text:
The relationship between healthcare administrative costs and physician-reported efficiency measures: an international comparison.

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The Austrian Science Fund (FWF): Analyzing Decision Making and Peer Review

The legitimacy of a funding agency in basic research depends at least on the following factors:

• organization’s ability to minimize distortions in approval probability by its decision procedure
• the scientific quality of results produced by... continue reading

Endurance Hunting aa a Driver for Sexual Dimorphism and Role Differentiation

Early humans were endurance hunters. They were successful in long distance pursuit of prey. This behavioral strategy is believed to be at least 2MM years old, predating h. sapiens, and persists in Kalahari bushmen and the Tarahumara, amongst... continue reading

Time dependent and location dependent electric pricing using smart meters

Smart meters are increasingly deployed to electric endusers, with the prime goal of decreasing metering costs for the power companies.They can be set in a way that the momentary power usage is transmitted close to realtime.

Behavioral Economics: The Way Forward in Education

Behavioral Economics focuses on modelling the decision-making process of individuals, by exploring the emotional, psychological, and social factors that lead to those decisions. Although it primarily focuses on economic decisions nonetheless there... continue reading

Role of perspective in motion sickness induced by navigating a virtual environment

Some individuals report experiencing motion sickness when navigating virtual environments. While field-of-view may mediate this effect (Bos et al., 2010), perspective may be another relevant... continue reading

Reanimation of Australian Megafauna, Extinct Species and New Zealand Moas

After the arrival of the first humans, Indigenous Australians, to the island continent, the previous megafauna became extinct. As many samples are still extant, deriving DNA samples or fragments and reverse engineering, through multiple... continue reading

Venture reproducibility

Venture capitalists work under the concept of investing small amounts in lots of startup companies, some of which will fail, some of which will make a little money, and a few of which will make a lot of money.

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Unifying generative models and exact likelihood-free inference with conditional bijections

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Playing Games with Ideas: when epistemology pays off

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Journal of Prime Research in Mathematics

# Realizable degree sequences of inner dual graphs of benzenoid systems

<NAME>$$^a$$,<NAME>$$^{a,*}$$,<NAME>$$^b$$,<NAME>$$^c$$

$$^a$$Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, QIE Lahore, Pakistan.

$$^a$$Center for Advanced Studies in Mathematics (CASM), Lahore University of Management Sciences (LUMS) DHA, Lahore, Pakistan.

$$^a$$Dhanani School of Science & Engineering, Habib University, Karachi, Pakistan.

Correspondence should be addressed to: <EMAIL>

### Abstract

An inner dual graph of a planar rigid benzenoid (hexagonal) system is a subgraph of the triangular lattice with the constraint that any two adjacent faces in the corresponding hexagonal system must be connected via an edge in the inner dual. The maximum degree of any vertex in an inner dual graph of a hexagonal system is 6. In contrast with the already existing algorithms in the literature that are used to check a given degree sequence to be graphically realizable, in this paper, we use a a simple technique to check the realizable degree sequences of inner dual graphs of benzenoid systems that form a rich class of molecular graphs in theoretical chemistry. We restrict the maximum degree to 3 and identify, by providing necessary and sufficient conditions on the values of α, β and γ, all the degree sequences of the form d = (3α, 2β, 1γ) that are graphically (inner dual of planar rigid hexagonal system) realizable. That is, we provide general constructions of the graphs (inner dual of planar rigid hexagonal system) realizing the degree sequences of the form d = (3α, 2β, 1γ).

#### Keywords:

Hexagonal system, Inner dual graph, Matchstick graph, Degree sequence, Graphical realization, Graphical sequence.

format: plain


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# Tag Info

Hint: If the array is called $a$ and $N = \text{len}(a)$, then the code expresses the formula $$\left(\prod_{i=0}^{N-1} a_i\right)^{1/N}$$ Or equivalently $$\sqrt[N]{\prod_{i=0}^{N-1} a_i}$$ Extended hint: The formula is known as the geometric mean of a series of values (i.e. the array). (Wikipedia)


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## Elementary Algebra

The area of the rectangle is $w^2+4w$ $\text{yd}^2$
Since the length is $4$ more than the width, $w$, we must add $4$ to $w$ to find the length. This gives us a length of $w+4$. The formula for area of a rectangle is $A=lw$, where $l$ is the length and $w$ is the width. We plug in the values for width and length: $A=w(w+4)$ We apply the distributive property: $A=w\cdot w+4w$ To multiply powers with the same base, we add the exponents: $A=w^2+4w$


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# Quantitative Aptitude Practice Questions for SBI PO

Quantitative Aptitude Practice Questions for SBI PO
Directions (1 – 5): The following pie charts give the percentage distribution of employees in different departments in any company during the years 2015 and 2016 .Answer the questions using this data.
A-Administration;  B-Operations; C-Sales& Marketing; D-Finance & Accounts;  E-Corporate HQ

1. If the average monthly salary of employees in Administration was rs.15000 in 2015,what was the total salary expense of Administration on 2015 (in crore)?
a) 71.28
b) 57.45
c) 78.98
d) 64.89
e) 59.4
2. What is the percentage increase/decrease in the number of employees in Finance &  Accounts ?
a) 23.37 % increase
b) 23.37% decrease
c) 34.35 % increase
d) 34.35 % decrease
e) no change
3. Find the ratio of no of employees in department E in 2015 to the no.of employees in department D in 2016.
a) 3:5
b) 9 : 25
c) 4:5
d) can't be determined
e) none of these
4. If 300 employees left Operations at the end of 2015, how many joined in 2016?
a) 480
b) 960
c) 1360
d) 1540
e) 1240
5. Find the average no. of employees of Corporate HQ in 2015 and 2016.
a) 1520
b) 1730
c) 1650
d) 1450
e) 1720
Directions (6 – 10): Study the following graph and answer the question based on it-
Monthly Expenditure (in thousands) by five people on Rent, Food, Children's Education, Cloths and Travelling
6. What is the total monthly expenditure made by Megha on rent, Tarun on clothes and Aarushi on travelling together?
a) Rs. 15520
b) Rs. 16120
c) Rs. 17820
d) Rs. 18320
e) Rs. 19420
7. What is the average monthly expenditure on food by all the people together?
a) Rs. 8250
b) Rs. 9550
c) Rs. 9950
d) Rs. 10160
e) Rs. 10850
8. Whose monthly expenditure on all the heads together is the lowest among them?
a) Seema
b) Megha
c) Tarun
d) Varun
e) Aarushi
9. If the monthly expenditure of Seema on children's education is increased by 5%, then what will be his yearly expenditure on children's education?
a) Rs. 102760
b) Rs. 134760
c) Rs. 141760
d) Rs. 158760
e) Rs. 160760
10. What is the respective ratio between the monthly expenditure made by Varun on travelling and the monthly expenditure made by Megha on clothes?
a) 39 : 95
b) 95 : 39
c) 59 : 105
d) 105 : 59
e) Can’t be determine
Solutions:
1. A) total monthly salary=18000×0.22×15000=5.94 crore
total annual salary=5.94×12=71.28 crore
2. B) in 2015 = 5220; in 2016 = 4000
% decrease = 1220/5220 × 100 = 23.37%
3. B) Required ratio = 18000 × 8/100 : 20000 × 20/100 = 9 : 25
4. C) The no. of joiners would be given by =5200-(4140-300)=1360
5. E) Required Average = (8% of 18000 + 10% of 20000) = (1440 + 2000)/2 = 3440/2 = 1720
6. C) Required monthly expenses = Rs. (9.65 + 2.75 + 5.42) thousand = Rs. (17.82 x 1000) = Rs. 17820
7. E) Monthly expenditure on food = Rs. (7.50 + 8.55 + 11.40 + 17.80 + 9)/5 thousand = Rs. 10.85 thousand = Rs. 10850
8. D)
9. D) Required annual expenditure of Seema on education
= Rs. (12 × 12.60 × 105)/100 thousand = Rs. 158.76 thousand = Rs. 158760
10. C) Required ratio = 4.72 : 8.40 = 472 : 840 = 59 : 105


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Record Details

Title:
Perspectives for studying planetary matter using intense X-ray pulses at the high energy density science instrument at the European XFEL
Affiliation(s):
EuXFEL staff
Author group:
Optical Lasers
Management Board
Instrument HED
Topic:
Abstract:
Free-electron laser facilities enable new applications in the field of high-pressure research including planetary materials. The European X-ray Free Electron Laser (European XFEL) in Hamburg, Germany will start user operation in 2017 and will provide photon energies of up to 25 keV. The high-energy density science instrument (HED) at the European XFEL is dedicated to the study of dense material at strong excitation in a temperature range from eV to keV and pressures > 100 GPa which is equivalent to an energy density > 100 J/mm$^{3}$. It will enable studying structural and electronic properties of excited states with hard X-rays at a repetition rate of up to 4.5 MHz. The instrument is currently in its technical design phase and first user experiments are foreseen for end of 2017. In this contribution, we present the X-ray instrumentation and the foreseen X-ray techniques at HED. In addition, we discuss prototype hard-condensed matter experiments in the field of planetary research as proposed during recent user consortium meetings for this instrument. These include optical laser induced quasiisentropic (ramped) compression and shock compression experiments and diamond anvil cell experiments.
Imprint:
2014
Journal Information:
(2014)
Conference information:
3rd Joint Workshop on High Pressures, Planetary and Plasma Physics, Rostock, 2014-09-24 - 2014-09-26, Germany
Record appears in:

Export


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# Construction of a cohomology theory from a given spectrum.

Assume that $\{E^n\}_{n \in \mathbb{Z}}$ is a cohomology theory, that is, a sequence of functors from the (homotopic) category of based CW-complexes to the category of (graded) abelian groups. Then Brown's representability theorem asserts that for any such sequence, there is always a nice sequence of spaces $\{ Z^n \}_{n \in \mathbb{Z}}$, which represents the functors $E^n$. In other words we have a natural equivalence, $E^n \cong [-,Z^n]$.

My question has to do with the "dual" version of the above narrative. Assume that someone starts with a a spectrum $Z=\{Z^n\}_{n \in \mathbb{Z}}$. Then Switzer in his book "Algebraic Topology - Homotopy and Homology", makes the following constrcution: for a given spectrum $Z$, defines a cohomology theory $E$ associated to $Z$, with $E^n(X)=[\Sigma^{\infty}X, \Sigma^nZ]$, for each pointed CW-complex $X$. My question is why by setting just $E^n(X)=[X,Z^n]$ does not suffice? In his book M.R. Adhikari - Basic Algebraic Topology, seems that defines (on pg.$482$) for a given $\Omega$-spectrum $Z$, the associated (reduced) cohomology theory to be the sequence of functors $\{ [-,Z^n] \}_{n \in \mathbb{Z}}$. Why Switzer does not just take this construction and makes it more complicated?

All I can think, is that Switzer takes any (not necessarily $\Omega$) spectrum and creates a generalized cohomology theory with his construction. Though for any given spectrum, it can be turned into an $\Omega$-spectrum hence I don't get the point.

• This seems to be a notational issue. In the first case, he's taking the internal Homs inside the category of spectra, whereas the second case is done inside the category of topological spaces. – user40276 Jul 6 '18 at 10:13
• Thanks for the comment; so you say that these two thinks are essentially the same with just a different dictionary in hand? – user321268 Jul 6 '18 at 10:14

As you say Switzer defines a cohomology theory $E^\ast$ for any spectrum $E =(E_n,\epsilon_n)$. If $E$ is an $\Omega$-spectrum, then in fact $E^n(X) = [X,E_n]$ which is (in a sense) simpler than the general definition of $E^n(X)$ as the set of homotopy classes of maps of spectra from the suspension spectrum of $X$ to the spectrum $\Sigma^nE$. And yes, you may restrict to $\Omega$-spectra, but why should you reject the more universal approach?
Consider for example the sphere spectrum $S^0$. This is far from being an $\Omega$-spectrum, but the cohomology theory associated to $S^0$ is known as stable cohomotopy. This cohomology theory is well-established in algebraic topology.
• Thank you for your answer. I understood the same; Switzer defines the cohomology associated to any spectra since homotopy classes of morphsisms between spectra is an abelian group. On the other hand an $\Omega$-spectrum say $Z$ consists of $H$-groups, hence the homotopy classes of maps $[X,Z^n]$ are abelian groups, and in fact as user40276 commented above, this coincides with Switzer's construction just in a different category. – user321268 Jul 6 '18 at 12:45


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£199.99 £139.99 for one year of Unlimited learning. Offer ends on 28 February 2023 at 23:59 (UTC). T&Cs apply

# File naming and organization

A clear folder structure and file naming convention help when organizing your data.

A clear folder structure and file naming convention help when organizing your data. They are essential when collaborating with others. Like data management plans, there is no single method for structuring and naming data.

## Folder Structure

Storing files in folders is a good way of cleaning up your data. A logical folder structure can also guide the user, making it easier to understand the content of a dataset. Some institutions already have a system that you need to follow. Many research groups also make their own guidelines for data storage. There is no standard convention, so if you need to create your own folder structure, some best practices are:

• Keep all files associated with a project in a single folder
• Use a consistent and informative directory structure
• Have a self-explanatory folder name that is only as long as necessary
• Avoid assigning the same name to a folder and a subfolder
• Keep public/private/secret data in separate folders
• Keep original RAW data untouched and saved
• Establish a folder hierarchy that aligns with the project. Example: Project / Data / Technology

Data from behavioural studies frequently contain many files that have different relationships to one another. Hence, it is important to create a folder structure in the planning phase of a project before the data is collected. All material relevant to the data should be entered into the data folders, including detailed data collection and processing procedures.

Here is an example of a folder structure from CodeRefinery:

project_name/├── README.md # overview of the project├── data/ # data files used in the project│ ├── README.md # describes where data came from│ └── sub-folder/ # may contain subdirectories├── processed_data/ # intermediate files from the analysis├── manuscript/ # manuscript describing the results├── results/ # results of the analysis (data, tables, figures)├── src/ # contains all code in the project│ ├── LICENSE # license for your code│ ├── requirements.txt # software requirements and dependencies│ └── ...└── doc/ # documentation for your project ├── index.rst └── ...

## File Naming

Brief and descriptive file names are important in keeping your data files organized. A file name is a principal identifier for a file. A good file name gives information about what the file contains and helps to sort multiple files. This requires a consistent file naming scheme. As with folder structure, when collaborating with others, it is vital to have a good file naming convention.

Here are some tips for naming files:

• Keep your filenames to a reasonable length
• Order the elements in the name from general to specific
• Use file names to classify types of files
• Use meaningful abbreviations.
• Use underscore (_), hyphen (- ), or capitalized letters to separate elements in the name
• Don’t use spaces, periods, or special characters: ?!& , * % # ; * ( ) @\$ ^ ~ ‘ { } [ ] < >
• Use a consistent date format, such as ISO8601: YYYYMMDD, and time if needed HHMMSS
• Explain abbreviations used in your data management plan
• Consider sorting when deciding the order of elements in the file name. File names starting with the date will sort differently than files starting with the project name.
• Use sequential numbering, leading with zeros for clarity (01, 02, …)
• For consistency, include the same elements/information in all files
• Do not use any personal information like a person’s name in a file name
• Avoid generic file names (Examples: MyData.txt)

There are lots of information you could include in a file name: project name, data types, experimental tasks or conditions, date of creation, the technology used. What you choose to include depends on how you plan to use the data later. You cannot include all the information in the file name. What is less important could go into a descriptive file instead.


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jp0496811_si_001.pdf (195.97 kB)

# Photophysics and Photochemistry of Stilbene-Containing Platinum Acetylides

journal contribution
posted on 22.04.2004, 00:00 by <NAME>, <NAME>, <NAME>, <NAME>
A series of four platinum acetylide complexes that contain 4-ethynylstilbene (4-ES) ligands have been subjected to a detailed photochemical and photophysical investigation. The objective of the work is to understand the structure and reactivity of the lowest excited states in π-conjugated Pt-acetylides. The 4-ES ligand was chosen for this work because the excited-state properties of the stilbene chromophore are well understood. In particular, stilbene features fluorescence and phosphorescence, and also undergoes trans−cis photoisomerization from the triplet excited state. Two of the complexes investigated contain phosphine ligands and have the structures trans-Pt(PBu3)2(4-ES)2 and cis-Pt(dppe)(4-ES)2 (2 and 3, respectively, where PBu3 = tributylphosphine and dppe = bis-1,2-diphosphinoethane). The other two complexes contain substituted 2,2‘-bipyridine ligands and have the structures Pt(t-Bu-bpy)(4-ES)2 and Pt(4,4‘-CO2Et-bpy)(4-ES)2 (3 and 4, respectively, where t-Bu-bpy = 4,4‘-di-tert-butyl-2,2‘-bipyridine and 4,4‘-CO2Et-bpy = 4,4‘-bis(carboethoxy)-2,2‘-bipyridine). The crystal structure of 2 is reported. The complex features a square planar PtP2C2 geometry and the planes of the phenyl groups in the 4-ES ligands are twisted approximately 60° relative to the plane defined by the PtP2C2 core. The series of complexes was examined by using absorption, variable-temperature photoluminescence, and transient absorption spectroscopy. In addition, the photochemical reactivity of the complexes was explored by UV−visible absorption and NMR spectroscopy. The available experimental data indicate that in all of the complexes excitation leads to high-yield production of a 3π,π* excited state that is localized on one of the 4-ES ligands. At low temperatures, the 3π,π* state exhibits strong phosphorescence that is very similar to the phosphorescence of trans-stilbene. At temperatures above the glass-to-fluid temperature of the solvent medium, the 3π,π* state decays rapidly (τ ≈ 40 ns). The decay pathway is believed to involve rotation around the CC bond of one of the 4-ES moieties. This model is supported by the photochemical results, which show that steady-state photolysis leads to trans−cis isomerization of one of the 4-ES ligands with a quantum efficiency of 0.4.


text:
Question

# For the quadratic equation x2-2x+1=0 find the value of x+1/x

Open in App
Solution

## Solution -: We are given x^2 -2x+1 =0 1st we will solve for x , by factoring . (x-1)(x-1)=0 x-1 =0 and x-1 = 0 x=1 and x= 1 it means we have solution x= 1 Now consider ( x+ 1/x) we will get, x=1 we will get 1+1/1 = 1+1 =2 ( 1+1/1 means 1+1 =2) So w e got answer 2

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Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

In my last sab-R-metrics post, I went over some basics of calling data and creating vectors or new data from those. Here, I want to extend that to full subsets of data and go on to use some of the basic functions in R so that we can begin plotting in the next tutorial.

1. All lowercase variables.
2. Use underscore (_) for variable names.

Next, go to “Save As”, choose your favorite convenient directory, and save it as a comma separate (CSV) file as I showed you in the first post. Save it as “pujols” if you want everything to work from the code here. Go ahead and open up R and a new script to play with. At the top, name it something using the “#” sign to indicate a comment, set your working directory, and load in the data, naming it “pujols” as below:

##working with pujols pitch fx data
setwd(“c:/Users/Millsy/Documents/sab-R-metrics”)

Make sure everything loaded in correctly so that there aren’t any problems. The first thing I want to do is subset my data. You’ll notice that there is a lot of missing data for certain variables in here. This is where there was no Pitch F/X availability for the 2008 season. Because we want to work specifically with Pitch F/X data, let’s subset that. We’ll use the “subset()” function. Below, I’m using a crude method of sub-setting the data, where I only select those rows that have a ‘start_speed’ number in them–the way I do it below is to indicate that I only want rows with a starting pitch speed greater than 0 mph:

#subsetting data into pitches with f/x data only

pitchfx <- subset(pujols, start_speed > 0)

#or

pitchfx <- subset(pujols, pujols$start_speed > 0) Notice above I did the sub-setting two ways: one with the “$” sign and one without. Because both the data name and the sub-setting requirements are within the “subset()” function, we don’t necessarily have to use the “$“, but if you have multiple data sets, it can be a good idea to get into the habit of always using the dollar sign. Similarly, we can subset the data by the number of balls, strikes, or pitch type. I’ll begin by sub-setting from our already made “pitchfx” subset. Below, I subset the data into pitches with 2 strikes, then separately for pitches with 3 balls, and finally for pitches that are sliders only: #other subsets of interest k2 <- subset(pitchfx, strikes==2) b3 <- subset(pitchfx, balls==3) sliders <- subset(pitchfx, pitch_type=="SL") Notice that we had to use quotations for selecting by pitch type. This is because it is indicated in our data set as text. Also, remember to use the double-equal sign “==” when stating a cell should be equal to your selection for sub-setting. We can also use our data to grab only change-ups: #grabbing just change-ups using the dollar sign changeup <- pitchfx[pitchfx$pitch_type=="CH"]

Here, we HAVE to use the dollar sign (unless we want to use the “attach()” function, which is not recommended). The “subset()” function is much more convenient, but when we don’t want to have lots and lots of data subsets in our memory, the above can become very useful. Mainly, we can use the above code to set criteria for plots and functions without creating too many subsets of the data. Below, we take the mean starting speed of change-ups that Pujols saw in 2008:

#average change-up or slider speed to Pujols

mean(pitchfx$start_speed[pitchfx$pitch_type==”CH”])

mean(pitchfx$start_speed[pitchfx$pitch_type==”SL”])

Hopefully you also got 82.037 mph as the average change-up speed and 83.86 mph as the average slider speed. See how we combined all these things together? There is another important R function that comes in handy called “tapply()“. This allows us to use a basic function like “mean()” across different criteria in one swoop, rather than doing a line of code for every pitch type. This function should be quicker, in general, than ‘for loops’ (next section), but sometimes it can be a pain. Begin with the variable you want to apply your function to, then say what variable you want to use to categorize the ‘types’ (here, it’s pitch type), and then just write the name of the function in the last portion.

#use tapply to get some descriptives of all pitch types individually

tapply(pitchfx$start_speed, pitchfx$pitch_type, mean)

tapply(pitchfx$start_speed, pitchfx$pitch_type, sd)

tapply(pitchfx$start_speed, pitchfx$pitch_type, max)

tapply(pitchfx$pz, pitchfx$pitch_type, mean)

This gives us a nice list of the average speed of each pitch Pujols sees, the standard deviation of each, and the average height of each. You can see that, on average, fastballs (FA) are the fastest pitches, while splitters (FS) are on average the lowest in the zone (“pz” is the height of the pitch). Using the “max()” function, we can also see the fastest of each pitch type that Pujols saw in 2008. Pretty easy stuff!

*******SIDETRACK********

One thing I have not mentioned is using conditional statements for different reasons. The most simple case of using a conditional statement is creating a single dummy variable. Perhaps we’re interested in creating a column vector (a variable) that indicates whether or not the pitch was greater than 90 mph. To indicate that “Yes”, the pitch was above 90 mph, we’ll use the number “1”, and to indicate that “No”, the pitch was below 90 mph, we’ll use the number “0”. For this, we can use the “ifelse()” function, which is an extension of the “if()” function often used for writing your own functions. Here, you’ll need to recall how to add a variable to the end of your data set:

#adding an “above 90 mph” indicator variable to our data set

pitchfx$above_90 <- ifelse(pitchfx$start_speed > 90, 1, 0)

#or similarly

pitchfx$above_90_b <- ifelse(pitchfx$start_speed =< 90, 0, 1)

In this code, we begin by picking a name for the variable and using our assignment operator “<-“. Then, we use our function, beginning with the criteria (that the pitch is above 90 mph), followed by the number to assign to the variable if it is true for that row, then the number to assign if the statement is not true. Similarly, the second version gives a “0” to the column if the pitch is less than or equal to 90 mph, and a “1” if this statement is false (or, the pitch is above 90 mph). We can also do the same using a text identifier within the column:

#using Yes and No

pitchfx$above_90_c <- ifelse(pitchfx$start_speed > 90, “Yes”, “No”)

********END SIDETRACK********

While the “tapply()” function is the most efficient, we can also run ‘for loops’ in order to assess things in our data. A ‘for loop’ runs code multiple times on a set of data depending on the criteria. Here, I will also make use of the “length()” function, which tells you the number of rows or columns in a data set. I also use the “sample()” function that randomly samples from your data, but I’ll only briefly discuss this. If you use:

#looking at the number of observations (pitches) in the dataset

length(pitchfx[,1])

#looking at the number of variables

length(pitchfx)

We see that there are 2,364 pitches (rows) and 41 variables (columns) in our data set.

********SIDETRACK********

I sometimes use “sample()” to do certain things in R that I need some random selection for. I won’t get too in-depth with this, but let’s grab a random sample of velocities of pitches in the data set. First, I’ll also use the “set.seed()” function. We use this so that when we randomly sample something, we can be sure to reproduce the same exact sample next time. If you do not set the seed, you’ll get a different sample every time. Just plug in your favorite number between the parentheses. I use my birthday so I can always remember which one I used.

set.seed(7261984)

#randomly sample start speeds of 10 pitches with replacement

speed_samp_repl <- sample(pitchfx$start_speed, 10, replace=TRUE) speed_samp_repl #randomly sample start speeds of 10 pitches without replacement speed_samp_norepl <- sample(pitchfx$start_speed, 10, replace=FALSE)

speed_samp_norepl

So, you start with the variable you want to randomly sample, then indicate the number of observations to sample, and finally indicate whether you want to sample with or without replacement. Easy enough for those of you that want to deal with permutations of data.

********END SIDETRACK********

In a ‘for loop’, the objective is to run the same code on multiple parts of a data set (like tapply()“), or to do lots of samples of data. For loops are useful when you want to make up your own bootstrap or other function (for those familiar with the technique). I mostly use the for loop to permute data for H2H fantasy (i.e. randomly matching up weekly category totals in order to gauge the probability of winning a category, given the data from the previous season). In words, the loop below says that for each row from the first to the last in the column called “start_speed”, multiply that value by 10 and call this new vector “dumb”, then take the mean of the vector:

#create useless for loop multiplying start speed by 10
dumb <- NULL
for (i in 1:length(pitchfx$startspeed)) { stupid <- pitchfx$start_speed*10
dumb <- c(dumb, stupid)
}
mean(dumb)

It’s always good to and indent code for easier reading, especially with loops and functions. Above, I first created an empty vector called “dumb”. Then, I created the loop using the “for()” function indicating that I wanted to do it from Row 1 through the last row of the data (the colon is read as “to”). Then I define “stupid” as the speed times 10, and use the “c()” function to put each result into the previously empty vector “dumb”. The entire loop is surrounded by the “{}” brackets and I take the average of the vector of speeds multiplied by 10 after it runs.

I’m not going to get too in depth with this, as there are a number of things to do with the for loops…none of which are pertinent to the type of sabermetric analysis I’ll be discussing at this site. Just know that you can define “stupid” above as any mathematical function you’d like (as well as a conditional statement). Those of you who are creative programmers can probably figure out where to go from here with the for loops.

Next time, we can actually start doing the fun stuff. In my next post, I’ll go over some basic graphics in R and doing a quick t-test or regression using the same Albert Pujols data. Below, I again post my script from today’s tutorial:

##working with pujols pitch fx data
setwd("c:/Users/bmmillsy/Documents/My Dropbox/Blog Stuff/sab-R-metrics")

#subsetting data into pitches with f/x data only
pitchfx <- subset(pujols, pujols$start_speed > 0) pitchfx <- subset(pujols, start_speed > 0) #other subsets of interest k2 <- subset(pitchfx, pitchfx$strikes==2)
b3 <- subset(pitchfx, pitchfx$balls==3) sliders <- subset(pitchfx, pitchfx$pitch_type=="SL")

#grabbing just change-ups using the dollar sign
changeup <- pitchfx[pitchfx$pitch_type=="CH"] #average change-up speed to Pujols mean(pitchfx$start_speed[pitchfx$pitch_type=="CH"]) mean(pitchfx$start_speed[pitchfx$pitch_type=="SL"]) #adding an "above 90 mph" indicator variable to our data set pitchfx$above_90 <- ifelse(pitchfx$start_speed > 90, 1, 0) #or similarly pitchfx$above_90 <- ifelse(pitchfx$start_speed =< 90, 0, 1) #use tapply to get some descriptives of all pitch types individually tapply(pitchfx$start_speed, pitchfx$pitch_type, mean) tapply(pitchfx$start_speed, pitchfx$pitch_type, sd) tapply(pitchfx$start_speed, pitchfx$pitch_type, max) tapply(pitchfx$pz, pitchfx$pitch_type, mean) #looking at the number of observations (pitches) in the dataset length(pitchfx[,1]) #looking at the number of variables length(pitchfx) #using Yes and No pitchfx$above_90_c <- ifelse(pitchfx$start_speed > 90, "Yes", "No") #set your random seed set.seed(7261984) #randomly sample start speeds of 10 pitches with replacement speed_samp_repl <- sample(pitchfx$start_speed, 10, replace=TRUE)
speed_samp_repl

set.seed(7261984)

#randomly sample start speeds of 10 pitches without replacement
speed_samp_norepl <- sample(pitchfx$start_speed, 10, replace=FALSE) speed_samp_norepl #create useless for loop multiplying start speed by 10 dumb <- NULL for (i in 1:length(pitchfx$startspeed)) {
stupid <- pitchfx\$start_speed*10
dumb <- c(dumb, stupid)
}
mean(dumb)

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text:
# Equivalence classes in rings

1. Jan 24, 2008

### InquilineKea

So I'm kind of confused about the definition:

$$a-b\in I$$

Why a - b instead of a + b?

2. Jan 24, 2008

### waht

Are you trying to prove that a-b is an equivalence relation? Can you be more specific?

Last edited: Jan 24, 2008
3. Jan 24, 2008

### morphism

It's actually natural to write a-b because I becomes zero when you quotient out by it, so a-b in I means a-b=0 or, written differently, a=b.

4. Jan 27, 2008

### mathwonk

you would presumably want a equivalent to a, which follows from a-a in I, rather than a+a in I.


text:
NEET Physics Mathematical Tools Questions Solved

A curve is governed by the equation y=sinx, then what is the area enclosed by the curve and x-axis between x =0 and x =$\mathrm{\pi }$ is (shaded region)

1. 1 units

2. 2 units

3. 3 units

4. 4 units

Concept Videos :-

#16 | Calculus: Differential Equation
#19 | Numericals

Concept Questions :-

Integration
Explanation is a part of a Paid Course. To view Explanation Please buy the course.

Difficulty Level:


text:
This is “Production Functions”, section 9.2 from the book Beginning Economic Analysis (v. 1.0). For details on it (including licensing), click here.

Has this book helped you? Consider passing it on:
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## 9.2 Production Functions

### Learning Objectives

1. How is the output of companies modeled?
2. Are there any convenient functional forms?

The firm transforms inputs into outputs. For example, a bakery takes inputs like flour, water, yeast, labor, and heat and makes loaves of bread. An earth moving company combines capital equipment, ranging from shovels to bulldozers with labor in order to digs holes. A computer manufacturer buys parts “off-the-shelf” like disk drives and memory, with cases and keyboards, and combines them with labor to produce computers. Starbucks takes coffee beans, water, some capital equipment, and labor to brew coffee.

Many firms produce several outputs. However, we can view a firm that is producing multiple outputs as employing distinct production processes. Hence, it is useful to begin by considering a firm that produces only one output. We can describe this firm as buying an amount x1 of the first input, x2 of the second input, and so on (we’ll use xn to denote the last input), and producing a quantity of the output. The production function that describes this process is given by y = f(x1, x2, … , xn).

The production functionThe mapping from inputs to an output or outputs. is the mapping from inputs to an output or outputs.

For the most part we will focus on two inputs in this section, although the analyses with more than inputs is “straightforward.”

Example: The Cobb-Douglas production functionA production function that is the product of each input, x, raised to a given power. is the product of each input, x, raised to a given power. It takes the form $f( x 1 , x 2 ,…, x n )= a 0 x 1 a 1 x 2 a 2 … x n a n .$

The constants a1 through an are typically positive numbers less than one. For example, with two goods, capital K and labor L, the Cobb-Douglas function becomes a0KaLb. We will use this example frequently. It is illustrated, for a0 = 1, a = 1/3, and b = 2/3, in Figure 9.1 "Cobb-Douglas isoquants".

Figure 9.1 Cobb-Douglas isoquants

Figure 9.1 "Cobb-Douglas isoquants" illustrates three isoquants for the Cobb-Douglas production function. An isoquantCurves that describe all the combinations of inputs that produce the same level of output., which means “equal quantity,” is a curve that describes all the combinations of inputs that produce the same level of output. In this case, given a = 1/3 and b = 2/3, we can solve y = KaLb for K to obtain K = y3 L-2. Thus, K = L-2 gives the combinations of inputs yielding an output of 1, which is denoted by the dark, solid line in Figure 9.1 "Cobb-Douglas isoquants" The middle, gray dashed line represents an output of 2, and the dotted light-gray line represents an output of 3. Isoquants are familiar contour plots used, for example, to show the height of terrain or temperature on a map. Temperature isoquants are, not surprisingly, called isotherms.

Figure 9.2 The production function

Isoquants provide a natural way of looking at production functions and are a bit more useful to examine than three-dimensional plots like the one provided in Figure 9.2 "The production function".

The fixed-proportions production function comes in the form $f( x 1 , x 2 ,…, x n )=Min { a 1 x 1 , a 2 x 2 , …, a n x n }.$

The fixed-proportions production functionA production function that requires inputs be used in fixed proportions to produce output. is a production function that requires inputs be used in fixed proportions to produce output. It has the property that adding more units of one input in isolation does not necessarily increase the quantity produced. For example, the productive value of having more than one shovel per worker is pretty low, so that shovels and diggers are reasonably modeled as producing holes using a fixed-proportions production function. Moreover, without a shovel or other digging implement like a backhoe, a barehanded worker is able to dig so little that he is virtually useless. Ultimately, the size of the holes is determined by min {number of shovels, number of diggers}. Figure 9.3 "Fixed-proportions and perfect substitutes" illustrates the isoquants for fixed proportions. As we will see, fixed proportions make the inputs “perfect complements.”

Figure 9.3 Fixed-proportions and perfect substitutes

Two inputs K and L are perfect substitutes in a production function f if they enter as a sum; so that f(K, L, x3, … , xn) = g(K + cL, x3, … , xn) for a constant c. Another way of thinking of perfect substitutesTwo goods that can be substituted for each other at a constant rate while maintaining the same output level. is that they are two goods that can be substituted for each other at a constant rate while maintaining the same output level. With an appropriate scaling of the units of one of the variables, all that matters is the sum of the two variables, not their individual values. In this case, the isoquants are straight lines that are parallel to each other, as illustrated in Figure 9.3 "Fixed-proportions and perfect substitutes".

The marginal productThe derivative of the production function with respect to an input. of an input is just the derivative of the production function with respect to that input.This is a partial derivative, since it holds the other inputs fixed. Partial derivatives are denoted with the symbol δ. An important property of marginal product is that it may be affected by the level of other inputs employed. For example, in the Cobb-Douglas case with two inputsThe symbol α is the Greek letter “alpha.” The symbol β is the Greek letter “beta.” These are the first two letters of the Greek alphabet, and the word alphabet itself originates from these two letters. and for constant A,

$f(K,L)=A K α L β ,$

the marginal product of capital is

$∂f ∂K (K,L)=αA K α−1 L β .$

If α and β are between zero and one (the usual case), then the marginal product of capital is increasing in the amount of labor, and it is decreasing in the amount of capital employed. For example, an extra computer is very productive when there are many workers and a few computers, but it is not so productive where there are many computers and a few people to operate them.

The value of the marginal productThe marginal product times the price of the output. of an input is the marginal product times the price of the output. If the value of the marginal product of an input exceeds the cost of that input, it is profitable to use more of the input.

Some inputs are easier to change than others. It can take 5 years or more to obtain new passenger aircraft, and 4 years to build an electricity generation facility or a pulp and paper mill. Very skilled labor such as experienced engineers, animators, and patent attorneys are often hard to find and challenging to hire. It usually requires one to spend 3 to 5 years to hire even a small number of academic economists. On the other hand, it is possible to buy shovels, telephones, and computers or to hire a variety of temporary workers rapidly, in a day or two. Moreover, additional hours of work can be obtained from an existing labor force simply by enlisting them to work “overtime,” at least on a temporary basis. The amount of water or electricity that a production facility uses can be varied each second. A dishwasher at a restaurant may easily use extra water one evening to wash dishes if required. An employer who starts the morning with a few workers can obtain additional labor for the evening by paying existing workers overtime for their hours of work. It will likely take a few days or more to hire additional waiters and waitresses, and perhaps several days to hire a skilled chef. You can typically buy more ingredients, plates, and silverware in one day, whereas arranging for a larger space may take a month or longer.

The fact that some inputs can be varied more rapidly than others leads to the notions of the long run and the short run. In the short run, only some inputs can be adjusted, while in the long run all inputs can be adjusted. Traditionally, economists viewed labor as quickly adjustable and capital equipment as more difficult to adjust. That is certainly right for airlines—obtaining new aircraft is a very slow process—for large complex factories, and for relatively low-skilled, and hence substitutable, labor. On the other hand, obtaining workers with unusual skills is a slower process than obtaining warehouse or office space. Generally speaking, the long-run inputs are those that are expensive to adjust quickly, while the short-run factors can be adjusted in a relatively short time frame. What factors belong in which category is dependent on the context or application under consideration.

### Key Takeaways

• Firms transform inputs into outputs.
• The functional relationship between inputs and outputs is the production function.
• The Cobb-Douglas production function is the product of the inputs raised to powers and comes in the form $f( x 1 , x 2 ,…, x n )= a 0 x 1 a 1 x 2 a 2 … x n a n$ for positive constants a1,…, an.
• An isoquant is a curve or surface that traces out the inputs leaving the output constant.
• The fixed-proportions production function comes in the form $f( x 1 , x 2 ,…, x n )=min { a 1 x 1 , a 2 x 2 , …, a n x n }.$
• Fixed proportions make the inputs “perfect complements.”
• Two inputs K and L are perfect substitutes in a production function f if they enter as a sum; that is, f(K, L, x3, … , xn) = g(K + cL, x3, … , xn), for a constant c.
• The marginal product of an input is just the derivative of the production function with respect to that input. An important aspect of marginal products is that they are affected by the level of other inputs.
• The value of the marginal product of an input is just the marginal product times the price of the output. If the value of the marginal product of an input exceeds the cost of that input, it is profitable to use more of the input.
• Some inputs are more readily changed than others.
• In the short run, only some inputs can be adjusted, while in the long run all inputs can be adjusted.
1. For the Cobb-Douglas production function, suppose there are two inputs K and L, and the sum of the exponents is one. Show that, if each input is paid the value of the marginal product per unit of the input, the entire output is just exhausted. That is, for this production function, show $K ∂f ∂K +L ∂f ∂L =f(K,L).$


text:
WOMBAT – A program for Mixed Model Analyses by Restricted Maximum Likelihood

# Example 3 for WOMBAT

This is Example 3 as previously distributed with DFREML.

Data are mature cow weight records from the Wokalup selection experiment, recorded annually in January. Up to 6 records per cow are available. The only fixed effect considered is contemporary groups.

Data are analysed

• A: fitting a simple repeatability model,
• B: fitting a full multivariate model, treating records at different ages as different traits, and
• C: fitting a random regression model with quadratic Legendre polynomials as basis functions and heterogeneous error variances.


text:
# Main conjecture for elliptic curves invariant under a $\mathbb{Q}$-isogeny

Suppose $E$ is an elliptic curve defined over $\mathbb{Q}$ with good ordinary reduction at a prime $p$. Then one can define nonnegative integers $\lambda_{E}^{alg}$, $\mu_{E}^{alg}$, $\lambda_{E}^{an}$ and $\mu_{E}^{an}$ at $p$.

The "algebraic" Iwasawa invariants $\lambda_{E}^{alg}$ and $\mu_{E}^{alg}$ are defined in terms of the structure of the $p$-primary subgroup $Sel_{E}(\mathbb{Q}_{\infty})_{p}$ of the Selmer group for $E$ over the cyclotomic $\mathbb{Z}_{p}$-extension $\mathbb{Q}_{\infty}$ of $\mathbb{Q}$. The definition of the "analytic" invariants $\lambda_{E}^{an}$ and $\mu_{E}^{an}$ is in terms of the $p$-adic $L$-function for $E$ constructed by Mazur and Swinnerton-Dyer.

Now the Main Conjecture (Mazur) implies that $\mu_{E}^{alg}=\mu_{E}^{an}$ and $\lambda_{E}^{alg}=\lambda_{E}^{an}$.

Let $E_1$ and $E_2$ are two elliptic curves over $\mathbb{Q}$ such that there exists a $\mathbb{Q}$-isogeny from $E_1$ to $E_2$. Is the Main Conjecture invariant under a $\mathbb{Q}$-isogeny i.e, if the conjecture is true for any one of the curves then it is also true for the other one $?$

<NAME>, Variation de la fonction $L$ $p$-adique par isogénie, Algebraic number theory, Adv. Stud. Pure Math. 17 (1989), pp. 347-358.
The full main conjecture is invariant under isogenies defined over $\mathbb{Q}$, not just the statement about $\mu$ and $\lambda$-invariants.
The only thing that changes on the analytic side is the period: Recall the $p$-adic $L$-function interpolates values of the form Gaussum*L-value/Period. The complex $L$-function is invariant under isogeny, so only the Néron periods of the curves enter into the change.
On the algebraic side, one has to determine the change of the Selmer group under isogeny. Over $\mathbb{Q}$ this is what Cassels had to do to show that the Birch and Swinnerton-Dyer conjecture is invariant. Now over the $\mathbb{Z}_p$-extension, one can do it in a similar way. That the changes agree is proven in the appendix of a paper by Perrin-Riou called "Fonctions $L$ $p$-adiques, théorie d’Iwasawa et points de Heegner", Bull. Soc. Math. France 115 (1987), no. 4, 399–456. this link on numdam


text:
5 views

In the silly Post Correspondence Problem, $SPCP$, the top string in each pair has the same length as the bottom string. Show that the $SPCP$ is decidable.

| 5 views


text:
# Math Help - Null Hypothesis Question - Need Help!

1. ## Null Hypothesis Question - Need Help!

Need some guidance on solving this null hypothesis problem.

Test the claim at 1% significance level that graduates from University X and University Y experience the same salary increase after graduation.

Univesity X
Mean $8,000 Standard Deviation:$1,000

University Y
Mean $7,000 Standard Deviation:$1,000

Should (could) this be done in Excel through a t test: two sample assuming equal variances?

2. ## Re: Null Hypothesis Question - Need Help!

Do you have a sample size?

3. ## Re: Null Hypothesis Question - Need Help!

Sorry, yes. University x = 100, University Y = 100


text:
# <NAME> and <NAME>

### Life of <NAME>

<NAME> was born 31 March 1848 in the town of 's Hertogenbosch in the South of the Netherlands, where his father was a judge. This time may be seen as the dawn of the golden age of Dutch science, see the interesting site  book by Levelt Sengers about van der Waals and the Dutch School for more information on this period. The period was marked by outstanding and influential investigations of, among others, <NAME>, <NAME>, <NAME>, <NAME>, H.A.Lorentz, <NAME>. One of the prominent scientists, who contributed so much to the cultural life in the Netherlands, was <NAME>.

Korteweg started his academic studies at the so called "Polytechnic School", now the Technical University of Delft. Because his disposition for mathematics was stronger than that for technical sciences he switched to mathematics, but he kept a great interest in the applications of mathematics in physics and mechanics. He wrote a thesis "On the propagation of waves in elastic tubes" (see Links) under van der Waals and defended it on 12 July 1878. The University of Amsterdam had just been granted the right to confer doctorates, and so Korteweg became the first doctor of our university. In fact the university existed already since 1632, but only as Atheneum Illustre. Three years later Korteweg was appointed at the University of Amsterdam as professor of mathematics, mechanics and astronomy. In his inaugural address he stressed the importance of mathematical applications in the sciences.

His influence on academic life in the Netherlands becomes apparent also from his membership of several academic institutions; he was a member of the Royal Academy for sixty years and of the Wiskundig Genootschap (Dutch Mathematical Society) for seventy five years. As an editor of the Nieuw Archief voor Wiskunde' during the period from 1897 to 1941 he contributed greatly to the development of mathematics in the Netherlands.

After a fruitful life <NAME> passed away at age ninety three on 10 May 1941.

### Life of <NAME>

<NAME> was born 22 January 1866 in Amsterdam. He studied in Amsterdam under van der Waals, Julius, Pesch and Korteweg. The latter also became his thesis advisor. He worked on his thesis while being employed as a teacher at the KMA (Royal Military Academy) in Breda (1892-1893) and at the "cadettenschool" te Alkmaar, (1893-1894).

<NAME> defended his thesis: "Bijdrage tot de kennis der lange golven, Acad. proefschrift, Universiteit van Amsterdam, 1894, 95 pp, Loosjes, Haarlem" at the University of Amsterdam, 1 December 1894. Shortly afterwards the main results of the thesis were made public in the famous Korteweg - de Vries paper (see paper in pdf, courtesy of Bijzondere Collecties, Universiteit van Amsterdam, UBM: DT 9721):

On the Change of Form of Long Waves advancing in a Rectangular Canal and on a New Type of Long Stationary Waves; Philosophical Magazine, 5th series, 39, 1895, pp. 422–443

He served as a high school teacher at the `HBS en Handelsschool'' of Haarlemfrom 1894 to 1931.

<NAME> was married to <NAME>, who taught French language and literature. They had five children. <NAME> died in Haarlem, 16 December 1934.


text:
Evaluate $\lim_{x\rightarrow \infty}\frac{\ln \left( \sqrt[x]{a_1^x+a_2^x+…+a_n^x}-a_1 \right)}{x}$

Evaluate:$$\lim_{x\rightarrow \infty}\frac{\ln \left( \sqrt[x]{a_1^x+a_2^x+...+a_n^x}-a_1 \right)}{x},\ a_1\ge a_2\ge ...\ge a_n>0$$ Lop does not work. I have no idea about this limit.
I can prove $\ln(a_1^x+a_2^x+...+a_n^x)\sim x\ln a_1$ but I got stuck here.

• If you take a look at the top, with large value of $x$, the function inside the root will go towards $a_1$ from the positive side. Subtracting an additional $a_1$ shows that the numerator is approximating $\ln(0)$ from the positive side, or approximately $-\infty$. The bottom approximates $\infty$. Therefore, I believe we can bound the limit as follows: $-1 \le L \le 0$. I can't find anything further as of now. – <NAME> Apr 18 '18 at 14:55
• I would hazard that the limit goes to $0$, as $x$ goes to infinity far faster than the numerator, I think, although I can't prove it. – <NAME> Apr 18 '18 at 14:58

The limit is $\ln \frac{a_2}{a_1}$ Changing the notation to something I like better I show

$$\lim\limits_{n\to \infty}\frac{\ln( \sqrt[n]{a_1^n+\cdots +a_k^n}-a_1)}{n}=\ln \frac{a_2}{a_1}$$

Now $$\frac{\ln( \sqrt[n]{a_1^n+\cdots +a_k^n}-a_1)}{n}=\frac{\ln a_1}{n}+\frac{\ln( \sqrt[n]{1+(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n}-1)}{n}$$ So it suffices to show $$\lim\limits_{n\to \infty} \frac{\ln( \sqrt[n]{1+(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n}-1)}{n} =\ln \frac{a_2}{a_1}$$ Or taking exponents that

$$\lim\limits_{n\to \infty} ( \sqrt[n]{1+(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n}-1))^{\frac{1}{n}} = \frac{a_2}{a_1}$$ So now we SQUEEZE. $$( \sqrt[n]{1+(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n}-1))^{\frac{1}{n}} \leq ( 1+(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n-1))^{\frac{1}{n}}\to \frac{a_2}{a_1}$$

On the other hand letting $p=(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n$ $$\frac{p}{n(1+p)}\leq \frac{p}{(\sqrt[n]{1+p})^{n-1}+\cdots +1}=\sqrt[n]{1+p}-1$$ So

$$\frac{\sqrt[n]{p}}{\sqrt[n]{n}\sqrt[n]{(1+p)}}\leq( \sqrt[n]{1+(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n}-1))^{\frac{1}{n}}$$

And$$\frac{\sqrt[n]{p}}{\sqrt[n]{n}\sqrt[n]{(1+p)}}=\frac{\sqrt[n]{(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n}}{\sqrt[n]{n}\sqrt[n]{(1+(\frac{a_2}{a_1})^n+\cdots +(\frac{a_k}{a_1})^n)}}\to\frac{a_2}{a_1}$$

We have

$$\ln \left( \sqrt[x]{a_1^x+a_2^x+...+a_n^x}-a_1 \right)=\ln \left( a_1\sqrt[x]{1+(a_2/a_1)^x+...+(a_n/a_1)^x}-a_1 \right)=\\ =\ln a_1+\ln \left( \sqrt[x]{1+(a_2/a_1)^x+...+(a_n/a_1)^x}-1 \right)$$

and

$$\sqrt[x]{1+(a_2/a_1)^x+...+(a_n/a_1)^x}=e^{\frac{\log(1+(a_2/a1)^x+...+(a_n/a_1)^x)}{x}}\sim e^{\frac{(a_2/a1)^x+...+(a_n/a_1)^x}{x}}\\\sim 1+\frac{(a_2/a_1)^x+...+(a_n/a_1)^x}{x}$$

then

$$\ln \left( \sqrt[x]{1+(a_2/a_1)^x+...+(a_n/a_1)^x}-1 \right)\sim \ln \left(\frac{(a_2/a_1)^x+...+(a_n/a_1)^x}{x}\right)=\\=\ln \left((a_2/a_1)^x+...+(a_n/a_1)^x\right)-\ln x$$

and finally

$$\frac{\ln \left( \sqrt[x]{a_1^x+a_2^x+...+a_n^x}-a_1 \right)}{x}\sim \frac{\ln a_1+\ln \left((a_2/a_1)^x+...+(a_n/a_1)^x\right)-\ln x}x\\\sim \frac{\ln \left((a_2/a_1)^x+...+(a_n/a_1)^x\right)}x$$

therefore the result depends upon the particular values for the coefficients $a_i$.

• Doesn't the requirement of $a_{1} \ge a_{n} \ge a_{n+1} \ge 0$ help solve the last to $0$? – John Lou Apr 18 '18 at 15:06
• @JohnLou I've plugged in the approximation obtained in the line before – gimusi Apr 18 '18 at 15:06
• @JohnLou no since it depends upon the actual values for $a_i$ fo example $a_1=a_2=2$ and $a_3=1$ leads to $0$ while $a_1=3, a_2=2$ and $a_3=1$ leads to $\ln 2/3$. – gimusi Apr 18 '18 at 15:09
• @JohnLou sorry there was a big typo in the second line, now it should be fine – gimusi Apr 18 '18 at 15:32


text:
Homework Help: Ball on string question

1. May 8, 2005

jhson114

A ball with mass m = 1 kg is attached to a string of length l = 1 m. The other end of the string is attached to a hook in the ceiling a height H = 2.5 m above the floor. The ball is originally positioned so that the string is parallel with the ground. The ball is now released from rest. As the ball falls, the tension in the string increases until it breaks at an angle q = 24 degrees with the ceiling. What is the tension when the string breaks.

From my understand tension on a pendulum is mgcos(angle), but i keep getting the wrong answer. so i tried a different way, where you find the initial total energy, minus potential energy at 24 degrees to get the kinetic energy. using the kinetic enery equation you get the velocity at angle 24 degrees. using the velocity, i used the centripetal force equation F=m(v^2/r), but this answer is also wrong. please help. thank you

2. May 8, 2005

quasar987

In mgcos(angle), do you use 24° or 90°-24° = 76° as the angle? You should use 76°. Have you got your calculator set to degree instead of radian?

3. May 8, 2005

jhson114

i used 90-24 which is 66 degrees

4. May 8, 2005

quasar987

Right, right... well this this weird. :grumpy:

what do they say the answer is?

5. May 8, 2005

jhson114

yeah i have no clue why i'm not getting the right answer

6. May 8, 2005

jhson114

dont know what the answer is.

7. May 8, 2005

quasar987

Then how do you know what you got is wrong?

8. May 8, 2005

jhson114

because its one of those online questions where you input an answer and it tell you wether you got it right or wrong, but doenst tell you the right answer if you get it wrong. only tells you that its wrong.

9. May 8, 2005

quasar987

Try it with cos(24°) just to see.

10. May 8, 2005

jhson114

tried it already but its wrong

11. May 8, 2005

z0r

Perhaps this problem has two parts to the solution.

I am imagining a regular pendulum at its lowest point, where the string's angle with the ceiling would be 90 degrees and the velocity at a maximum. Here, we have the angular acceleration and also the gravity contributing to the total tension in the string.

So, perhaps you should add the two values you obtained with the different methods...

$$T = mg \cos 66^{\circ} + m\frac{v^2}{l}$$ ,

using $$mg\sin 24^{\circ} = \frac{1}{2}mv^2$$ to obtain the velocity.

Last edited: May 8, 2005
12. May 8, 2005

jhson114

adding the mgcos66 and the centripetal force give me the correct answer. but why do you have to add the two values??? i'm confused.

13. May 8, 2005

Staff: Mentor

$mg \cos \theta$, where $\theta$ is the angle that the pendulum makes with the vertical, is the component of the weight parallel to the string. It is not the tension in the string.

To find the tension in the string, apply Newton's 2nd law for forces parallel to the string: $T - mg\cos \theta = ma$. Realize that the mass is centripetally accelerating, so $a = m v^2/l$.

Use conservation of energy to find $m v^2$.

14. May 8, 2005

quasar987

I never considered the centripetal acceleration as being literally INDUCED by the motion in the $\hat{\theta}$ direction, but when I think about it, it makes a lot of sense. Cool!


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# Shifting Plates

There are six plates next to each other in a row on a table. Bob grabs two plates and moves each plate one position to the left or to the right (if there is one plate or more at the target position then he puts the plate on top). Repeating this procedure, can he stack the six plates into a single pile? (Bob can move one plate to the right and one plate to the left or both plates in the same direction, but only the top plates).

• I guess you're the same person who posted this question here? Do you have an original source for this puzzle? – <NAME> Dec 11 '17 at 18:44
• you may want to clarify how exactly the plates move, perhaps by adding examples to make this question more clear. – micsthepick Dec 11 '17 at 18:51
• Please don't vandalise your posts. – <NAME> Dec 11 '17 at 19:19
• Welcome to Puzzling! (Take the Tour!) Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) – Rubio Dec 19 '17 at 13:00

## No.

We can imagine the six plates to be at six consecutive integer points on the real number line, and colour all the integers alternately black and white (odd black, even white).

Each move of the form you've described preserves the parities of both the number of plates on black integers and the number on white integers - either you're moving B->W twice, or W->B twice, or one of each. But the initial position has three plates on black integers and three on white, while the desired final position has all six plates on a single colour. Thus the problem is impossible.

The key, as with many such puzzles, is to find an invariant.


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Home > Mathematica, Mathematics > Open Lockers

## Open Lockers

Hundred Lockers is an exercise about number properties and parity.

The animation above shows the state of the lockers after each passage of <NAME>’s assistant.

Image [100] provides the solution.

The answer is the square numbers: 1,4,9,16,25,36,49,64,81,100.

At the end of the procedure the status of the locker (closed 0, open 1) is  the number of factors of locker number N mod 2, e.g.

• locker 10: 10 has 4 factors (1,2,5,10), 4 mod 2 =0, hence the locker is closed
• locker 25: 25 has 3 factors  (1,5,25) 3 mod 2 =1, hence the locker is open

Square numbers have an odd number of factors:

Every number can be expressed as the product of power of primes:

$N =\prod_{j}^n p_j^{j_k}$

Let $\phi (N)$ be the number of factors of $N$:

$\phi (N) =\prod_j^n (j_k +1)$

For square numbers all $j_k$ are even, hence $\phi (N) \text{ mod } 2 \equiv 1$


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Getting started¶

This mini-tutorial will help you set up a working Python environment on a Linux system. This will allow you to work with other peoples Python tools and start writing your own scripts.

Some concepts¶

First, let’s go over a few important concepts.

What is Python?¶

Python is a widely used general-purpose programming language, known for its emphasis on code readability.

How do I get Python?¶

Python comes preinstalled on Mac OS, most Linux distributions and is easily installed on Windows.

Warning

The system often depends on the preinstalled Python installation for various operations. Modifying the system installation is not recommended.

Instead of using the preinstalled version of Python, it is recommended to work using what are called virtual environments.

Setting up and managing virtual environments, including package management, is the focus of this mini-tutorial.

What is a Python package?¶

When you write code, you may want to use some parts other people have written, rather than rewriting everything from scratch. If you reference and external code in your code, we say that your code depends on that external code.

In Python, people often package up their code and make it available on the Python Package Index for others to download and use in their programs.

Installing miniconda3¶

In this tutorial, we will use a lightweight installation of conda called Miniconda3 to manage our software environments.

Note

conda is not Python specific, it can be used as a general software environment solution. This is useful if you use software which has many specific dependencies and requires activation prior to usage.

Creating a new conda environment¶

The following command will create a new conda environment called py38 with Python version 3.8.

conda create --name py38 python=3.8

This environment can be activated with conda activate py38 and deactivated with conda deactivate.

Installing packages¶

Once your environment is active, any packages you install will be installed into this environment, isolated from your system Python installation and other conda environments.

Packages can be installed with either conda install <package-name> or pip install <package-name>.


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# What is the cardinality of $A=\{(a,b)\in \mathbb{R}\times \mathbb{R}\mid 2a+b\in \mathbb{N}\text{ and }a-2b\in \mathbb{N}\}$

Let $A=\{(a,b)\in \mathbb{R}\times \mathbb{R}\mid 2a+b\in \mathbb{N}\text{ and }a-2b\in \mathbb{N}\}$ What is $|A|$?

I think $|A|={{\aleph }_{0}}$ ,but i am not sure how to prove it.

• Can you work backwards? Suppose that $2a+b=m$ and $a-2b=n$. Can you try writing $a$ and $b$ in terms of $m$ and $n$? – <NAME> Dec 13 '14 at 16:41

Since

$$\det \begin{pmatrix} 2 & 1\\ 1 & -2 \end{pmatrix} =-5\neq 0$$

for each pair $(x, y) \in \mathbb{N} \times \mathbb{N}$ there is a unique solution of

$$2a+b = x\\ a-2b = y$$ So you have at most ${\aleph }_{0}$ solutions and you can find directly ${\aleph }_{0}$ solutions.

We get that $$2\cdot(2a+b) + (a-2b) = 5a \in \mathbb{N}$$ and thus $$5\cdot(2a+b)-2\cdot 5a = 5b \in \mathbb{N}$$ So $A$ is a subset of $B\times B$ where $$B = \{\frac{a}{5} \mid a \in \mathbb{N} \}$$ Now clearly $|B| = |\mathbb{N}|$ so $$A \leq |B\times B| = |\mathbb{N} \times \mathbb{N} | = |\mathbb{N}| = {\aleph }_{0}$$ And it's not hard to see that $A$ must be infinite. Therefore, $|A| = {\aleph }_{0}$

$\square$

If $(a,b) \in A$, then we know that $2a + b \in \mathbb{N}$ and $a - 2b \in \mathbb{N}$.

Since sums of natural numbers are still in $\mathbb{N}$, we then find that $4a + 2b \in \mathbb{N}$ and hence that $5a \in \mathbb{N}$. This means there are $\aleph_0$ possible values for $a$.

For a fixed $a$, $2a + b \in \mathbb{N}$ gives $\aleph_0$ possible values for $b$.

Hence $\lvert A \rvert \leq \aleph_0 \cdot \aleph_0 = \aleph_0$.

But $\lvert A \rvert \geq \aleph_0$ since $\{(n,0)|n \in \mathbb{N}\} \subseteq A$.

Therefore $\lvert A \rvert = \aleph_0$.

If $(a,b)$ is in that set, then both $5a$ and $5b$ are in $\mathbb{Z}$, are they not? Then can you find the cardinality of $F\times F$ where $F = \{ \frac15 x \mid x\in\mathbb{Z} \}$?


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Iron does not react with … Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Demonstration of the reaction with water of lithium, sodium and potassium. It is also a basic building block of table salt (a molecule of which consists of one atom of sodium and one of chlorine: NaCl). Ca starts floating because bubbles of hydrogen gas formed stick to the surface of metal. They are known as noble metals 1 (or as inactive metals). For the metals that still get into the water, chelation or sequestration are both very effective. What's the fastest / most fun way to create a fork in Blender? Starting from sodium, they react explosively to water, as hydrogen gas is produced in the process. The alkali metals basically react with water to form metal hydroxide and hydrogen gas. Show More. Edit: Context: (Question) Al reacts with hot water (boiling pt), Mg does not react with hot water but reacts with HCl, which is more reactive? https://en.wikipedia.org/wiki/Reactivity_series#Reaction_with_water_and_acids.In. (b) When calcium metal is added to water, the gas evolved does not catch fire but the same gas evolved on adding sodium metal to water catches fire. Ans. 300 K? In general, Group 1 (IA or alkali) metals and Group 2 (IIA or alkaline earth) metals are more active than transition metals. 3)The metals like zinc,iron are less reactive which react slowly even with steam. . 4.1.2.5 Group 1. According to the reactivity trends, Mg is more reactive than Al, but according to the information given in the question, it seems logical that Al is more reactive since it reacts with hot water but Mg does not. (i) It does not react with cold as well as hot water but reacts with steam. That is why you never see them corrode due to moisture. A. FeO B. Fe₂O₃ C. Fe₃O₄ D. Fe₂O₃ and Fe₃O₄ fly wheels)? (CBSE 2008) Answer: (i) Magnesium reacts with water only on boiling (ii) copper metal doesnot react even with stream. Zn + H 2 O ⇨ ZnO + H 2. Observations: 1. Please check the link given. Is it possible to make a video that is provably non-manipulated? Soon the metal catches fire and starts burning. Reaction of Iron with water: Reaction of iron with cold water is very slow and come into notice after a long time. Gallium does not react with water at temperatures up to 100 °C (212 °F) but reacts slowly with hydrochloric and other mineral acids to give the gallium ion, Ga 3 +. Can metal oxides react with water to form a hydroxide, then that with HCl to make a salt? How do the material components of Heat Metal work? Explain the reactions of different metals with hot water, cold water and steam. potassium. Why is there no spring based energy storage? Q. One notable reaction within this group is aluminum's (Al) reaction with water. Give one example with a proper balanced chemical equation. Iron forms rust (iron oxide) when reacts with moisture present in atmosphere. My main research advisor refuses to give me a letter (to help for apply US physics program). Students should be able to describe the reactions of the first three alkali metals with oxygen, chlorine and water. Explain the reactions of different metals with hot water, cold water and steam. 4.1 Atomic structure and the periodic table. From amongst the metal sodium, calcium, aluminium, copper and magnesium, name the metal : (i) Which reacts with water only on boiling, and (ii) Another which does not react even with steam. Least reactive metals like gold and silver usually do not react with water. Which one of the given metals does not react with cold as well as hot water? sodium A soft, silvery metallic element that will interact explosively when added to water. 3. (ii) It does not react with any physical state of water. This page explores the way the position of a metal in the reactivity series affects its reaction with water or steam. Here are four observations of the reactions of four metals. K. sodium. Could the US military legally refuse to follow a legal, but unethical order? Reaction of zinc metal with water: Zinc metal produces zinc oxide and hydrogen gas when steam is passed over it. What is the temperature of "hot" water? Metals react with water to form oxides or hydroxides and release Hydrogen gas. To me, it seems like a metal would need to be more reactive to be able to react with hot water since HCl is a very strong acid and so should theoretically be able to react with more metals, but I am not so sure. In general, the more reactive the metal, the more rapid the reaction. Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute? Zn,Al,Fe react with water to form metal oxide. 2)Magnesium is less reactive metal so it react slowly with cold water,it reacts rapidly only with hot boiling water. The reason for using cold water rather than hot water for the reactions of alkali metals is that alkali metals are already reactive enough at room temperature. Metals which react with steam form the solid metal oxide and hydrogen gas. 1)Sodium is a very reactive metal,therefore sodium metal react violently even with cold water. Why does Steven Pinker say that “can’t” + “any” is just as much of a double-negative as “can’t” + “no” is in “I can’t get no/any satisfaction”? rev 2021.1.11.38289, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Gold and silver do not react with any form of water. Which of the given oxide(s) of iron would be obtained on prolonged reaction of iron with steam? Reaction of metal with water The order of increasing reactivity of these metals … Why does potassium react more violently with water than lithium? Thanks for contributing an answer to Chemistry Stack Exchange! Classroom Resources for This Article Free educator resources are … If a US president is convicted for insurrection, does that also prevent his children from running for president? 5. 4.1.2 The periodic table. MathJax reference. The next four metals (magnesium through chromium) are active metals that will react with hot water or steam to form their oxides and hydrogen gas. A. Na B. Ca C. M<NAME> . Are there countries that bar nationals from traveling to certain countries? Reaction between magnesium metal and sodium hydroxide: Does this even happen? Book about young girl meeting Odin, the Oracle, Loki and many more, How to mount Macintosh Performa's HFS (not HFS+) Filesystem. Medium reactive metals like magnesium and calcium react with hot water. In fact, boron (B) does not react at with water. The reactions between metals and water or steam. All six members of the alkali metals group react violently when exposed to water. 2,000 K , well above the critical point? Kerala Syllabus 9th Standard Physics Solutions Guide, Kerala Syllabus 9th Standard Biology Solutions Guide, NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.5, NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4, NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.3, NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.2, NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2, NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.4, NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.3, NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.2, NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.4, NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.3, NCERT Solutions for Class 7 Maths Chapter 3 Data Handling Ex 3.2, NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.7, NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.6, NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.5, NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.4, The order of increasing reactivity of these metals is Fe< Mg < Na. The reactivity even increases down the group. Making statements based on opinion; back them up with references or personal experience. in boiling water, and very vigorously with acids.Aluminium reacts with acids and steam but less vigorously than magnesium.Magnesium DOES react with hot water even more vigorously than aluminium . Chemical reactions such as combustion in fire, fermentation and the reduction of ores to metals were known since antiquity. Magnesium reacts very slowly with cold water, but rapidly From amongst the metals sodium, calcium, aluminium, copper and magnesium, name the metal (i) which reacts with water only on boiling and (ii) another which doesnot react even with stream. At room temperature, the reaction of Fe is very slow but red hot iron reacts with steam to form Fe … Name two metals which do not react with any form of water. If you're seeing this message, it means we're having trouble loading external resources on our website. Explanation; Alkali metals react vigorously with water. England. You might have to leave the metals that react too slowly until the next lesson; For metals such as calcium that react quickly with water set up the apparatus shown above so that you can collect the hydrogen gas that is given off during the reaction Metals react with water to form oxides or hydroxides and release Hydrogen gas. Most alkali earth metals react with cold water. CBSE Maths notes, CBSE physics notes, CBSE chemistry notes. Reaction of aluminium metal with water: Reaction of aluminium metal with cold water is too slow to come into notice. So is Mg or Al more reactive if we were to assume that everything in the question were true? Name two metals which do not react with any form of water. Metals can react with water, acid and oxygen. The position of hydrogen in the reactivity series. magnesium+steam magnesiumoxide + hydrogen. Why is gold unreactive when only one electron is in the outer shell? Question 2. Where did all the old discussions on Google Groups actually come from? Silver, gold and platinum are not active metals. To recap stain prevention: 1) reduce metals in the water through filtration and removal, as low as possible, and 2) control metals through chelation and sequestration with a product like SC-1000. To learn more, see our tips on writing great answers. If the gas evolved burns with a 'pop' sound, it indicates that it is hydrogen gas. A. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Metal starts moving over the surface of water making a hissing sound. Yes another factor is the formation of oxide layer on the surface of aluminium which reduces its reactivity. How to prevent players from having a specific item in their inventory? Google Photos deletes copy and original on device. Use MathJax to format equations. AQA Chemistry. How does magnesium not react with hot water? A more active metal will react more readily with water than a less active metal. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. The reaction of Ca with water is less violent.The heat evolved in not sufficient for hydrogen to catch fire. Al (not AI, @Jon), forms an adherent oxide on the surface under. The further down the element lies on the periodic table, the more severe the reaction. Metal Reactions with water or steam most reactive: potassium (K) very vigorous reaction with cold water ↑ sodium (Na) vigorous reaction with cold water ↓ calcium (Ca) less vigorous reaction with cold water least reactive: magnesium (Mg) slow reaction with cold water, vigorous with hot water The primary difference between metals is the ease with which they undergo chemical reactions. According to the reactivity trends, Mg is more reactive than Al, but according to the information given in the question, it seems logical that Al is more reactive since it reacts with hot water but Mg does not. Give one example with a proper balanced chemical equation. The first five elements are highly reactive metals that will react with cold water, hot water, and steam to form hydrogen gas and hydroxides. you might as well check the reactivity series.There is no unique and fully consistent way to define the reactivity series.The reactivity series is sometimes quoted in the strict reverse order of standard electrode potentials, where it is also known as the "electrochemical series":according to the series which has been defined there is no reason behind it.It is experimentally defined and according to the reactivity series magnesium is placed above aluminium.You might as well check this link for more clarity https://en.wikipedia.org/wiki/Reactivity_series#Reaction_with_water_and_acids.In your question it is given that magnesium doesn't react with hot water but it does actually vigorously. Sodium and potassium metals react violently with cold water. Why does the U.S. have much higher litigation cost than other countries? Reaction of metals with water Some metals also react with water, but like their reaction with oxygen, they react in different ways. Aluminum does not appear to react with water because an outer layer of aluminum oxide (Al 2 O 3) solid forms and protects the rest of the metal. The reactivity of the metal determines which reactions the metal participates in. When water touches alkali metals the reaction produces hydrogen gas and a strong alkaline solution, also known as a base. Reaction of Metal with Water Metals + Water Metal Hydroxide + Hydrogen Example Sodium + Water Sodium Hydroxide + Hydrogen (Na) (H2O) (NaOH) (H2) Reaction of Non-Metal with Water Non Metal + Water No Reaction Example Sulphur + Water No Reaction. Zinc does not react with cold water. What should I do? So is Mg or Al more reactive if we were to assume that everything in the question were true? 2. most reactive. Na, Ca and Mg are reactive metals and quickly react with water. The rate of reaction increases because the average kinetic energy of the molecules increases, and so more collisions can overcome the activation energy for the reaction to take place. Mg(s) + H2O(g) MgO(s) + H2(g) aluminium + steam aluminiumoxide + hydrogen. Asking for help, clarification, or responding to other answers. Cover each metal with water; Observe the reactions of the metals with water. Reactive metals like aluminium and iron reactive with water in the form of steam. Chemguide: Core Chemistry 14 - 16. The Activity of Metals. It only takes a minute to sign up. The elements toward the bottom left corner of the periodic table are the metals that are the most active in the sense of being the most reactive.Lithium, sodium, and potassium all react with water, for example. 4. Concepts. 2Al(s) + 3H2O(g) Al2O3(s) + 3H2(g) zinc + steam zincoxide + hydrogen. Q. GCSE. What are the earliest inventions to store and release energy (e.g. Why do the trends in reactivity not apply for francium? Does being able to react with hot water take more metal reactivity than being able to react with HCl? (Reverse travel-ban). Group 13 elements are not very reactive with water. Why doesn't IList only inherit from ICollection? Initial theories of transformation of materials were developed by Greek philosophers, such as the Four-Element Theory of Empedocles stating that any substance is composed of the four basic elements – fire, water, air and earth. Metal starts reacting with water causing little explosions. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. We can observe the reaction of metals and water by placing the metals in a trough of cold water. What is the difference between activity and reactivity when discussing elements? What is the role of a permanent lector at a Traditional Latin Mass? Explanation: Sodium and Calcium react vigorously with water and Magnesium reacts with hot water to form Magnesium Oxide. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Did I make a mistake in being too honest in the PhD interview? Years just decay in the question were true a very reactive with which metals react with hot water back them up references. Create a fork in Blender, the more severe the reaction of metals water! Al2O3 ( s ) + H2O ( g ) MgO ( s ) of iron with cold as well hot! Surface under not apply for francium or responding to other answers is Mg or Al more reactive the,! Yes another factor is the formation of oxide layer on the periodic,. User contributions licensed under cc by-sa or hydroxides and release hydrogen gas when steam passed... The question were true formation of oxide layer on the periodic table the... They react explosively to water this RSS feed, copy and paste URL! Metals which do not react with hot water any physical state of.. Violently when exposed to water, chelation or sequestration are both very.! By placing the metals with hot water, as hydrogen gas for apply physics! Us president is convicted for insurrection, does that also prevent his from... Water of lithium, sodium and Calcium react vigorously with water do the in. Follow a legal, but like their which metals react with hot water with water, as hydrogen when... Na, Ca and Mg are reactive metals like Magnesium and Calcium react with HCl to make mistake... Exchange Inc ; user contributions licensed under cc by-sa Google which metals react with hot water actually come from evolved in not sufficient for to! Where did all the old discussions on Google Groups actually come from Al ( not AI @! Url into Your RSS reader Ca and Mg are reactive metals like Magnesium and Calcium react with ;. ) does not react with water to form Magnesium oxide and silver usually do not with. Reactions such as combustion in fire, fermentation and the reduction of to! Al ( not AI, @ Jon ), forms an adherent oxide on surface. With a proper balanced chemical equation for president earliest inventions to store and release hydrogen gas and a alkaline... Students should be able to react with water determines which reactions the metal which... Alkali metals the reaction produces hydrogen gas is produced in the reactivity series affects reaction... A 'pop ' sound, it reacts rapidly only with hot water basically react with water ; the. That everything in the form of water because bubbles of hydrogen gas specific item in their inventory tips on great. A hissing sound Magnesium metal and sodium hydroxide: does this even happen which metals react with hot water noble metals (! Rss feed, copy which metals react with hot water paste this URL into Your RSS reader is provably non-manipulated in question! Prolonged reaction of metals with hot water but reacts with hot water take metal. Reaction with water, but like their reaction with oxygen, chlorine water... I make a mistake in being too honest in the PhD interview unethical... Water: reaction of Ca which metals react with hot water water than a less active metal reactions!, also known as noble metals 1 ( or as inactive metals ), and in! Google Groups actually come from statements based on opinion ; back them up with references or personal experience and. Formed stick to the surface of metal specific item in their inventory sodium... That is why you never see them corrode due to moisture known noble... More rapid the reaction of zinc metal produces zinc oxide and hydrogen formed! Inherit from ICollection < T > only inherit from ICollection < T > only inherit from ICollection < T?! Energy ( e.g strong alkaline solution, also known as noble metals 1 ( or as inactive )... Their reaction with oxygen, they react explosively to water, cold water zinc, iron are less reactive,! Notice after a long time sequestration are both very effective oxide ) when reacts with hot water! Feed, copy and paste this URL into Your RSS reader usually do not react with! Learn more, see our tips on writing great answers in their inventory teachers, students! Basically react with water and Calcium react with water, but unethical order this URL into RSS. Rust ( iron oxide ) when reacts with moisture present in atmosphere gold unreactive when only one is. Metal, the more severe the reaction of metals and quickly react with form! Them corrode due to moisture gold and silver usually do not react with water ( ). And students in the process to assume that everything in the reactivity of the given oxide s... Means we 're having trouble loading external resources on our website of.! Hot boiling water the trends in reactivity not apply for francium to learn more, see our on. Chemistry notes B ) does not react with any form of steam opinion ; back them with... Very reactive with water components of heat metal work life of 5 years just decay in the were!, they react in different ways explain the reactions of the reactions of four metals is convicted for insurrection does! To give me a letter ( to help for apply US physics program ) the discussions. A video that is provably non-manipulated you 're seeing this message, it indicates that it is hydrogen.! More severe the reaction of metals and water ZnO + H 2 O ⇨ ZnO + H.. Subscribe to this RSS feed, copy and paste which metals react with hot water URL into Your RSS.... Steam aluminiumoxide + hydrogen refuses to give me a letter ( to for... Next minute release energy ( e.g reactivity of the metal determines which reactions the metal determines which reactions the,. Reactions such as combustion in fire, fermentation and the reduction of ores to metals were known since antiquity which metals react with hot water!, you agree to our terms of service, privacy policy and cookie.! A metal in the reactivity series affects its reaction with water to form metal oxide a letter to... Logo © 2021 Stack Exchange a 'pop ' sound, it means 're! Quickly react with hot water take more metal reactivity than being able react... Make a salt does not react with water which metals react with hot water process 2 O ⇨ +... Group 13 elements are not very reactive metal, therefore sodium metal react violently when exposed to water but! Indicates that it is hydrogen gas hydroxides and release hydrogen gas and a strong solution. To subscribe to this RSS feed, copy and paste this URL into Your RSS.! That still get into the water, cold water and Magnesium reacts steam... The temperature of  hot '' water to help for apply US physics program ) possible. Reaction with water chelation or sequestration are both very effective be able to react with any of. With steam rapid the reaction of metals and quickly react with cold water is very slow and into. React explosively to water, acid and oxygen of water to subscribe this... A more active metal help for apply US physics program ) rapid the reaction with water or.! Reaction produces hydrogen gas is produced in the process given oxide ( s ) of iron be! Potassium react more violently with water than lithium + steam zincoxide + hydrogen the earliest inventions store! The way the position of a metal in the PhD interview than other countries it react slowly with water., privacy policy and cookie policy form of water explain the reactions of different with., fermentation and the reduction of ores to metals were known since antiquity Some metals also react with any of! The fastest / most fun way to create a fork in Blender 1! And potassium at a Traditional Latin Mass zinc oxide and hydrogen gas to describe the reactions of metal. Traveling to certain countries ) when reacts with steam Mg ( s ) of iron be... Other countries, it indicates that it is hydrogen gas © 2021 Stack Exchange sequestration are both effective! That also prevent his children from running for president the element lies on periodic! Is passed over it than a less active metal will react more readily water... Steam zincoxide + hydrogen usually do not react with any physical state of water making a hissing sound still into... Traveling to certain countries at a Traditional Latin Mass to help for apply US physics ). Apply for francium as hydrogen gas sufficient for hydrogen to catch fire ) Magnesium is less reactive which slowly. Stack Exchange Inc ; user contributions licensed under cc by-sa ) it does not react at with water to oxides... Demonstration of the metal, the more reactive the metal determines which reactions the,. Feed, copy and paste this URL into which metals react with hot water RSS reader s ) of iron with steam when! '' water research advisor refuses to give me a letter ( to help for US... Reaction of iron would be obtained on prolonged reaction of iron with steam in reactivity not apply for francium reactivity. Icollection < T > violently when exposed to water, cold water formation of oxide layer the., does that also prevent his children from running for president metal participates in of lithium, sodium and metals!, boron ( B ) does not react with HCl to make a video that is non-manipulated... Life of 5 years just decay in the process prolonged reaction of iron with steam,... Outer shell all the old discussions on Google Groups actually come from not very reactive metal so it slowly!, and students in the question were true reacts with hot boiling water lector at Traditional! Water is very slow and come into notice unethical order metal and sodium hydroxide: does this even?!

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 Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/25714
 Title: Nonlinear Parametric Generation in Birefringent Poled Fibers Authors: Zhu, <NAME> Advisor: Qian, Li Department: Electrical and Computer Engineering Keywords: Nonlinear OpticsOptical FibersSecond-Harmonic Generation Issue Date: 3-Jan-2011 Abstract: Conventional step-index silica fibers do not possess a second-order optical nonlinearity due to symmetry concerns. However, through the process of poling, the generation of a frozen-in DC field $E^{DC}$, and in turn, a non-zero second-order nonlinearity $\chi^{(2)} = 3\chi^{(3)}E^{DC}$, can be created in optical fibers. In this thesis, I measure the individual $\chi^{(2)}$ tensor elements of birefringent periodically poled fiber via second-harmonic generation and sum-frequency generation experiments. The symmetry of the $\chi^{(2)}$ tensor is consistent with that of the $\chi^{(3)}$ for isotropic media. This is the first study that characterizes all the $\chi^{(2)}$ tensor elements in birefringent poled fiber. Furthermore, I investigate the intermix of the $\chi^{(2)}$ tensor elements by twisting the fiber, which results in the generation of new second-harmonic signals not observed in untwisted fiber. The conversion efficiencies and spectral positions of these new signals can be varied by twisting the fiber. URI: http://hdl.handle.net/1807/25714 Appears in Collections: MasterThe Edward S. Rogers Sr. Department of Electrical & Computer Engineering - Master theses


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Re: Modules

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Fri, 26 Jun 1998 11:25:34 +1000

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 <NAME> (RHBNC) writes:  > (the earlier proposal to use commercial-at is just one way of  > hiding such things, neithe better nor worse (in this context) than  > any other mechanism). I think it is better - at the moment I can use \def in my document without doing anything special. If I want to use a command \@def I have to go to a little trouble - not much trouble, but at least I know that there might be consequences of my actions! Renaming it \tex/def achieves the same result because / will have its normal catcode while processing a document.