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I cannot figure out why the camera displays and renders a portion of the image, but not entirely. I am attaching an image image of what the camera is actually displaying, and will try to figure out how to attach a 2nd image of the scene I am trying to accomplish Thanks for your help | A scene I made is not rendering, at all. This grey screen stays the same and nothing changes. Here are my settings: [ |
Show:$$\lim_{n\to\infty}\frac{\sqrt[n]{n!}}{n}= \frac{1}{e}$$ So I can expand the numerator by geometric mean. Letting $C_{n}=\left(\ln(a_{1})+...+\ln(a_{n})\right)/n$. Let the numerator be called $a_{n}$ and the denominator be $b_{n}$ Is there a way to use this statement so that I could force the original sequence into the form of $1/\left(1+\frac{1}{n}\right)^n$ | I'm trying to find $$\lim_{n\to\infty}\frac{n}{\sqrt[n]{n!}} .$$ I tried couple of methods: Stolz, Squeeze, D'Alambert Thanks! Edit: I can't use Stirling. |
Is it necessary to prove this ??? Can it not be shown simply like 2Z is not ring isomorphism to 3Z , when n=2 and m=3. | Show that if $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$. Can I get some help to solve this problem |
Is there a way to store my password when ssh'ing on a server? I tried to change the variables BatchMode and PasswordAuthentication in my file /etc/ssh/ssh_config, but to no avail. Could someone indicate me how to proceed? | I want to communicate between several computers on my network (static Ethernet), through SSH. In order to do that I need to run ssh-add every time I log in on a specific machine, how can I do it so that it's set up once and it doesn't ask me for the passphrase every time I log in or reboot my machine? I know that there is a way that you should add some lines to the bash_profile file, but I still need to type the password every time I reboot/log in to a specific machine. if [ -z "$SSH_AUTH_SOCK" ] ; then eval `ssh-agent -s` ssh-add fi |
As part of an exercise I needed to decompose the Jordan form of a complex matrix into nilpotent and diagonalizable parts, and also explain why they commute. The decomposition is trivial since strictly triangular matrices are nilpotent, but I don't see - why do these matrices commute? | Let $A$ be an $n \times n$ complex matrix. Prove that there exist a diagonalizable matrix $D$ and a nilpotent matrix $N$ such that a. A = D + N b. DN = ND and show that these matrices are uniquely determined. I think I've solved the part a but don't have an idea to continue. Here is what I've tried: Let $D = \begin{bmatrix} a_{11} & 0 \\ * & a_{nn} \\ \end{bmatrix}$ and $N = \begin{bmatrix} 0 & * \\ 0 & 0 \end{bmatrix}$. Since D is a lower triangular matrix, its determinant is equal to product of its diagonal entries and hence its characteristic polynomial is $(x-a_{11})...(x-a_{nn}).$ Then D is diagonalizable. Similarly, characteristic polynomial of $N$ is $x^n$ then by Cayley-Hamilton $N^n = 0$. Update: My assumption for D to be diagonalizable was wrong, eigenvalues need not to be distinct. Update after answers: Thank you all for your help. It was just a question asked in the end of the chapter "Canonical Forms". So I just know Jordan form, Rational form, etc. I don't know anything about the Lie Algebra, Semi simple matrices, Representation theory, Perfect field mentioned in the answers. Honestly, answers didn't help me to understand the solution but they seem useful so maybe they help other people. Thanks. |
I read this story in Omni magazine about 25 years ago. In researching a few months ago, I believe I found info on this site, but can’t find again, and browser history was cleared. Written in the 40’s, I think. Starts with one scientist coming to visit another about an experiment and upon arrival (an island, I think, tropical) finds a man just standing and staring. The scientist finds that his colleague had found a drug that slows body functions to the speed of trees, making people seem like zombie-statues. I don’t remember how it ends, so would like to read it again. | I'm looking for the title of a short story by Ursula Le Guin about a scientist (?) who is given a drug that slows the timescale of his perception enormously, so that he can perceive that an alien (?) forest is actually behaving as a sentient being, reacting to current events, but at an enormously slow (from a normal human point of view) timescale. It might be in , but I don't remember the title (and it doesn't jump out at me from the list of titles) and don't have access to that collection right now. It is not "The Word for World is Forest", nor "Direction of the Road" (from ), nor "Vaster than Empires and More Slow", the latter two of which look at similar plant perception/time-scale issues. Update: it turns out that the description was right, but I had most of the details wrong: not Le Guin, not alien, not a scientist ... |
I have Matlab running in a Linux session for almost 2 days, and afraid to lose the computations if my network connection fails. Will moving Matlab to the background and starting 'screen' be the answer for that? | I have a running program on a SSH shell. I want to pause it and be able to unpause its execution when I come back. One way I thought of doing that was to transfer its ownership to a screen shell, thus keeping it running in there. Is there a different way to proceed? |
This is a multipart linear algebra textbook question. Let $A, P_1, P_2, N_1, N_2$ be $n$ × $n$ matrices with real entries such that $I_n$ = $(t I_n − A) \big(\frac{N_1}{(t-1)^3} + \frac{N_2}{(t-1)^2} + \frac{P_1}{(t-1)} + \frac{P_2}{(t-2)}\big)$ Then, I'm asked to show the following: If $\lambda$ is an eigenvalues of $A$, then λ ∈ {1, 2}. I'm not really sure what my first steps here should be. Given the initial equation, I don't really know what matrix algebra I can apply. I'm wondering first of all how I can even take the determinant of both sides to connect it to eigenvalues Any assistance on this question would be much appreciated! | Thanks everyone for viewing my question! I'm getting stucked on this problem: Suppose $A,B,C,D,E$ are real $n\times n$ matrices such that for any real number $t\neq 1,2$: $$ I_n=(tI_n-A)(\frac{B}{(t-1)^3}+\frac{C}{(t-1)^2}+\frac{D}{t-1}+\frac{E}{t-2}) $$ The problem asks me to prove $C=(A-I)D=D(A-I)$. My progress: Multiply $t-1$ to both sides we obtain: $$ (t-1)I_n=(tI_n-A)(\frac{B}{(t-1)^2}+\frac{C}{t-1}+D+\frac{(t-1)E}{t-2}) $$ Then take limits when $t\rightarrow 1$: $$0=\lim_{t\rightarrow1}(I_n-A)(\frac{B}{(t-1)^2}+\frac{C}{t-1}+D) \\(A-I_n)D=\lim_{t\rightarrow1}(I_n-A)(\frac{B}{(t-1)^2}+\frac{C}{t-1}) $$ This is really close to the required form but I do not know how to continue, I saw some answer concluding that: $$ \lim_{t\rightarrow1}(I_n-A)(\frac{B}{(t-1)^2}+\frac{C}{t-1})=C $$ I don't know if this is correct and it makes no sense to me. Thanks so much for your answers in advance! |
I'm trying to show that the kernel of the homomorphism $$\varphi: \mathbb{K}[X,Y]\rightarrow \mathbb{K}[t^2,t^3],$$ $$X\mapsto t^2,$$ $$Y\mapsto t^3,$$ is the ideal $I=\langle Y^2-X^3\rangle$ in $\mathbb{K}[X,Y]$, where $\mathbb{K}$ is a field. I can show that $I$ is contained in $\ker \varphi$, but not the other way around. For a given polynomial $p(X,Y)$ such that $\varphi(p(X,Y))=0$, I wrote it as $$ p(X,Y)= \sum_{i=1}^n a_iX^i + \sum_{j=1}^mb_jY^j + \sum_{r,s>0}c_{rs}X^rY^S +d, $$ but that didn't help me as much as I hoped. At least I can show that $d=0$, but that was it. The change of variables made by $\varphi$ suggested some integer relationships between $i$, $j$ and $r,s$ but I could not conclude anything. This was a part of an example seen in a Commutative Algebra online course under the section of Integral Extensions with a spoiler from what owuld be seen in an Algebraic Geometry course (I can provide link for the Youtube video, if needed, though I believe it's not necessary) | How to prove that the ideal $I=(x^3-y^2)$ in $k[x,y]$ is prime? I have constructed a map from $k[x,y]$ to $k[t]$, which maps $x$ to $t^2$, and $y$ to $t^3$. Then, I want to show that the kernel is exactly $I$. But the difficulty is that how to prove the kernel is contained in $I$. Could you help me? Thanks a lot! |
I changed my admin user name using System Preferences/User and Groups, but the name didn't change and the Admin user account was changed to standard and lost the admin rights. I've read similar questions here and solutions using single-user mode, but it seems like the /sbin/fsck -fy and the rm /var/db/ .AppleSetupDone commands are not working on my MacbookPro 2012 running on High Sierra. Any help would be appreciated. Thanks | On my mac I have 2 accounts and the both are normal account. So in this moment I don't have a Administrator account, only one that was in the past a administrator, but now is not. How I can have again a Administrator account? |
This question is specifically for I work to nearly get success, but the question is also asking in general. I shouldn't use nearly to get because that would detract from from my purpose of working. | Mark's generosity in this crisis seems to more than make up for his earlier stinginess. Should those sentences always be avoided, or are there cases where they are valid? |
I'm writing the thesis for my master degree, some of the very very old articles I have to cite are in a foreign language I don't understand (usually German and French). Most of them have been translated in my native language and/or English, but in some cases I didn't find a translation. Even if I'm asking it for the thesis I think it does apply in more serious cases of research too. An example would be for example if I write that the Friedman Lemaitre Robertson Walker metric in general relativity was first derived by Lemaitre in 1922. If I cite his original article in French at this point, would I be doing something wrong since I don't understand French and I can't understand what's written there? This is just an example, I'm pretty sure an English version of Lemaitre article exists, I just didn't check. I mean I assume that when someone cites an article he' read and understood it. My opinion is that I shouldn't cite the original article at all but cite someone else who cites it, knowing what was written in the original article. Am I overthinking it and I should just simply cite these articles or is there a better procedure? I don't know if it can be relevant but these articles appears mainly in the very beginning of the work, which is just an introduction to the topic of the work | Some months back I got into a situation where a paper with information that I considered important to prove a point was in a language I cannot understand. Since it was important but not crucial, I ended up not using the paper. Except for its abstract, which was in English, the entire paper was in this other language. It had graphs and images that I could understand without knowing the language. At the time, I was tempted to use Google Translate in order to get the general idea of the paper (in more detail than what is given in the abstract), while not necessarily trusting on the specific information that the translation gave me (). Since this would still leave me with some measure of uncertainty — there was no way for me to be sure exactly what it was saying — I thought it better to just let the paper go. But say that in a future situation I find a crucial paper in a language I don't understand: if I use Google Translate, using the paper in a situation that does not require specific information but only it's general gist, would citing it be ethically acceptable? (It's almost the same situation as , but I'm not concerned with translating the entire paper, for this would take time/resources that I simply don't have access to.) |
I have a MacBook pro and have downloaded bootcamp Windows 7, and was trying to dual boot Ubuntu. I got it to download and start and went into the installation setup and it asked me to do something with the partitions and I was messing around and accidentally marked the Windows folder as biosgrub. It then froze and I forced it to shutdown, but when it rebooted, it said missing operating system and I can't boot Windows anymore. I can get into system recovery and can still see the files, but it just won't boot. I could restore OS X and buy another Windows disk, but I was wondering if there was another way. | I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install. What can I do to fix this? |
A simple textbook reference would probably suffice here; I’m just not sure where to look, as I haven’t done much set theory. Let $C$ be a class that is not a set. Is it true/provable/whatever that for any set $S$, there is an injection from $S$ to $C$? (I’m not even totally sure what the right way to phrase the question is, but hopefully the intuitive idea is clear.) | Some proper classes are "too big" to be a set in the sense that they have a subclass that can be put in bijection with $\alpha$ for every cardinal $\alpha$. It is implied in post that every proper class is "too big" to be a set in this sense, however I have been unable to prove it. It's true if every two proper classes are in bijection, but it's consistent with ZFC for there to be a pair of non-bijective classes. So, is the following true in ZFC: For all proper classes, $C$, and $\alpha\in\mathbf{Card}$, $\exists S\subset C$ such that $|S|=\alpha$? If not, is there something reasonable similar that preserves the intuition about classes that are "too big to be sets"? |
Here I is what I have so far: And I am NOT SURE WHY Hakre closed this because it has to do with dropping MySQL events from the MySQL Event Scheduler NOT with using table names with PDO. My code is as follows: public function dMySQLEvent($my_env, $my_event_name) { $my_success = 0; $my_message = ''; try { # declare & set variables using $my_env list ($db_dbdriver, $db_hostname, $db_database, $db_username, $db_password) = Connection::dbConnect($my_env); # set default timezone # create & set connection # WORKS # $conn->exec("DROP EVENT IF EXISTS " . $my_event_name . ";"); # DOES NOT WORK # Prepare an SQL statement $my_sql = "DROP EVENT IF EXISTS :My_Event_Name"; $stmt = $conn->prepare($my_sql); # bind parameters to prevent SQL Injection $stmt->bindValue(':My_Event_Name', $my_event_name); # execute the SQL statement $stmt->execute(); # closes the cursor, enabling the statement to be executed again $stmt->closeCursor(); # close & unset the connection $stmt = null; unset($stmt); $conn = null; unset($conn); # Set success value to TRUE $my_success = 1; $my_message = 'success'; } catch(PDOException $e) { # Append error message to error log } return array($my_success, $my_message); } | Why can't I pass the table name to a prepared PDO statement? $stmt = $dbh->prepare('SELECT * FROM :table WHERE 1'); if ($stmt->execute(array(':table' => 'users'))) { var_dump($stmt->fetchAll()); } Is there another safe way to insert a table name into a SQL query? With safe, I mean that I don't want to do $sql = "SELECT * FROM $table WHERE 1" |
Complex numbers are used widely in quantum mechanics and the waveform, is there a physical interpretation of what this means about the structure of the universe? Why is it not used in macro physics? Do physicists really think that calling imaginary numbers a 90 degree rotation is a good enough answer? It seems to be used in many areas to mean similar things. Is there an explanation to do with dimensions as I have tried in this conversation a better way to understand them? | The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: Is the use of complex numbers simply to make the process of derivation easier, or is it an essential ingredient, without which it would be impossible to derive some results? I can identify two different settings where the answer may be different: It doesn't look like it is mandatory for results in Newtonian mechanics, General Relativity and classical electrodynamics. Can we say the same thing about quantum mechanics either way for sure? Could this be a difference in quantum mechanics over the classical picture? |
I have written a simple function that nullifies itself after its first call: var nullify = function(){ nullify = null; return 1; }; If I call it two times, like this: console.log(nullify()); console.log(nullify); Then the 1st expression will return 1, and the other will evaluate to null. All clear up to this point. If I however do it in a single expression and wrap it in a function: var fun = function(f){ return f() && !f; } Then, for some reason: console.log(fun(nullify)); evaluates to false, while I would expect it to be true, since 1st operand will return 1 and the other, as a negation of null, true. The evaluation of the right-hand operand occurs when the nullify functiion has already called nullify = null, is that right? What am I missing? | The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself). Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this? |
My mom’s old passport has only a Surname and no Given Name. The USA Visa was also issued this way. Example: Surname: Lakshmi Vishnu Given Name: FNU My mom’s new passport has changed the way the information is structured. Example: Surname: Vishnu Given Name: Lakshmi The old visa is still Valid and she is visiting me next month. She has traveled to the US before. Will this change of surname and given name pose a problem? | I have valid US B1/B2 Visa on an expired Indian passport. My passport has my surname as blank and hence I was issued a US Visa with given name as FNU and Surname "My First Name" . I need to apply for new passport and I am planning to get my given name and the surname correct in the new passport. My questions are: Will I have problems travelling to US if my new passport says my given name as "my first name" and surname as "My last name" but my valid visa on old passport says given name as FNU and Surname as "my first name" Or should I again apply for my new passport with just my first name and keeping my surname as blank, which I am not in favor of. |
I am looking for the mean and variance of a bernoulli distribution of two normally distributed random variables. An example would be as follows: A coin flip heads: draw from a $N(\mu1,\sigma1)$ tails: draw from a $N(\mu2,\sigma2)$ For the expected value of the coinflip I would think it equals $p*\mu1+(1-p)*\mu2$. Where $p$ is 0.5 in this case. But I have no idea how to compute the variance of this bernoulli distribution. Could somebody help me with this? | Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know that the mean of this mixture would be $\mu_{AB} = (p\times\mu_A) + (q\times\mu_B)$. What would the variance be? A concrete example would be if I knew the parameters for the distribution of male and female height. If I had a room of people that was 60% male, I could produce the expected mean height for the whole room, but what about the variance? |
When I add a loop cut I get this cross hatching effect. If I add one to the other side as well, then the whole object gets that effect. I've tried changing the shading from flat to smooth, and back. I've recalculated normals, I've removed doubles(0). It doesn't seem to affect the render at least, but i'm not sure if it'll affect anything else like the materials. Or is it just a random glitch that wont do anything else. I've restarted my blender and it didn't take it away either, so I'm lost. | For instance, here I have two cubes that are offset only on the x-axis. When I render them (using Blender's internal renderer), the overlapping faces interfere with each other and the result looks awful. A quick and easy solution would be to offset them by just a smidget, but is there another solution that allows faces to overlap and not exhibit this graphical glitch? |
I have a Netherlands texts saved in my table. They show well in MySQL table like this Wilt u hoogstens één of twee kinderen, ook al kunt u zich qua gezondheid en inkomen meer kinderen permitte When I select that text and do an echo with PHP I get Wilt u hoogstens ��n of twee kinderen, ook al kunt u zich qua gezondheid en inkomen meer kinderen permitte. I tried to set the PHP page to use <meta http-equiv="content-type" content="text/html; charset=utf-8"> and also tried to do echo utf8_decode($text) but the text is still not showing as in the table. Any help on this please? Thanks. Note: the table field collation where the text is stored is utf8mb4_general_ci To select the text from my table I'm using PHP PDO: function get_questions($userBrowserLanguage, $dbh) { $query = "SELECT Frage, FrageNr FROM `tbl_fragen` WHERE Language = ? AND Test = ? AND Frage != ? ORDER BY FrageNr ASC"; $parameters = array('nl', 'OCA55', '');//$userBrowserLanguage $sth = do_query($query, $parameters, $dbh); $questions = array(); while ($question = do_fetch_result($sth)) { array_push($questions, array($question['FrageNr'], $question['Frage'])); } return $questions; } | I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1. Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur? This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2. |
I've attached an image below of artifacting that happens with 3D text when you push the 'depth' parameter to extremes. The artifacts look as if a vertex on the letters has been pulled out really far resulting in large spikes. I want to understand why this is happening because I would like to know how to fix this issue If I ever wanted to use this effect for stylistic purposes I want to know how to recreate it. Thanks! | I exported an svg 1.1 file from Adobe Illustrator CS6. I joined all the shapes by pressing Ctrl+J. I set the curve shape to 2D. Then I extruded using the right hand side panel: So far so good. But when I try to apply even a slight bevel, all hell breaks loose: It does get less insane if I bring the bevel down by multiple factors of 10... But then I really don't have much of a bevel. Am I doing something wrong? Am I using the wrong kind of object? Should I be doing this with meshes? Do my curves just need cleaning up? |
can any one help in changing the onclick javascript button to lightning component?..becasuse javascript button are not supported in lightning. {!REQUIRESCRIPT("/soap/ajax/37.0/connection.js")} var Suite = '{!Contract__C.Suite__c}'; var check = '{!Contract__C.Notification_check__c}'; var amount= '{!Contract__C.amount__c}'; var blackReview = '{!Contract__C.black_Review__c}'; var blackReview= blackReview!= '' && blackReview!= 'No'; var Suite = Suite != ''; var amount= Number(amount.replace(/[^0-9\.]+/g,"")); amount = amount>=1000.00; //alert(blackReview+" "+ amount+" " +Suite ); if ((amount|| blackReview|| Suite)&& check == 0){ var con= new sforce.SObject("Contract__C"); con.id = "{!Contract__C.Id}"; con.Notification_check__c = 1; result = sforce.connection.update([con]); } | We depend on a javascript button to allow our salesforce screens to interact with another web application. We read some elements from the salesforce contact, and then call a js func hosted on another web site to pass that contact info to the other web site. The js func has a call back, so when the other web site is finished, our js in salesforce can save some data to the salesforce contact. But.... as lightning lacks javascript buttons, we have been locked out of lightning. I just found this: But it is not clear: Can I do a javascript button now in lightning, or do I still need to wait for more pieces from salesforce? We would love to have a path forward with lightning. |
It's weird that creating desktop shortcuts is currently so primitive. I found the following: That helps. However, if there's something wrong with the shortcut, it just doesn't do anything. For instance, I tried to create a shortcut for this command line to create a shortcut. When I double-click it, it just does nothing. This is the resulting text of my "Create Desktop Shortcut.desktop" file on the desktop: [Desktop Entry] Version=1.0 Type=Application Terminal=false Icon[en_CA]=gnome-panel-launcher Exec=/usr/bin/gnome-desktop-item-edit ~/Desktop/ --create-new Name[en_CA]=Create Desktop Shortcut Name=Create Desktop Shortcut Icon=gnome-panel-launcher As I said, when I double-click this, or right-click it and select Open, nothing happens. Is there a log file where something about this would be written to? | In older versions it was easy to create a launcher on my desktop. All I had to do is right click on my desktop and select the "create launcher" option. How can I create such launchers now? |
Complex numbers are essentially 2-dimensional vectors with product defined such that the set is a field and extends real product. So, is there an analogous definition for 3, or higher, dimensional vectors such that the Euclidean space becomes a field also? | If complex numbers are in some sense 2 dimensional numbers, would it be useful or logical to extend the complex number system to a system of 3-dimensional or even n-dimensional numbers? If this does not make sense in general, why does it make sense only to extend from the 1st dimension to the 2nd dimension? What is special about 2-dimensional numbers that they are needed but n-dimensional numbers are not? I know that we have $R^k$, which is in some sense a field of $k$ dimensional numbers, but that is very different from the way in which complex numbers are constructed. So my question is could the complex numbers be extended to a 3rd dimension (or even an nth dimension) in the same way that the real numbers are extended to the complex numbers, in which the properties of complex numbers are preserved as a subset of this higher dimensional space? |
I'm trying to select calendar event titles that have a specific word and use this to change the background colour of the event. Please see my code below. This changes all events to have the background colour of red even if event title doesn't contain the word 'Test'. I've even changed 'Test' to 'uhrguqhergoieqhrgeurgherogih' but it still changes everything. Unfortunately I can't see anything similar on SO so hopefully one of you could help me out please! :) Thanks in advance! $(window).on('load', function() { if($(".fc-event-title:contains('Test')")) { $('.fc-event').css('background-color', 'red'); } }); | How can I check the existence of an element in jQuery? The current code that I have is this: if ($(selector).length > 0) { // Do something } Is there a more elegant way to approach this? Perhaps a plugin or a function? |
I know this is a rlly dumb question (sorry) but is there a way to set up parental controls on my ubuntu 14.04 computer? Thanks in advance | I bought my kids a PC and installed 12.04 (Unity) on it. The bottom line is, I want my children to use the computer unsupervised while I have confidence they cannot access anything inappropriate. What I have looked at: I was looking at Scrubit a tool which allows me configure my wifi router to block content and this solution would also protect my other PC and mobile devices. This may be overkill as I just want the solution to work on one PC. I also did some Google searches and came across the application called . My experience of OSS is that the best solutions frequently never appear first on a Google search list and in this case I need to trust the methods therefore my question is very specific. I want to leverage your knowledge and experience to understand What is the best way to restrict adult content on 12.04 LTS as this is important to me. It maybe a combination of things so please don't answer this question "try this or that", then give me some PPA unless you can share your experience of how good it is and of course if there are any constraints. |
I am a non-native speaker and I was just wondering whether it is stylistically and grammatically correct to write something like "smart me made the same mistake again" or "Intelligent me could not solve the riddle" is this similar to saying "fifteen-year-old me?" Can I say "my smart self" instead ? | I'm trying to find out how come we say lucky me and stupid us rather than lucky I and stupid we. My understanding is that this is not a recent invention, but a relic from the distant past where it was a dative construction. However, I don't see the reason for using any case other than the nominative in this construction to begin with. He went surfing. → Lucky him went surfing. I got pulled over. → Stupid me got pulled over. They bought a house. → Thoughtless them bought a house. This is rather intriguing. After thinking about it for a while, I couldn't come up with any other language, Germanic or otherwise, where simply introducing an adjective would dictate a change of grammatical case. This appears to be an English peculiarity. How far can it be traced back? Can anyone comment on its background? |
ETA: In case someone notices the similarity, this question is not a duplicate of . Which statement is true about the sequence $\{f(n)\}$: $$ \left\{ \begin{array}{l} f(1)=1 \\ f(2n)=f(n) \\ f(2n+1)=f(n)+f(n+1) \end{array} \right. $$ a)All prime numbers appear in $\{f(n)\}$ b)All Mersen primes appear in $\{f(n)\}$ c)A finite set of primes appear in $\{f(n)\}$ d)Just primes of the form $4t-1$ appear in $\{f(n)\}$ It's seen that $f(2n)=1$ but I'm not sure that $f(2n+1)$ generates which primes... | An arithmetic function is defined as follows:$f(1)=1$, $f(2k)=k$ and $f(2k+1)=f(k)+f(k+1)$. When (for which $k$) is $f(k)$ even? While it is obvious that $f(4n-1)=f(4n)=2n$, therefore $f(k)$ is even for $k=4n$ and $k=4n-1$, which is possible to prove using induction (isn't it?), I don't know how to prove the converse. I tried to solve the recurrence or make use of constant difference between certain elements of the sequence $\ldots$ What am I missing? Thank you. |
I'm looking for a way to know if the cpu of my linux system is running in 64 bit mode. I've got to programm it for the university. My idea was to create something like an function that provides me that information. I'm not sure how should I start. Can somebody give me an idea?. My university give me a code, but I'm not able to check the length of the parameter that the main is sending to the funktion is64bit. My code is this: int main() { uint32_t msr = assembleMSR( 0, 0, 0, 0 ); printf("assembled MSR is %#x, should be 0\n", msr); printf("is64BitMode(&msr) should be 0, is %d\n", is64BitMode(&msr)); printf("is64BitMode(&msr) should my EXAMPLE, is %d\n", is64BitMode(&msr2)); enableInts( &msr); printf("MSR with ints enabled is %#x, should be 0x8000\n", msr); return 0; } int is64BitMode ( uint32_t *MSR ) { int longi=sizeof(MSR); printf("longi de size of%d\n", longi); printf("%d\n", __WORDSIZE);// with this sentence i know that my cpu is running on 64 bits. (void) MSR; return 0; /* TODO */ } | When I type uname -a, it gives the following output. Linux mars 2.6.9-67.0.15.ELsmp #1 SMP Tue Apr 22 13:50:33 EDT 2008 i686 i686 i386 GNU/Linux How can I know from this that the given OS is 32 or 64 bit? This is useful when writing configure scripts, for example: what architecture am I building for? |
In order to create one USB stick with 18.04 for 32 bit, can someone tell me where is the iso file and its name for 32bit architecture PC to install ubuntu 18.04 as I am unable to find the exact link for 32 bit. Ubuntu desktop 18.04 is saying its for 64bit. | Why is there no 32 bit ISO for the new Ubuntu 18.04? |
I am writing a project which makes use of the MS Chart for .net 3.5 utility. However, either all users will also need to install this, or I need to package the dll with the program. I can get Visual Studio to copy the dll to the folder with the program, but is it possible to make it embed the dll, so that there is only the one file? I have seen several external programs out there, but surely there must be a way in Visual Studio - and would it work with a MS .net dll? | Is it possible to embed a pre-existing DLL into a compiled C# executable (so that you only have one file to distribute)? If it is possible, how would one go about doing it? Normally, I'm cool with just leaving the DLLs outside and having the setup program handle everything, but there have been a couple of people at work who have asked me this and I honestly don't know. |
I've always heard of such statements as $SU$ group describing our world even before I seriously learned physics. When learning about spin, someone spoke of $SU(2)$ but did not seriously explain. When learning isospin and hypercharge for particles made of $u, d, s,$ someone spoke of $SU(3)$ but did not give detailed explanation. When talking about the discovery of J/ψ, teacher (a experimentalist) say, well now with the charm quark, we need $SU(4)$. I am crazy, $SU$ is just special unitary matrix group, what are they talking about when relating these matrix with spin or particles? I hope someone could give me a detailed explanation about how these group is related to real world substances or recommend a book. | I was hoping someone could give an overview as to how the Lie groups $SO(3)$ and $SU(2)$ and their representations can be applied to describe particle physics? The application of Lie groups and their representations is an enormous field, with vast implications for physics with respect to such things as unification, but I what specifically made these groups of physical importance and why there study is useful. I have just started studying these two groups in particular, but from a mathematical perspective, I'd very much appreciate understanding some sort of physical motivation. |
I came across the following example from the textbook Advanced Grammar in Use by Martin Hewings. To say that we think a past situation actually happened, we use will have + past participle: As it was cloudy, few people will have seen last night’s lunar eclipse. Why isn't the past simple or past perfect used in the aforementioned example? As it was cloudy, few people saw last night’s lunar eclipse. | Non-native speakers often get confused about what the various tenses and aspects mean in English. With input from some of the folk here I've put together a diagram that I hope will provide some clarity on the matter. I offer it as the first answer to this question. Consider it a living document. Input is welcome, and good suggestions will be incorporated into the diagram. Nota bene: What this is not is a discussion of whether there are more than two tenses in English. , to which this question is not intended to supply arguments one way or the other. Here, the aim is to provide an overview of what constructions English-speaking people use for conveying information about actions referring to past, present, and future, and to provide it first and foremost to precisely the people who are likely to use "tense" as a catch-all term in their search, rather than to linguists who know better. Breaking News There is now an excellent ELU blog article titled . It is highly recommended reading. |
change the order of integration in $$\int_0^{2a}\int_0^{\sqrt{2ax-x^2}}\frac{\phi'(y)(x^2+y^2)x}{\sqrt{4a^2x^2-(x^2+y^2)^2}}dy\,dx$$ I was able to change the order of integration here to $$\int_0^a\int_{a-\sqrt{a^2-y^2}}^{a+\sqrt{a^2-y^2}}\frac{\phi'(y)(x^2+y^2)x}{\sqrt{4a^2x^2-(x^2+y^2)^2}}dx\,dy$$ Now i am stuck with the integration here w.r.t $x$. I tried substituting $(x^2+y^2)^2$ with $t$ but then replacing value of $4a^2x^2$ becomes a problem. I was thinking of substituting both $x$ and $y$ as $k\cos\theta$ and $k\sin\theta$ but then $y$ won't be constant w.r.t $x$, so that too I believe is out of the question! | Change the order of integration in: $$\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x }{\sqrt{4a^2x^2-(x^2+y^2)^2}}dxdy$$ and hence evaluate it. I changed the order of integration and got the limits $y=0$ to $a$ and $x=a-\sqrt{a^2-y^2}$ to $a+\sqrt{a^2-y^2}$. I then tried changing to polar coordinates, but it is only making the integrand more complex. |
Suppose $X\sim \bf{N}_m(\bf{\mu}, \bf{\Sigma})$ where the covariance matrix $\bf \Sigma$ is positive definite. Show that the distribution of $X^T{\bf{B}}X \sim \chi^2(\bf{tr(B\Sigma)})$where $\bf B$ satisfies $\bf{B\Sigma B}=\bf{B}$ $\bf\mu^TB\mu=0$ Now, previously I had done this result, when $\Sigma$ was replaced by $\bf{I}$ and $B$ was idempotent. This one is where I am stuck. I have found that $\bf B\Sigma$ and $\bf \Sigma B$ are idempotent. Now, I tried to find some $U\sim \bf{N_{\text{tr}(B\Sigma)}}(0, I)$ such that $U^TU=X^T{\bf{B}}X$ then we would be done, but I can't seem to find such an $U$. Can someone help me? Thanks. | Suppose $\underline{X}$ is an $m$-dimensional vector following multivariate Normal distribution i.e. $\underline{X}$~$N_m(\underline{\mu},\Sigma)$ where $\Sigma$ is positive definite. Let $B$ be a symmetric $m$ by $m$ matrix, having the following properties: $B\Sigma B=B$ $\underline{\mu}'B\underline{\mu}=0$ $trace(B\Sigma)=k$, where $k<m$ Prove that $\underline{X}'B\underline{X}$ follows chi-squared ($k$). I proceeded a lot but got stuck in one last step where I think linear algebra is troubling me. Kindly have a look at my "solution". The second condition can be written as $\underline{\mu}'B\Sigma B\underline{\mu}=0\implies B\underline{\mu}=\underline{0}$ as $\Sigma$ is Positive definite. Then after a little algebra and considering condition 2, we can write $\underline{X}'B\underline{X}=(\underline{X}-\underline{\mu})'B(\underline{X}-\underline{\mu})=(\underline{X}-\underline{\mu})'B\Sigma B(\underline{X}-\underline{\mu})$ But $\Sigma$ is positive definite hence we can have a symmetric matrix $\sqrt{\Sigma}$ defined such that $\sqrt{\Sigma}\sqrt{\Sigma}=\Sigma$. Using this, we can write $(\underline{X}-\underline{\mu})'B\Sigma B(\underline{X}-\underline{\mu})=(\sqrt{\Sigma}B(\underline{X}-\underline{\mu}))'(\sqrt{\Sigma}B(\underline{X}-\underline{\mu}))$ We want to show that this follows chi-squared ($k$). Now, it is obvious that as $(\underline{X}-\underline{\mu})$~$N(\underline{0},\Sigma)$, $\sqrt{\Sigma}B(\underline{X}-\underline{\mu})$~$N(\underline{0},\sqrt{\Sigma}B\Sigma B\sqrt{\Sigma})=N(\underline{0},\sqrt{\Sigma}B\sqrt{\Sigma})$ Now, $trace(\sqrt{\Sigma}B\sqrt{\Sigma})=trace(B\Sigma)=k$ and $\sqrt{\Sigma}B\sqrt{\Sigma}$ is idempotent (verified). So its eigenvalues are only $0$ or $1$. Since its trace is $k$, there are $k$ eigenvalues with value $1$ and other $m-k$ eigenvalues are $0$. Now here is the thing I want to prove: I want to show that$\sqrt{\Sigma}B\sqrt{\Sigma}$, which is the covariance matrix, is diagonal and has only $k$ $1$'s and remaining $m-k$ diagonal entries $0$. The reason is, then I will be able to say that $k$ components of $\sqrt{\Sigma}B(\underline{X}-\underline{\mu})$ are independent standard normals whose sum of squares is our quadratic form and thus it follows chi-squared ($k$). But I really could not show that $\sqrt{\Sigma}B\sqrt{\Sigma}$ has the desired property i.e. it is diagonal with rank $k$. But this is crucial, it is the finale. If this does not happen, then some components will be correlated with each other and we cannot say that our quadratic form has chi-squared ($k$). I would really appreciate if someone helped me to prove this final part. |
I recall a short story I read many years ago about a soldier or scientist being sent forward in time to see if man survives overpopulation and if we do, how we solved the overpopulation problem. The answer was a literal "war of the sexes". The protagonist even has to drop his pants at one point to prove he's a man so some guy guarding a library (?) won't shoot him. I can't remember the title or the author's name but I believe it was in a short story collection about time travel. | Here's what I remember about it: The protagonist is sent a relatively short distance into the future (maybe a year? I've forgotten). When he arrives in this "future" he finds himself in a completely different world, with non-human inhabitants. The inhabitants use a machine to teach him their torturous language. He tries to return home, and (eventually) finds himself in a realm of chaos/nothingness. He laboriously reconstructs in his mind everything he can remember about his home and finds himself back there somehow. The twist is that in his "home" reality everyone speaks the language he was taught by the non-human inhabitants at his first stop. |
I read the Wikipedia article about Cell Potency Totipotency is the ability of a single cell to divide and produce all of the differentiated cells in an organism. while pluripotency means a stem cell that has the potential to differentiate into any of the three germ layers: endoderm, mesoderm, or ectoderm. I don't quite understand the difference, then, between a totipotent and a pluripotent cell. | Both develop into specialized cells.Then how are they different? |
I have a question that I don't know how to solve. For which $n \in \mathbb{N}$ do we have $$\sum\limits^n_{k=0} k^3 = (\sum\limits^n_{k=0} k)^2\quad ?$$. Here's what I've tried: \begin{align*}\sum\limits^n_{k=0} k^3 = (\sum\limits^n_{k=0} k)^2 & \Leftrightarrow 1+8+27+\cdots+n^3 = (1+2+3+\cdots+n)^2\\ & \Leftrightarrow \sqrt{1+8+27+\cdots+n^3} = 1+2+3+\cdots+n \end{align*} | I recently proved that $$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k \right)^2$$ using mathematical induction. I'm interested if there's an intuitive explanation, or even a combinatorial interpretation of this property. I would also like to see any other proofs. |
Is there an easy and efficient way to put multiple venn-diagrams in a single line? Either force the compiler to ignore the line break or shift all of the coordinates in the second one? I'm open to any solution. \documentclass{article} \usepackage{tikz} \def \setA{ (0,0) circle (1cm) node {$A$}} \def \setB{ (1.5,0) circle (1cm) node {$B$}} \def \myrectangle{ (-2, -1.5) rectangle (3.5, 1.5) } \begin{document} \begin{center} \begin{tikzpicture}[scale=0.6] \draw \myrectangle node[below left]{$U$}; \fill[gray] (0,0) circle (1cm); \fill[gray] (1.5,0) circle (1cm); \draw \setA; \draw \setB; \end{tikzpicture} \begin{tikzpicture}[scale=0.6] \draw \myrectangle node[below left]{$U$}; \begin{scope} \clip \setA ; \fill[gray] \setB ; \end{scope} \draw \setA; \draw \setB; \end{tikzpicture} \end{center} \end{document} | I like my code to look like this: \documentclass{article} \begin{document} \begin{enumerate} \item test text \begin{enumerate} \item 1 \item 2 \item 3 \item 4 \item 5 \end{enumerate} \end{enumerate} \end{document} For the sake of readability I like to put a blank line before a new environment starts. In the particular case I'm considering, the blank line adds some vertical space between the item from the first level enumerate and the first item from the second level enumerate. So my question is: is there a best practice to format code related to blank lines before environments start? Should I avoid it? Should I comment out the blank line? Clarification: I'm talking about the vertical space between "test text" and "1". But, I'm not asking for a way to remove the extra space added by the blank like, I already know how to do that. My reasoning is the following: Since adding a blank like before a new enumerate adds vertical space, it means that that blank line is meaningful for TeX. Since it is meaningful for TeX, is it OK to use it for the mere purpose of formatting code or should I avoid it? |
Not sure if I should use crime science or Crime Science throughout my essay. When should I capitalize the term? | Do I say "I study computer science," or "I study Computer Science"? Similarly, "I really liked that computer science course," vs. "I really liked that Computer Science course." |
So I was trying to mount a drive on boot. I was editing /etc/fstab and then I rebooted to see if my drive would mount on boot. Now I can't do anything. The prompt I see Give root password for maintenance (or press Control-D to continue): When I press Control-D this prints: sulogin: cannot read /dev/tty1: Operation not permitted I've tried all kinds of root passwords but none of them work. I tried to tap shift while it boots and nothing happens. EDIT: This question is not a duplicate because when I press Control-D at the prompt I get an error message I'm on a Pine64. Is there any way to salvage the device or save the files? Bootable USB's do not work | I need to reset my password. I have followed these steps: However, then I go to "root" or "netroot" recovery options, it tells me: Give root password for maintenance (or type Control-D to continue) Clearly, I do not know the root password. If I type CTRL+D, I return to the list of options. From I read: Under chapter 'The Other Way': 4. Highlight the line that begins kernel and press 'e' to edit` But in the grub configuration file I have no line that starts with kernel. Only: setparams 'Ubuntu...' recordfail set gxfpayload... insmod part_msdos insmod ext2 set root=... search --no-floppy... linux /boot/vmlinuz-2.6.38... initrd /boot/initrd.img-2.6.... Those are all lines in my GRUB. Which line should I edit? Or is there another way to reset my password? |
Over a long enough time, everybody who has asked a half-decent question, or posted a half-decent answer, will gain access to the moderation tools. There is a natural "inflation" to the rep system in regards to the features that unlock. The rep system was supposed to only unlock features for users who have proven themselves "trusted" through high-ranking activity on the site... but over time, that will eventually include just about everyone, whether they've been good members or not. Is this a problem? If not, why not? | Overall reputation scores are headed nowhere but up. Pretty soon there will be thousands of mods. What to do? Thoughts on possibilities: Thousands of mods is fine. Carry on. Adjust the threshold values for high-level SO privileges. Do a straight-up inflation adjustment. You had x rep, then at the turn of the year we applied the Consumer Rep Index to all scores, now you have (x / inflation) rep. Implement a rep decay mechanism, so that inactivity sheds some of the overall rep that's built up. |
I bought a domain name for new site. Within a month, on a domain, there was nothing but an empty root directory of the page something like "Index of / [ICO] Name Last modified Size Description". I read that for new domains until developing is best to make a page with a brief description of the future site. Very soon I will publish my site on hosting, will i have a negative seo impact for last month with a blank page? Pretty nice domain, but as long as there is a possibility I can change him beforehand. Is there at least some sense to me to do so? | I am currently developing a website which is going to take some time to finish. I need to move some 'stuff' to production frequently, while maintaining a under construction status. My front page will clearly mention that my website is under construction. I know crawlers will access my URL before I am ready to go live. Should I tell them my site is under construction (no need to index)? If yes how? P.S.: Eventually, I am ok to let them see my under construction front page. |
Why is ${\rm d}\vec{A}_1$ pointing up and ${\rm d}\vec{A}_2$ pointing down? Electric field ${\rm d}\vec{E}_1$ is pointing up so isn't it supposed to be perpendicular to the surface? | Why does S3 equal to 0 ? for E3 dot dA = 0? Could I also know why does dA1 and dA2 point up and down? while dA3 point to the right? |
$$\begin{cases} \frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} = 0, &x\in\mathbb{R},\ t>0\\ u(x,0) = u_0(x), &x\in\mathbb{R}. \end{cases}$$ Which choices of the following functions for $u_0$ yield a $C^1$ Solution $u(x,t)$ for all $x\in\mathbb{R}$ and $t>0$ $1)$ $u_0 (x) = \frac{1}{1+ x^2}$ $2)$ $u_0(x) = x$ $3)$ $u_0(x) = 1+x^2$ $4)$ $u_0(x) = 1+2x$ My answer key says the answer is $2$ and $4$. My question is why we should reject option $1$ and $3$? $$\frac{dt}{1} =\frac{dx}{u}= \frac{du}{0}$$ gives me $u=c_1$ and $ut-x=c_2$ where $c_1$ and $c_2$ are constants. Now by condition given in Option $1$ I get a relation between constants I.e $$c_1= \frac{1}{1+(c_2)^2}.$$ Then I have the solution $$u = \frac{1}{1+ (ut-x)^2}.$$ Then why we reject option $1$? | Consider the Cauchy Problem of finding $u(x,t)$ such that $$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=0,x\in\mathbb{R},t>0$$ $$u(x,0) = u_0(x), x\in\mathbb{R}$$ Which choices of the following functions for $u_{0}$ yield a $C^{1}$ solution $u(x,t)$ for all $x\in\mathbb{R},t>0$ $u_{0}(x)=\frac{1}{1+x^{2}}$ $u_{0}(x)=x$ $u_{0}(x)=1+x^{2}$ $u_{0}(x)=1+2x$. If I use the existence and uniqueness theorem for Cauchy problem i get the corresponding determinant is non zero so all are true according to me. But in answer key only option 2nd and 4th is given. Please help me to solve the problem. Thanks a lot. |
Let $f\in C(\mathbb{R})$ be a function that satisfies $\displaystyle\lim_{x\to\pm\infty}f(x)=+\infty$. Show that $f$ attains its absolute minimum, i.e. there is a point $x_0\in\mathbb{R}$ such that $f(x)\geq f(x_0)$ for all $x\in\mathbb{R}$. I was thinking about studying the set $M=\{L\in\mathbb{R}: f(x)\geq L, \forall x\in\mathbb{R}\}$. But I'm not sure if this is the right way to proceed. | If $f:\mathbb{R}\to\mathbb{R}$ is continuous and $$\lim_{x\to\infty}f(x)=\lim_{x\to-\infty}f(x)=\infty$$ Prove that $f$ has a minimum on $\mathbb{R}$; that is, there is an $x_m\in\mathbb{R}$ such that $$f(x_m)=\inf_{x\in\mathbb{R}}f(x)<\infty$$ I think the best approach would be to prove the existence of a lower bound, that is $\exists M\in\mathbb{R}:M<f(x),\forall x\in\mathbb{R}$, but I don't know how to do this. I am probably supposed to use the extreme value theorem or the intermediate value theorem, but I don't know how to do that. |
I come from a scripting background and the preprocessor in C has always seemed ugly to me. None the less I have embraced it as I learn to write small C programs. I am only really using the preprocessor for including the standard libraries and header files I have written for my own functions. My question is why don't C programmers just skip all the includes and simply concatenate their C source files and then compile it? If you put all of your includes in one place you would only have to define what you need once, rather than in all your source files. Here's an example of what I'm describing. Here I have three files: // includes.c #include <stdio.h> // main.c int main() { foo(); printf("world\n"); return 0; } // foo.c void foo() { printf("Hello "); } By doing something like cat *.c > to_compile.c && gcc -o myprogram to_compile.c in my Makefile I can reduce the amount of code I write. This means that I don't have to write a header file for each function I create (because they're already in the main source file) and it also means I don't have to include the standard libraries in each file I create. This seems like a great idea to me! However I realise that C is a very mature programming language and I'm imagining that someone else a lot smarter than me has already had this idea and decided not to use it. Why not? | I recently had cause to work with some Visual Studio C++ projects with the usual Debug and Release configurations, but also 'Release All' and 'Debug All', which I had never seen before. It turns out the author of the projects has a single ALL.cpp which #includes all other .cpp files. The *All configurations just build this one ALL.cpp file. It is of course excluded from the regular configurations, and regular configurations don't build ALL.cpp I just wondered if this was a common practice? What benefits does it bring? (My first reaction was that it smelled bad.) What kinds of pitfalls are you likely to encounter with this? One I can think of is if you have anonymous namespaces in your .cpps, they're no longer 'private' to that cpp but now visible in other cpps as well? All the projects build DLLs, so having data in anonymous namespaces wouldn't be a good idea, right? But functions would be OK? |
A random variable $X$ is lognormal if ln $X$, the natural logarithm of $X$, is normally distributed. Find the mean and variance of a lognormal random variable with $ln X ∼ N(µ, σ^2)$ How should I solve this using the moment generating function of normal distribution, without differentiation? | The computed moments of log normal distribution can be found . How to compute them? |
I am trying to call methods of one class in another class but every time I am getting the same Exception in thread "main" java.lang.NullPointerException error... Please look into the code below and guide me.... Class: 1 public class CurrencyConverter { double[] exchangeRates; void setExchangeRates(double[] rates) { //set instance methods exchangeRates = rates; } void updateExchangeRates(int arrayIndex, double newVal) { exchangeRates[arrayIndex] = newVal; } double getExchnageRates(int arrayIndex) { return exchangeRates[arrayIndex]; } double computeTransferAmount(int arrayIndex, double amount) { return amount * getExchnageRates(arrayIndex); } void printCurrencies() { System.out.println("\nrupee: " + exchangeRates[0]); System.out.println("dirham: " + exchangeRates[1]); System.out.println("real: " + exchangeRates[2]); System.out.println("chilean_peso: " + exchangeRates[3]); System.out.println("mexican_peso: " + exchangeRates[4]); System.out.println("_yen: " + exchangeRates[5]); System.out.println("$australian: " + exchangeRates[exchangeRates.length-1]); } public static void main(String[] args){ CurrencyConverter cc = new CurrencyConverter(); double[] rates = {63.0, 3.0, 3.0, 595.5, 18.0, 107.0, 2.0}; cc.setExchangeRates(rates); //calling setExchangeRates methods rates = new double[]{65.0, 3.0, 3.0, 595.5, 18.0, 107.0, 2.0}; rates = new double[]{65.0, 3.0, 3.0, 595.5, 18.0, 107.0, 2.0}; cc.setExchangeRates(rates); cc.printCurrencies(); cc.updateExchangeRates(0, 66.0); cc.printCurrencies(); double amount = cc.computeTransferAmount(0, 1000); System.out.println("\nTransferred Amount: " + amount); } } Class 2 : public class MoneyTransferService { CurrencyConverter cc = new CurrencyConverter(); double computeTransferAmount(int countryIndex, double amount) { return cc.computeTransferAmount(countryIndex, amount); } double computeTransferFee(int countryIndex, double amount) { double transferAmount = computeTransferAmount(countryIndex,amount); double transferFee = transferAmount * 0.02; return transferFee; } public static void main(String[] args) { MoneyTransferService transferService = new MoneyTransferService(); double transferAmount = transferService.computeTransferAmount(0, 1000); double transferFee = transferService.computeTransferFee(0, 1000); System.out.println("transferAmount: " + transferAmount); System.out.println("transferFee: " + transferFee); } } | What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them? What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely? |
I have a country drop down, and on change of it I return a div containing the same country drop down with additional fields. I replace this entire div using the below code. But after the replace of div is done, the on change event stops working further. How can I fix this ? $("#country).on("change", function(){ var str = $("#myform").serialize(); $.ajax({ type: 'POST', data:str, url:'../changeme', success: function(data){ debugger; var html = $.parseHTML(data); var arrSelector = $(html).find('div[data-refresh=true]'); var i; for(i=0;i<arrSelector.length;i++) { $('#' + arrSelector[i].id).replaceWith($($(data)).find('#' + arrSelector[i].id)); } }, done:function(data){ }, error:function(data){ }, complete:function(data){ } }); }); }, | I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off. This happens on page ready and works just fine. The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound. I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option. |
I am trying to remember the name of a Fantasy series from the 1980's. It contained at least 7 novels. I remember it was about a magic bottle that was entered by use of the ring. Each novel, whilst a separate story, was connected to the others, building the story of the bottle from different perspectives. Went to re-read them but found they had been "tidied away" during a house move. Any ideas on either title of the series or one of the books? | I have vague recollection of a book (possibly a short series) that involved a bottle trap. When you interacted with the bottle, you were sucked into it and found yourself in a multi-level 'dungeon'. I think there might of been a bottle at that bottom to get yourself out. The same book might have had something about having slow conversations with stones, but it might not and I am really just interested in the bottle concept. It certainly was not written this century. If I had to guess, I would say the 80's, but that is only a guess. |
The date is not displayed correctly in the inferior part of my slides. \documentclass{beamer} \mode<presentation> { \usetheme{Madrid} % or try default, Darmstadt, Warsaw, ... \usecolortheme{default} % or try albatross, beaver, crane, ... \usefonttheme{serif} % or try default, structurebold, ... \setbeamertemplate{navigation symbols}{} \setbeamertemplate{caption}[numbered] } \usepackage[utf8]{inputenc} \usepackage[spanish]{babel} \usepackage{chemfig} \usepackage[version=3]{mhchem} \usepackage{caption} \usepackage{epstopdf} \usepackage{comment} \usepackage{graphicx} \usepackage{subfig} \definecolor{ao(english)}{rgb}{0.0, 0.5, 0.0} \usepackage{pgfpages} \pgfpagesuselayout{resize to}[% physical paper width=8in, physical paper height=6in] \title[Unal%iversidad Nacional de Colombia ]{} \author{Juan Muñoz } \date{\today} \begin{document} \begin{frame} \titlepage \end{frame} % These three lines create an automatically generated table of contents. \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \end{document} | When the number of slides of my beamer is more than 10, the date is not displayed correctly in the inferior right corner of my slides. \documentclass{beamer} \mode<presentation> { \usetheme{Madrid} % or try default, Darmstadt, Warsaw, ... \usecolortheme{default} % or try albatross, beaver, crane, ... \usefonttheme{serif} % or try default, structurebold, ... \setbeamertemplate{navigation symbols}{} \setbeamertemplate{caption}[numbered] } \usepackage[utf8]{inputenc} \usepackage[spanish]{babel} \usepackage{chemfig} \usepackage[version=3]{mhchem} \usepackage{caption} \usepackage{epstopdf} \usepackage{comment} \usepackage{graphicx} \usepackage{subfig} \definecolor{ao(english)}{rgb}{0.0, 0.5, 0.0} \usepackage{pgfpages} \pgfpagesuselayout{resize to}[% physical paper width=8in, physical paper height=6in] \title[Unal%iversidad Nacional de Colombia ]{} \author{Juan Muñoz } \date{\today} \begin{document} \begin{frame} \titlepage \end{frame} % These three lines create an automatically generated table of contents. \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \begin{frame} \end{frame} \end{document} ¿How could I fix it? |
If the gcd(s, t)=1, prove $F_s F_t$ divides $F_{st}$ for all s,t > 1 $F_n$ is the Fibonacci sequence, such that $$F_n = F_{n-1} + F_{n-2}$$ I know that it needs to be shown that $F_s F_t\mid F_{st}$ which has the implication that $F_{st} = F_s F_tk$. I considered that it may be useful to use the theorem that states: the gcd of two fibonacci numbers is also a Fibonacci number with the form $\gcd(F_s,F_t)= g$ where $g= \gcd(s,t)$ or a Corollary relating to this theorem. But I cannot see how this directly applies to the problem. Is it valid to say that because a theorem states for any $s>1, t>1$, $F_{st}$ is divisible by $F_s$ then that is an implication for $F_s F_t\mid F_{st}$ because the $\gcd(s,t) =1$? | Can any one give a generalization of the following properties in a single proof? I have checked the results, which I have given below by trial and error method. I am looking for a general proof, which will cover the all my results below: Every third Fibonacci number is even. 3 divides every 4th Fibonacci number. 5 divides every 5th Fibonacci number. 4 divides every 6th Fibonacci number. 13 divides every 7th Fibonacci number. 7 divides every 8th Fibonacci number. 17 divides every 9th Fibonacci number. 11 divides every 10th Fibonacci number. 6, 9, 12 and 16 divides every 12th Fibonacci number. 29 divides every 14th Fibonacci number. 10 and 61 divides every 15th Fibonacci number. 15 divides every 20th Fibonacci number. |
Suppose I want to cast Dispel Magic (at 3rd level) on a target that has one beneficial spell on it and one harmful spell on it. I only want to dispel the harmful spell and leave the beneficial spell intact. Clearly, if the beneficial spell is 3rd level or lower, I am out of luck, since it is dispelled automatically. However, if the beneficial spell is of a higher level, it is only dispelled with a successful spellcasting ability check. Can I choose to fail this check on purpose to ensure that the beneficial spell is not dispelled while still attempting to dispel the harmful spell? Another less likely context where this might come up would be if I was being forced under duress to dispel a spell, and I wanted to pretend to try and fail. This seems somewhat similar to about destroying a spell scroll by intentionally misreading it, but it also seems different enough that I can't quite tell how to apply that answer here. | Here are the general guidelines regarding ability checks: The GM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results. In some cases, you could want to fail an ability check. If you are climbing a wall an want to drop off, you fail simply because you stop attempting to climb, but in other cases, success and failure are both tied to the actual action and may both have desirable outcomes. Example 1: Spell scrolls An evil adversary wants you to cast a spell scroll for him, but you have him figured out and want to destroy his spell scroll instead, seemingly by accident. The rules on spell scrolls read: If the spell is on your class’s spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + the spell’s level. On a failed check, the spell disappears from the scroll with no other effect. A failure means that you successfully destroy the spell scroll. Example 2: Amulet of the Planes You are in possesion of the Amulet of the Planes. Your party is being overrun by terrible monsters, and the only way to save your party is to sacrifice yourself by sending yourself and the monsters to another plane of existence. While wearing this Amulet, you can use an action to name a location that you are familiar with on another plane of existence. Then make a DC 15 Intelligence check. On a successful check, you cast the Plane Shift spell. On a failure, you and each creature and object within 15 feet of you travel to a random destination. Roll a d100. On a 1-60, you travel to a random location on the plane you named. On a 61-100, you travel to a randomly determined plane of existence. By walking up to the monsters and failing the check, you and the monsters would be sent to another plane of existence. The question The rules seem to assume that you always want to succeed when you perform an ability check. Sometimes, however, you could want to fail on purpose. A sensible DM would rule that if you are skilled enough to succeed the check, then you would undoubtly be able to fail it on purpose as well. What does the rules as written say -- if anything -- about this circumstance? According to RAW, is it possible to attempt an ability check and intentionally fail? |
I'm pretty new to Ubuntu. I just want to open the most common ports namely FTP (port 20 TCP/UDP) HTTP (port 80 TCP/UDP) SMTP (port 25 TCP) ETC I've tried all the ways in iptables, ufw, and gufw. In the end, it still remains unchanged with the same error: Connection refused. I can't even access the home page on HTTP port: 80 from the other device. | My SoulSeek client Nicotine+ checks my open ports during initial configuration and promts that the one port number it needs is closed, cutting me off frmo about 50% of the users. Is there anyway I can open that particular port for the application to use? RUnning ubuntu desktop 13.04. I have not manually installed any firewalls, but not sure if its included in the default installation. |
I have a sample with data and I would like to compare the result I get from Monte Carlo integration and by analytically computing the marginal likelihood. Now I know that in many cases this is a challenging computation, but in this case apparently it is possible. I have the code for doing it, but I don't understand how it is done, and the code doesn't make me wiser. So, let $Y \sim N(\theta,1)$ and the prior on $\theta \sim N(0,1)$. How would I analytically compute the marginal likelihood $p(y)$ $$p(y) = \int p(y|\theta)\,p(\theta)\, d\theta$$ | Given that $a$~$\mathcal{N}(\mu, \Sigma)$ and $\mu$~$\mathcal{N}(0, \sigma^2 I)$, Is $p(a|\Sigma, \sigma)=\int p(a|\mu, \Sigma)p(\mu|\sigma)d\mu$ again a Normal distribution? And how to estimate the mean and variance respectively? Thanks a lot! |
I was just trying to shorten a code snippet in python and came across the strange way of working of the following code. sample = [[]] * 3 # OUTPUT - [[], [], []] - Simple enough to understand sample[0].append(1) # OUTPUT - [[1],[1],[1]] - Why is this happening? sample[1].append(2) # OUTPUT - [[1,2],[1,2],[1,2]] - Why is this happening? sample[2].append(3) # OUTPUT - [[1,2,3],[1,2,3],[1,2,3]] - Why is this happening? Why is appending to a nested list appending to all the nested lists in the list? Are all the nested lists pointing to one list? If so where is the original copy of the list? | I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3 The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]] Then I changed one of the innermost values: my_list[0][0] = 5 Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]] which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it? |
Some background info I'm running a dual boot with Windows 10 and Ubuntu 20.04 I did something stupid like this because I've used Windows my whole life so I didn't realize what apt can do if I'm not careful (I guess sudo is needed for a reason) No, I did not read the documentation, yes it wasn't a good idea, no I will not do it again. Why I would want to use Kali is because I was asked by a teacher to install Kali, so I thought about just using Katoolin to install Kali tools on Ubuntu What happened: I ran Katoolin 3 and told it to install everything I ran sudo apt-get update and sudo apt-get dist-upgrade It began to throw a bunch of errors, so I used sudo apt --fix-broken install, then used sudo apt-get dist-upgrade again Repeated this process until I got tired of the errors, so I tried restarting my laptop, only to be greeted with "Kali GNU/Linux" instead of the usual "Ubuntu" on the Grub menu After selecting "Kali GNU/Linux", it showed the following messages: [FAILED] Failed to start Anonymizing overlay network for TCP [FAILED] Failed to start Anonymizing overlay network for TCP [FAILED] Failed to start Anonymizing overlay network for TCP [FAILED] Failed to start Service for snap application canonical-livepatch.canonical-livepatchd I selected the Ubuntu recovery option and told it to resume normally, this time it didn't show anything at all, just a blinking white rectangle. Pressing the power button shows a log though. What I need help with: All I want is to at least get my Ubuntu partition working, I have no important data there so I'm okay with doing a reset, but I'm not sure how to do that while making sure my Windows install stays safe. I've seen some threads explaining it but I'm not sure if the presence of Katoolin will mess things up. If there is any other information you need, please let me know. Thanks in advance. | Updated Ubuntu 16.04 today using the software updater. Now my PC is running Kali? There were something like 2Gb of updates, which I thought at first was because I haven't updated in a while. Now I'm thinking that it was downloading Kali. Here's a of the new boot-up process. The screen will continue to flicker for another 30 seconds or so, then stop flickering leaving the text on the screen. I tried switching the display manager from gdm to lightdm, which will boot me straight to the console and without flickering, but still no desktop. I'm not altogether sure how I managed to accomplish this. It must have been when I was trying to get Katoolin running. Any tips as to how I can either get the desktop or revert the updates? Contents of cat /etc/lsb-rolling: DISTRIB_ID=Kali DISTRIB_RELEASE=kali-rolling DISTRIB_CODENAME=kali-rolling DISTRIB_DESCRIPTION="Kali GNU/Linux Rolling" |
When dealing with abstract classes in Java it is not possible to create an object of that class. So this would not work AbstractClassName object = new AbstractClassName();. Why this is working AbstractClassName object = new NonAbstractClassName(); ? Can you tell me what am I doing by using a constructor from a non abstract class (that extends the abstract one) and assign the object to a abstract class type? | I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this? I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly. Is it just so if you were to do: IInterface classRef = new ObjectWhatever() You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that. Also, how could you write a method that takes in an object that implements an interface? Is that possible? |
I have found many different Q/A regarding installation of various versions of TeXlive and uninstalling (). To be honest, I might have be a bit lazy.. Will see. To my best knowledge I am running Ubuntu 14.04.4 LTS and I have installed TeXlive 2013, tex --version gives me TeX 3.1415926 (TeX Live 2013/Debian).... I had troubles running the package leadsheets and found some issue thread, that TeXlive 2013 might be missing some features, the exact error is E: /home/quapka/Development/ZpevnikMladez/tex_songs/template.tex:60 "kernel/command-not-defined"! Control sequence \prop_item:Nn undefined. ...ate_variant:Nn \prop_item:Nn { NV } Anyway, I decided to install 2015. But I was lazy and just followed . But did not do the clean up (since this was the first time I was installing TL2015), but I also did not do anything about the previous version (2013). So, after downloading and running sudo ./install-tl I hoped I was done, obviously not. After quick search I've updated PATH, like anywhere I could. I am using zsh, soo, I changed PATH in /etc/environment, ~/.zshrc, ~/.profile. Obviously, running pdflatex outputs This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) and not 2015 version. It seems 2015 is installed correctly, at least /usr/local/texlive/bin/2015/bin/x86_64-linux/pdflatex outputs This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) (preloaded format=pdflatex) , so hey, it's something. Last note, TL 2013 is not in /usr/local/texlive/bin/2013/.. the only thing I could find is in /usr/share/texlive/ (with release notes for 2013 version. In desperate move (it already took me two days, since I lost connection installing TL2015 yesterday) I ran sudo apt-get remove texlive, something was removed but not what I hoped. My question here is. How to switch to 2015 version? What should I uninstall (or, I worry, uninstall, remove, remove more, install..). Disclaimer: I know I should be more careful and etc. But I got used to simply run sudo apt-get install/update/upgrade whenever I need to install/update/upgrade something, but all this work because of one package stopped me from being reasonable. If this is dupe of some sort I am happy to delete it and educate myself elsewhere. Thanks! | Debian and Ubuntu have very good texlive packaging. But I'd like to use tlmgr to have a more fine-grained control about upgrades and which packages I want to be installed. So how do I install "vanilla" TeXLive on Debian/Ubuntu? Also how do I make dpkg aware that I have TeXLive installed? |
I need to write a script that prints out a statement stating whether an IP is valid or invalid. IP addresses are made up of four bytes (each with a valid range of 0-255). valid examples: 127.0.0.1 , 123.244.100.1 , etc. invalid examples: 124,44,2,2 , 127.0.2,4 , 355.23.24.43 , etc. I'm guessing the easiest way would be to use regex? but i am having some trouble with that. I also thought about using split(), but im not sure how I would handle any other special characters that aren't a "." Any help or advice would be great, thanks | What's the best way to validate that an IP entered by the user is valid? It comes in as a string. |
Problem: Find prime solutions to the equation $p^2+1=q^2+r^2$ I welcome you to post your own solutions as well I have found a strange solution which I can't understand why it works(or what's the math behind it.) Here it is through examples Put $r=17$(prime) Now $17^2-1=16\times 18=288=2 \times 144$ (a particular factorization) $\frac {2+144}{2}=73$ $\frac {144-2}{2}=71$ Solution pair $(p,q,r)=(73,71,17)$ Put $r=23$, $23^2-1=22\times 24=8\times 66$ $\frac {8+66}{2}=37$ $\frac {66-8}{2}=29$ Solution pair $(37,29,23)$ It works for each prime except for $2,3,5$ Which generate $(2,2,1),(3,3,1),5,5,1)$ Please explain me how it's working | Are there integral solutions to the equation $x^2+y^2-z^2=1$? |
This is a question for those out there working in data scientist roles within your organizations. How many variables in acceptable to use within models that are going to be deployed in production for marketing or other purposes? The reason I ask is this, we have four analysts, two of whom have been with the company for 10 years, and two of us who are recently graduated with our Masters in Predictive Analytics. Our senior analysts primarily build with linear / logistic regression models, and think that using the least amount of variables (regardless of technique) is always best, usually trying to use around 10-15 variables. Us newer analysts work primarily with random forest and xgboost, and are comfortable using 100-800 variables in our models. I havnt encountered anything to say that using this many variables in random forest or xgboost should cause any concern, but we cannot come to an agreement. Even if holdout results are better using 100+ variables, we are still encouraged to use less. Can anyone provide any information regarding this topic that might help shape our decision making progress? Thank you, Nate | Just a thought: Parsimonious models have always been the default go-to in model selection, but to what degree is this approach outdated? I'm curious about how much our tendency toward parsimony is a relic of a time of abaci and slide rules (or, more seriously, non-modern computers). Today's computing power enables us to build increasingly complex models with ever-greater ability for prediction. As a result of this increasing ceiling in computing power, do we really still need to gravitate toward simplicity? Sure, simpler models are easier to understand and interpret, but in the age of ever-growing data sets with greater numbers of variables and a shift towards a greater focus on prediction capability, this might no longer even be achievable or necessary. Thoughts? |
I want to order my steam games by "unearned achievments" aka achievements I haven't gotten yet because I am trying to 100% every game I have. Does anyone know how to do that? If that's not possible can you somehow sort every game in the Categories by hand? | I play several games on Steam and I love the achievement system. It would be great to get an overview of all the achievements ever gained in Steam games. Does Steam support this? I haven't found such an overview. If such a feature does not exist, I would already be happy with an easy way to calculate the sum of all my achievements automatically. Edit: I stumbled upon an interesting website called today. Unfortunately it only works for XBox-Achievements. Does anyone know of a similar service for Steam? This would solve my question right away. Implementing my own solution based on the links posted in the answers didn't work because the APIs are not sufficient for my needs. |
the radio antennas receives millions of signals. how our radio selects the appropriate signal as it's input? which characteristics of the signal are involved for this selection. | I have some understanding of what frequency modulation entails - it entails "adding" a new frequency to the frequency spectrum of a signal. But how, exactly, is a modulated signal selected in the receiver? Say you're listening to your car radio and want the radio signal modulated at 80 Hz or something. How does the actual system select it? In general, not in car radios specifically. |
I was wondering, when exactly can I use the foreach loop? Do I have to implement IEnumerable? | This is in C#, I have a class that I am using from some else's DLL. It does not implement IEnumerable but has 2 methods that pass back a IEnumerator. Is there a way I can use a foreach loop on these. The class I am using is sealed. |
What's the correct one of the following sentences? Here they come. or Here come they. Consider for example: Here comes the sun. This is the title of a famous Beatles song. Also consider: Here the post office is. Here is the post office. Number (5) seems more natural than number (4). So which is better, or more natural, (1) or (2)— and why? | It's very common to say: "Here he comes." "Here comes the man." But what about: "Here comes he." "Here the man comes." Is there a rule about the order of noun and verb in inversion? It will be too much if all the inversions are considered, so let us talk about adverb inversions only, such as: "Here comes the rainbow." "Off we go." "In the room is the man lying." |
I plan to shut off the main water supply to my 2 story house before leaving for a week on vacation. I have an AO Smith gas 'powervent' water heater in the garage that I would like to set to 70*F rather than turning it off. Since there are no issues with freezing pipes here in the SF Bay Area, I wasn't planning to drain the water lines within the house. Would the cold water feed on top of the water heater need to be turned off also? | I have a brand new AO Smith 50gal gas water heater. Today there was a burst pipe from the cold spell we're having currently, so I had to turn off the water main to the house until the plumbers get here tomorrow. With that, nobody had used any hot water all day so it should be full, but do I need to turn the water heater off until the water can be turned back on tomorrow to avoid any damage etc? |
I want to sort a HashMap of timestamps . Here is my timestamps hashmap. Map<String, DateTime> timestamps = new HashMap<> (); I dont know which method i should use to sort this type of hashmaps . So I cant provide any additional code. Thank you for ur help ! | I am relatively new to Java, and often find that I need to sort a Map<Key, Value> on the values. Since the values are not unique, I find myself converting the keySet into an array, and sorting that array through array sort with a custom comparator that sorts on the value associated with the key. Is there an easier way? |
The following error occurred while opening software updater/Ubuntu software center/sypnatic package manager/software sources. E:Encountered a section with no Package: header, E:Problem with MergeList /var/lib/apt/lists /ppa.launchpad.net_atareao_atareao_ubuntu_dists_quantal_main_i18n_Translation-en, E:The package lists or status file could not be parsed or opened. How to solve this problem?. Any help please. | The computer gave me this output in a window: E: Encountered a section with no Package: header E: Problem with MergeList /var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_natty_main_binary-i386_Packages E: The package lists or status file could not be parsed or opened. How can I fix this? |
How might I evaluate this integral: $$\int_0^\infty \frac{\log\ x}{1+x^2}dx$$ I tried substituing $x = \tan\ v$ but that didn't get me anywhere. Any suggestions as to a thought process for this one? | I want to show that $\int_{0}^{\infty}\frac{\log x}{x^2+1}dx=0$, but is there a faster method than finding the contour and doing all computations? Otherwise my idea is to do the substitution $x=e^t$, integral than changes to $\int _{-\infty}^{\infty}\frac{t e^t}{1+e^{2t}}dt$. Next step is to take the contour $-r,r,r+i\pi,-r+i\pi$ and integrate over it... |
I was doing this problem for self study in rotational dynamics: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on the rods. The discs have identical thickness and are made of the same material, but have differing radii $p$ and $q$. The discs are given angular velocities of magnitudes $x$ and $y$, respectively, and brought into contact at their edges. After the discs interact via friction it is found that both discs come exactly to a halt. Which of the following must hold? Ignore effects associated with the vertical rods. Answer choices: $(x^2)p = (y^2)q$ $xp = yq$ $x(p^2) = y(q^2)$ $x(p^3) = y(q^3)$ $x(p^4) = y(p^4)$ I got the answer $x(p^4) = y(p^4)$ by setting the angular momentum of the two discs equal to each other (because of conservation of momentum) and solving, but the answer is $x(p^3) = y(q^3)$. How do I solve this problem? | Problem #25 from the 2009 $F=ma$ contest: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on the rods. The discs have identical thickness and are made of the same material, but have differing radii $r_1$ and $r_2$. The discs are given angular velocities of magnitudes $\omega_1$ and $\omega_2$, respectively, and brought into contact at their edges. After the discs interact via friction it is found that both discs come exactly to a halt. Which of the following must hold? [...] Ignore effects associated with the vertical rods. Diagram here: Probably conservation of angular momentum is useful here, but I am not clear how it can be applied. There are two distinct axes of rotation, one for each disc, so we cannot talk about conservation of angular momentum about one axis. If the two disks rotated about the same axes then the solution is straightforward, but this is not the case. |
How to avoid null insertion in ArrayList while inserting element? ArrayList<String> al=new ArrayList<String>(); al.add(null);//should avoid . . . al.add("Ramesh"); | I use object != null a lot to avoid . What is an alternative to: if (someobject != null) { someobject.doCalc(); } |
Is there any canon indication (books, films or any additional materials) that Harry Potter is in any way related to Albus Dumbledore? There seem to be some similarities between them like Ancestors of both were always placed in Gryffindor. Both have connections with Godrics Hollow. | There were a lot of family connections between everyone and everyone in HP... Harry and Ignotus, Voldemort and Slytherin, the Blacks and everyone else (Tonks, Weasleys, etc...) Was there any info (canon or JKR) that Dumbledore was related to anyone? He lived in Godric's Hollow, but that is not necessarily a basis for any leaps of logic. |
I'm trying to get the greatest value of just 1 row (mult columns). All of the tutorials I've watched are for multiple rows. How can have just the greatest value (4943) returned? Thanks! | How do you return 1 value per row of the max of several columns: TableName [Number, Date1, Date2, Date3, Cost] I need to return something like this: [Number, Most_Recent_Date, Cost] Query? |
For example, A 9mm bullet travels 380 m/s. Preconditions: The spark from the primer ignites the gunpowder. Gas converted from the burning powder rapidly expands in the cartridge. The expanding gas forces the bullet out of the cartridge and down the barrel with great speed. A photon travels 299,792,458 m/s. Preconditions: What are they? Why does it travel at exactly that speed? Why not faster/slower? Thanks. | I was told that the Galilean relative velocity rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them. How and why is this possible? Also, why can't anything travel faster than light? |
The below error I get after I run my stand alone application developed in JAVA. Please help # A fatal error has been detected by the Java Runtime Environment: # EXCEPTION_PRIV_INSTRUCTION (0xc0000096) at pc=0x04730008, pid=1872, tid=2248 # JRE version: 6.0_30-b12 # Java VM: Java HotSpot(TM) Client VM (20.5-b03 mixed mode, sharing windows-x86 ) # Problematic frame: # C 0x04730008 # If you would like to submit a bug report, please visit: # http://java.sun.com/webapps/bugreport/crash.jsp # The crash happened outside the Java Virtual Machine in native code. # See problematic frame for where to report the bug. I get this error after I run my stand alone application developed in JAVA. Please help | When a Java VM crashes with an EXCEPTION_ACCESS_VIOLATION and produces an hs_err_pidXXX.log file, what does that indicate? The error itself is basically a null pointer exception. Is it always caused by a bug in the JVM, or are there other causes like malfunctioning hardware or software conflicts? Edit: there is a native component, this is an SWT application on win32. |
I'm new to Linux, currently using Kubuntu and trying to switch to Solus. So, I was trying to format the usb stick I used as a bootable pendrive to install Kubuntu, but I can't seem to recover my 8GBs. I've tried the KDE partition manager and GParted, but there is no direct mention of "Format" anywhere in both. I've mounted and unmounted the drive several times, tried to create a partition, GPT, MSDOS, ext4, FAT32, etc. FYI, I created the bootable pendrive using Ubuntu's Startup Disk Creator. I don't understand how this works but I think there is a section of the drive that this program reserved that I can't access in any way. Or can I? If yes, how? | i started installing ubuntu and took out windows 10 completely during the installation.. but after the installation, when i checked my disk partitions 927gb on linux filesystem 3 gb on linux swap 512 mb on efi but my hard disk size is 1tb (1024gb so now rest 94 gb is missing can anyone help me out. i tried if the windows 10 is still existing on the disk, but i didnt get any method and while booting the system i get a message on the top left corner /dev/sda2: clean,223062/60760064 files, 5079494/243030464 blocks ... so does this mean. |
$A$ is a set of $n$ arbitrary natural numbers. We know that $|A|=n$, so $\forall a_i\in A; a_i=nq+j(i)\ \ \ \ (0\le j(i)\lt n)$. If there exists an $a_k$ such that $j(k)=0$, then the subset $\{a_k\}$ is the answer. If not, then $\forall a_i\in A; a_i=nq+j(i)\ \ \ \ (0\lt j(i)\lt n)$. Then I can say there exist at least two members of $A$ such that $n \mod a_a=n\mod a_b$. But I can't go further. Help needed. Guys sorry. It's "divisible by $n$". :-shame | I assume this is correct to any size set, not 2015 in particular... it's obviously true for 2. I know from pen and paper it's true for 3, and 4.... I understand that I should look at the reminders, and build pigeonholes from them. If one of the numbers has a 0 reminder obviously the entire set is divisible, so the possible reminders go from 1 to (n-1). i have n numbers hence one of the reminders repeats. the sums of the reminders go from 1 to n*(n-1).... And that's it... Any and all help would be appreciated. Of course I mean non empty set... |
When Ripley was in Cryo-sleep between Alien and Aliens did she age at all? The person in Cryo is still alive, reduced heart rate etc, but given that you wouldn't normally be 'asleep' for so long any small ageing would be unnoticeable surely one as long as 57 years would show some ageing on Ripley? (Looking 7 years older due to filming dates doesn't count) | As Parker repeatedly asks after they bring the face-hugged Kane aboard, why don't they freeze him? I understand that Ash doesn't want to, but neither Dallas nor any other crew member provide any reason for not putting Kane in cryo and dealing with him later. |
how to prove this formula $\int_{0}^{\infty}\frac{e^{-\frac{x^2}{2}-\frac{z^2}{2x^2}}}{x^2}dx=\sqrt{\frac{\pi }{2}}\frac{ze^{-|z|}}{|z|}$? i have tried residue theorem, but it seems not to work | Given $$\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$$ evaluate: $$\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx. $$ I can find that $$\left(ax+\frac{b}{x}\right)^2 = a^2x^2+2ab+\frac{b^2}{x^2}$$ therefore: $$\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx = e^{2ab}\int_0^{\infty}e^{-\left(ax+\frac{b}{x}\right)^2}dx$$ but I can't find any clue then. |
So I am quite new to using PDO and although I have to it to work using static settings I would like to be able to change the table name in a statement. and saw the highly up voted answer. So I attempted to recreate a simple version which would just dump all the information within a column. Question: Why is my edited version of that persons example not work and return this error below. Fatal error: Uncaught exception 'PDOException' with message 'SQLSTATE[42000]: Syntax error or access violation: 1064 You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '' at line 1' in C:\xampp\htdocs\ *****\database.php:84 Stack trace: #0 C:\xampp\htdocs\ *****\database.php(84): PDOStatement->execute() #1 C:\xampp\htdocs\ *****\database.php(88): buildQuery(1) #2 {main} thrown in C:\xampp\htdocs\ *****\database.php on line 84 The code from the example linked with my small alterations. function buildQuery( $get_var ) { switch($get_var) { case 1: $tbl = `r16.7`; break; } global $db; $sql = "SELECT * FROM $tbl"; $stmt = $db->prepare($sql); $stmt->execute(); $result = $sth->fetchAll(PDO::FETCH_COLUMN, 1); var_dump($result); } buildQuery(1); | Why can't I pass the table name to a prepared PDO statement? $stmt = $dbh->prepare('SELECT * FROM :table WHERE 1'); if ($stmt->execute(array(':table' => 'users'))) { var_dump($stmt->fetchAll()); } Is there another safe way to insert a table name into a SQL query? With safe, I mean that I don't want to do $sql = "SELECT * FROM $table WHERE 1" |
How can I get an old version of the YouTube application for Samsung Galaxy Tab 2? The new update is slow and poor display. | Is is possible to download older versions of Android applications? Is there some kind of online archive for all versions of Android apps? Like how you can find older versions of some Windows app. |
There was a bug fix awhile back for this problem: . My problem is the opposite of this bug fix. On my test partition when I try to upgrade 16.04 to 18.04 and I run: ~$ sudo do-release-upgrade Checking for a new Ubuntu release Get:1 Upgrade tool signature [819 B] Get:2 Upgrade tool [1,253 kB] Fetched 1,254 kB in 0s (0 B/s) authenticate 'artful.tar.gz' against 'artful.tar.gz.gpg' extracting 'artful.tar.gz' It is selecting Artful (17.10) and not Bionic (18.04). If I change /etc/update-manager/release-upgrades last line from: Prompt=normal to: Prompt=lts and rerun do-release-upgrade I get this: $ sudo do-release-upgrade Checking for a new Ubuntu release No new release found. Assuming 18.04 has been properly populated into Canonical Repositories, what am I doing wrong??? | I'm following the , but on launching the upgrade tool I get this response: Checking for a new ubuntu release No new release found Am I doing something wrong? Is there a workaround? |
I'd like to (resp. have to) ident the text of all section headings in a document (+ the abstract and quote enviornments, but that should be easy--by comparison) to 0.4" from the left margin of the page (like using a tab in a word processor). The headings should look like this: So far, I have: \def\@seccntformat#1{\csname the#1\endcsname.\quad} My guess is that there should be a way to replace \quad with something that works like a \absoluteposition or \tabto? Is there any onboard way to do this in Latex I'm also using the sectsty package for some other reason but couldn't find anything about this in the documentation. | I like to recreate the layout of an official template, in order to get rid of Word. Because the template is from the government, I must recreate it 1:1. In the end, the document should look like this: Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata. 1. First Section Title Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren. 1.1 First Subsection Title Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren. 1.1.1 First Subsubsection Title Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren. My main problem is the spacing between the section numbers and the titles. All section titles must begin on a fixed indent defined by the template, so the spacing between the numbers and the titles must be dynamic. With plain latex and titlesec I was only able to specify a fixed space. I also tried the memoir package with hangsecnum, but with this option the numbers will be aligned left, also with a fixed space between the section numbers and the title. Would it be possible to give me a hint how to create such a layout? |
I've come across all kinds of sites that are just scraping SE sites and taking the info for themselves, usually with a crappy UI. The most recent I've come across is , which seems to be scraping SU. Are we doing anything about them? Do we even care? | of Stack Overflow, all content posted on Stack Exchange sites by their users (i.e. you wonderful people) has been provided to the whole universe under . For my fellow non-lawyers, that license basically means: Anyone can use any Stack Exchange posts at any time without having to ask for permission Making money off of the copied content is permitted You don't even have to copy stuff from here verbatim; you can just use it as a starting point and make whatever edits you want There are just two rules you have to follow: You have to provide . Simple links to the original post and author info are just fine. You have to and allow other people to use your content, as long as they follow these very same rules. How meta! (If you ever forget any of that, and want to refresh your memory, the license info is linked to in the footer of every page.) There are, in fact, a lot of people who republish varying amounts of our content for assorted reasons. Unfortunately, there are some Stack Content Republishers Attributing Poorly and/or Excelling at Ranking (SCRAPERs, for short). In this context, "attributing poorly" means any use that doesn't follow our attribution rules or make any other reasonable attempt at give credit. This can get pretty egregious; I've seen SCRAPERs that not only don't link back to SE originals, but also use fake author info and post dates to make it harder to find originals. By "excelling at ranking," I'm referring to copycat sites that end up higher in Google results than the original SE sites do for the same content. That's not necessarily wrong, but in some cases, it indicates inappropriate SEO hackery. So, the question is: what can you do if you spot a SCRAPER? |
I have installed opencart 1.5.6.1 on Digital ocean ubuntu14.04 I have used "demo" as username and login by tightvnc opencart requird "www-data" as owner and group: $ sudo chown -R www-data:www-data /var/www/html $ sudo chmod -R a=r,a+X,u+w /var/www/html $ cd /var/www/html/ $ ls -la drwxr-xr-x+ 6 www-data www-data 4096 Aug 17 07:19 catalog -rw-r--r--+ 1 www-data www-data 0 Aug 15 13:14 config-dist.php $ sudo getfacl /var/www/html/ # file: var/www/html/ # owner: www-data # group: www-data user::rwx group::r-x other::r-x Then I change the ACL by adding demo as owner as well: $ sudo setfacl -R -m u:demo:rwx /var/www/html/ # file: var/www/html/ # owner: www-data # group: www-data user::rwx user:demo:rwx group::r-x mask::rwx other::r-x which allowed demo the edit the files and folders in vnc. but this has also changed the permission of those files: $ ls -la drwxrwxr-x+ 6 www-data www-data 4096 Aug 17 07:19 catalog -rw-rwxr--+ 1 www-data www-data 0 Aug 15 13:14 config-dist.php the group has been chhanged to rwx.... If I change the group permission by: $ sudo chmod -R g-x /var/www/html The ACL mask changed.... # file: var/www/html/ # owner: www-data # group: www-data user::rwx user:demo:rwx #effective:rw- group::r-x #effective:r-- mask::rw- other::r-x If I change the mask: $ sudo setfacl -R -m m:rwx /var/www/html/ the group returned to rwx! So the question is: Whenever I changed using chmod, ACL changed! When I changed using ACL, group permission changed! It may be related to : may need to use -n sudo setfacl -nR -m u:demo:rwx /var/www/html/ may be" The group class permission bits that would be displayed by ls -dl mydir now correspond to the mask entry." which mean the rwx displayed is referred to the mask permission instead of the group permission | To backup the "/home" directory tree of a server, I've created a 'backup' account and used setfacl to make the whole directory readable by it. My cron job runs this command as root each night: setfacl -R -m u:backup:rx,d:u:backup:rx /home Great, except for one problem: whenever I run this command, it changes the group permissions of my ssh key. me@myserver:~/.ssh$ ls /home/me/.ssh/id_rsa -l -rw-r-x---+ 1 me me 1679 Jan 8 18:35 /home/me/.ssh/id_rsa Well, this causes my ssh program to barf because it is now group readable. Strangely, getfacl disagrees with the permissions. me@myserver:~/.ssh$ getfacl /home/me/.ssh/id_rsa getfacl: Removing leading '/' from absolute path names # file: home/me/.ssh/id_rsa # owner: me # group: me user::r-- user:backup:r-x group::--- mask::r-x other::--- getfacl thinks the file is not group readable. If I run the obvious command chmod 400 id_rsa the permission is fixed, but reverts every time I re-run the original command (setfacl -R -m u:backup:rx,d:u:backup:rx /home). What's going on? Note: I do want my id_rsa to backup up, so let's not worry about those security implications. |
How can I set up multiple desktops (i.e. workspaces) in the new Ubuntu 18.04? I cannot find the "appearances" control that used to be in older versions. | Any idea how to have more than 2 workspaces on Ubuntu 18.04.1? |
In Ubuntu 17.04, there was an option to save a screenshot to a specific location. I understand that it's now in /home by default. In Ubuntu 17.10 (I've found solutions for 17.04 only), is there a way to specify another location and make it permanent? Thanks in advance. | I want to change the default location of "Save a screenshot to Pictures" to save it to Desktop. If that is not possible, is there any other way to do it? I am using Ubuntu GNOME 17.04. NOTE: I don't want to change the location with dconf-editor as it changes the location of screenshot applet and not of the shortcut I require. |
I installed 12.04 on an ancient Toshiba laptop several years ago, and it worked quite well. One of my acquaintances recommended that I upgrade to 14.04. This I did, but only with great difficulty, and this installation has been very buggy the entire time I've used it. Recently it failed entirely and eventually I gave up on trying to fix it and reinstalled 12.04, which works just fine. I realize that this is an obsolete installation and will reach its end of life in April, but since it works for me, is there any compelling reason that I should try upgrading again? Jim | What different Ubuntu derivatives are there? And what is special with them? |
I am Iranian and I have Irish visa. I am going to Cork from Tehran. I will have one stop in LHR London Heathrow airport for 7 hours. Do I need any type of visa to stay in airport in London? Could I leave the airport in these 7 hours? There is another flight that needs changing airport in London (LTN London Luton to LHR London Heathrow). Could I use this flight? I found some similar questions but I couldn't get the exact answer. | I am Lebanese Citizen and am planning a trip to Ireland this month. A valid Irish visa is already in hand and I am willing to reach there through the UK. Will I need a transit visa in the UK for few hours for flight connections to Ireland? |
Apostol 5.9.35 Given $P_0(x) = 1,\; P_n'(x) = nP_{n-1}(x),\; \int_0^1{P_n(x) \ dx} = 0 \enspace \forall \:n\geq 1$ (f)Prove that $$ P_n(1-x) = {(-1)}^n P_n(x)$$ if $n\geq 1$ | Consider the Bernoulli polynomials $B_n(x)$ given by the expansion $$\frac{te^{xt}}{e^t-1} = \sum\limits_{n=0}^{\infty}B_n(x)\frac{t^n}{n!}.$$ I want to prove the identity $$B_n(1-x)=(-1)^nB_n(x).$$ This formula is given in a lot of books, but unfortunately without any proof. Therefore I'm wondering how to prove it. Do you have any idea? I tried for instance: $\sum\limits_{n=0}^{\infty}B_n(1-x)\frac{t^n}{n!}=\frac{te^{-xt}}{e^t-1}e^t=\left(\sum\limits_{n=0}^{\infty}B_n(-x)\frac{t^n}{n!}\right)\sum\limits_{n=0}^{\infty}\frac{t^n}{n!}=\sum\limits_{n=0}^{\infty}\left(\sum\limits_{l=0}^n\binom{n}{l}B_{l}(-x) \right)\frac{t^n}{n!}$. Hence $B_n(1-x)=\sum\limits_{l=0}^n\binom{n}{l}B_{l}(-x)$. But I do not know how to proceed. On the other hand I know that $B_n(x+1)-B_n(x)=n x^{n-1}$. Hence $B_{n}(1-x)=B_{n}(-x)-n(-x)^{n-1}$. But again, I do not know how I can go further. Hopefully someone can help me. Best regards |
I don't know anything about Unix/Linux. I am primarily a web programmer. I am running the following command in my code: exec("tar -caf '/backups/_structure.tar.gz' --ignore-failed-read -C /source ."); This code makes a file backup of all the contents of my /source directory and stores it in the /backup directory. This code works fine, except for the fact that sometimes my files are HUGE. I would like to split the tar file by 100MB segments. In this single line, what would I add to do that? I've read some things about | split -b 100MB, but I don't know where in the line to put it and I'm very confused. | I need to backup a fairly large directory, but I am limited by the size of individual files. I'd like to essentially create a tar.(gz|bz2) archive which is split into 200MB maximum archives. Clonezilla does something similar to this by splitting image backups named like so: sda1.backup.tar.gz.aa sda1.backup.tar.gz.ab sda1.backup.tar.gz.ac Is there a way I can do this in one command? I understand how to use the split command, but I'd like to not have to create one giant archive, then split it into smaller archives, as this would double the disk space I'd need in order to initially create the archive. |
I'm a bit confused about how to solve a problem in which these two conservative quantities appear at the same time. Say for example, a pendulum with mass being hit by a particle with mass on its free spinning end. I understand that both linear momentum and angular momentum are conservative, and know how to apply that to solve a variety of only-linear or only-angular problems, but i don't seem to understand what happens when you have to take on account both at the same time, is there a link between the mv and Iw equations I'm missing? | I am trying to understand conservation linear momentum with in angular momentum Herewith i just explain what i am looking for. Imagine an object of mass(M), velocity(V), is undergoing circular motion with radius(R) Angular momentum L = RMV (R-radius M-mass- V- tangential velocity) Mass is constant here Since L is conserved so when R is decreased tangential velocity(V) has to be increased to keep angular momentum constant. Does this mean linear momentum not conserved when radius of rotation changes? When linear momentum is not conserved then what is the force that increases the velocity of object when R decreases. Could anyone clarify this. or could any one say is my basic understanding about momentum is wrong. for easy understanding i am only considered magnitude of momentum's not cross product of vectors |
I'm new at Java and I came across a problem I couldn't find a solution to, so maybe somebody can help me out. When I write this code: ArrayList<String> Liste = new ArrayList<>(); String Name; Liste.add("Harry"); Name = Liste.get(0); Name = "Dieter"; System.out.print(Liste.get(0)); System.out.print(Name); The output is, as expected: Harry Dieter However, if I change the type to a custom object: ArrayList<Names_Class> Liste = new ArrayList<>(); Names_Class Name; Liste.add(new Names_Class()); Liste.get(0).First_Name = "Harry"; Name = Liste.get(0); Name.First_Name = "Dieter"; System.out.print(Liste.get(0)); System.out.print(Name); The output becomes: Dieter Dieter So it seems Java only copies a references or something. Could somebody explain what happens here, and how I can get a complete copy of a single item out of an ArrayList? | I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation? |
I have a custom content type. I would like to limit that each user can only create one node of this content type. How can I achieve this? | How can I restrict various roles with limit in creating nodes of a particular content type? |
EDIT: I want to prove it with "converges absolutely" and not something else. I want to prove that the sequance $\sum _{n=1}^{\infty \ }\left[n^3\sin \left(\frac{1}{n}\right)-n^2+\frac{1}{6}\right]$ converges. I thought of trying converges absolutely, but I don't even know how to start. Also, trying to derivate the inside function doesn't help showing that the function is a non-negative one. Any ideas? Thanks! | Let $t\in \mathbb R$. Prove that $\displaystyle{\sum_{n=1}^{\infty}n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+t}$ converges iff $t=\frac{1}{6}$. While the $(\Rightarrow)$ direction was fairly easy (as $a_n$ should converge to $0$, forcing $t=\frac{1}{6}$), i'm facing some hard time trying to prove the second direction, that is $\displaystyle{\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})}$ converges. I did notice that $a_n=a_{-n}$ and tried to write this series as a Leibnitz series, but had no luck since the sequence doesn't decrease. I also tried to prove absolute convergence but then again, no luck. Thanks. |
I have the following question on a worksheet: Consider the finite complement topology τf on N. Does this topology have a countable base? If so give one such base and if not prove your claim. Been trying to solve this for several hours but I have got nowhere. I think that there is no countable basis because it seems like to construct a basis you would need to take the entire topology, but I have no idea if that's right or how to show that. Thanks | I am working on the problems from the textbook "Topology without tears". I am stuck with problem number $4$ in Exercise $2.2$. Could anyone suggest some hints on how to proceed? The question goes as follows. A topological space $(X,\tau)$ is said to satisfy the second axiom of countability or to be second countable if there exists a basis $\mathcal{B}$ for $\tau$, where $\mathcal{B}$ consists of only a countable number of sets. Prove that the discrete topology on an uncountable set does not satisfy the second axiom of countability. Let $(X,\tau)$ be the set of all integers with the finite-closed topology. Does the space $(X,\tau)$ satisfy the second axiom of countability? For the first problem, I tried to argue by contradiction assuming that the basis for the topology is countable. But I did-not know what I need to look at to prove the contradiction. For the second one, I do not know where to start. I have not thought deeply on the second one though. Thanks, Adhvaitha |
If I have an HDD with some bad sectors and I format the disk (from Windows) or re-partition the disk, will bad sectors still be marked as bad? | Assuming I'm not concerned with the data on it. |
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