\nSS(error), also referred to as Sum of\nSquares within groups, is a sum of squares\nrepresenting the variability that is assumed\nto be common to all the populations being\nconsidered.\nS\nS\ne\nr\nr\no\nr\n\n\n\n\n1\nn\n\n1\nn\n1\nn\ns\n\ns\n\ns\n1\n2\nk\n2\n1\n\n1\ns\nn\n\n\ni\n2\ni\n2\n2\n2\nk\nKey Components of\nAnalysis of Variance\nGiven the previous expressions for\nSS(total), SS(treatment), and SS(error),\nthe following relationship will always\nhold.\nSS(total) = SS(treatment) + SS(error)\nMean Squares (MS)\nMS(treatment) is a mean square for\ntreatment, obtained as follows:\nMS(treatment) =\nSS (treatment)\nk–1\nMS(error) is a mean square for error,\nobtained as follows:\nMS(error) =\nSS (error)\nN–k\nN = total number of values in all samples combined\nIdentifying Means That Are Different\nF=\nMS (treatment)\nMS (error)\nAfter checking a significance of the\nratio F of mean squares (MS), we\nmight conclude that there are\ndifferent population means. But it\ncannot show that any particular\nmean is different from the others.\n```\nRelated documents"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.92805076,"math_prob":0.94965184,"size":4293,"snap":"2019-51-2020-05","text_gpt3_token_len":940,"char_repetition_ratio":0.13103287,"word_repetition_ratio":0.06486487,"special_character_ratio":0.21476823,"punctuation_ratio":0.08038977,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99583787,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-07T03:35:13Z\",\"WARC-Record-ID\":\"<urn:uuid:b0c23a9b-3cae-4b84-b57f-dc1fe9a9ccad>\",\"Content-Length\":\"94486\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:bef4fff2-5cd9-4a40-978a-bcc15f201983>\",\"WARC-Concurrent-To\":\"<urn:uuid:eb45a756-2940-4a4d-bd33-6bcce33a548d>\",\"WARC-IP-Address\":\"104.28.20.25\",\"WARC-Target-URI\":\"https://studyres.com/doc/8530431/chapter-3\",\"WARC-Payload-Digest\":\"sha1:6GZDJ3URWH6M5KDX45BEP42TQPDEAJBO\",\"WARC-Block-Digest\":\"sha1:RUDGO6VM27NBJKNDU2ZHU5KMUP4BCNIP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540495263.57_warc_CC-MAIN-20191207032404-20191207060404-00160.warc.gz\"}"}
|
https://www.jobduniya.com/Placement-Papers/Tata-Infotech/Technical-Resources/Java/Infosys-Puzzles-Part-2.html
|
[
"# Tata Infotech Java Questions: Infosys Puzzles Part 2\n\nExamrace Placement Series prepares you for the toughest placement exams to top companies.\n\n1 I participated in a race. 1/5th of those who are before me are equal to 5/6th of those behind me. What were the total number of contestants in the race (3 Marks)?\n\n2 Find the 3 digit number. Third digit is square root of first\n\ndigit. Second digit is sum of first and third digits. Find the\n\nnumber (3 Marks)\n\n3This problem is of time and work type. i dont remember the exact question. The question goes like this. Some A and some B are able to produce so many tors in so many hours (for example 10 A and 20 B are able to produce 30 tors per hour). Like this one more sentence was given. We have to find out the rate of working of A and B in\n\ntors/hour (4 Marks).\n\n4 A and B play a game of dice between them. The dice consists of colours on their faces instead of numbers.\n\nA wins if both dice show same color. B wins if both dice show different colors. One dice consists of 1 red and 5 blue.\n\nwhat must be the color in the faces of other dice (i.e.how many blue and how many red?).\n\nChances of winning for A and B are even (5 Marks).\n\n1. This question is of anals type. The question goes like this. I dont remember the question. Some sentences reg tastes of people to poetry are given like all who like A's Poem like the poems of B like this 7 or 8 sentences were given\n\n5 A girl has 55 marbles. She arranges them in n rows. The nth row consists of n marbles, the n − 1th row consists of n − 1 marbles and so on. What are the number of marbles in nth row (3 Marks)?\n\nquestions were based on this (8 Marks).\n\n7This question is also of anals types. Four persons are there A, B, C, D. Each of the for persons own either\n\nP, Q, R, S. 10 sentences using if clause were given. We have to find out which belongs to whom (8 Marks).\n\n8 This question involves oercentage. i dont remember the question (5 Marks).\n\n9 problems on ages (6 Marks).\n\n10 Problmes on time and distance (5 Marks)."
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.95157456,"math_prob":0.8912545,"size":2046,"snap":"2020-24-2020-29","text_gpt3_token_len":528,"char_repetition_ratio":0.12144956,"word_repetition_ratio":0.024813896,"special_character_ratio":0.2605083,"punctuation_ratio":0.10722101,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9531053,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-12T21:59:33Z\",\"WARC-Record-ID\":\"<urn:uuid:336eabeb-d812-41f0-afed-58523ebd3919>\",\"Content-Length\":\"22205\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d37b338b-3496-48e7-886b-5558f2a85237>\",\"WARC-Concurrent-To\":\"<urn:uuid:51a414a1-ed16-4741-b959-8182bb0a172a>\",\"WARC-IP-Address\":\"172.67.188.50\",\"WARC-Target-URI\":\"https://www.jobduniya.com/Placement-Papers/Tata-Infotech/Technical-Resources/Java/Infosys-Puzzles-Part-2.html\",\"WARC-Payload-Digest\":\"sha1:CO2YGOQMN57WO7AOLHYQ2E5LZ74RY4ST\",\"WARC-Block-Digest\":\"sha1:COU4GGW6QZ6UQAB4QCUTQY5GRWOXSQLX\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657140337.79_warc_CC-MAIN-20200712211314-20200713001314-00430.warc.gz\"}"}
|
https://www.php.net/manual/ro/ds-vector.allocate.php
|
[
"PHP 8.1.0 RC 4 available for testing\n\n# Ds\\Vector::allocate\n\n(PECL ds >= 1.0.0)\n\nDs\\Vector::allocateAllocates enough memory for a required capacity\n\n### Descrierea\n\npublic Ds\\Vector::allocate ( int `\\$capacity` ) : void\n\nEnsures that enough memory is allocated for a required capacity. This removes the need to reallocate the internal as values are added.\n\n### Parametri\n\n`capacity`\n\nThe number of values for which capacity should be allocated.\n\nNotă:\n\nCapacity will stay the same if this value is less than or equal to the current capacity.\n\n### Valorile întoarse\n\nNu este întoarsă nici o valoare.\n\n### Exemple\n\nExample #1 Ds\\Vector::allocate() example\n\n``` <?php\\$vector = new \\Ds\\Vector();var_dump(\\$vector->capacity());\\$vector->allocate(100);var_dump(\\$vector->capacity());?> ```\n\nExemplul de mai sus va afișa ceva similar cu:\n\n```int(10)\nint(100)\n```",
null,
""
] |
[
null,
"https://www.php.net/images/[email protected]",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.58371544,"math_prob":0.6809744,"size":666,"snap":"2021-43-2021-49","text_gpt3_token_len":176,"char_repetition_ratio":0.1691843,"word_repetition_ratio":0.0,"special_character_ratio":0.25975975,"punctuation_ratio":0.15873016,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9555761,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-19T16:24:44Z\",\"WARC-Record-ID\":\"<urn:uuid:16186abd-c5f9-475c-ab6a-a1cfeb8beb7b>\",\"Content-Length\":\"25609\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:366c3592-964e-459c-a0e5-79dda3af7589>\",\"WARC-Concurrent-To\":\"<urn:uuid:69e00216-ce7d-4ca7-9292-250d75eabdae>\",\"WARC-IP-Address\":\"185.85.0.29\",\"WARC-Target-URI\":\"https://www.php.net/manual/ro/ds-vector.allocate.php\",\"WARC-Payload-Digest\":\"sha1:YFVUIXOMWUP44LURGDEGKR6QC5XCJDHB\",\"WARC-Block-Digest\":\"sha1:CPNNOD2AQAFY4TY374W4CFHTGYV3XI6K\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585270.40_warc_CC-MAIN-20211019140046-20211019170046-00492.warc.gz\"}"}
|
http://www.ebooklibrary.org/articles/eng/Dilaton
|
[
"",
null,
"#jsDisabledContent { display:none; } My Account | Register | Help",
null,
"Flag as Inappropriate",
null,
"This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate? Excessive Violence Sexual Content Political / Social Email this Article Email Address:\n\n# Dilaton\n\nArticle Id: WHEBN0000564961\nReproduction Date:\n\n Title: Dilaton",
null,
"Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:\n\n### Dilaton\n\nIn particle physics, the dilaton is a hypothetical particle that appears in theories with extra dimensions when the volume of the compactified dimensions is allowed to vary. It appears for instance in Kaluza–Klein theory's compactifications of extra dimensions. It is a particle of a scalar field Φ, a scalar field that always comes with gravity. For comparison, in standard general relativity, Newton's constant, or equivalently the Planck mass is a constant. If this constant is promoted to a dynamical field, the result is the dilaton.\n\nIn Kaluza–Klein theories, after dimensional reduction, the effective Planck mass varies as some power of the volume of compactified space. This is why volume can turn out as a dilaton in the lower-dimensional effective theory.\n\nAlthough string theory naturally incorporates Kaluza–Klein theory (which first introduced the dilaton), perturbative string theories, such as type I string theory, type II string theory and heterotic string theory, already contain the dilaton in the maximal number of 10 dimensions. However, on the other hand, M-theory in 11 dimensions does not include the dilaton in its spectrum unless it is compactified. In fact, the dilaton in type IIA string theory is actually the radion of M-theory compactified over a circle, while the dilaton in E8 × E8 string theory is the radion for the Hořava–Witten model. (For more on the M-theory origin of the dilaton, see .)\n\nIn string theory, there is also a dilaton in the worldsheet CFT(Conformal field theory). The exponential of its vacuum expectation value determines the coupling constant g, as ∫R = 2πχ for compact worldsheets by the Gauss–Bonnet theorem and the Euler characteristic χ = 2 − 2g, where g is the genus that counts the number of handles and thus the number of loops or string interactions described by a specific worldsheet.\n\ng = \\exp(\\langle \\phi \\rangle)\n\nTherefore the coupling constant is a dynamical variable in string theory, unlike the case of quantum field theory where it is constant. As long as supersymmetry is unbroken, such scalar fields can take arbitrary values (they are moduli). However, supersymmetry breaking usually creates a potential energy for the scalar fields and the scalar fields localize near a minimum whose position should in principle be calculable in string theory.\n\nThe dilaton acts like a Brans–Dicke scalar, with the effective Planck scale depending upon both the string scale and the dilaton field.\n\nIn supersymmetry, the superpartner of the dilaton is called the dilatino, and the dilaton combines with the axion to form a complex scalar field.\n\n## Dilaton action\n\nThe dilaton-gravity action is\n\n\\int d^Dx \\sqrt{-g} \\left[ \\frac{1}{2\\kappa} \\left( \\Phi R - \\omega\\left[ \\Phi \\right]\\frac{g^{\\mu\\nu}\\partial_\\mu \\Phi \\partial_\\nu \\Phi}{\\Phi} \\right) - V[\\Phi] \\right].\n\nThis is more general than Brans–Dicke in vacuum in that we have a dilaton potential."
] |
[
null,
"http://read.images.worldlibrary.org/App_Themes/wel-mem/images/logo.jpg",
null,
"http://read.images.worldlibrary.org/images/SmallBook.gif",
null,
"http://www.ebooklibrary.org/images/delete.jpg",
null,
"http://www.ebooklibrary.org/App_Themes/default/images/icon_new_window.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.83467,"math_prob":0.93024343,"size":4720,"snap":"2019-43-2019-47","text_gpt3_token_len":1115,"char_repetition_ratio":0.13019508,"word_repetition_ratio":0.0055788006,"special_character_ratio":0.22118644,"punctuation_ratio":0.15706214,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98148286,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-13T00:33:17Z\",\"WARC-Record-ID\":\"<urn:uuid:b6464da8-cca6-4fed-a41e-a455e660e4d2>\",\"Content-Length\":\"148109\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4af3d734-9a1f-4e50-b37f-04c0ee133950>\",\"WARC-Concurrent-To\":\"<urn:uuid:166c2577-b410-452e-9b81-50d8d3a906e5>\",\"WARC-IP-Address\":\"66.27.42.21\",\"WARC-Target-URI\":\"http://www.ebooklibrary.org/articles/eng/Dilaton\",\"WARC-Payload-Digest\":\"sha1:E55F7HRJKJV4ZZFXIDW6LPDCUBQWX5CQ\",\"WARC-Block-Digest\":\"sha1:CEFA7U77BMDKT64DTMIPGNGDXQJBR744\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496665809.73_warc_CC-MAIN-20191112230002-20191113014002-00410.warc.gz\"}"}
|
https://www.cazoomy.com/number/ordering-decimals/
|
[
"# Ordering Decimals Worksheets\n\n## Cazoomy Ordering Decimals Worksheets\n\nOrdering decimals worksheets for gcse foundation maths. Ordering decimal worksheet 1 asks students to write the correct position of each decimal in the tables. Ordering decimals worksheet 2 contains questions using a maze. Ordering decimals worksheet 3 asks students to correctly put the decimals in the correct place on the number line.\n\n## Ordering Decimals Worksheet Example\n\nBelow shows an example of ordering decimals using a maze. The yellow squares shows the order of the decimals smallest to largest starting from the green square which is 0.01 and ending at the red square which is 0.7.",
null,
"## Ordering Decimals Best Practice Advice\n\nWhen Ordering decimals it is important to notice how many zero's occur after the decimal point. The more zero's after the decimal point, the smaller the number is.\nIf you're looking for all decimals worksheets try here: Decimals Worksheets.\n\n## Ordering Decimals Worksheet Starter\n\nThe ordering decimals worksheet starter asks students to identify the smallest number. The teacher may circle the largest number on the board after a popular vote.",
null,
"#### Ordering Decimals Worksheet Starter Answer\n\n• 0.0069\n\nIf you're looking for all decimals worksheets try here: Decimals Worksheets.\n\n## Enjoy 50 Free Ordering Decimals Resources !\n\nAccess 100s of Ordering Decimals Worksheets, including Ordering Decimals questions and answers for gcse maths, 9-1 gcse mathematics, key stage 3 and key stage 4 maths.\nSignup FREE.\n\n•\n•\n•\n•\n•\n•\n•\n•\n•"
] |
[
null,
"https://cdn.shortpixel.ai/client/q_lqip,ret_wait,w_638,h_479/https://www.cazoomy.com/math-practice/decimals/ordering-decimals-worksheet.png",
null,
"https://cdn.shortpixel.ai/client/q_lqip,ret_wait,w_638,h_479/https://www.cazoomy.com/math-practice/decimals/ordering-decimals-worksheets.png",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.74729174,"math_prob":0.9404964,"size":1707,"snap":"2020-10-2020-16","text_gpt3_token_len":350,"char_repetition_ratio":0.26776278,"word_repetition_ratio":0.06225681,"special_character_ratio":0.18746339,"punctuation_ratio":0.09897611,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99835575,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-21T04:04:37Z\",\"WARC-Record-ID\":\"<urn:uuid:3228044b-c789-4eee-a35f-6cc1cf92ac3c>\",\"Content-Length\":\"62141\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e148e78e-7f22-454d-8948-f90fcdf70e1b>\",\"WARC-Concurrent-To\":\"<urn:uuid:24f3095c-d960-4262-a954-ea993cc04e29>\",\"WARC-IP-Address\":\"185.119.175.239\",\"WARC-Target-URI\":\"https://www.cazoomy.com/number/ordering-decimals/\",\"WARC-Payload-Digest\":\"sha1:NNY422LVTYLYUMNE7QPNKC6QLWJ3XRWI\",\"WARC-Block-Digest\":\"sha1:RBKBSAPHR5ZCWCVLS6HTPRQQNQT6XOBP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145438.12_warc_CC-MAIN-20200221014826-20200221044826-00399.warc.gz\"}"}
|
http://www.softmath.com/math-com-calculator/graphing-inequalities/where-can-you-find-the-answer.html
|
[
"Search Engine visitors came to this page today by entering these algebra terms:\n\nSolve: log2=5th root of 8, translating words to expressions math worksheets for primary students, prealgebra worksheet, factoring monomials calculator.\n\nMcdougal littell math practice workbook, grammer the ninth grade, algebra worksheet, java code that counts the digits, conversion from cubics to square feet, algebra slope calculator, Solving Radical Equations-Equation Solver.\n\nDna report 6th grade, precalculus linear programming examples, roots of cubic function, calculator, ti-84 emulator, FREE BOOLEAN ALGEBRA SOLVER, formula for solving cubic meters, math prentice hall workbook pre-algebra florida.\n\nMerrill Algebra One Book Teachers, games one and two step solving for variable, manually calculate logarithms, HOLT PHYSICS chapter 4 test A, ti-89 programs laplace inverse.\n\nTrigonometry and word problems and printable, Solving trigonometric equations printable worksheets, Algebrator website, are all exothermic equations spontaneous.\n\nAlgebra two factoring with two variables, 7th grade math mid year exam georgia, ti 89 sat study cards, mcdougal littell answer key, Free Printable Algebra Worksheets.\n\nMatlab solving homogeneous systems of equations, algebra help radicals, completing cube square examples, 9th grade english worksheets with a answer key, Methods for comparing fractions.\n\nGlencoe PreAlgebra Workbook, algebra formulas exponents, cheats for algebra 2, calculator online with logarithm, automatic algebra solutions.\n\nEven answers elementary statistics third edition, how do find the vertex of a parabola using the linear and quadratic system, hard calculas problems, online calculator factoring polynomials, coordinate graphing lessons printable, Solve an Algebra Equation, algebra software.\n\nOnline fraction solver, graphing nonlinear inequalities with absolute value, college algebra solutions, Free past exam papers gcse year 11 maths.\n\nCommon denominators worksheet, \"Using letter symbols\" year 7 resource, Free Algebra problem solver, LCM Java Codes, Factoring quadratic games, sum and difference of two binomial, binary calculator java code example.\n\nMath square cube cube root, sample accounting problems and answers, free year 9 algebra quizz, online simultaneous equations solver, harvard math placement test sample, free games to download for you TI-84 calculator.\n\nUsa tutor needing students, bionomial theorem for any real exponent, Algebra and Trigonometry Structure and Method Book 2 answers.\n\nAlgebra quadratic equation solver, sixth grade math least common denominator worksheet, mathematical analysis walter rudin homework solutions, rational expression - trivia.\n\nWriting expression and equations,mathematics, grade 7, power point, dummit and foote chapter 7 solutions, printable online graphing calculator.\n\nText to Ti-84 Program compiler, grade 10 exam practise, solving binomial expressions.\n\nTi-84 plus factor program, symbolic method, algebra software for kids, convert fraction to percent notation.\n\nMathamatical exercices, square cube root chart, programming midpoint formula in TI-83 Calc, classical mathimatics, pdf, roots and exponents, worksheets for turning decimals into fractions.\n\nNonlinear programming ti-89, online algebra solver, simplifying algebra worksheets.\n\nHomework cheats, tutorial quiz for kids for surds, past perfect execises, free downloadable ebook for grade 6 math, How to show equations in presentations, solving radical equations online calculator.\n\nHow to work out equations on TI-84, DOWNLOAD APTITUDE TEST PAPERS, the difference between simplifying an algebraic expression and solving an algebraic equation, how can you tell if the functions is linear by an equation, begining algebra factoring tutor, distributive property using fractions.\n\nTRICK ALGEBRA QUESTIONS, volume of elipse, t-83 online calculator, online algebra textbook.\n\nDividing Integers Worksheet, integral calculas, mathematical equations percents.\n\nLeast common multiple of algebraic expressions, square root and radical problems, addition and multiplication chart for z7, pre algebra prentice hall multiple choice practice, simplifying radicals calculator, precalculus proving trigonomic identities.\n\nSubtracting Fractions Like Denominators, math story scale, trigonomic function cheat sheet, mcdougall littell + math worksheets.\n\nFree 8th grade writing exercices, ti84 algebra pdf, factoring calculators.\n\nMix numbers, download programs interpolation texas Ti82, georgia eoct algebra online practice test, Integrated Mathematics Course I: Second Edition answer key, mathmatic convertion, transforming formula in algebra, cpm algebra 2 answers.\n\nRules for adding and subtracting negative integers, answers to hrw biology ch 6 test, solution of simultaneous algebraic equations.ppt, convert Exponential to polar ti89.\n\nSolving chemistry on the TI-84, free solved logarithm problems, algebra for beginners worksheets, practise KS3 maths sats questions, addition and subtraction inequalities worksheet.\n\nSummation identity formula sheet, algeb everyday life, slope printables, how to figure greatest common factor, solving nonlinear differential equations, free online calculator with square root key, t1 89.\n\nMathpower 10 download, math, cubed, squared, equation, Problems for Algebra Substitution, easy way to learn decimals in grade 1, simple worksheets on simultaneous equations, differentiation exponetial function.\n\nAdding and subtracting worksheet, compass test idiots guide, sdaie reading r*, geometric progression sample quiz, baldor pdf, Factoring Polynomials calculator, dividing decimal venn diagrams.\n\nPrintable Math worksheets, foil, adding negatives and positives worksheet, root calculator simplify variable, factoring by grouping calculator, adding and subtracting integers game, gauss-jordan for dummies.\n\nMATHEMATICAL APTITUDE QUESTIONS & ANSWERS, coordinates powerpoint presentation KS2 year6, \"algebraic expression\"+\"percent\", homogeneous differential equation solution matlab, Algebra test paper, free online algebra 2 calculator, revision websites for yr nine sats.\n\nFree printable addition algebra problems, math tutor cdrom, how do you convert a mixed fraction into a decimal notation, distributive property algebra problem worksheets, SAT algebra problems.\n\nMiddle school math work book course 2, algebra for college students, Quadratic Formula program for TI-83 Calculators, holt physics 1 answers, algebra problem helper, free ti 83 plus apps.\n\nAn equivalent logarithmic equation automatic solver, free answer algebra equations, simplifying square root.\n\nTI-83 cubed roots, algebra word problem cheats enter problem, Rational Expressions that have the same denominators lesson plan, simplyfing radical exponent, mcdougall littell algebra lesson plans, \"Discrete Mathematics with Applications third\" homework, \"university physics with modern physics\" solution manual.\n\n\"answers for saxon algebra\", ti-89 conjugate, pre algebra state test, free dividing fractions worksheets for 5th grade, hrw \"modern chemistry\" tests and answer keys, free trigonometric calculator, simplifying multiple variable quadratic equation.\n\n\"Math for 12 years olds\", cheats for solving math equations, answers to Mark Dugopolski College Algebra, math trivia with answers mathematics, rudin, solution, calculate a gcd, looking for percent formulas.\n\nBEGINING TRIG, summation ti 83 plus, free 6th grade O level paper, aptitude test paper for free, TI-84 FAQs, absolute value, inequality math worksheet, time tables blackline chat printables for teachers.\n\nExponential function.ppt, printable multiplying polynomial worksheets, factoring trinomials if a=cubed.\n\nMultiplying by the lcd with free answers, multiplying in algrebra, polynom formula in excel, dividing equations, writing factored binomials in standard polynomial form.\n\nPositive and negative numbers worksheets, math \"factorial word problem\", Saxon Algebra 1 answers, college algebra for dummies, hillsborough NJ homework, intermediate algebra solver.\n\nMath test paper ks3, free maths trivia questions pdf, prealgebra problems, square root division solver.\n\nPerimeter worksheets ks2 free, 2nd order equation calculator, highschool worksheets for computer app, free quadratic formula calculator.\n\nGeorgia eoct algebra free online practice test, Sample answeres KS3 English SATS, algebra 2 apply properties of rational exponents examples from mcdougal, quadratic graphics in matlab.\n\nActivity/lesson on commutative and associative properties for grades 3-5, Arithmetics for accounting, algebra factor calculator, algebra 101 problem solvers.\n\nCombination math formula, ks3 test paper online, sats paper online for YR 9.\n\nHungerford,algebra,solution, interactive games for simplifying variable expressions, integer worksheet, calculate mod, cryptography activities for first graders, systems of linear equations ti-83.\n\n\"unit rate\" Powerpoint lesson, \"gallian abstract algebra\", a lgebra math trivia.\n\nPolynomial solver, free trigonometry test papers level 3, mathpower 7 pg 92.\n\nHow to solve polynomials, solving complex fractions, square root method, table of contents, \"structure and method course 2\", McDougal Littell, Dolciani, contents.\n\nPrintable secret code sheets, fractions decimals percents filetype;ppt, math solving software, free algebra answers, prentice hall mathematics book answers, Aptitude Questions & Answers.\n\nTransforming formulas - algebra, two variable factoring, caculator multiplying mix fractions, algetiles, cubed route symbol, bittinger introductory algebra 10th edition tests.\n\nI just need to know if you can answer this pre-algabra problem for a free answer?, complete the square ti 89, colleg algerbra.\n\nFree KS2 SATS comprehension English, Glencoe/McGraw-Hill math double-digit division with decimals games, programs that help with college algebra, aptitude test papers of software companies.\n\nTI 84 Plus Silver Edition Cross Product program, third order equation solver, trigonometric proofs solver, aptitude questions and solutions, trigonometry answers, modern world history mcdougal littell answers.\n\n+\"visual Basic 6\" +\"cheat Sheet\", creative story for Algebra simplifying, integration by parts calculator, calculator with square root.\n\nTi-89 calculate factorial, algebra-online factoring-binomials, Beginning Algebra Lial ebook, conversion lineal meters, solving quadratic formula ti-81.\n\nOnline logarithmic calculator, science past sats paper, calculator codes TI-83 plus, homework help problem solver, solving fraction equations, multiplication, grade five math practise on perimeter.\n\nWorksheet on inequalities for elementary, solve simultaneous nonlinear equations in matlab, TI-84 chemistry tutorials, EOCT economics answers, Preparing for the Texas Algebra 1 Midterm Exam.\n\nSaxon algebra 2 an incremental development second edition online study guid, \"linear differential equation\" + \"first order\" + \"trigonometric\", percent discount worksheets, simplifying and solving equations calculator.\n\nTutoring on graphing calculator, gre math formulas, algerbra formulas, \"glencoe\" biology \"word search\" answers.\n\nKumon+Mathmatics+Ottawa, factoring polynomials online, discret mathmatics, solution for ordered pairs for the equation x-y=4, tutorial simultaneous equations ti-84 complex numbers, aptitude test download, ti-30x iis solve equation.\n\nPre-assessment quiz - lowest common denominator, online problem solver + word problems, calculating LOG base 5 TI-84.\n\nDo algebra for you, college algebra software, precalculus poem, problem solver for precalculus online, factoring diamond math, Ti83 msn download, Difference of Two nth Powers.\n\nTheory of pie-MATHS, algebra 1 answers in mcdougal book, Solving third order Differential Equations, ks2 negative numbers lesson plans.\n\nAlgebra 2 problems and answers, permutation worksheet, root solver, math help, trigonometry course homework solution, graph parabola inquality.\n\nExamples of math trivia, free math worksheets calculating the mean, mode, median and range, 7th grade math negative exponential example, the hardest math algebra problem, easy ways to solve squared polynomials, \"Math Pre Algebra Worksheet\" Finding Circumference area circle.\n\nWhat is the diffrence when the square of 17 is subtracted from the squre of 18, matlab solving simultaenous equations, sheets on probability, combination and permutation, free download ti-84 calculator emulator, 6th grade math trivia, multiplying mixed number: answers to problems, abstract algebra fraleigh solutions.\n\nJava random number 5050, free accounting exercises, worksheet equations with algebraic fractions, McDougal Littell quiz language.\n\nMath induction solver, multiplying and dividing decimals tests, factorising calculator, third order linear Differential Equations.\n\nPratice ged test, ks2 free online learning, combinations and permutations in matlab, \"kumon level i\", math help polynominals, Algebra equation solver.\n\nOnline activity, factoring polynomial, 8th grade, inequality math solver show work, equations of completing the squares algebra.\n\nPermutations and combinations percentages, maths rotation worksheet, help with elementary algebra, finding volumes of cuboids worksheet free download, College algebra parabola test answers, complex numbers conversion on the casio fx-115Ms, least common denominator worksheets printables.\n\nExamples of math elimination & sustitution, '*8th Grade Math\" + reasoning, ti-89 log, Combining Like Terms Worksheets, pre algebra quizzes and work sheets, solving a system of equations, linear combination, worksheet, printable maths worksheets that are ks3.\n\nFactoring quadratics applet, ti 89 programs trigonomic equations, partial sums, Visual Basic code cumulative binomial equation.\n\nHalf-life problems solving, problem sheet on compound interest for gcse, answers to prentice hall pre-algebra book page 183.\n\nPolynomial factoring online calculator, Permutation and Combination, ninth grade math problems, programming a calculator, \"matlab 7\" solutions manual\", glencoe history test online printouts.\n\nThe break down of minutes into fractions, boolean algebra, problem sheet,pdf, 4th grade pictograph worksheets.\n\nUnderstanding algebra, learn algebra 2, calculator algebra expressions.\n\nLiniar equations interactive, solving quadratic equations regression of a parabola, ANSWERS TO ALGEBRA 2 PROBLEMS, ti 89 integral solver, root solver.\n\nMaths-completing the square, combination math problems, merrill algebra 1, factoring quadratic eqautions, integers and order of operation and exponets, simplify radical expressions, solving for second order linear differential equation.\n\nFactors in a square root, Quadratic equation game, glencoe algebra 1 book online.\n\nRules for adding & subtracting negative factors, t83 calculator, addition and subtraction algabraic expressions, free examples of 8th grade math problems, homework and practice workbook Holt Middle School math course 1 answers.\n\nFactoring polynomials work sheet, dividing and simplifying exponents, free printable worksheets for 6th grade.\n\nAlgebra answers free, Factor by Grouping Chapter 7 Practice Answers, simplifying fractions calculator.\n\nFind the cubed route calculator, trigonometry practice sheet, ti-89 decimals into fractions, solving non linear simultaneous equations in matlab, calculation for radical equations, Dividing/Multiplying and other Monomials.\n\nFree worksheets for math with composite and prime numbers and GCF, pre ged math worksheet download, solving quadratic systems by substitution, calculator rom.\n\nFree online help for elementary algebra, test on itergers for grade 7 math, solve algebra free, rational expressions solver, trigonomic ratios calculator.\n\nEnglish and maths for 8 yr old, sample math test for 5th grade decimals and fractions, harold r. jacobs geometry test.\n\nAlgebra help for freshman, Math Answers Cheat, mathpower gr.7 mean,median,mode,range test sheet, Operations with Radical Expressions Problem Solver, advanced algebra questions, Excel trigonometry download, multiplying fractions by wholes.\n\nFinding quadratic equation given three points calculator, Rational Expression Practice problems, matlab \"decimal to binary array\", TI-89 to solve logs, division w/remainder problems, how do we divide fraction?, Multiplying decimals 5th grade worksheets.\n\nAdding,multiplying,subtracting,and dividing fractions, maths games-probability, application of algebra, free printable writing integers worksheet.\n\nFree intermediate algebra software, greatest common factor table, multiplacation sheet second grade, adding integers worksheets, 3d symmetry ks2 worksheet, factorize trinomials sum of cubes difference of cubes hand out tutorial questions, different important of alkali earth metals with formula and uses.\n\nKs3 science papers free, ontario math syllabus for 7th grade, trigonomic functions chart.\n\nEasy \"algebra 2\" \"help\", simultaneous equations transpose 3 3, \"Math and exponents\", mathsquare nets.\n\nOnline trigonometry chapters pdf, year 10 mathmatic lessons, proportions worksheets 6th grade.\n\nHow to change fractions to percents manually, homework help algebra word problems solving radical equations, math help on sqare feet.\n\nTriangle worksheets, mathmatic dictionary, teachers glencoe accounting first year course, Linear Systems of equations with the TI-89, instructions on how to find the LCD of two rational expressions.\n\nDownload algebra 2 mcdougal littell book, program solve simultaneous equation, how can we graph quadriatic equation, CUBE ROOT OF NON PERFECT NTH ROOTS, golden sheet trigonometry.\n\nExamples of math trivia students, math quizes on division and multiplacation facts, \"casio 9850\" +tips, Texas Instruments TI-82 calculating Mod, highschool prealgbra, math equation signs, math calculator first grade printable.\n\nSOLVING NONLINEAR DIFFERENTIAL EQUATIONS, algebra three printable exponent equations, algerba dummies, adding/subtracting integers math worksheets, simultaneous equations excel, free online pre-algebra practice websites.\n\nMathmatics.com, cheat gcse, algebra help - writing linear equations, balancing chemical equations ks4 games, softmath.\n\n\"teaching slope\" \"elementary school\", grade 2 adding and subtracting test worksheet, GRE sample question papers pdf, FREEE FONTS DOWNLOAD, what two numbers are the greatest common factor of 9 and the sum of 99?, fraction equations, working with rational exponents worksheet.\n\nInverse log TI-84 plus, physic journal for elementry school, ti-84 plus downloads unit circle, multiplying square roots calculator, simplifying rational exponential expressions.\n\nGrade eleven accounting games, solve polynomial equations calculator, factoring out quadratic equations calculator, Finding vertex of Standard Form Equations, TI 84 finding slope, ks2 maths work sheets to print.\n\nEquation solver logarithms, math eoct help, factorising tool, solving two-step equations worksheets, FREE ALGREBRA PRE TEST, how do you type exponets in word.\n\nMultiplying and dividing radical expressions, interpreting quadratic word problem equations, prentice hall mathematic, Solving Higher Ordinary Differential Equations with Matlab, algebra vertex form.\n\nTrigonomic equations, code to convert decimal value to char in java, printable pre algebra worksheets, algerbra for dummies, Learning Basic Algebra, Fun Completing the Square Lessons, Instant Algebra Homework Help.\n\nChapter 6 test, chemistry,holt rinehart and winston,printout, algebra1 problems with answers, calculator for rational exponents.\n\nAlgebra simplifying programs, combining like terms calculator, Pizzazz Worksheet #225, Solution for Abstract Algebra by Hungerford, free worksheets multiplying by 1.2,3, download maths formulas cat, KS3 Maths SAT papers.\n\nTemperature worksheets for 4th grade, 5th grade inequality worksheets, Free Ti 89 Trig programs, help on equivelent fractions, multiplying decimal lesson plans/ elementary.\n\nBasic Math Algbra Problems, solving algebra equation common denominator, pre calc factoring machine, algebra 2 homework help matrices.\n\n\"graph paper\"\"plotting pictures\", decimal printable, beginning algebra math tutor, how to solve equations with fractional coefficients, analys poem, fraction and decimal math poetry, practice elementary algebra worksheets.\n\nSolving trinomials, 9th Grade Algebra TextBooks, cubed polynomial factors, teaching exponents, printable worksheets plotting points, math help- slopes y intercepts printouts, \"kumon method\" +online +worksheets.\n\nAlgebra word problem solver enter your problem, math 4th grade taks, simultaneous equations solver, Mcdougal Littell textbook chapter 8, casio-fx115ms directions, algebra applications of linear systems online help, applications of algebra in life.\n\nSolving logarithms, ks2 maths books downloads, free math practice worksheets and laws of exponents, prentice hall math quiz websites, college alg work and uniform motion problems.\n\nOnline calculator dividing polynomials, online TI-38, completing the square differential equations, The nature of roots math, 4th square root tutorials, elemantry school worksheets, difinition and use of pie roots for highschool students.\n\nMath sheets yr 7, steps to solving an equation for 7th grade, THE USE OF ARITHEMATIC.\n\nOnline graghing calculator, prentice hall mathematics algebra 1 workbook answers, math solver for simplifying rational expressions free.\n\nCoversion real estate feet moles, factoring cubed polynomials, solve nonlinear differential equations.\n\nAptitude question, basic algebra formulas, combination in college allgebra, graph linear equations, simplifying quadratic equations calculator.\n\nHow to convert mixed number to decimals, sat exam third grade sample worksheets, maths help in combination, find free worksheets on adding fractions with the same denominator, \"math probability worksheets\".\n\nAlgebra work sheets, ti-89 complete the square, multiplying decimals 5th grade worksheet, teach yourself math, kumon answers.\n\nSolving Radicals for dummies, determinant ti-89 instruction manual, converting equations to vertex form, \"how to rationalize the denominator\", Solving Rational Equations Problem Solver, pre-algebra graphing slop worksheet.\n\nDistributive Property Radical Expression Calculator, partial fraction ti 89, sixth graders linking verbs free programs, how to solve an equilateral hyperbola.\n\nLinear diophantine programs for calculator, quadratic equations word poblems, ti-84 plus trig downloads, math formulas annual percentage difference, math homework help from the mcdougall pre-algebra book.\n\nMath lesson plan exponents, rational expression calculator, free least common denominator calculator, how to use a calculator for factoring polynomials.\n\nOnline grading curve calculator, LU factorization with \"TI 89\", solving difference equations non homogenous case, NY 6th grade worksheets, lcm ti-83.\n\nBinary multiplacation and division of binary codes, beginners algebra, ti 84 graphing calculator error messages, multiplying and dividing integers worksheet, font+Dowload, abstract algebra math help, \"combining like terms\" + lesson plan.\n\nInverse log t183, calories worksheet, vertex form standard form, mathmatical drill sheets, British Method algebra.\n\nMixed Number Calculator, free printable worksheets and exponents, algebra year 8 online test.\n\nPre algebra with pizzazz, exponents for dummies, rudin principles of mathematical analysis solutions to exercises, interval notation calculator.\n\nSimultaneous equations in two variables, \"answers to mastering physics problems\", college algebra clep, algebra balancing method, ERB test sample questions, multiplacation charts.\n\nMiddle school math inequalitiy tests, fraction expression calculator, test preparation for 6th graders for free, download simple calculator gui matlab, ti 83 cost accounting, convert standard to vertex form.\n\nPre algebra problem solver, algebra equation solver, free math work sheet.\n\nMerrill chemistry book answers, hard algebra problems, GCSE physic sheet, how do you add integers, engineering mathematic*free books*pdf.\n\nHow to graph absolute value equations, balancing equation cheater, online maths exercises for ks3, explaining radical equations, houghton mifflin algebra Trigonometry online california.\n\nSubtracting fractions with different denominators worksheet, 9th grade beginning algebra lesson, Saxon Math Answers.\n\nAdd integers quiz, matlab wronskian, online inequality graphing calculator, Algebra 1 EOCT practice.\n\nIntermediate Algebra concepts and applications answers, elementary math trivia, McDougal Littell Algebra 2 Answers, MCDOUGAL LITTELL ALGEBRA 1 ANSWERS, level 6-8 maths revision online, free 4th grade worksheets on volume, Trigonomic Identities and equations.\n\nSolutions rudin, college algebra problem solver, 3 unknowns quadratic equation solver, free past sats questions for 11 years, 7th grade math texas percent proportions, practice combination permutation.\n\nHow do you solve monomial problems, binomial coefficients tartaglia triangle difference equation, easy math trivia, logarithms on ti-89.\n\n\"real world applications & connections\" \"answer key\", sample program for permutation and combination, solving third order polynomials, glencoe + algebra 2 + answers, algebra problem examples, online free clep guide.\n\nUsable online TI-84 silver, solutions algebra pdf, fractional adding and subtracting, seventh grade taks formula chart, polynomials exam multiple choice, math prentice hall workbook pre-algebra.\n\nFree print off ks3 tests, ks3 maths difficult angels, calculate lcm, third order polynomial equation, root, Algebra1 interactions cheats, powerpoint completing the square.\n\nFree math percentage worksheets, hrw \"advanced algebra trigonometry\", algebra with pizzazz answers, Printable lessons MCdougal littell, online factoring solver, complex fraction simplifier.\n\nFree training of accountancy, online slope calculator graph, algebra exponent in excel.\n\nImportance variables algebra, \"permutations and combinations worksheet\", solving systems by addition, solve an absolute value inequality with fractions, adding and subtracting decimals worksheets.\n\nAlgebra 1 explorations and applications answers, +ti82 +manual, simplify rational expressions using a calculator, algebra 1b cheats, how to simplyfy fractions.\n\nPrincipal right eigenvector ti-86, pre algebra workbooks year seven Australia, java applet for permutation combination, Mutiply zero+ printable worksheet.\n\nSolve factorization in excel, UCSMP TRANSITION MATHEMATICS Scott, Foresman and Company worksheet answers, Boolean Algebra Calculator mac, division of polynomials calculator, hard algebra problem, fraction to decimal lesson, polynomials online activities for grade 8.\n\nMath 60 tutorial intermediate algebra fractions, abstract algebra chapter 3 homework solutions, mcdougal littell algebra 2 ch 6 test.\n\nExponential expression, Exponents Simplify Expressions Worksheets, \"The C Answer book\" ebook, word problems fo first grade, beginner subrating negitive numbers, Inverse Laplace Transformation ti-89.\n\nHelp with advanced algebra, excel cube root of a percentage, calculas, algebra equation solver, root method and equation, 5th grade equation activities.\n\nFree online adding calculator, factors and greatest common factors in algebra equations, solving algebra problems in a fast way.\n\nRADICAL CALCULATOR, free EOCT review, answers to algebra with pizzazz, quizzes for introductory algebra bittinger 10th edition.\n\nSimplify variable radical expressions, algebra 2 mcdougal littell answers, decimels to fractions, synthetic division solver.\n\nMath Scale factor, convert each decimal to fraction or mix number, how to add logarithms with different bases, worksheet simplifying expressions with radicals.\n\nHIGHEST COMMON FACTOR, plotting ordered pairs, worksheet, physics practise class 9th, \"TI-83 plus accounting\", factoring quadratic equations online, first order differential calculation, TI-89 logarithmic function.\n\nCalculating log using TI-84 plus, free worksheet on adding subtracting integers, Least Common Denominator finder.\n\nPolynomials quizzes online for grade 9, easy lesson for year 1 about fraction with work sheet, KS3 english & online game.\n\nAnswers for McDougal Littell Modern World History, matrice answer, texas lesson plans for sixth grade mathematics, online graphic calculator + factoring.\n\nHow to do algebraic math, partial product method, using ti-83 plus for complex numbers.\n\nQuadratic equations + sample questions, www.jamesbrennan.org, Solving Ordinary Differential Equations with Matlab, math pizzazz worksheet, math helper.com, Pre-Algebra Stories & Word Problems; inequalities.\n\nMath cheats, algebra 2 tutor, downloadable square root calculater, calculator for synthetic division, simplify quadratic calculator, graphing calculator worksheets + free printouts.\n\nGlencoe alg 1 fl book, VB + quation and answer, solving equations using direct substitution method, free pre-algebra helpers, pre algerbra exams, free online basic english structures for begginers, multiplying fractions handouts free.\n\n\"UCSMP\" Geometry \"Integrated mathematics\" +answer key, solving algebra 1 An Incremental Development, algebra 1 gateway sample questions, algebra 1 calculater, give example of combination vs permutation in college algebra.\n\nAnswers Linear Systems by Substitution, sguare feet to linear feet, Abstract Algebra Test and solutions, Exponet worksheets, printable gragh paper, math graphing calculator division online, \"download mathcad 12\".\n\nFree aptitude question paper, qudratic equation backgrounds backgrounds, \"free printable math worksheets\" measurement, \"math\" + \"scale factor.\n\nSolving inequalities ti 89, dividing fractions calculator, internet factorer.\n\nOnline graph coordinates, \"volume of a cube\" worksheet print, TI-89 in College Algebra, online aptitude papers, trigonometry poem, advanced reducing/simplifying coefficients and exponents.\n\nAlgebra 1 lesson 82 answers, factoring and solving polynomial equations calculator, how to solve fractional exponets, Free Math Answers Problem Solver, math solver, Ontario Math test Examples, algebraic radical calculator.\n\n\"finding scale factor\", algebra-horizontal lines, plotting points pictures, algebraic expressions worksheets, aptitude question.\n\nLesson plan for solving linear equations for 5th grade, Rudin Principles of mathematical analysis solution, answer plato pathways learner chem 65, free online tutor for algebra 2, 6th grade adding and subtracting worksheet.\n\nL-u decomposition ti-83, quadratic equations formulas rules, what is a scale factor ks3, standard form to vertex form, Thinking Mathematically third edition tutor, dividing polynomials worksheets, \"how to calculate ratio\".\n\nKS3 SAT math, multiplication of radicals calculator, root locus plus on graphing calculator, Algebra--Expanding binomials, how to find a scale factor, subtracting integers worksheet, GCF calculation program example.\n\nLearning algebra online, square root antiderivatives, the cheats for math stars, calculating LOG base 2 with TI-84 plus, permutation combination equation.\n\nPrograming exponents in excel, balancing chemical equations worksheets, integration calculator polynomials, Answers to Intermediate Algebra, prentice hall middle grade homework sheets.\n\nHow to solve algebraic equations with exponents, what is lineal metre?, printable 2nd grade star test practice, free worksheets subtracting fraction with same denominator.\n\nFree books on fluid mechanics, caculator download, solve my algebra equations, math problem solver, \"7th grade equations\".\n\nMcdougal littell pre-algebra practice answers, ti 89 parabolas vertex, free pre-algebra worksheets.\n\nAlgebra structure and method book 2 ch. 6, online polynomial factor, year nine maths worksheets, Algebra 1 Holt Rinehart Winston.\n\nFactoring TI-84, \"order of operations worksheets\" + exponents, fractional formula, free help with completing the square and graphing it pre-calculus, exampapers of mat.\n\nMoving from vertex to standard form, basic kids sheet mathe, ti-92 how to change decimal to fraction, pdf ti 89, Texas TI89 software download, quizes in math trivia, how to work out algebra problems.\n\nOnline pre algabra math games, algebra solving multiple variables, ti-86 fraction conversion, +\"ti-84\" +\"graphing instructions\", simplified square roots.\n\n\"solving trigonomic equations\", free 6th grade maths help, sample papers on sets in maths for practice online, common denominator solver, root calculator simplify.\n\nTaks test practice online free for third grade, how to simplifying radicals, algebra helper, matlab, solve simultaneous equations, texas instruments/TI-83 plus/software, multiplacation made easy.\n\nDiscriminant TI-84 plus, simplify calculator, introduction to algebra worksheets.\n\nCompleting the square mod, Develop an equasion in slope intercept format, answers of calculus book conics, partial sums worksheet grade 2, fraction exponent calculator.\n\nPearson prentice hall calculus answers, texas 89 convert binary to decimal, how to solve logarithms on ti-89.\n\n[pdf]+\"SAT II: PHYSICS\"+freeware, how to solve fraction with different denominator?, using sylow theorems to solve algebraic equations, Least common multiples games, radical solver.\n\nAlgebra substitutions, free equation calculator for exponents, Math lessons on Permutations and combinations, steps to solving algebra 2 problems, \"saxon algebra\" answers.\n\nFree algebra calculator, Trivia Questions About Math, expression and equations, grade 7, powerpoint, how do you convert a decimal to a radical.\n\nHow to do quadratic function on TI 89, free algebra worksheets, GCSE albegra.\n\nSlope-Intercept Form for Dummies, radican into trig, solving 3rd order equations with TI-83, free math factoring solver, How do you divide radical expressions?, free GED math help with pretests and anwsers, algebra 2 elimination method.\n\nSubtracting fractions worksheet, origin of exponets, solve math problem tool, balancing chemical equations solver.\n\nFree help with intermediate algebra problems, algebra easy way programming, c aptitude questions, History of Pie Mathamatical, how to solve 3rd order system, \"factor tree worksheet\".\n\nTI-83 + instructions for logarithms + free, solving polynomial equations online tool, fraction calculator emulator, linear variations math help, roots of real numbers solver, maths work out scale online calculator.\n\nFREE LINEAR EQUATION SOLVER, middle school math answers mcdougal, free tutorial on advanced excel formulaes.\n\nA working online TI-83 Plus calculator, changing a fraction into a decimal as itergers, third root, trigonomic substitution.\n\nNumber sequence brain teaser solver, solving ratios worksheets, online algebra 2 book.\n\nPermutation and combinations tutorials applets, Addison Wesley Biology 9th grade, trigonometry poems, convert mixed fraction into decimal, JAVA Aptitude Papers, \"convert decimal to fraction\".\n\nFree herstein students solutions, free algebrator, \"free pre algebra math problems\", Gaussian elimination online solver 3x3, ti calculator rom download, 3rd root calculator.\n\nHow cheat with the ti-84, ti 86 download excel, algebra practice for 6th graders, algerbra GCD, exponents worksheets + free, solve for x squared = 100.\n\nEquation solvers with steps online, how to make a decimal into a mixed number, downloadable algebra helpers, Sample questions and answers on relational algebra, math practice workbook for 8th grade, graphing T1-83 guide help, addition and subtraction equations worksheet.\n\nGr.10 math help, free work sheets for 2nd graders, algebraic proportions worksheets, Integers quadratic equations, lineal metre conversions, glencoe geometry answer key, mathematics exam papers grade 9.\n\nSquare root formula, evaluating expressions with variables worksheets, free basic fractions worksheets, quadratic equations two variables, what is the greatest common factor of 81, anwsers to math hw.\n\nAnswers abstract algebra gallian fifth, percentage caculator, how to do logs on a TI 84, GCF and lcm calculator, ti-84 online graphing calculator, mathamatics symbols, gre problems on permutation combination.\n\nOnline homework cheat- dividing monomials, \"square root simplifier\", Houghton Mifflin English Grade 6 Workbook Plus answers, factored form of the difference of two squares, finding common denominator worksheets, sat past paper yr 6.\n\nFactor tree worksheet, english eoct, mathematica Dsolve second order equation, solving nonlinear systems equations in matlab, free worksheets for 9th graders, ratio proportion worksheets for elementary.\n\n\"simplifying radical expressions\", congruence gcse, probability powerpoint ks3, polynomial square root calculator, free Algebra 1 EOCT review, pdf for ti 89.\n\nWorksheet on combining like terms, find vertex ti84, online complex number solver, mathamatics learning.\n\nSimplifying fractions with exponents, t1-83+programmer, Basic math for 12 grade work sheet, matlab function for finding quadratic equations, mathpower 8 online tests, answers algebra 1 glencoe, algebra calculating ratios example.\n\n\"iowa test\" samples free 3rd, free sats paper ks3 online, algebra calculater, fortran programming+freebook+download, radical math problems calculator, the university og chicago school mathamatics projects transition mathamatics integrated mathmatics text book, free college algebra problem solver.\n\nTutoring in intermediate algebra, how to simplify square roots, free printable worksheets for 7th grade, algebra square root polynomials, ks2 sats paper to do online for free, Adding and Multiplying positive and negative integer Worksheets.\n\nAlgebra simplification, saxon geometry worksheets, Binomial+algorithim+pdf, Completing the Square Equation Solver, domain range of absolute value equations, mathamatics on fraction test, how to get the lowest common multiple on a graphing calculator.\n\nMathematics Objective Question paper download, greatest common factor + table method, algebra homework helper, sats print out papers for ks2.\n\nDecimals to percent online calculater, printable worksheets algebra distributive property, java convert decimal to fraction, simple algebra equations, McDougal Littell Algebra online pages.\n\nOne-step equation free worksheets, fractional coefficient practice worksheets, samples of algebra pretests for 5th grade.\n\n\"convert fractions\" percent chart, c# modular division, ordering fractions cheating machine.\n\nAlgebra homework, quadratic functions discriminant homework solvers, aptitude questions+pdf, convert decimal to a fraction, free math balanced equations worksheets, simplify square roots expression.\n\nEnd-of-course algebra test, multiplying mix fractions, GEOMETRY cHAPTER 4 Resource Book Mcdougal, binomials and expansion year 9 maths test, Factoring Cubes, math tutors vancouver bc.\n\nElementary statistics larson 3rd edition quiz, polynomial solver with steps, 6th grade practice problems for algebraic expressions, maths solver, radical expression solver.\n\n6th grade proportions work sheet, glencoe math workbook answers, How to solve algebraic equations, level boundaries math sats KS3, adding and reducing mixed numbers worksheet.\n\nSolving graphing inequalities problems free online, answers pre-algebra with pizzazz, interactive quadratic formula, calculation of GCD, free algebra 2 answers for homework, free fraction solver.\n\nSimultaneous equation solver, \"cross-multiplication\" to solve inequalities lesson plans, excel equation.\n\nPolynomial factoring worksheets, printable algebra tiles, \"simple algebra\" + games + online, QUADRATIC EQUASION.\n\nAlgebra year 8 basics, definition and use of pie in maths in india, maths problems in squared metres, trigonometric answers, \"ontario real estate exam\", greatest common factor of 45, 90, 13.\n\nGcf and lcm practice, extra algebra slope practice, online algebra calculator.\n\nAlgebraic expression games, solve algebra problems, standard form of a linear equation ppt, \"data structures and algorithm analysis in c\" \"solutions manual\", orleans hanna sample questions, eqation editor.\n\nUndamped spring-mass system, how to calculate to the power on T1-83 calculator, statitics+exam paper, \"completing the square problems\", math problem solver online, second order linear.\n\nQuadratic equations applying word problem, worksheet +dividing +decimals, mcdougal littell online worksheets, algebra final exam tip, math poems.\n\nPoems in algebra, Writing Equations in Vertex Form, \"solve this formula\" height, \"c programing\" multiplication, \"Balancing equations\" +worksheets.\n\nHow to work Matrix on a TI82?, algebra 1 extra practice worksheets, prealgebra \"mcdougal little\", free parabola worksheet, prime number tester java code, pre algebra exams.\n\nQuadratic equations parabolic graphing practice, free online math homework help with factors between 1-110, caculator ON liNE AND Easy, equations algebraic fraction, Finding the LCD of Rational Algebraic Expressions, homework helper_ algebra 2.\n\nGeneral rule for multiplying integers, summation formula 12 days of christmas, laplace + TI-89, McDougal Littell Geometry chapter 5 vocabulary, Chapter 5 test answers CA, san jose - 6th grade, glencoe california geometry textbook answers.\n\nBasic algebra practice sheets for kids, multiple regression ti-86, real life gcf, trig answers, ti-84 plus, saving formulas, algebra 1 relating graphs to events.\n\nAdding and subtracting with unlike denominators calculator, find the volume of cube worksheet third grade, checking of solving equations with rules of exponents and logarithms, gateway pratice Algebra 1.\n\nMaths questions powerpoints for yr 8, multiplying integers worksheet equations, factoring algebra.\n\nPrime factorization for dummies, student solution manual for prealgebra tussy online, algebra Chapter 11 rational expressions and Functions Prentice-Hall, Inc. worksheet, how to simplify square roots quiz, Calculas Mathematics, Holt, Rinehart, and Winston-Algebra 1, math worksheets on combining like terms.\n\nExample math trivia, equasions with absolute value + Math, solve 3rd order polynomial, intermediate alegabra operations of polynomials.\n\nAnswers to McDougal Littell Pre-Algebra, online graphing cubics, \"Math Work Sheets\", algebra+simplest form+year7+examples, review worksheets for adding subtracting and multiplying decimals, log with TI 83, least to greatest integers.\n\nAlgebra worksheets combinations, examples linear equations, \"economics answers\" EOCT, class 10 projects on maths-pie chart.\n\nMean median mode hellp, java input number calculate the sum, simplifying complex numbers calculator.\n\nDividing integers games, chicago math 7th grade syllabus, indices maths yr 8, cheating on algebra with pizzazz.\n\nTaks practice tests, grade 9 mcdougal littell inc, kumon Answers english K, Free Algebra II math homework help, online coordinate graphing worksheets for 3rd grade, adding a coefficient to a square root, trigonometric addition.\n\nHow to find asymptotes on a ti-84, free algebra 2 homework solver, Pearson Education> Algebra 1 Book> Free worksheets.\n\nCheating GMAT, permutation combination calculator, log using ti-84, consumer math worksheets 9th grade, find real roots (tk solver), ks2 sats papers to do on the computer.\n\nEquation solveing calculator, negative and postive numberline worksheets, how to do rational equations on ti 89.\n\nMaths tricky questions, answers to algebra 1 workbook McGraw-Hill, Algebra 2: An Integrated Approach, free algebrator download, grade 8 mathematic polynomial test, t1-83 graphing calculator online.\n\nClear way to find slope and y-intercept for linear equation, pre-algebra, balancing equation helper, solving equation games, subtracting with variables + elementary worksheets.\n\nPrintable Fraction-Decimal-to Percentage Games, free intermediate algebra websites, english aptitude questions, equation of completing the squares algebra.\n\nMultiplying and dividing integers, activities for finding properties of square roots, solving logarithmic functions using quadratic formula, math printables expressions and equations, Mathcad11 download free, self help courses in algebra.\n\nSimplifing equations, radical expressions calculator, simple algebra expressions.\n\nPrintable 8th algebra math worksheets on linear equations, TI calculator program solve polynomial, solving math problems sixth grade reflections free lesson plans, two step multipication problem solving.\n\nTest printsof SATS practice, Algebra and Trigonometry, Structure and Method, Book 2 tests, free test papers Singapore.\n\nSolving equations containing radicals, pre-Algebra.com, SOLVING SYSTEMS OF LINEAR EQUATIONS ACTIVITIES, resource book in algebra 1 McDougal Littell, rudin solutions, positive negative math worksheets.\n\nActivities on adding equations, GRE online maths revision, \"College Physics fifth edition\" .pdf, multiply polynomial applet, ti-89 linear algebra tutorial, two equations fractions.\n\nInverse log ti-83, algebra fx hacks, integer worksheets, rational exponents, elementary 4th and fifth grade graphing ordered pairs worksheets, free worksheets ks2 maths, free math assignments in division with remainders.\n\nHow to factor algrebra, greatest common factor variables, how to solve square root of 7, TI-86 Error 13 Dimension, online synthetic division calculator javascript, free algebra answers for radicals.\n\nTi 89 solve trigonomic, Synthetic Division GCF, algebra, FOIL printable worksheets, algebrator software, substitution method calculator, square roots worksheets, Super ellipse circumference math work.\n\nMathworksheets, free area/perimeter worksheets, what is the diffrence when the square of 17 is subtracted from the square of 18?, RADICAL FORM IN MATH, learn TI-84 for sixth grade, rational numbers and deciamals.\n\n\"solving equations with rational expressions\", Rational numbers multiplication and division, online graphing calculator TI usable, school mathimatics homework, t1-83 online calculator, biology formula cubed.\n\nSearch Engine users found our website today by typing in these keywords :\n\nYahoo users found our website today by entering these keyword phrases :\n\n• root calculation two variables\n• complex numbers and ti 89\n• first order differentiation method for rational and radical form\n• free 7th grade inequalities online\n• level of questions in Iowa Algebra\n• solve arbitrary second order ode\n• permutations and combinations AND elementary school\n• boolean algebra applet\n• fraction calulator\n• prentice hall homeschool curriculum\n• texas t1 83 how do you use log\n• examples of math trivia with answer\n• online physics graphing calculator\n• exponents and variables distributive property\n• adding and subtracting polynomials worksheets\n• answers to prentice hall mathematics algebra\n• coordinates ks2\n• exponents power point\n• slope activity game printout\n• the process of elimination in algebra yahoo answers\n• the hardest math problem in the world\n• Programming quadratic formula ti 84\n• boolean online calculator\n• maths test online for year 8\n• squares and square roots, cubes and cube roots, fourth power and fourth root etc.\n• convert decimal to fraction\n• ELIPSE,LINEAR\n• algebra 2 projects logarithm\n• free online fraction and decimal calculator\n• trigonometric raito power points\n• solve algebra problems software\n• is 9.42 rational\n• mixed number to decimal calculator\n• plato learning english cheat sheet\n• solve rational expressions calculator\n• orleans hanna algebra prognosis test DVD\n• 10th standard mathematics formulae list\n• how to solve radical on the ti-84 plus calculator\n• simplifying square root epressions\n• permutation videos for kids\n• algebra solver\n• examples of different kinds of slopes worksheet\n• Mathematica Tutorial pdf\n• converting quadratic functions to vertex form\n• combinations and permutations practice\n• printable math worksheet on adding negative and positive fraction\n• mathematics investigatory games\n• maths multiplication sheet for year 2\n• how do you put a sqrt signs in the algebrator program\n• Holt Science and Technology Directed Reading Online Worksheet A 7th grade life science\n• www. I have probloms in math. com\n• the mcgraw-hill cheat sheet\n• log 2 ti 84\n• program formulas in TI\n• adding and subtracting positive and negative fractions\n• eighth grade math problems pre algebra chapter 8\n• human proportions worksheet\n• chemical equation product calculator\n• solve for x fractions calculator\n• how to convert a decimal to fraction formula\n• expression simplifying calculator\n• simplifying complex fractions calculator\n• basic evaluating expressions worksheets\n• glencoe algebra 2 lesson plans\n• What is the greatest common factor of 525 and 833\n• free addition and subtraction inequalities worksheets\n• online calculator decimals to percents\n• number game for rational expressions\n• system first order differential equations adjoint homework\n• college algebra for dummies\n• powerpoint presentation of using equation in solving age problem\n• online college algebra math problem solver step by step\n• work sheet for addition and subtraction of negative numbers\n• math symbol refrence sheetsfor 6th grade\n• free math problem help\n• rational exponents practise questions\n• free help to solve mixed numbers and decimals on number lines\n• algebra one math poems\n• simplify -9x w exponent of 3 *9\n• basic algebra questions\n• exponential function and quadratic equations\n• slope of parallel calculator\n• square number activities\n• adding, subtracting, dividing and multiplying integers worksheet\n• LaPlace + Differential equation solver package version 1.2.4 to TI-89 download\n• decimal equivalent of a mixed fraction 37/8 is\n• algebra equations vertex form\n• Finding the square - easy\n• worksheet application systems of three equations\n• solutions of problems by method of completing the squares\n• convert decimal to root\n• square root algerba\n• percentage formulas\n• algebra program\n• substitution method on ti-89\n• algebra work and answer sheet\n• equation to standard form calculator\n• how do u press the square root key on a ti 83 calculator\n• algebraic expressions x on one side fraction\n• dividing integers online caculator\n• nonlinear equations equal 0\n• factorize fractions\n• MATH GAMES FOR EQUATIONS FOR 5TH GRADE\n• polar equations worksheet\n• solving code games for 5th grade\n• Math Solutions for 2 unknowns\n• factoring study print off grade 9 math\n• introductory algebra test 9th grade\n• prentice hall complete algebra 1 test for indiana\n• how to write a equation in vertex form by completing the square\n• graph number sentence\n• Chapter 5: Polynomials and Polynomial Functions worksheet answers mcdougall littell\n• the most hardest math problem in the world\n• how solve differential equations TI89\n• java divisible\n• abstract algebra online test\n• answers for ordering decimals cheat\n• how to simplify 7 squared\n• year 7 mathematics worksheet for algebra\n• non-homogeneous second order equation solution\n• mathematics further equations worksheet\n• factoing worksheet\n• algebra 2 cheat test\n• solving systems of linear equations 3 variables\n• algebra of a triangle\n• math worksheets multi step\n• algebraic expressions worksheets free grade 7\n• prentice-hall mathematics self-instruction\n• simplify by combining like terms worksheet\n• solving equations by multiplying video\n• ti-89 graphing parabola\n• online area and perimeter tests for grade 8 free\n• plotting linear functions cheats\n• free worksheets for subtracting integers\n• how to check your answers in the online algebra 1 book\n• mixed fraction java code\n• glencoe- substitution algebra 1 answers\n• equation trinomials calc\n• zoom algebra registered key TI-83 Plus\n• rules for adding and subtracting positive and negative numbers\n• how to rewrite a division expression as an equvilant multiplacation expression?\n• algebra with pizzazz multiply binomials mentally\n• solving single rational expression in lowest terms\n• java multiple square roots\n• glencoe algebra 2 practice book answer sheet\n• simplifying variables with exponents\n• 6th grade math brain teasers\n• expressions and variables lessons in 5th grade\n• online least common denominator practice\n• college algebra multiplying cubed cubed by squared\n• geography worksheets grade 6 Line Scale\n• Integrated Algebra 1 answers factoring\n• holt physics problem workbook\n• solving implicitly for y using graphing calculator\n• what are the pros and cons of each method when using the systems of equations by graphing or by using substitution of elimination?\n• free order of operation worksheets\n• help with pre-algebra Writing Inequalities: problem solving solutions\n• system of equations problems adding subtract worksheets\n• Practice doing 9th grade scientific notation\n• LCM calculator online\n• vertex form if you do not know \"a\"\n• finding the scale factor\n• simplify year 8 algebra\n• minumum common multiplier matlab\n• TI-83 Plus slope\n• difference between evaluation and simplification of an expression\n• online year 7 algerbra test\n• discrete mathematics and its applications\" solution ebook\n• how to simplify a square root with an exponent\n• solving 2 step equations fractions calculator\n• CONVERT FROM POLAR TO RECTANGULAR FORM/TI-83\n• powerpoints for maths for year 7\n• trigonometry trivia\n• answers to algebra glencoe mcgraw workbook\n• lowest common multiple form\n• give us sample problem college math and the solution\n• one step eqations\n• fraction to decimal formula\n• inverse operations worksheets addition and subtraction\n• quadratic equation formula ti 89\n• multiply and simplify square roots of powers\n• fouth Grade SAT sample worksheets\n• ti-84 matrix solve complex\n• \"partial fraction\" calculator OR Solver\n• Lowest Common Denominator Online Calculator\n• find an equation using given asymptotes\n• divideing fractions - printouts\n• What Is the Definition of a Dimension in Mathmatical terms?\n• write a mixed number as a decimal\n• 9-6 Paul A. Foerster Algebra and Trigonometry answers\n• free solving promble for intermidiate algebra\n• square root method\n• writing algebraic expressions worksheet\n• free algebra worksheets\n• linear inequalities worksheet\n• prentice hall algebra one tests and quizzes torrent\n• graphing inequalities worksheet\n• learning foil in algebra\n• how to find a common denominator in a ratio\n• Logarithmic equation solver\n• free slope intercept form of the equation worksheets\n• hard mathematical equation\n• solve equation for a variable with multiple variables\n• online parabolic graphing calculator\n• can you add a whole number to a square root?\n• easy way to calculate vectors\n• the hardest math question in the world\n• polynomdivision englisch casio\n• free introduction to elementary algebra\n• graphing cube roots+ti 83\n• how to calculate log base 2 TI 83\n• 5th class maths\n• Mathematical Induction for dummies\n• free math practice tests online for 7th graders\n• EXAMPLES OF 10TH GRADE MATH\n• finding the equation to an elipse\n• sophbmath\n• mixture compoud worksheet ks3\n• symbolic method\n• free lesson plans plotting ordered pairs\n• \"order of operations\" worksheets free printable\n• maths question paper for 5th grade\n• factor the polynomial completely. if not type prime calculator cheat\n• math-secrets-ppt\n• Free Worksheets With Negative Numbers\n• practice papers for class viii\n• solving fractional equations\n• free dividing polynomial worksheets\n• gcse maths bearings worksheet\n• free algebra solver with steps\n• prentice hall algebra 1\n• median and mode worksheets 4th grade\n• Algebra principles solver\n• Describe the similarities and/or differences you find between the different methods for solving quadratic equations. Can you develop a strategy or pattern to solve the quadratic equations?\n• simplify a(2) +b(2)\n• calculating density and volume worksheet + sixth grade level\n• 8th grade algebra give the line of symmetry\n• extracting square root quadratic formula calculator\n• fraction formulas\n• Mcdougal Littell algebra 2 answer key\n• math sheets - order of operations\n• ti-89 fractions\n• algebra with pizzazz objective 3-c answers\n• worksheets on using expression when reading\n• how do you solve the square root of multiple variables\n• algebra 2 lesson master answers\n• scince sats papers year 9\n• elementary math formula sheets\n• online Subtraction problems for third grade\n• calculator addition,subtraction,minus,division sample coding in vb.net\n• KS3 maths subtracting fractions worksheets\n• practice paper on adding and subtracting negative numbers\n• convert decimal to decimal\n• what is a symbolic method\n• algebraic expression question exponent\n• operations with integers worksheet\n• \"binomial fraction\" fractions\n• simplify A trinomial calculator\n• equations with fractions and exponents\n• square roots with fractions\n• mixed number as a decimal\n• basic calculas\n• algebra tiles worksheets\n• Step how to use graphing calculater intering function TI 84\n• how to solve factorial expressions\n• maths Percentages as fractions Tests year 8\n• solving college algebra\n• free printable 8th grade math worksheets\n• a sum of cubes plus a number\n• solver for exponents\n• free probability worksheets\n• cool maths sheets\n• intercepts fractions maths\n• solving 3rd order polynomials\n• balanced equations worksheets for 5th grade\n• math trivia examples\n• automatic math problem solver\n• absolute equation solver\n• expression calculator\n• math problem solver bearings\n• real life examples of undefined equations\n• squared and cubed maths games\n• solving two step equations in 7th grade math\n• chemistry math problem solver\n• Holt Math equations\n• Free Math Solver\n• how do you solve multiplying radical expressions\n• exponential notation worksheets\n• cheat codes algebra i cognitive tutor\n• log base 2 texas\n• adding and subtracting positive ans negative number test questions\n• math 6TH GRADE TEST book 2\n• dilation geometry free worksheet\n• vb program of inequality of an addition property\n• factoring calc\n• convert lineal metre to square metre\n• resolution equation non linear matlab\n• second order runge kutta matlab\n• solving inequalities worksheet\n• teacher's guide online free practice workbook with examples algebra 1 answers mcdougal littell chapter 9 2001\n• how to find the sum of the roots of a cubic\n• lcd of polynomial\n• how to determine if a square root can be simplified\n• rational expression math games\n• matlab simplify\n• sample matlab codes for newtons method for solving non linear pde\n• How to solve for p-values using TI-83+\n• how to turn an uneven fraction into a mixed number\n• first order linear differential equation calculator\n• binomial expansion exponential\n• free maths work booklets\n• question papers for grade 12 history\n• second order differential equation homogeneous\n• fractions greatest to least answer key\n• mastering physics workbook solutions ga\n• solution nonlinear differential equations\n• graph two variable equations\n• parabola calc\n• second order differential equation solver\n• linear equations with fractions and exponents\n• how do I write a mixed decimal for a fraction?\n• math sover pre algebra\n• Convert 8 in decimal to binary calculator\n• mixed number converted to a decimal\n• least common multiple 5th grade\n• how to convert mixed numbers to dicimals\n• mathcad solve simultaneous equations in program loop\n• algerator\n• binary operations PPT in abstract algebra (seventh edition) by john b. fraleigh\n• simplify ration expression with ti-83 plus\n• worksheet algebra combining like terms\n• fraction problem solver\n• number converter java code\n• iterative ti-89 solve\n• lowest common denominator calculator\n• rational root theorem power point Glencoe\n• addition and subtraction equation rules\n• free fractions step by step online\n• worksheet on solving systems of linear equations\n• factors worksheet for kids\n• find logarithm in science data book\n• free trial of ti 84 calculator\n• combinations and permutations\n• exponential expression practice\n• rationalize the denominator worksheet\n• sample algebra solving for a variable questions\n• simlutaneous equations calculator 3 variables\n• answers to just like fractions (multiply & divide) math worksheet algrebra 2\n• algebra quiz\n• \"non algebraic\" solve matlab\n• holt algebra ohio\n• very long hard algebra problems to solve\n• maths + squarring FRACTIONS\n• basic theory of systems of first order linear equation\n• completing the square + practice problems\n• three unknown equations calculator\n• special product and factoring\n• graphing linear equations worksheet\n• powell funktion jacobian matlab\n• math answers to merril algebra 2 with trigonometry\n• T1 83 Online Graphing Calculator\n• ged algebra questions\n• prentice hall pre algebra WORKBOOK\n• finding density worksheets for 5th grade\n• square root expressions\n• steps to chemical equations\n• aptitude test questions in g math\n• multivariable equations excel\n• college algebra calculator free\n• how to find the scale factor\n• log 2 and ti83\n• formula solver program for ti-83\n• nc holt rinehart and winston math grade 8 workbooks\n• picture of a mathdiameter\n• solving fractions in java\n• 4th grade simplest form fraction worksheet\n• inequalities fractions\n• solving by factoring calculator\n• completing the square for dummies\n• completing the square in two variables calculator\n• programs for TI 84 synthetic division\n• wronskian work backwards\n• solving nonlinear first order differential equations\n• solve quadratic equations in matlab\n• beginers algerbra\n• algebra help prentice hall algebra 1 california edition chapter tests tutoring\n• five simultaneous equations solver\n• college algebra clep prep free\n• perfect square root calculator\n• those roots are radical TI\n• cubing numbers on a ti-83 plus calculator\n• solving greater than less than worksheet\n• how to divide exponents with unknowns\n• balancing equations worksheet\n• instructions on a hard math equation\n• enrichment activities in radical expressions\n• pre algebra problem solver\n• 5th grade function tables worksheets\n• math for dummies online\n• VBA project to solve for the real roots of the quadratic equation excel\n• algebra calculator with fractions\n• homework solution to Linear Algebra Done Right\n• Free College Algebra Calculator\n• glencoe mathematics algebra 1\n• 3rd grade free algebra worksheet\n• how to find the square root of a number if you don't have a square root symbol\n• mathematics for dummies\n• how to print sum of a cube with java\n• square cube roots what used for\n• basic algebra cube square triangle\n• ti-84 log base 2\n• tricky maths in permutation and combination\n• free algebra equation calculator\n• california star practice 9th grade\n• fractions + ordering from least to greatest + grade 4 + worksheet\n• differential equation convolution\n• using fortran to solve a polynomial equation\n• free worksheets decimals to fractions\n• how to solve vertex on TI-89 calculator\n• Grade 9 questions using polynomials in triangles\n• Free adding and subtracting word problems/printable\n• solve linear equations with 3 variables with TI-84\n• javascript calculator with exponent and +squareroot\n• solution of second order non homogeneous differential equation\n• converting mixed fractions to decimals\n• aptitude questions on English language\n• answers to glencoe mcgraw-hill algebra 1 workbook\n• TI-84 graphing linear equations\n• 9th std algebra sums\n• algebra games for beginners\n• permutation and combination worksheet\n• 4th grade algebra lesson Base Ten\n• solving quadratic equations by factorisation\n• algebraic processes in factorization of quadratic equation\n• input 10 digits and determine larger number java\n• Addition and Subraction of Trigonometric Expression\n• multiply and reduce to lowest term calculator\n• is there a way to find the greatest common factor on the ti-89\n• linear combination method generator\n• solve using cramer's rule worksheet\n• Permutation lessons for grade 6\n• division properties exponents calculator\n• glencoe 1999 life science chapter test\n• Algebra Calculator with exponents\n• square root formula\n• sign( absolute value derivative ti 89\n• procedure for graphing a line given its equation\n• how to calculate z probability with ti85\n• mcdougal littell algebra 1 book chapter 10 answer key\n• basic algebra for 9th grade level\n• holt key code\n• algebra 2 holt\n• how do you simplify the the square root of 13\n• algebra with pizzazz sheets\n• equation inverse solver\n• java GCF&LCF simulation\n• worksheet on scientific notation\n• online math problem solver Solve by factoring\n• how to dividing polynomials for dummies\n• domain and range printable free worksheets\n• linear algebra cheat sheet\n• free test for simplifying fractions with exponents\n• largest common denominator\n• convert decimal to square root\n• standard vertex form tool\n• hardest physics formulas\n• solving equations with cube roots worksheet\n• complex to exponetial form ti83\n• gauss elimination in visual basic\n• free worksheets on negative numbers\n• ladder method multiplication chicago math\n• how to find logs on ti 89\n• inequality worksheet\n• options problems examples\n• \"free\" online \"step by step integration calculator\"\n• practice workbook algebra 1 answers mcdougal littell chapter 9\n• teach me algebra now\n• easy way to understand ratios\n• math trivia with solution and answer\n• multiplication Properties of Exponents lesson plans\n• EQUATIONS WITH TWO VARIABLES power point\n• a +calaulator changing decimals into fractions\n• algebra 2 answer key mcdougal\n• common denominators ks2 maths problems primary resources\n• how to input behavior polynomial on graphing calculator\n• hard substitution in maths\n• one step linear equations printables\n• online ti-83\n• highschool homework solver\n• dividing fractions worksheet and answer\n• factor binomials calc\n• free consumer math worksheets\n• how do make 55% a fraction\n• grade 11 college math fractions\n• graphing ellipses help\n• pre algebra with pizzazz answers worksheets\n• java program to convert time\n• convert square meters to lineal metres\n• one step equations for 4th grade\n• uniform motion word problem\n• algebraic fractions in daily life\n• power points lesson on degree of polynomials\n• power point presentation for maths lessons for 7 th class from india\n• how to do problem solving polynomials grade 11\n• why can't you not use the LCD method when simplifying rational equations\n• printable circumference and pi worksheet\n• zeros solver\n• glencoe math grade 6 permutations\n• interactive writing algebraic expressions\n• simplifying radical expressions rationalizing the denominator worksheet\n• doing exponents on the ti-83\n• prentice hall chemistry workbook answeres\n• simplifying square root fractions rationalizing denominators\n• free online ti 84 calculator\n• combining like terms worksheet\n• from where can i find free mathematics o/l exam papers\n• introductory algebra worksheet\n• rational expression simplifier\n• online calculator-square\n• adding subtracting dividing multipy fractions\n• adding and subtracting positive and negative intergers\n• graphing linear functions worksheets\n• linear equations worksheets 5th grade\n• ALGEBRAIC EXPRESSIONS 4TH GRADE WORKSHEETS\n• online solve maths problems class viii\n• glencoe algebra 2 solutions manual\n• pictures parabolas\n• Glencoe worksheet on sequences\n• 4th grade order of operations lesson plan\n• simplifying exponential expressions\n• ti-83 plus cube roots\n• math double cross worksheet\n• solver change to radical form\n• algerbra work to do\n• Practice Hall worksheets for math Practice 9-6\n• how to learn math for 7th graders negative and zero exponits\n• finding common denominator worksheet\n• binomial calculator (a+b)^2\n• aptitude test tutor\n• math grade 9 rational expressions\n• basic math for dummies\n• Practice SAT tests for 6th graders\n• factorizing cube roots\n• easiest way to factor cube root\n• print string 100 times java loop\n• algebra 1 holt practice workbook\n• holt algebra lesson plans\n• free Intergers work sheet\n• high school free printable algebra\n• 10th grade trigonometry flash cards online\n• plato interactive mathematics pre algebra book\n• aptitude questions in c language\n• formula of the slope\n• inventor kids worksheet\n• math cheats linear and nonlinear equations\n• function order rossover in matlab\n• online calculator with INT divide\n• Multiply Devide Fractions Worksheets\n• convert square roots\n• find a slope using fractions\n• how do you find formula the greatest common factor\n• solve for x worksheets\n• problem scale factor\n• mutiplying and dividing fractions test\n• how to simplify square root expressions\n• something fun for rearranging formulae ks3\n• adding and subtracting fraction and decimals calculator\n• online calculator with variables\n• on-line videos for 8th grade algebra\n• integers workshheet\n• how to grapg the equation with one variable\n• how do I solve for variables withe a caculator\n• factoring a cubed polynomial\n• algebra calc exponents\n• howdo i find the y intercept of (-4,-10)\n• parabola graphing tool\n• Prentice Hall Mathematics Geometry Answers\n• factor polynomial two variables\n• math trivia with solutions\n• solving roots\n• fortran error 13\n• how to do an algebra problem\n• how to add subtract multiply and divide fractions study sheet\n• solve simultaneous equations online\n• simultaneous equations calculator\n• \"proportion worksheet\"\n• adding subtracting integers with a number line worksheet\n• maths papers 10th\n• pre algebra basic subtraction equations\n• free printable pre-algebra worksheet\n• example of mixed number as a decimal\n• glencoe algebra 1 worksheet answers\n• math formula chart grade 7\n• algebra 2 homework help- multiplying and dividing radical expressions\n• factoring math problems\n• algebra 1 glencoe chapter test\n• Write net Bronsted equations and determine the equilibrium constants for the acid-base reactions that occur when aqueous solutions of the following are mixed\n• free fourth grade calculator activities\n• integration by algebraic substitution\n• trigonometry problem solver\n• holt mathmatics 6th grade chapter nine test\n• free intermediate algebra worksheets\n• convert mixed number into a decimal\n• do my math homework simplifying rational expressions\n• calculator formula for square root\n• year 11 mathmatic books\n• pre-alg with pizzaz\n• +INTERGRATION GEOMETRY TRANSLATIONS\n• free pictograph worksheets for kids\n• adding, subtracting, dividing and multiplying integers\n• liner graph\n• solution set calculators\n• square number rules\n• can you have a negative number in a radical\n• free online linear equation solver\n• multiple choice worksheet fraction operations\n• algebra 1 dividing fractions problems\n• how to solve polynomials with a ti 83 plus\n• free proprtions worksheet\n• combining like terms powerpoint\n• Free printable conic section worksheets\n• fraction to decimal worksheet\n• solve equation in excel\n• math solving programs\n• LU decomposition ti89\n• variables WROKSHEETS\n• first grade math printable worksheets\n• finding slope on a ti83\n• online fractions calculator\n• \"glencoe world history study guide\"\n• ebook for combination and permutation\n• logarithm solver\n• coordinates worksheets for 1st grade\n• calculator to divide polynomials\n• problem solver for trig identities\n• For what value of n, are the nth terms of two APs\n• free numeracy test on percentages for ks3\n• hot to simplify combinations and permutations\n• online factor trinomial calculator\n• solving simultaneous quadratic equation with 3 variables\n• trinomial factor calculator\n• graphing a parabola on a ti-86 calculator\n• an easy ellipse problem\n• mcdougal littell geometry free answers\n• solve equations with rational exponents ppt\n• trivias for math\n• do my logarithm problems online\n• Mcdougal littell note-taking copy master\n• mcdougal littell +TAKs Objective Review\n• worksheets area of composite figures with polygons honors geometry\n• factoring quadratics in two variables\n• glencoe math workbooks answers simple interest\n• square root worksheet\n• prentice hall algebra worksheets\n• slope worksheets free grade 9\n• solving simultaneous equation in excel\n• greatest common factor of polynomials worksheet\n• \"factoring trinomials\" \"word problems\"\n• square root problems for third grade\n• ks2 sats graphs\n• linear equations hard worksheets year 11\n• free algebra calculators vertex\n• 2nd grade area square worksheet\n• ordering fractions from least to greatest worksheet for third graders\n• math transformations worksheets\n• solving simultaneous nn linear equation in excel\n• problems for transforming formulas\n• solving equations by taking square roots calculator\n• Algebraic Expressions and Identities Start Test Not available\n• linear equations worksheets\n• mixed number to decimal\n• online linear algebra problem solver\n• how to solve 3rd order equation polynomials\n• online answers+ prentice hall mathmatics algebra 1\n• problem solver for rational equations and expressions\n• dividing exponent calculator\n• free prentice hall textbook answers\n• what is the key vocab for chapter 11 of glencoe mcgraw hill algebra 1\n• print out 8th grade Math work sheets\n• GCF conversation chart\n• sampling problems for 6th grade\n• roots of multiple variable system\n• how does a 6th grader calculate simple interest\n• percent equations\n• converting decimal to root\n• sample year-9 trigonometry question\n• percentage algebra formulas\n• solving systems linear equations worksheets\n• mcdougal littell algebra 2 answer key 7-3\n• rationalizing complex fractions+test\n• online book prentice hall algebra 2\n• elementary algebra practice problems help\n• teaching handwriting worksheets gard 6\n• rationalizing the denominator with variables\n• using parentheses in math worksheets\n• free algebra for worksheet 9th grade\n• logarithms and algebra for beginners\n• when to use permutation and combination in real life\n• pictures of steps to easy algebra problems\n• math problem solver 8th grade\n• intermediate algebra calculations\n• standard graphing calculator -deviation online\n• prentice hall pre algebra textbook answer key\n• partial sum algorithm worksheet\n• calculating log base 2 on a TI-30\n• how to input binomial formula into TI 83 calculator\n• worksheet on adding and subtracting integers\n• adding subtracting polynomials algebra 1 test c ch 10\n• Solve the following differential equations in matlab\n• 7th grade how to do conversion math\n• how to raise trig functions on ti-89\n• green globs cheat equation\n• non homogenous non linear differential equation\n• Why is it important to simplify radical expressions before adding or subtracting?\n• solving quadratic equation by synthetic method\n• challanging algebra qusetions for beginer gcse\n• online algebra courses sacramento\n• quiz questions for adding and subtracting polynomials\n• printable measuring rules for math homework\n• permutation trivia\n• algebra exponent multiple choice\n• elimination method for solving equations calculator\n• 5th grade algebra lesson plan\n• one step inequality worksheets\n• radical number calculator in fractions\n• any problem calculator\n• math hyperbola equation\n• special products factoring equation\n• create an example of a quadradic equations for solving the four\n• addition and subtraction equations worksheets\n• convert mixed number decimal\n• investigatory in math\n• integers review worksheet\n• FORMULA TO CONVERT DECIMAL TO FRACTION\n• t183 plus metric conversion functions\n• dividing fractions sheets\n• how to solve proportions with multiple variables\n• standard function form to vertex form\n• free college algebra help\n• free mathematics algebra book in pdf format\n• nc algebra 1A practice\n• parabola formula\n• FACTOR TREE WORKSHEETS\n• linear equations graphing ppt\n• equation to solve for variables\n• adding subtracting whole numbers and fractions free worksheets\n• college level math equation worksheets\n• free math reviewer for TAKS test\n• slope-intercept form worksheets\n• easy algebra maths sheets\n• video math tutor polynomials, free on line\n• solve equations with x as denominator\n• step by step way on how to balance equations\n• solving radical equations on calculator\n• multiplication of rational expressions calculator\n• multiplying positive and negative numbers worksheet\n• standard into slope intercept form worksheet\n• standard form to vertex form calculator\n• how add subtract multiply and divide fractions and decimals\n• math tutor - hs, bellevue, wa\n• how to write a math equation 5th grade\n• step by step instructions on solving ratio tables elementary\n• algebrator+4.0\n• simplify x to the -1/7 power = 1/5\n• Integer Worksheets\n• simultaneous equations solver\n• practicing equation balancing worksheet dividing\n• mix numbers\n• algebra pie formula\n• easy geometry worksheets gre\n• subtracting like mixed numbers worksheets\n• least to greatest math fraction and decimal sheet\n• Qualifiers math\n• FREE online Introductory algebra eighth edition teachers edition\n• beginner algebra lessons\n• distributive property worksheets\n• printable system of equation word problems\n• COmpleting the squares multiple variables\n• cramer's rule calculator\n• simplify t algebraic expression by combining like terms\n• answers to page 486 in a prentice hall algebra-1 book\n• second-order runge-kutta matlab\n• algebra cheat cheats for parabola characteristics\n• quadratic equasion given 2 points\n• free prinable plus sums\n• solution to trinomial equations hard\n• log ti-89\n• how to simplify cubics trinomials\n• prentice hall algebra 1 georgia\n• hyperbola solver\n• Maths Trivia Kids\n• algebra square root calculator\n• solve equations matlab\n• rational expression calculator\n• Printable algebra tile worksheets\n• solving fractional equations worksheets\n• printable chemical equation balancing quizzes\n• rudin Real and Complex Analysis solution\n• free online math solver\n• \"Why is it important to simplify radical expressions before adding or subtracting?\"\n• algebraic expressions worksheets\n• Graphing Algebra Equations\n• challanging algebra qusetions for pre gcse\n• 5th grade algebra: rate of growth\n• worlds hardest math equation\n• log base 2 on ti-89\n• two step word problems 3rd grade\n• how to convert a fraction to a decimal\n• reference book in college algebra with author\n• solving cubed root functions\n• multiplying and dividing decimals worksheet\n• Aptitude question\n• rules for algebra\n• y6 translations worksheet"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.7745746,"math_prob":0.9898381,"size":89832,"snap":"2020-34-2020-40","text_gpt3_token_len":19483,"char_repetition_ratio":0.23493788,"word_repetition_ratio":0.013081395,"special_character_ratio":0.19222549,"punctuation_ratio":0.112827204,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.99992335,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T06:58:06Z\",\"WARC-Record-ID\":\"<urn:uuid:ea815510-18cd-4b0e-9e91-f4adb61e7b64>\",\"Content-Length\":\"138513\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9157a125-ea44-4ecf-8f63-20602fd1270f>\",\"WARC-Concurrent-To\":\"<urn:uuid:32ee468f-d18b-4205-b3b9-e2bd548d3db0>\",\"WARC-IP-Address\":\"52.43.142.96\",\"WARC-Target-URI\":\"http://www.softmath.com/math-com-calculator/graphing-inequalities/where-can-you-find-the-answer.html\",\"WARC-Payload-Digest\":\"sha1:ENKQLN6G7BX2N4GKMK43ZVLZP5G5RT6Q\",\"WARC-Block-Digest\":\"sha1:DZ3YTMKK7RYQGQYWXEA4GCNH7OZAK5B5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400196999.30_warc_CC-MAIN-20200920062737-20200920092737-00467.warc.gz\"}"}
|
https://arxiv.org/abs/1712.05495
|
[
"math.ST\n\n# Title:Minimax estimation of a p-dimensional linear functional in sparse Gaussian models and robust estimation of the mean\n\nAbstract: We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of these means are equal to zero. We show that, up to a logarithmic factor, the minimax rate of estimation in squared Euclidean norm is between $(s^2\\wedge n) +sp$ and $(s^2\\wedge np)+sp$. The estimator that attains the upper bound being computationally demanding, we investigate suitable versions of group thresholding estimators that are efficiently computable even when the dimension and the sample size are very large. An interesting new phenomenon revealed by this investigation is that the group thresholding leads to a substantial improvement in the rate as compared to the element-wise thresholding. Thus, the rate of the group thresholding is $s^2\\sqrt{p}+sp$, while the element-wise thresholding has an error of order $s^2p+sp$. To the best of our knowledge, this is the first known setting in which leveraging the group structure leads to a polynomial improvement in the rate.\nThe second problem studied in this work is the estimation of the common $p$-dimensional mean of the inliers among $n$ independent Gaussian vectors. We show that there is a strong analogy between this problem and the first one. Exploiting it, we propose new strategies of robust estimation that are computationally tractable and have better rates of convergence than the other computationally tractable robust (with respect to the presence of the outliers in the data) estimators studied in the literature. However, this tractability comes with a loss of the minimax-rate-optimality in some regimes.\n Subjects: Statistics Theory (math.ST) Cite as: arXiv:1712.05495 [math.ST] (or arXiv:1712.05495v4 [math.ST] for this version)\n\n## Submission history\n\nFrom: Arnak Dalalyan S. [view email]\n[v1] Fri, 15 Dec 2017 01:16:05 UTC (49 KB)\n[v2] Wed, 20 Dec 2017 18:35:10 UTC (50 KB)\n[v3] Wed, 9 May 2018 09:42:58 UTC (53 KB)\n[v4] Thu, 8 Nov 2018 20:59:49 UTC (53 KB)"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.9057568,"math_prob":0.97186816,"size":2297,"snap":"2019-26-2019-30","text_gpt3_token_len":549,"char_repetition_ratio":0.120366335,"word_repetition_ratio":0.0,"special_character_ratio":0.23770136,"punctuation_ratio":0.1002331,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9896632,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-17T01:49:02Z\",\"WARC-Record-ID\":\"<urn:uuid:e483b247-bb6d-4ef9-903b-5cee34588fc6>\",\"Content-Length\":\"20011\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2b65fb6a-4e63-4423-8682-976ade973e75>\",\"WARC-Concurrent-To\":\"<urn:uuid:c579551d-bc30-43c2-b94f-f8eecb5cd05f>\",\"WARC-IP-Address\":\"128.84.21.199\",\"WARC-Target-URI\":\"https://arxiv.org/abs/1712.05495\",\"WARC-Payload-Digest\":\"sha1:DOJXQUYS74GYMJBZ2YAPXVN5MA6Z4L4Y\",\"WARC-Block-Digest\":\"sha1:GQPNTNT4MHOUDPT3RVJJ5XWF3YMJKSAP\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525004.24_warc_CC-MAIN-20190717001433-20190717023433-00278.warc.gz\"}"}
|
http://adrian-tudor.com/blog/islandt-convert-hexadecimal-number-to-decimal-number-with-python-program/
|
[
"# Adrian Tudor Web Designer and Programmer\n\n## IslandT: Convert hexadecimal number to decimal number with Python program\n\nUse python program to convert hexadecimal number to the decimal number.\n\nHello and welcome back, in this article we are going to solve one of the programming problems on Codewars. This problem had been listed under the 8 Kyu category which means if we can solve that problem we will get two points. First I thought this should be an easy and simple question, I always select the 8 or 7 kyu questions not because they are hard but because they are simple. But after I have gone through this question, the only comment from me is “WHAT THE ****!”, man this question should be put under 6 kyu instead of the easiest category! Anyway, let us look at this question.\n\nWe will be given a string of hexadecimal number, for example, “C2a3”, we need to convert that hexadecimal number to the decimal number and return the answer to the caller.\n\nIf you are having a problem converting hexadecimal number to the decimal number, read this article. I will not go through all the details here because we will just concentrate on the programming part.\n\nHere are the steps we will need to do to solve the above problem.\n\n1. Convert all the characters in the hexadecimal string to lower case if there is any uppercase character in the string.\n2. Turn the new string into a list.\n3. Create a dictionary object with hexadecimal number as the key and the decimal number as the value.\n4. Reverse the list item (because the first hexadecimal letter starts from the right side of that hexadecimal string) and start to do the conversion within a for loop.\n```def hex_to_dec(s):\ns = s.lower()\ns_list = list(s)\nhex_dict = {\"0\" : 0,\n\"1\" : 1,\n\"2\" : 2,\n\"3\" : 3,\n\"4\" : 4,\n\"5\" : 5,\n\"6\" : 6,\n\"7\" : 7,\n\"8\" : 8,\n\"9\" : 9,\n\"a\" : 10,\n\"b\" : 11,\n\"c\" : 12,\n\"d\" : 13,\n\"e\" : 14,\n\"f\" : 15}\ncount = 0\nsum = 0\n\nfor item in reversed(s_list):\nsum += hex_dict[item] * (16 ** count) # read that hexadecimal post if you are lost\ncount+=1\n\nreturn sum\n```\n\nLeave your own solution in the comment box below this post, as always! But make sure you know what you are talking about, which means please don’t go beyond the subject of this post.\n\nBack Top"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.8682224,"math_prob":0.94426763,"size":2067,"snap":"2019-35-2019-39","text_gpt3_token_len":528,"char_repetition_ratio":0.14590402,"word_repetition_ratio":0.0076530613,"special_character_ratio":0.2805999,"punctuation_ratio":0.14252874,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.981951,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-18T11:26:22Z\",\"WARC-Record-ID\":\"<urn:uuid:98fe2aa8-e0f5-454b-82d0-66da0e12aae9>\",\"Content-Length\":\"14120\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:32a52e8c-db16-46cc-a183-f1b12b88069f>\",\"WARC-Concurrent-To\":\"<urn:uuid:573f1c74-91a3-4349-8e5c-8d5a45a70a62>\",\"WARC-IP-Address\":\"107.178.108.52\",\"WARC-Target-URI\":\"http://adrian-tudor.com/blog/islandt-convert-hexadecimal-number-to-decimal-number-with-python-program/\",\"WARC-Payload-Digest\":\"sha1:KO63FFUY6OE6XE2WF4O6HNYTJMUFIBF4\",\"WARC-Block-Digest\":\"sha1:HLMHLVZZ4YQNDFPQWVDJDI74C57EYKMS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514573284.48_warc_CC-MAIN-20190918110932-20190918132932-00019.warc.gz\"}"}
|
https://people.sissa.it/~laio/Research/Res_BE.php
|
[
"Bias-exchange metadynamics (see Ref. ) is an approach specifically designed for accelerating rare events/computing the free energy in very complex cases, in which the variables that are relevant for the process are more than 2-3. In these cases, normal approaches such as metadynamics or umbrella sampling are very inefficient.\nThe method works as follows:\n\n• One first lists all the collective variables that are expected to be relevant for the process under investigation. There is no limitation on the number of variables.\n• One runs in parallel several molecular dynamics simulations, each biased with a metadynamics potential acting on one of the collective variables of the list.\n• At fixed time intervals, swaps of the configurations between pairs of replicas are attempted. The swap is accepted according to the Metropolis criterion.\nThus, the dynamics of each replica is biased in a direction that changes stochastically with time. This allows the system exploring a complex (multidimensional) free energy landscape with great efficiency, even if the bias at each time is only one-dimensional.\n\nA two-dimensional example\n\nConsider a dynamics on a two-dimensional potential like the one in figure. If one perfoms metadynamics biasing x, one obtains an estimate of the free energy affected by large errors: indeed, the system jumps between the two wells at the bottom and the two wells at the top only due to (rare) thermal fluctuations, and obtaining the correct free energy would require taking the average over several transitions along y.",
null,
"We now perform two metadynamics simulations on two replicas, one biasing x, the other y. From time to time, we allow the two replicas exchanging configurations, accepting the exchange according to a Metropolis criterion (see Ref. ). Even if the computational cost has only dubled with respect to the simulation above, one observes a very significant reduction of the hysteresis:",
null,
"Now the metadynamics potential almost exactly compensates the free energy, both as a function of x and y: indeed, the profiles are practically flat lines. This means that the hysteresis is much reduced, and the metadynamics potential provides a very good estimate of the free energy.\n\n• The approach allows a parallel reconstruction of the free energy as a function of many variables. The computational cost scales LINEARLY with the number of variables.\n• The more variables one adds, the better the convergence is. However, if one forgets a relevant variable convergence is slow.\n• If one uses NR variable, the result of the simulation is not a free energy as a function of NR variables, but NR one-dimensional projections of the free energy. Obtaining the free energy as a function of all the variables requires a postprocessing of the results, described in Ref. .\n\nThe method has been successfully applied to study protein folding and protein-ligand docking.\nBibliography\n S Piana, A Laio,\nA bias-exchange approach to protein folding\nJOURNAL OF PHYSICAL CHEMISTRY B, 111, 4553 (2007)\n\n F Marinelli, F Pietrucci, A Laio, S Piana,\nA Kinetic Model of Trp-Cage Folding from Multiple Biased Molecular Dynamics Simulations\nPLOS COMPUTATIONAL BIOLOGY, 5, e1000452 (2009)"
] |
[
null,
"https://people.sissa.it/~laio/Research/Images/no_exch_x.gif",
null,
"https://people.sissa.it/~laio/Research/Images/exch.gif",
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.88898444,"math_prob":0.94449556,"size":2970,"snap":"2020-45-2020-50","text_gpt3_token_len":638,"char_repetition_ratio":0.13991909,"word_repetition_ratio":0.025641026,"special_character_ratio":0.1996633,"punctuation_ratio":0.10714286,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96580607,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-26T04:09:01Z\",\"WARC-Record-ID\":\"<urn:uuid:08665d82-6300-494d-addc-e33f3708e1b1>\",\"Content-Length\":\"7383\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7d613248-d315-4009-b060-e92006db2aff>\",\"WARC-Concurrent-To\":\"<urn:uuid:b21cd910-c3b7-40eb-bb53-5892ce603845>\",\"WARC-IP-Address\":\"147.122.1.145\",\"WARC-Target-URI\":\"https://people.sissa.it/~laio/Research/Res_BE.php\",\"WARC-Payload-Digest\":\"sha1:PJM4LPAGRBPSJBJS6XAS5IOLNTPZ2RNR\",\"WARC-Block-Digest\":\"sha1:QSXFRSVM6ZXBWZDGKEOSHK4VXMFHEIBZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107890273.42_warc_CC-MAIN-20201026031408-20201026061408-00104.warc.gz\"}"}
|
https://www.yhzq-blog.cc/bzoj-3012-usaco2012-decfirst/
|
[
"# bzoj 3012 [Usaco2012 Dec]First!\n\n### Description\n\nBessie has been playing with strings again. She found that by changing the order of the alphabet she could make some strings come before all the others lexicographically (dictionary ordering). For instance Bessie found that for the strings “omm”, “moo”, “mom”, and “ommnom” she could make “mom” appear first using the standard alphabet and that she could make “omm” appear first using the alphabet “abcdefghijklonmpqrstuvwxyz”. However, Bessie couldn’t figure out any way to make “moo” or “ommnom” appear first. Help Bessie by computing which strings in the input could be lexicographically first by rearranging the order of the alphabet. To compute if string X is lexicographically before string Y find the index of the first character in which they differ, j. If no such index exists then X is lexicographically before Y if X is shorter than Y. Otherwise X is lexicographically before Y if X[j] occurs earlier in the alphabet than Y[j].\n\n### Input\n\n• Line 1: A single line containing N (1 <= N <= 30,000), the number of strings Bessie is playing with.\n• Lines 2..1+N: Each line contains a non-empty string. The total number of characters in all strings will be no more than 300,000. All characters in input will be lowercase characters ‘a’ through ‘z’. Input will contain no duplicate strings.\n\n### Output\n\n• Line 1: A single line containing K, the number of strings that could be lexicographically first.\n\n• Lines 2..1+K: The (1+i)th line should contain the ith string that could be lexicographically first. Strings should be output in the same order they were given in the input.\n\n#### Sample Input\n\n4\n\nomm\n\nmoo\n\nmom\n\nommnom\n\nINPUT DETAILS: The example from the problem statement.\n\n#### Sample Output\n\n2\n\nomm\n\nmom\n\nOUTPUT DETAILS: Only “omm” and “mom” can be ordered first.\n\n### 题解\n\n#include <cstdio>\n#include <queue>\n#include <cstring>\n#define N 300010\nusing namespace std;\nstruct edge\n{\nint to,next;\n}e;\nint n,tot,cnt,ans,sums;\nint ch[N],is_end[N],can,st,len,d,root,sz;\nqueue<int> q;\nchar s;\n{\ne[++tot].next=st[x];\ne[tot].to=y,st[x]=tot;\n// printf(\"%d %d\\n\",x,y);\n}\nqueue<int>que;\nmain()\n{\nscanf(\"%d\",&n);\nfor (int i=1;i<=n;i++)\n{\nscanf(\"%s\",s[i]+1);\nint len=strlen(s[i]+1),now=root;\nfor (int j=1;j<=len;j++)\nif (ch[now][s[i][j]-'a'])\nnow=ch[now][s[i][j]-'a'];\nelse\nnow=ch[now][s[i][j]-'a']=++sz;\nif (!is_end[now])\nis_end[now]=i,can[i]=1;\n}\nfor (int i=1;i<=n;i++)\nif (can[i])\n{\nint len=strlen(s[i]+1),now=root;\nfor (int j=1;j<=len;now=ch[now][s[i][j]-'a'],j++)\nif (is_end[now])\ncan[i]=0;\nif (!can[i]) continue;\nmemset(st,-1,sizeof st);\nmemset(e,0,sizeof e);\nmemset(d,0,sizeof d);\ntot=0,now=root,sums=0;\nfor (int j=1;j<=len;now=ch[now][s[i][j]-'a'],j++)\nfor (int k=0;k<26;k++)\nif (k!=s[i][j]-'a' && ch[now][k])\nfor (int j=0;j<26;j++)\nif (!d[j])\nque.push(j);\nwhile(!que.empty())\n{\nint now=que.front();que.pop();\nsums++;\nfor (int j=st[now];~j;j=e[j].next)\n{\nd[e[j].to]--;\nif (!d[e[j].to]) que.push(e[j].to);\n}\n}\nif (sums<26)\ncan[i]=0;\nelse\nans++;\n}\nprintf(\"%d\\n\",ans);\nfor (int i=1;i<=n;i++)\nif (can[i])\nprintf(\"%s\\n\",s[i]+1);\n}"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.52003306,"math_prob":0.9701616,"size":3360,"snap":"2023-40-2023-50","text_gpt3_token_len":1209,"char_repetition_ratio":0.110846244,"word_repetition_ratio":0.03211009,"special_character_ratio":0.33184522,"punctuation_ratio":0.18481013,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99736595,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-06T14:20:55Z\",\"WARC-Record-ID\":\"<urn:uuid:890b6dfb-3a87-45c8-b2e8-2139b4230d8d>\",\"Content-Length\":\"31237\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:918e9c77-22ab-4ed0-8348-c3f6d0d83546>\",\"WARC-Concurrent-To\":\"<urn:uuid:5dc80944-9366-4e8a-9887-514db651aea1>\",\"WARC-IP-Address\":\"154.223.167.132\",\"WARC-Target-URI\":\"https://www.yhzq-blog.cc/bzoj-3012-usaco2012-decfirst/\",\"WARC-Payload-Digest\":\"sha1:CHDKPQEGWKXI5LMXBMF7GOGO3JJTR4RI\",\"WARC-Block-Digest\":\"sha1:26UWIEL6EMF62Q7XI2XC5AY5P2TSLVVE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100599.20_warc_CC-MAIN-20231206130723-20231206160723-00622.warc.gz\"}"}
|
http://mizar.uwb.edu.pl/version/current/html/proofs/ndiff_1/7
|
[
"let S be RealNormSpace; :: thesis: for seq being sequence of S holds\n( seq is non-zero iff for n being Nat holds seq . n <> 0. S )\n\nlet seq be sequence of S; :: thesis: ( seq is non-zero iff for n being Nat holds seq . n <> 0. S )\nthus ( seq is non-zero implies for n being Nat holds seq . n <> 0. S ) by ; :: thesis: ( ( for n being Nat holds seq . n <> 0. S ) implies seq is non-zero )\nassume for n being Nat holds seq . n <> 0. S ; :: thesis: seq is non-zero\nthen for x being set st x in NAT holds\nseq . x <> 0. S ;\nhence seq is non-zero by Th6; :: thesis: verum"
] |
[
null
] |
{"ft_lang_label":"__label__en","ft_lang_prob":0.88862246,"math_prob":0.9983468,"size":529,"snap":"2019-43-2019-47","text_gpt3_token_len":175,"char_repetition_ratio":0.20380953,"word_repetition_ratio":0.3828125,"special_character_ratio":0.35916823,"punctuation_ratio":0.14814815,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99389875,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-22T17:25:26Z\",\"WARC-Record-ID\":\"<urn:uuid:26046ada-d8c4-4b5b-879f-98dbe1bcc6d1>\",\"Content-Length\":\"6000\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a22661a9-6f35-4dd0-8a40-44ff0277b257>\",\"WARC-Concurrent-To\":\"<urn:uuid:80f45079-fc05-4ca7-b492-899ccce84650>\",\"WARC-IP-Address\":\"212.33.73.131\",\"WARC-Target-URI\":\"http://mizar.uwb.edu.pl/version/current/html/proofs/ndiff_1/7\",\"WARC-Payload-Digest\":\"sha1:NXUCGSL2TNVLMYK34UMTXPBFOQOUTGRH\",\"WARC-Block-Digest\":\"sha1:75GOQRJIG6JLZ7DS6MO4B7CKX6MPXVT4\",\"WARC-Identified-Payload-Type\":\"application/xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987822458.91_warc_CC-MAIN-20191022155241-20191022182741-00343.warc.gz\"}"}
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.