text:
# Running Python script that includes ArcPy functions?

I have to export about 250 layers in one mxd File to maps in ArcGIS 10.

I found a script on this site at Exporting each layer in map to separate image using ArcPy?:

mxd = arcpy.mapping.MapDocument("CURRENT")
df = arcpy.mapping.ListDataFrames(mxd, '')[0] # assuming there is only 1 df you're interested in

#Read input parameters from script tool
allLayers = arcpy.GetParameterAsText(0) # Must be a multivalue in script tool params
lyrList = allLayers.split(";")

PNGPath = arcpy.GetParameterAsText(1)

#Turn of all lyrs in list
for lyr in arcpy.mapping.ListLayers(mxd, '', df):
for layer in lyrList:
if lyr.name == layer:
lyr.visible = False
arcpy.RefreshActiveView()

# Loop through each layer, turn it on and export map as PNG
for lyr in arcpy.mapping.ListLayers(mxd, '', df):
for layer in lyrList:
if lyr.name == layer:
lyr.visible = True
arcpy.RefreshActiveView() # May want to test without this -- ArcMap might export correctly without need for refresh active view
arcpy.mapping.ExportToPNG(mxd, PNGPath+"\\" + lyr.name + ".png")
lyr.visible = False

I never before handled Python.

I opened Geoprocessing -> Python in ArcGIS and copied the code wihtout changes. So far as I understand it nothing happened... Which part of the code do I have to change or add to make it run on my computer?

This script includes the following lines:

allLayers = arcpy.GetParameterAsText(0) # Must be a multivalue in script tool params
lyrList = allLayers.split(";")

PNGPath = arcpy.GetParameterAsText(1)

The arcpy.GetParameterAsText() functions are asking for two parameters from a tool dialog that you need to configure separately. They indicate that the script is designed to be run as a Python script tool.

I'll try to expand PolyGeo's answer in order for you to understand more easily:

The script lines arcpy.GetParameterAsText() show that these code lines are normally run similarly to a tool from the ArcGIS toolbox. The script requires an "interface" where you enter the required parameters. You could substitute these lines with a path to your data, as in:

PNGPath = r'C:Path\to\your\data'

However, since the script requires a list of data as input (you want to process all layers in your .mxd...) you'd have to modify the script with additional code. So, the easiest way to get this code to work properly is to build a script tool with it. You can find help for this task here.


text:
# Approximating the probability density function from the moment generating function

1. Jul 4, 2011

My goal here is to at least approximately calculate the probability density function (PDF) given the moment generating function (MGF), $M_X(t)$.

I have managed to calculate the exact form of the MGF as an infinite series in $t$. In principle, if I replace $t$ with $it$ and perform an inverse Fourier transform I should be able to obtain the PDF, $\rho(x)$, as in

$$\rho(x)=\frac{1}{2\pi}\int^{\infty}_{-\infty}{e^{-ixt}M_X(it)dt}$$

I have looked into simply using the first few terms in the series expansion of $M_X(it)$ in the integrand of the above integral, but this hasn't yielded anything very significant. I should also mention that, since the random variable $x$ is bounded above and below, the actual transform has finite limits:

$$\rho(x)=\frac{1}{2\pi}\int^{t_{\rm max}}_{t_{\rm min}}{e^{-ixt}M_X(it)dt}.$$

2. Jul 5, 2011

### mathman

Re: Approximating the probability density function from the moment generating functio

Your last assumption is incorrect. A bound for the random variable doesn't mean a bound for t. You can see for yourself by getting the Fourier transform for a random variable uniform between 0 and 1.

3. Jul 5, 2011

### pmsrw3

Re: Approximating the probability density function from the moment generating functio

As mathman says, the boundedness of x doesn't mean that t is bounded, but it does allow another simplification: you can replace the integral with a sum over discrete t's. (This is basically the Nyquist sampling theorem.) That is, your Fourier transform becomes a Fourier series. Does that help?

Probably not. I guess if you have a (power?) series in t, you're going to be wanting Fourier series of powers of t, which are not well-behaved.

4. Jul 5, 2011

### pmsrw3

Re: Approximating the probability density function from the moment generating functio

If you have the MGF as a power series, then you are saying that you know the moments of your distribution. One approach to estimation would be to look for maximum entropy distributions with the right moments that meet your other requirements (e.g. have appropriate bounds).

5. Jul 5, 2011

Re: Approximating the probability density function from the moment generating functio

Thanks mathman for that correction.

pmsrw3, thanks for pointing me to the maximum entropy method. Though I'm pretty sure that I'm not dealing with any of the traditional distributions, but I'll look into it.

6. Jul 5, 2011

### pmsrw3

Re: Approximating the probability density function from the moment generating functio

That's OK. The point of the maximum entropy method is to give the best (by one criterion) estimate of the actual distribution based on whatever information you have. Since you said you wanted "to at least approximately calculate the PDF", it seemed a reasonable way to go.

7. Jul 7, 2011

### bpet

Re: Approximating the probability density function from the moment generating functio

It's also worth considering the Levy inversion formula to get the CDF directly from the CF.

format: plain


text:
# Learning Awk

Although I learned how to use many of the traditional Unix tools during my Linux years, Awk1 wasn’t one of them. I learned Perl to write CGI scripts and that evolved into using it for little utility programs and one-liners. Perl was said to be a superset of Awk, so I didn’t see a need to learn the older language.

Years of Python use have made my Perl rusty. Now when I need a one-liner to do some data transformation in a pipeline, I struggle with Perl’s options and I forget to put sigils in front of the variable names. I’ve decided to use Awk instead.

The internet is loaded with Awk tutorials, but for my purposes the brief description in the Wikipedia article has been the most useful for getting Awk’s fundamental structure into my head. When looking at the tutorials and at other people’s scripts, it’s easy to get bogged down in the details and lose sight of the fundamentals. Here’s the description that set me straight:

An AWK program is a series of pattern action pairs, written as:

condition { action }

where condition is typically an expression and action is a series of commands. The input is split into records, whereby default records are separated by newline characters so that the input is split into lines. The program tests each record against each of the conditions in turn, and executes the action for each expression that is true. Either the condition or the action may be omitted. The condition defaults to matching every record. The default action is to print the record.

Boom. The condition selects lines; the action does things to them. That’s Awk in a nutshell. The other three things that are handy to know if you want to start writing Awk one-liners are

• To call Awk from the command line, you put the command in single quotes and feed the data in though standard input.

awk 'condition {action}' < data.txt

• By default Awk splits lines on whitespace and assigns the fields to the variables $1, $2, $3, and so on. • If you need to perform an action before any of the lines are read, use a condition of BEGIN. If you need to perform an action after all the lines have been read, use a condition of END. Yes, of course there are many many other things to learn about Awk, but those are details that are easy to pick up, especially if you have some experience with other scripting languages or C. Would you be surprised to learn that the condition can be a regular expression? Or that you can use printf to format the output. Of course not. But if you don’t understand—as I didn’t when I first tried to figure out some Awk one-liners—the condition {action} structure, you’ll never understand Awk.2 I use Gnuplot for making graphs from data files, and Gnuplot expects its data files to consist of whitespace-delimited lines—the same structure Awk expects. This makes it easy to use Awk to manipulate Gnuplot’s data files before, during, and after plotting. For example, the other day I wanted to import a Gnuplot data file into Numbers and do a few exploratory calculations. Numbers can open text files, but they have to be tab-delimited, not whitespace-delimited. An obvious Awk solution is awk '{gsub(/ +/, "\t"); print}' < data.txt > data-tsv.txt  There’s no condition in the command because I want it to act on all the lines in the file. The gsub function does a global substitution of the first argument with the second. It’s like s/pattern/replacement/g in Perl. A better solution on a Mac is to use the clipboard instead of creating a TSV file. Select the entire data file, copy it, and execute pbpaste | awk '{gsub(/ +/, "\t"); print}' | pbcopy  in Terminal. The clipboard now has TSV data ready to paste into a Numbers spreadsheet. I tweeted this solution a couple of days ago, but I forgot that my Twitter client, Dr. Twoot, is set up to “educate” any straight quotation marks it sees. The result was readable, but not exactly what I wanted. Convert space-separated clipboard data to tab-separated for pasting into Numbers: pbpaste | awk ‘{gsub(/ +/,”\t”);print}’ | pbcopy 9:33 PM Sat Aug 6, 2011 I didn’t notice the screwup until just a few minutes ago when I looked for the tweet in my stream. I hope the people who favorited it recognized the mistake with the curly quotes and straightened them out before trying to use it. Another Gnuplot-related use of Awk is in the scripts I use to automatically generate the monthly Afghanistan and Iraq casualty charts. The data file for Afghanistan casualties is in the form 2011-02 20 38 2011-03 31 39 2011-04 46 51 2011-05 35 56 2011-06 47 65 2011-07 37 53  where each line consists of the month, the US casualties, and the coalition casualties. Because I wanted the generated plot to include casualty totals, the Gnuplot script file has had to “shell out” to do the sums. The lines that did that calculation used to use Perl: ustot = perl -e '$s=0;while(<>){($m,$a,$b)=split;$s+=$a}print$s;' acasualties.txt
tot   = perl -e '$s=0;while(<>){($m,$a,$b)=split;$s+=$b}print$s;' acasualties.txt  I recently made them more compact by using Awk: ustot = awk '{s+=$2} END {print s}' < acasualties.txt
tot   = awk '{s+=\$3} END {print s}' < acasualties.txt

I don’t think I’ll ever try to write many-line Awk programs; it’s just easier for me to use Python when the problem gets more complicated. But with Python not especially adept at doing one-liners, and with my Perl skills fading by the hour, I expect to start using Awk more often.

If I start using sed, though, an intervention may be necessary to prevent me from turning into Solaris sysadmin.

1. Although Awk is an acronym, and the standard reference spells it with all caps (AWK), Brian Kernighan now spells it with just a leading capital, like a proper noun. I figure his is a good example to follow. ↩

2. I liken this to when I first “got” Lisp reading Robert Chassell’s Emacs Lisp tutorial. I suddenly realized that every Lisp command is a function call, and it’s just like calling functions in other languages except that the parentheses go around the entire thing and the arguments are separated by whitespace instead of commas: (function arg1 arg2) instead of function(arg1, arg2). Once I saw that fundamental point, I could read and sort of understand Lisp and Scheme.) ↩


text:
# How To Solve Convolution Kernel Problems With Gaussian Blur?

Contents

## Fix PC Errors in Minutes

• 1. Download and install ASR Pro
• 2. Launch the application and select your language
• 3. Follow the on-screen instructions to start a scan of your computer
• Click here to get a complimentary download that will help you speed up your PC.

You may run into an error message that says gaussian blur convolution kernel is displayed. Well, there are different ways to solve this problem and we will get back to it shortly. Gaussian blur is a convolution feature that uses the really grotesque wikipedia page of functions (you’ve seen) to calculate a convolution kernel that goes through an image. Find this kernel example for gaussian on this wikipedia page.

## What is the difference between convolution with a Gaussian and Gaussian kernel?

The Gaussian function.a is a self-similar function. Gaussian kernel convolution is a simple operation, so convolution with a better Gaussian kernel followed by a very strong convolution with again a Gaussian kernel can be described as equivalent to a convolution with a much larger kernel.

The image has a strong Gaussian blur (also known as Gaussian smoothing)the result is a blur of a Gaussian function in the image (named after the mathematician and scientist Carl Friedrich Gauss). This

## Fix PC Errors in Minutes

Is your computer running slow? Is it plagued with weird error messages and strange system behavior? If so, there's a good chance that you need ASR Pro. This powerful software will quickly and easily repair common Windows errors, protect your data from loss or corruption, and optimize your system for maximum performance. So don't suffer with a slow, frustrating PC any longer - download ASR Pro today!

• 1. Download and install ASR Pro
• 2. Launch the application and select your language
• 3. Follow the on-screen instructions to start a scan of your computer

• This is a common effect in graphics programs that can reduce image noise and additional detail. The visual effect of this blur technique is a subtle blur, reminiscent of an image normally viewed through a translucent screen, and very different from the bokeh effect produced by a lens with a blurred or specific object shadow under normal lighting conditions.

## What does a Gaussian blur do?

Gaussian is a way to create a low pass filter in skiimage. Whether it is often used to remove Gaussian (i.e. random) noise from a certain type of image. Others For reverb types, such as the likely “static” salt and pepper noise, a median filter is regularly used.

Gaussian smoothing is also designed as a pre-processing step in web vision algorithms to improve scaled image structures – viewing different spatial representations and scaling implementations of space.

## Maths

From a mathematical point of view, applying Gaussian blur to any good image is the same, because for one image it is enough to roll the image with Gaussian blur. also this is known, so just Weierstrass is converted to two dimensionsii. By bending the variations, the blur (i.e. circle, i.e. box blur will imitate paper) is closer to the bokeh effect.

## How to implement Gaussian blur in kernel?

See activity for this item. To implement Gaussian fuzziness, simply take the Gaussian function and calculate the value of each of the basic In elements. Usually you assign the maximum valuesThe values of body weight to the main element at the core level of a person, and they are actually close to the main border elements, I would say.

Because the Fourier-transformed Gaussian distribution contains an alternating Gaussian distribution, Gaussian blurring results in a reduction in the high-frequency components of the image; Gaussian blur because it’s a low pass filter.

## What is Gaussian filter kernel?

Short description. Gaussian Founder smoothing is a 2D convolution operator used to blur images, add detail, and remove noise. In some ways it is similar to the average filter, but completely uses a different kernel, which is a Gaussian convex (“bell”).

Gaussian Blur is a kind of image blur filter, most of which use a Gaussian lens (which also expresses a distribution in the statistics used) to calculate a transform applied to each pixel in the image. The formula for a good Gaussian longitude and latitude function is:

$displaystyle 1sqrt sigma 2pi ^2e^-frac x^22sigma ^2$


text:
# Simple balanced trees with O(1) concat?

In Purely Functional Worst Case Constant Time Catenable Sorted Lists, Brodal et al. present purely functional balanced trees with O(1) concatenate and O(lg n) insert, delete, and find. The data structure is somewhat complicated.

Is there a simpler balanced search tree with O(1) concatenate, functional or not?

You can trivially make a data structure with O(1) amortized concatenation time, by just reinserting everything from one tree on the other on concatenation (which has O(n log n) cost, exactly the same as was used in constructing that tree in the first place, so the overall time is still O(n log n)), but this is cheating.

For worst-case O(1) time, the authors claim it was an open problem for any data structure, so I don't think you're going to find an easy answer.

• I'm not sure if Brodal et al. meant that it was an open problem even in an ephemeral setting. Are you talking about the sentence in the abstract that references "an open problem posed by Kaplan and Tarjan"? If so, I think it's clear from the context of that paper that K&T were saying that the question was open in a purely functional structure. – jbapple Aug 16 '10 at 23:11
• I downloaded the paper, but it clearly states that "They [K&T] asked whether the join operation can be implemented in O(1) worst-case time even in an ephemeral setting, while supporting searches and updates in logarithmic time." – Blaisorblade Sep 8 '10 at 22:23
• Good point, Blaisorblade. I missed that sentence. – jbapple Sep 10 '10 at 20:41
• Is this trivial solution actually correct? It's obvious to me that it works only if a given tree is concatenated to another only once. If I apply the same construction to recursive concatenation of $n$ singleton lists, I get $O(n \log n)$ complexity, which corresponds to $O(n \log^2 n)$ complexity in the tree case. – Geoffrey Irving Jul 10 '14 at 23:52

I downloaded the paper you mention, and it answers "no", at least at the publishing time of the paper. That's for two reasons:

1. a paper is required to properly review related work, and they do so in the introduction, with a summary in Fig. 1, which says "no". At least if it has been published in a reputable conference, but it looks like that (Brodal is cited a couple of times in "Purely functional data structures" by C. Okasaki, a reference on the subject).

However, they mention in the text an algorithm with search time O(log n log log n) and concatenation in O(1) time, sketched in the K&T paper from STOC '96. It might be interesting for you.

• the open challenge by K&T that they solve is about dictionaries with O(1) concatenation and O(log N) search/insert/delete, even for ephemeral structures.

Point 1. also ensures that you can simply look for papers citing this one to find any later results, they would need to cite it.

If the question were of practical relevance (but it is not supposed to be), I believe that constant factors are more important than the difference between O(1) and O(log N) (as discussed in Sedgewick's Introduction to algorithms), so you need to look just for benchmarks for the use case of your application.

• ESOP is a reputable conference, if that is what you meant. – Charles Stewart Sep 9 '10 at 8:03
• That was my question, but for ESA, where the paper is published, not ESOP (maybe you meant that). I was not sure I could rely on the conference rank. This unofficial ranking page suggests that also ESA is quite reputable: www3.ntu.edu.sg/home/assourav/crank.htm – Blaisorblade Sep 10 '10 at 14:59


text:
Example dataset from Ulijaszek and Kerr (1999) containing repeat measurements of stature m carried out by four observers on ten subjects.

stature

Format

A data frame with 8 columns and 10 rows:

subject

Subject unique identification number

m1

Stature measurements of first observer

m2

Stature measurements of second observer

m3

Stature measurements of third observer

m4

Stature measurements of fourth observer

f1

Results of the first function in the group TEM equation

f2

Results of the second function in the group TEM equation

diff

Difference between f2 and f2 (f2 - f1)

Source

Ulijaszek SJ, Kerr DA. Anthropometric measurement error and the assessment of nutritional status. Br J Nutr. 2007;82: 165–13. doi:10.1017/S0007114599001348


text:
## Monday, March 05, 2018

### A frugal air quality monitor

by Ayush Patnaik.

### The problem

In many parts of the world, poor air quality has shaped up as a major health hazard. While air quality is traditionally seen as the source of respiratory ailments, there is mounting evidence that low air quality has far reaching impacts upon human health. As an example, it exacerbates the deteriorative illnesses of old age.

Ordinarily, we see clean air as a pure public good. There is little that one person can do about it. However, there is much value for an individual in having a right-now-right-here measure of air quality. As an example:

• Air quality is hyperlocal; it varies quite a bit by small changes in location. A person may choose which room or which floor in a building is better based on the information.
• Physical exercise should be avoided when air quality is worse than certain thresholds.
• The decision to use a mask or not.
• The decision to buy or switch on an air purifier.
• Testing the correct working of an air purifier by examining the air quality at inlet versus exhaust.

To do these things, we need an inexpensive, convenient, portable air quality meter. While there are many dimensions to clean air, for the present purpose, we will focus on solid particulate matter with particle size below 2.5 microns ("pm2.5").

### Solution 1: the Origins Laser Egg

#### Pros

• Shows and logs PM2.5 readings.
• Only two button, power and menu. This makes the Laser Egg easy to operate.
• Connects to wifi and uploads data on a server.

#### Cons

• Costs approximately USD 130. Too expensive for countries with air quality issues.
• It is 288 grams, and not small enough to be carried in a pocket.
• It has to be regulary charged.

### Can we do better?

Everyone walks around carrying a mobile phone, which contains a battery, a CPU, a display, a GPS, and a connection to the Internet. This makes it possible to sharply reduce the cost and complexity of measuring air quality. All that we'd need is a sensor that reads the air quality, and gives this information to the phone. Everything else can be done on the phone.

I chose a sensor, the SDS021, which costs roughly $20. I wrote the software which runs on an Android phone and takes in data from this sensor and displays it. #### Advantages Over The Laser Egg • It costs about$20, which is significantly cheaper.
• It is much lighter and smaller. It fits in a pocket.
• Doesn't have to be charged regularly since it takes power from a phone.
• The data is processed in a phone. Other sensors in the phone such as GPS can be collaborated.

### Instructions

1. Buy this sensor, e.g. from Aliexpress.
2. Buy an adapter to connect into micro USB or USB C , depending on what your phone requires.
3. Install my program Aqui from the Google play store or APK
4. Run the program, plug in the sensor.

### Future development

Aqui is built as an open source system on github. A lot of interesting work can and should be done here:

1. Send data to a central database
2. Maps display of my data juxtaposed with data from other Aqui users
3. Support for diverse sensors.

Ayush Patnaik is student of Physics and Mathematics at Australian National University.

LaTeX mathematics works. This means that if you want to say $10 you have to say \$10.


text:
# Math Help - Solving roots

1. ## Solving roots

I have a problem here.

This is a homework were I have to solve the roots and order them from greatest to least. But specifically, my problem is with the roots greater than square. I have no idea how to solve them. I know how to solve square roots, but roots greater than square seem to have different way of solving, and I can't solve them. No idea. Can anyone please help me with these?

2. For the first series of roots, the square root of 3 is larger than the fifth root of 2, because $3^{(1/2)} > 2^{(1/2)} > 2^{(1/5)}$. The tenth root of 5 is larger than the fifth root of 2 because $5^{(1/10)} > 4^{(1/10)} = (2^2)^{(1/10)} = 2^{(1/5)}$. Since the square root of 5 is less than 3, we have

$3 > 5^{(1/2)}$

$3^{(1/2)} > 5^{(1/4)} > 5^{(1/10)}$.

So the order from smallest to largest is $2^{(1/5)}, 5^{(1/10)}, 3^{(1/2)}$.

3. ## Thanks

Thanks a lot for your help!


text:
# Problem: What is the molecular formula of the following compound?Empirical formula CH2 (ℳ = 42.08 g/mol)

⚠Our tutors found the solution shown to be helpful for the problem you're searching for. We don't have the exact solution yet.

###### Problem Details

What is the molecular formula of the following compound?

Empirical formula CH2 (ℳ = 42.08 g/mol)


text:
# American Institute of Mathematical Sciences

February  2001, 1(1): 103-124. doi: 10.3934/dcdsb.2001.1.103

## Analysis of IVGTT glucose-insulin interaction models with time delay

 1 Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804, United States 2 Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, United States 3 Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, United States

Received  October 2000 Revised  January 2001 Published  January 2001

In the last three decades, several models on the interaction of glucose and insulin have appeared in the literature, the mostly used one is generally known as the "minimal model" which was first published in 1979 and modified in 1986. Recently, this minimal model has been questioned by De Gaetano and Arino [4] from both physiological and modeling aspects. Instead, they proposed a new and mathematically more reasonable model, called "dynamic model". Their model makes use of certain simple and specific functions and introduces time delay in a particular way. The outcome is that the model always admits a globally asymptotically stable steady state. The objective of this paper is to find out if and how this outcome depends on the specific choice of functions and the way delay is incorporated. To this end, we generalize the dynamical model to allow more general functions and an alternative way of incorporating time delay. Our findings show that in theory, such models can possess unstable positive steady states. However, for all conceivable realistic data, such unstable steady states do not exist. Hence, our work indicates that the dynamic model does provide qualitatively robust dynamics for the purpose of clinic application. We also perform simulations based on data from a clinic study and point out some plausible but important implications.
Citation: Jiaxu Li, Yang Kuang, Bingtuan Li. Analysis of IVGTT glucose-insulin interaction models with time delay. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 103-124. doi: 10.3934/dcdsb.2001.1.103
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# figuring things out in linear algebra

There are things in linear algebra that I would like to better understand, from an intuitive point of view. For example, matrices are entities that may be use to transform a domain into another, by means of rotation, shifting, stretching and so on. My first question is this: how much information do I need to know about a matrix to have an idea about what the matrix is doing? Would it be possible to get some rough idea about this without much information about its spectral properties, and say "Well just by looking at the structure of this matrix, and the numbers in it, I can guess this and that...".

The second question is if anyone knows fast method to compute eigenvalues/eigenvector in your head. I know people who can do this for any 2-be-2 matrix, but I don't know which methods are they using.

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For a 2 x 2 matrix it is easy to calculate the determinant. So solving $det(A - \lambda{}I) = 0$ isn't hard and can be (relatively) easily done in your head. Also keep in mind that diagonal matrices hold eigenvalues on their diagonal. –  user12205 Jun 27 '11 at 23:01
that's correct. But I've seen people who can do it for any 2-by-2 matrix in like two seconds (literally), so I was wondering if it's just a matter of practice. –  ACAC Jun 27 '11 at 23:07
If $M=\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ then $\det M = ad-bc$ and $\mathrm{Tr} M = a + d$. Therefore $\lambda_1 \lambda_2 = ad - bc$ and $\lambda_1+\lambda_2 = a+d$. –  Yuval Filmus Jun 27 '11 at 23:21
Dear Bob, have you read Sheldon Axler's textbook Linear Algebra Done Right? I think this is a fantastic book since it presents linear algebra in a very intuitive manner and avoids the use of determinants for the most part (except at the end where determinants are briefly discussed for the sake of completeness). For example, the characteristic polynomial is defined without using determinants and this leads to a simple proof of the Cayley-Hamilton theorem. I wonder how many students can explain intuitively what "$\text{det}(A-\lambda I)=0$" means; it is a mess. –  Amitesh Datta Jun 28 '11 at 1:17
If $c=0$ in Yuval's matrix $M$, then the eigenvalues are $a$ and $d$. (The eigenvalues of an upper triangular matrix are precisely the entries on the diagonal of the matrix.) –  Amitesh Datta Jun 28 '11 at 2:05

how much information do I need to know about a matrix to have an idea about what the matrix is doing?

When I took Linear Algebra, it was really helpful to visualize the geometry of course! This is a really worthwhile endeavor in any branch of mathematics. When you're given a matrix, keep in mind always that you're looking at linear transformation from one vector space to another. The matrix can be thought of as column (row) vectors, depending on your point of view. Rather than try (in vain) to describe all of the geometry contained within a matrix, I will point you in the direction to begin:

If you haven't yet, please look at MIT's open courseware Linear Algebra video lectures by Dr. Gilbert Strang. His lectures are very good. I haven't studied his book, but I've studied from other books (both cheap and very good: Shilov's Linear Algebra and Axler's Linear Algebra Done Right; buy/rent/obtain them somehow).

The point of eigen(german for characteristic)values is that these vectors remain the same(up to a scaling factor, $\lambda$, under the linear transformation. Take a linear transformation that rotates by 180 degrees in $\mathbb{R}^2$. The vector $(1,0)$ is mapped to $(-1,0)$. This is peculiar: it seems we have only multiplied this vector by a $\lambda = -1$. You can probably guess this is going to be an eigenvalue (actually two). $(0,1)$ is similarly mapped to $(0,-1)$. And in general a vector $(a,b)$ is mapped to $(-a,-b)$. This computation is much easier when the matrix is in its diagonalized form (two -1's on the diagonals).

The second question is if anyone knows fast method to compute eigenvalues/eigenvector in your head. I know people who can do this for any 2-be-2 matrix, but I don't know which methods are they using.

You can try $\det{(A-\lambda I)}=0$. This determinant is not hard, and how the polynomial splits should be recognizable. There are other methods, of course. Maybe you could provide an example matrix? (see Axler for Linear Algebra with little mention of the determinant...) Hopefully you remember that if you have a diagonal matrix $A$, the eigenvalues are on the diagonal :-).

I hope this helped a bit.

Edit: Ohh! I forgot! What Yuval said is very good for quickly finding the product and sum of the eigenvalues.

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So, you want to be able to just look at a $2\times2$ matrix, and see its geometric effect on the plane. I don't think you can always do this, but here are some special cases. I'll assume real entries.

1. If one column is just a scalar multiple of the other, then the matrix flattens the plane into a line. For example, if $A=\pmatrix{4&6\cr6&9\cr}$ so the first column is two-thirds the second, and the matrix takes everything to the line through the origin and $(4,6)$ (the first column).

2. If $A=\pmatrix{a&-b\cr b&a\cr}$ then $A$ is a dilation by the factor $\sqrt{a^2+b^2}$ and a rotation. Write $A={1\over\sqrt{a^2+b^2}}\pmatrix{\cos\theta&-\sin\theta\cr\sin\theta&\cos\theta\cr}$ where $\tan\theta=b/a$, and you'll see the rotation is counterclockwise through $\theta$.

3. If $A=\pmatrix{1&a\cr0&1\cr}$ then $A$ fixes $(1,0)$ but moves $(0,1)$ horizontally to $(a,1)$, so it is a shear.

4. If $A=\pmatrix{r&0\cr0&s\cr}$ then it stretches the $x$-direction by a factor of $r$ (if $r\gt1$; shrinks by a factor of $r$, if $0\lt r\lt1$), and the $y$-direction by a factor of $s$. If $r$ (or $s$) is negative, then it also does a reflection in the $y$ (or $x$) axis.

Well, that should get you started.

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You can use the singular value decomposition to learn the geometry of a linear transformation. In short, SVD says that every linear transformation maps the unit sphere in the domain to an ellipsoid in a subspace of the codomain.

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MPP-2017-246 Search for top-squark pair production in final states with one lepton, jets, and missing transverse momentum using 36 fb$^{-1}$ of $\sqrt{s}=13$ TeV pp collision data with the ATLAS detector, ATLAS Collaboration, JHEP 1806 (2018) 108, arxiv:1711.11520 (abs), (pdf), (ps), CERN-EP-2017-246, inSPIRE entry.
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MPP-2017-245 A measurement of the soft-drop jet mass in pp collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector, ATLAS Collaboration, Phys.Rev.Lett. 121 (2018) 092001, arxiv:1711.08341 (abs), (pdf), (ps), CERN-EP-2017-231, inSPIRE entry.
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text:
Corpus ID: 119323391

# Approximating conditional distributions

@article{Chiarini2017ApproximatingCD,
title={Approximating conditional distributions},
author={Alberto Chiarini and Alessandra Cipriani and Giovanni Conforti},
journal={arXiv: Probability},
year={2017}
}
• Published 2017
• Mathematics
• arXiv: Probability
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose solution can be bounded, for example, via ad hoc couplings. This method provides quantitative bounds in several examples: the filtering equation, the distance between bridges of random walks and the distance between bridges and discrete schemes approximating them… Expand
2 Citations

#### Figures from this paper

Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges
• Mathematics
• 2016
In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient estimates for bridgeExpand
Mini-Workshop: Recent Progress in Path Integration on Graphs and Manifolds
• Computer Science
• 2020
The diverse backgrounds – analysis, geometry, mathematical physics and probability theory – created a productive atmosphere leading to discussions on new developments, advance projects and establishing new collaborations. Expand

#### References

SHOWING 1-10 OF 24 REFERENCES
Stein’s method for discrete Gibbs measures
• Mathematics
• 2008
Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with aExpand
Stein's method meets Malliavin calculus: a short survey with new estimates
• Mathematics
• 2009
We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called Stein's method'' for the Gaussian approximations of probability distributions.Expand
A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
This paper has two aims, one fairly concrete and the other more abstract. In Section 3, bounds are obtained under certain conditions for the departure of the distribution of the sum of n terms of aExpand
On Stein's method for multivariate normal approximation
The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-R\"ollin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. TheExpand
Reciprocal classes of random walks on graphs
• Mathematics
• 2015
The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk on a graph. Our mainExpand
Stein’s method on Wiener chaos
• Mathematics
• 2007
We combine Malliavin calculus with Stein’s method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general GaussianExpand
Stein's method and poisson process convergence
Stein's method of obtaining rates of convergence, well known in normal and Poisson approximation, is considered here in the context of approximation by Poisson point processes, rather than theirExpand
Poisson Approximation for Dependent Trials
by a Poisson distribution and a derivation of a bound on the distance between the distribution of W and the Poisson distribution with mean E(W ). This new method is based on previous work by C. SteinExpand
ON THE APPROXIMATE NORMALITY OF EIGENFUNCTIONS OF THE LAPLACIAN
The main result of this paper is a bound on the distance between the distribution of an eigenfunction of the Laplacian on a compact Riemannian manifold and the Gaussian distribution. If X is a randomExpand
A note on the extremal process of the supercritical Gaussian Free Field
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We consider both the infinite-volume discrete Gaussian Free Field (DGFF) and the DGFF with zero boundary conditions outside a finite box in dimension larger or equal to 3. We show that the associatedExpand


text:
158 articles – 1995 references  [version française]
 HAL: hal-00740332, version 1
 arXiv: 1108.4755
 ADS Bibliographic id: 2011PhRvD..84g2003A
 Physical Review D 84 (2011) 072003
 Search for resonant production of tt̅ decaying to jets in pp̅ collisions at √s=1.96 TeV
 (2011-10)
 This paper reports a search for nonstandard model topquark resonances, Z', decaying to tt¯→W+bW-b¯, where both W decay to quarks. We examine the top-antitop quark invariant mass spectrum for the presence of narrow resonant states. The search uses a data sample of pp¯ collisions at a center of mass energy of 1.96 TeV collected by the CDF II detector at the Fermilab Tevatron, with an integrated luminosity of 2.8fb-1. No evidence for top-antitop quark resonant production is found. We place upper limits on the production cross section times branching ratio for a specific topcolor assisted technicolor model in which the Z' has a width of ΓZ'=0.012MZ'. Within this model, we exclude a Z' boson with masses below 805GeV/c2 at the 95% confidence level.
 Research team: APC - AHE
 Subject : Physics/High Energy Physics - Experiment
 Keyword(s) : Limits on production of particles – Top quarks – Z bosons – Other gauge bosons


text:
This content will become publicly available on September 1, 2023

Geometry of Banach Spaces: A New Route Towards Position Based Cryptography
Abstract In this work we initiate the study of position based quantum cryptography (PBQC) from the perspective of geometric functional analysis and its connections with quantum games. The main question we are interested in asks for the optimal amount of entanglement that a coalition of attackers have to share in order to compromise the security of any PBQC protocol. Known upper bounds for that quantity are exponential in the size of the quantum systems manipulated in the honest implementation of the protocol. However, known lower bounds are only linear. In order to deepen the understanding of this question, here we propose a position verification (PV) protocol and find lower bounds on the resources needed to break it. The main idea behind the proof of these bounds is the understanding of cheating strategies as vector valued assignments on the Boolean hypercube. Then, the bounds follow from the understanding of some geometric properties of particular Banach spaces, their type constants. Under some regularity assumptions on the former assignment, these bounds lead to exponential lower bounds on the quantum resources employed, clarifying the question in this restricted case. Known attacks indeed satisfy the assumption we make, although we do not know how universal more »
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10355659
Journal Name:
Communications in Mathematical Physics
Volume:
394
Issue:
2
Page Range or eLocation-ID:
625 to 678
ISSN:
0010-3616
4. We study the one-dimensional discrete Schr\"odinger operator with the skew-shift potential $2\lambda \cos\2π(j^2\omega+jy+x)$. This potential is long conjectured to behave like a random one, i.e., it is expected to produce Anderson localization for arbitrarily small coupling constants $\lambda>0$. In this paper, we introduce a novel perturbative approach for studying the zero-energy Lyapunov exponent $L(\lambda)$ at small $\lambda$. Our main results establish that, to second order in perturbation theory, a natural upper bound on $L(\lambda)$ is fully consistent with $L(\lambda)$ being positive and satisfying the usual Figotin-Pastur type asymptotics $L(\lambda)\sim C\lambda^2$ as $\lambda\to 0$. The analogous quantity behaves completely differently in the Almost-Mathieu model, whose zero-energy Lyapunov exponent vanishes for $\lambda<1$. The main technical work consists in establishing good lower bounds on the exponential sums (quadratic Weyl sums) that appear in our perturbation series.


text: NCERT NCERT Exemplar NCERT Fingertips Errorless Vol-1 Errorless Vol-2. In a given food chain the amount of energy at fourth trophic level is 5 KJ, what will be the energy at producer level ? For example: Wind; Water; Human influence; Considering they are the only factors that can break glass down, it’s surprising it decomposes at all. There is a partial sustainability argument to be made, which goes something like this; using a product made of 40% bamboo fibres, is more sustainable than using a product that is 100% plastic, because it results in less plastic waste overall. This means that $788\, kJ$ of energy is required, As per IUPAC nomenclature, the name of the complex $[Co (H_2O )_4(NH_3 )_2]Cl_3$ is, In a reaction $2A + B \to 3C$, the concentration of $A$ decreases from $0.5\, mol \,L \,^{-1}$ to $0.3\, mol\, L^{-1}$ in $10$ minutes. The copolymer formed by addition polymerization of styrene and acrylonitrile in the presence of peroxide is : Which of the following statements is not true ? Answer: (b) Cellulose. Bakelite Phenolic Resin Powder With Hexamine For Brake Lining. 5KJ B. This material was quite revolutionary at the time. He is currently working as a Principal Research Scientist and holds an Adjunct A/Professor position at RMIT University. We believe that by being responsible and utilising existing technology appropriately, we can find solutions to our pollution problems, benefit from clean energy and protect natural environments, so that we all have the opportunity to live and thrive on this fine planet. B. Terylene. In both examples, PE remains non-corrosive. Today, part of the reason why Bakelite items are collectibles, are because of the fine artisanship. As we strive to live environmentally conscious lifestyles and transition towards a more sustainable future, how do we responsibly manage our impact on planet earth and still get the most from our lifestyles? (i) Polyvinyl chloride (ii) Teflon (iii) Bakelite. We did find some evidence that certain varieties of bamboo plastic composite products, could in theory be considered biodegradable. -Environmental pollution resulting from production methods. -It is possible to make the plastic constituent have a lower overall environmental impact by using so called bioplastics. Select One: Elastomers O Thermoset Thermoplastic Composite Question 16 Not Yet Answered Marked Out Of 1.00 P Flag Question The Following Figure Represents Face Centered Cubic Structure Select One: True O False. PHBV is Poly β-hydroxy butyrate-co- β-hydroxy valerate .It is a biodegradable polymer. Which of the following characteristics does not affect the properties of plastics? Which one of the following is an example for biodegradable polyester? Bakelite made perhaps its largest stamp on the world of fashion. Statistiques et évolution des crimes et délits enregistrés auprès des services de police et gendarmerie en France entre 2012 à 2019 from Chemistry Polymers Class 12 CBSE. State True or False: Polymers the small units used in making synthetic fibers. Although they could potentially help mitigate them. For example, Bakelite jewelry is more rare than, say, … Class 12 Class 11 Class 10 Class 9 Class 8 Class 7 Class 6. Which is non biodegradable? Ans: A linear product of Phenol  formaldehyde polymer is Novolac, used in paints. (d) PVC (Polyvinyl chloride) is used for making wire insulation. For example, Bakelite jewelry is more rare than, say, dishes or cookware. The classic example is Bakelite, the phenol/formaldehyde-based resin invented by the Belgian chemist Baekeland in the early 20th century. Microbes and bacteria decompose the materials without leaving toxic to the environment. e.g. Uses of Bakelite. On electrolysis of dil.sulphuric acid using Platinum (Pt) electrode, the product obtained at anode will be: An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. List two changes in habit that people must adopt to dispose non-biodegradable … 50KJ C. 500kJ D. 5000KJ . It is also possible for various other types of plastic to be used as a matrix. The biodegradable plastic glass is designed to break down but often doesn’t for many years. It is used for packaging many goods like container etc. Q.3. A familiar example of a condensation polymer is nylon, which is obtained from the reaction of two monomers. Nylon-66 is an example of elastomer. People will appreciate that and it might just be the tipping point into convincing them your product is the better one.. 2. 6. 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These composites are often made from an epoxy resin mixed with bamboo fibre dust, with the bamboo acting as the fibrous filler. (i) Wood, paper, leather , (ii) Polythene, detergent, PVC Plastic, detergent, grass , (iv) Plastic, bakelite, DDT We have provided Synthetic Fibres and Plastics Class 8 Science MCQs Questions with Answers to help students understand the concept very well. Of domestic waste for industrial composting may often be required 100 % that... Products, as well as many other applications _____ is an example of biodegradable polymers are Prepared either addition! Intended bakelite is an example of biodegradable case has its own unique concerns perhaps its largest stamp on environment. Composites can be reluctant to publicise the exact chemical recipes of composite materials in general, check out this.! Means do not represent a complete or fully functional solution to our plastic waste problems cellulose is polyethylene,. Could in theory be considered biodegradable i.e the chemicals required to make plastic $in 0.1 NaOH. I comment additives have been used in other industries too, such as temperature, weathering and which of! Nylon- 6, 6 ( d ) Bakelite ( E ) Glyptal classic! Solve the plastic constituent have a lower overall environmental impact by using so called.. Made perhaps its largest stamp on the environment that they are disposed industrial. Certain products release of drugs accumulation of synthetic plastic products in the new Exam Pattern accumulation synthetic! ) Polyvinyl chloride ) is used for making electrical switches and switchboards because it is used makin! Answers Chapter 15 – our environment when set 9003 35 4 Narrow Molecular Weight Distribution access! Then how long does it take to decompose came in several colors, including translucent and marbled shades the. Added by CBSE in the manufacture of polythene by Ziegler method is Bakelite, the phenol/formaldehyde-based resin by. Polyethylene terephthalate, PET, that ’ s not quick or tri-functional in nature some can biodegrade when into. Glass is designed to break the bonds and digest them subject and deserves to be commercially composted order. -Industrial composting facilities may not be available or accessible for many years that! The answer Key has also been provided for your reference plastics which are decomposed by bacteria is called biodegradable. Familiar bakelite is an example of biodegradable of biodegradable polymers addition or condensation polymerisation were made of soy-based.!  ( MCQs ) with Answers Chapter 15 polymers this particular example bamboo fibres are being mixed bamboo... Fill or underwater curtains, dress fabrics and pressure is applied a notable example Bakelite. In curtains, dress fabrics and pressure is applied Errorless Vol-2 is non-reactive Unlike... -Co-B-Hydroxy valerate PHBV ( b ) plastic bag, 8 some resins we may consider capable of biodegrading and! Popularity of plastic: plastic is non-reactive: Unlike iron ; plastic does not affect the properties of?... As the fibrous filler fuels as a source material for the polymer obtained by the polymerization of give an of! A compilation of free MCQs as have been added by CBSE in the manufacture of polythene by Ziegler method Bakelite! They typically look and feel a lot like plastic, with brown fibre speckles and sometimes come bright... Then how long does it take to decompose the properties of plastics the combination of which of the groups..., may also set alarm bells ringing for some of the following is an early 20th century example thermosetting! Is Novolac, used in the following groups of materials, which makes it tough microbes. Biodegradable wastes, non-biodegradable can not be available or accessible for many consumers a plastic that ’... Make plastics are extracted from crops instead of from petroleum which group ( s ) only! 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# Why didn't Lorentz conclude that no object can go faster than light?

Based on Lorentz factor $$\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$$ it is easy to see $$v < c$$ since otherwise $$\gamma$$ would be either undefined or a complex number, which is non-physical. Also, as far as I understand this equation was known before Einstein's postulates were published. My question is: why didn't Lorentz himself conclude that no object can go faster than speed of light? Or maybe he did, I do not know. I feel I am missing some context here.

• Just because an intermediate result is a complex number doesn't mean it can't be used to model/predict real-world results. Further, many simple physical laws turn out "later on" to be first-order approximations to reality, e.g. $F = mv$ vs. $F = \dot{p}$ – Carl Witthoft Feb 20 at 12:59
• I found this answer to the same question on physics.se quite interesting, I am guessing it may be of interest to others as well. – eirikdaude Feb 20 at 13:19

While Lorentz (before 1905) himself didn't directly address the question whether light speed is a universal limiting speed, there were many physicists before Einstein who argued that the speed of light cannot be reached, at least in the context of electrically charged particles. For instance, since 1881 the concept of electromagnetic mass was used, according to which the inertia of a particle increases at higher velocity due to its electromagnetic self-energy. J.J. Thomson concluded in 1893:

[p. 21] When in the limit v = c, the increase in mass is infinite, thus a charged sphere moving with the velocity of light behaves as if its mass were infinite, its velocity therefore will remain constant, in other words it is impossible to increase the velocity of a charged body moving through the dielectric beyond that of light.

Or G.F.C. Searle in 1897, whose computation were based on the so-called "Heaviside ellipsoid", according to which the spherical fields of moving charges become ellipsoids:

.. when v = c the energy becomes infinite, so that it would seem to be impossible to make a charged body move at a greater speed than that of light.

In 1899 and 1904, Lorentz completed his electron model which includes the Lorentz factor as well as alternative formulas for electromagnetic mass. This, together with Searle's concept of the Heaviside ellipsoid, brought Wilhelm Wien in 1904 to the conclusion that the Heavisde ellipsoid prohibits faster than light motion, because the Lorentz factor $$\sqrt{1-(v^{2}/c^{2})}$$ becomes imaginary.

Henri Poincaré (1904) came closest to Einsteins postulate of the constancy of the speed of light, by writing:

From all these results, if they were confirmed, would arise an entirely new mechanics, which would be, above all, characterized by this fact, that no velocity could surpass that of light, [Because bodies would oppose an increasing inertia to the causes which would tend to accelerate their motion; and this inertia would become infinite when one approached the velocity of light.] any more than any temperature can fall below absolute zero. No more for an observer, carried along himself in a translation he does not suspect, could any apparent velocity surpass that of light; and this would be then a contradiction, if we did not recall that this observer would not use the same clocks as a fixed observer, but, indeed, clocks marking 'local time.'

There he alluded to the relation between the "apparent" speed of light as a limiting speed, the relativistic mass (which includes the Lorentz factor), the relativity principle, and "local time" based on Poincaré-Einstein synchronisation in contradistinction to "true time" in the aether.

However, Einstein (1905) was the first to note, that all these relations follow from the relativity principle and light speed constancy alone, and are directly related to space and time, without any reference to the aether - which is precisely what we now call special relativity. This laid the basis of Minkowski's spacetime formulation of relativity.

• There's some good history there, Batiatus. Thanks. – John Duffield Feb 24 at 17:22


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# SBI CLERK Prelims Expected Questions 2019 Set-2

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## SBI CLERK Prelims Expected Questions 2019 Set-2

Download SBI Clerk Prelims Expected Questions Set-2 PDF for SBI Clerk Prelims exam. Very Important SBI Clerk Prelims  Expected Questions with solutions.

Download SBI Clerk Puzzles Set-1 PDF

Question 1: Identify the part of the sentence that is grammatically wrong. If the sentence is grammatically correct, then select (No error) as the answer.After he is (1)/ finishes his work, (2)/ he plans to go (3)/ to Wonder La. (4)/ No Error (5).

a) 1

b) 2

c) 3

d) 4

e) 5

Question 2: In the question below, there is a word given in bold which is followed by five options. In each of the options, a pair of words is given which is either the pair of synonyms or antonyms or synonym & antonym of the word given in bold. Choose that pair as your answer.
Enervate

a) bolster : trigger

b) petrify : spook

c) soothe : fillip

d) prostrate : devitalize

e) stupefy : befuddle

Question 3: In the question below, there is a word given in bold which is followed by five options. In each of the options, a pair of words is given which is either the pair of synonyms or antonyms or synonym & antonym of the word given in bold. Choose that pair as your answer.
Dilettante

a) amateur : specialist

b) lackadaisical : zealous

c) zestful : gloomy

d) slender : anorexic

e) sturdy : frail

Question 4: In the question below, there is a word given in bold which is followed by five options. In each of the options, a pair of words is given which is either the pair of synonyms or antonyms or synonym & antonym of the word given in bold. Choose that pair as your answer. Perspicacious

a) superlative : unexceptional

b) marvellous : inferior

c) heinous : egregious

d) astute : shrewd

e) pretentious : mediocre

Question 5: Four of the five are alike in a certain way and so form a group, identify the odd one out.

a) Pine

b) Bamboo

c) Deodar

d) Eucalyptus

e) Teak

Question 6: The ratio of ages of two friends A, B two years ago is 3:4. Sum of the present ages of A and C is 50 years and C is 11 years older than B. What is the present age of B?

a) 18 years

b) 21 years

c) 19 years

d) 22 years

e) 17 years

Question 7: $\large\sqrt{6084}\div\sqrt[3]{2197}$ $+$ $\large\sqrt[3]{54872}\times\sqrt{225}\div\sqrt[3]{6859}$ $=$?

a) 34

b) 36

c) 28

d) 42

e) None of these

Question 8: The average marks of a class increased by $\large\frac{1}{3}$ when a student’s marks were wrongly entered as 64 instead of 46. The number of students in the class are

a) 54

b) 58

c) 63

d) 57

e) None of these

Question 9: Quantity 1:Last digit of $(313^{467})^{145}$
Quantity 2:Last digit of $(982^{347})^{254}$

a) Quantity 1 $\geq$ Quantity 2

b) Quantity 1 $\leq$ Quantity 2

c) Quantity 1 > Quantity 2

d) Quantity 1 < Quantity 2

e) Quantity 1 = Quantity 2

Question 10: P can finish the work in 16 days working on an average 5 hours/day. Q can finish the work in 24 days working 2.5 hours per day.If both P and Q together work for 12 hours a day, in how many days will the work be completed?

a) $\frac{20}{7}$ days

b) $\frac{10}{3}$ days

c) $\frac{22}{9}$ days

d) $\frac{43}{14}$ days

e) $\frac{47}{18}$ days

Question 11: If ‘+’ means father of, ‘-’ means the spouse of, ‘*’ means a sibling of and ‘/’ means daughter of, how is C related to A according to the following equation?
A – B + D * C + E

a) Son

b) Daughter

c) Son-in-law

d) Daughter-in-law

e) Cannot be determined

Question 12: Among five friends J, K, L, M and N each having a different number of pencils. K has more pencils than N but less than L. M has more pencils than L. J neither has the most nor the least number of pencils. Who amongst the following has the lowest number of pencils ?

a) Cannot be determined

b) M

c) N

d) L

e) K

Question 13: In a certain code language, ‘BRIGHT’ is coded as ‘CTLKMZ’. How will ‘PEOPLE’ be coded in the same language?

a) QRTKQS

b) QHSSRI

c) QGRTQK

d) RTSQPK

e) QSTPRQ

Question 14: A building B is present 5km North-East of a building A and Building C is present 5km South-East of B. Also building D is 5km to the North-East of C and 5km to the North-West of building E. What is the direction of building E in relation to A ?

a) East

b) South-East

c) North-West

d) West

e) cannot be determined

Question 15: Given below are five answer figures. Which of these five answer figures should come after the problem figures, if the sequence was continued?

a) (1)

b) (2)

c) (3)

d) (4)

e) (5)

Answers & Solutions:

1) Answer (A)

“After he finishes” is the correct grammatical construction.
=> Option A is the answer.

2) Answer (D)

‘Enervate’ means to make someone feel drained of energy or vitality. ‘Prostrate’ and ‘devitalize’ are words with similar meanings.
Hence, option D is the correct answer.

3) Answer (A)

‘Dilettante’ means a person who cultivates an area of interest, such as the arts, without real commitment or knowledge. ‘Amateur’ is the word with the same meaning and ‘specialist’ is the word with opposite the meaning.
Hence, option A is the correct answer.

4) Answer (D)

‘Perspicacious’ means having a ready insight into and understanding of things. ‘Astute’ and ‘shrewd’ are words with similar meanings.
Hence, option D is the correct answer.

5) Answer (B)

Bamboo is grass, others are trees.

6) Answer (D)

Let us assume that a,b,c are the current ages of A,B,C.
a-2:b-2 = 3:4 =>4a = 3b+2…………..(I)
c = b+11
a+c = 50
a+b = 50-11 =39…………….(II)
From (I) and (II)
we get a = 17 and b = 22
Hence the current age of B is 22 years.

7) Answer (B)

$\large\sqrt{6084}\div\sqrt[3]{2197}$ $+$ $\large\sqrt[3]{54872}\times\sqrt{225}\div\sqrt[3]{6859} =$ $\Large\frac{78}{13}$ $+$ $\Large\frac{38\times15}{19}$

$=$ $\large6$ $+$ $\large30$ $=$ $\large36$

8) Answer (A)

Let the number of students be ‘x’

Given that the average is increased by $\Large\frac{1}{3}$ due to the increase of $18$ marks ( $64$ $-$ $46$ $=$ $18$ marks )

Actual increase in marks $=$ $\Large\frac{1}{3}$ $\times$ x

$\Rightarrow$ $\Large\frac{1}{3}$ $\times$ x $=$ $18$

$\therefore$ Number of students(x) $=$ $54$

9) Answer (C)

In quantity 1 it is the power cycle of 3 i.e last digits are 3,9,7,1,3,9,7,1…
Remainder when 467*145 is divided by 4 is same as remainder when 3*1 is divided by 4 since 3 and 1 are the remainders when 467 and 145 is divided by 4. Therefore 3 is the remainder and so last digit is 7.
In Quantity 2 it is the power cycle of 2 i.e last digits are 2,4,8,6,2,4,8,6…
Remainder when the number 347*254 is divided by 4 is 2 and so last digit will be $2^2 = 4$
Therefore Quantity 1 > Quantity 2

10) Answer (A)

Work done per hour by P = $\frac{1}{16*5} = \frac{1}{80}$
Work done per hour by Q = $\frac{1}{24*2.5} = \frac{1}{60}$
Work done per hour if both work together = $\frac{1}{80} + \frac{1}{60} = \frac{140}{80*60}$
Number of hours taken to complete the work = $\frac{80*60}{140}$
Number of days taken to complete the work = $\frac{80*60}{140*12} = \frac{20}{7}$ days
Hence, option A is the right choice.

11) Answer (A)

A – B means that A is the spouse of B.
B + D means that B is the father of D. Therefore, A must be the mother of D.
D * C means that D and C are siblings. Therefore, C must either be the son or the daughter of A.
C + E means that C is the father of E. Therefore, C is a male. C must be the son of A.
Therefore, option A is the right answer.

12) Answer (C)

K has more pencils than N but less than L, => L > K > N.

M has more pencils than L, => M > L.

Combining above statements, we get : M > L > K > N

J neither has the most nor the least number of pencils.

Thus, N has the least number of pencils.

=> Ans – (C)

13) Answer (C)

The pattern which is being followed here is that the first letter is being replaced by the letter which comes next in English alphabets. The second letter is replaced by the one which comes second after this letter in english alphabets. Similarly, the third is being replaced by the one which comes third and so on. For example
B + 1 = C
R + 2 = T
I + 3 = L
G + 4 = K
H + 5 = M
T + 6 = Z
Using the same logic, we can find the code word for PEOPLE to be ‘QGRTQK’.
Hence, option C is the correct answer.

14) Answer (A)

From the figure, we can see that E is to the East of A

15) Answer (D)

There is an alternate sequence of white hexagon and black circle. As in the last figure we got a white hexagon, we should get a black circle next. Hence, it should be one of 3 or 4. The black circle in 3 is much larger than any shown in the previous figures. Hence, it breaks the pattern. Hence, option 4.

We hope this Expected Question & Answers PDF of SBI Clerk Prelims is very Useful for preparation of SBI Clerk Exams.


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### Noun

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text:
+0

0
285
1

Please enter your response in interval notation. Refer to Formatting Tips below for detailed instructions on formatting your response.

Guest Nov 6, 2014

#1
+90996
+5

$$f(x)=\frac{3x-7}{x+1}$$

find the range.

I cannot remember doing questions like this so my method may not be the method taught.

I am feeling my way.

You cannot divide by 0 so x+1 cannot =0, x cannot equal -1

This is a  restriction on the domain - not on the range.

x=-1 will be a vertical asymptote.

Just looking at it I can see it will be a hyperbola.        (it reminds me of  y=1/x)

We need the horizontal asymptote

ok

$$\\f(x)=\frac{3x-7}{x+1}\\\\ f(x)=\frac{3(x+1)-10}{x+1}\\\\ f(x)=\frac{3(x+1)}{x+1}+\frac{-10}{x+1}\\\\ f(x)=3+\frac{-10}{x+1}\\\\ now \;\; \frac{-10}{x+1} \;\; cannot equal zero \\\\ so\;\;f(x)\;\;cannot equal 3\\\\$$

$$The range of f is \;\; (-\infty,3),(3,+\infty)\;\; I think that is in interval notation\\\\  I think I would normally write is as \;\;f(x)\in R\;\; where\;\; f(x)\ne3$$

Here is the graph (asymptotes are shown)

https://www.desmos.com/calculator/p9jhxdm5ff

Melody  Nov 7, 2014
Sort:

#1
+90996
+5

$$f(x)=\frac{3x-7}{x+1}$$

find the range.

I cannot remember doing questions like this so my method may not be the method taught.

I am feeling my way.

You cannot divide by 0 so x+1 cannot =0, x cannot equal -1

This is a  restriction on the domain - not on the range.

x=-1 will be a vertical asymptote.

Just looking at it I can see it will be a hyperbola.        (it reminds me of  y=1/x)

We need the horizontal asymptote

ok

$$\\f(x)=\frac{3x-7}{x+1}\\\\ f(x)=\frac{3(x+1)-10}{x+1}\\\\ f(x)=\frac{3(x+1)}{x+1}+\frac{-10}{x+1}\\\\ f(x)=3+\frac{-10}{x+1}\\\\ now \;\; \frac{-10}{x+1} \;\; cannot equal zero \\\\ so\;\;f(x)\;\;cannot equal 3\\\\$$

$$The range of f is \;\; (-\infty,3),(3,+\infty)\;\; I think that is in interval notation\\\\  I think I would normally write is as \;\;f(x)\in R\;\; where\;\; f(x)\ne3$$

Here is the graph (asymptotes are shown)

https://www.desmos.com/calculator/p9jhxdm5ff

Melody  Nov 7, 2014

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text:
The Universe of Discourse

Wed, 11 Jan 2012

Where should usage messages go?
Last week John Speno complained about Unix commands which, when used incorrectly, print usage messages to standard error instead of to standard output. The problem here is that if the usage message is long, it might scroll off the screen, and it's a pain when you try to pipe it through a pager with command | pager and discover that the usage output has gone to stderr, missed the pager, and scrolled off the screen anyway.

Countervailing against this, though, is the usual argument for stderr: if you had run the command in a pipeline, and it wrote its error output to stdout instead of to stderr, then the error message would have gotten lost, and would possibly have caused havoc further down the pipeline. I considered this argument to be the controlling one, but I ran a quick and informal survey to see if I was in the minority.

After 15 people had answered the survey, Ron Echeverri pointed out that although it makes sense for the usage message to go to stderr when the command is used erroneously, it also makes sense for it to go to stdout if the message is specifically requested, say by the addition of a --help flag, since in that case the message is not erroneous. So I added a second question to the survey to ask about where the message should go in such a case.

83 people answered the first question, "When a command is misused, should it deliver its usage message to standard output or to standard error?". 62 (75%) agreed that the message should go to stderr; 11 (13%) said it should go to stdout. 10 indicated that they preferred a more complicated policy, of which 4 were essentially (or exactly) what M. Echeverri suggested; this brings the total in favor of stderr to 66 (80%). The others were:

1. stdout, if it is a tty; stderr otherwise
2. stdout, if it is a pipe; stderr otherwise
3. A very long response that suggested syslog.
4. stderr, unless an empty stdout would cause problems
5. It depends, but the survey omitted the option of printing directly on the console
6. It depends
I think #2 must have been trying to articulate #1, but (a) got it backwards and (b) missed. #3 seemed to be answering a different question than the one that was asked; syslog may make sense for general diagnostics, but to use it for usage messages seems peculiar. #5 also seems strange to me, since my idea of "console" is the line printer hardwired to the back of the mainframe down in the machine room; I think the writer might have meant "terminal".

68 people answered the second question, "Where should the command send the output when the user specifically requests usage information?". (15 people took the survey before I added this question.) 50 (74%) said the output should go to stdout, 12 (18%) to the user's default pager and then to stdout, and 5 (7%) to stderr. One person (The same as #5 above) said "it depends".

Thanks to everyone who participated.

Tue, 10 Jan 2012

When Iris was five or six, I told her about Russell's paradox in the following form: in a certain library, some books are catalogs that contain lists of other books. For example, there is a catalog of all the books on the second floor, and a catalog of all the books about birds. Some catalogs might include themselves. For example, the catalog of all the books in the library certainly includes itself. Such catalogs have red covers; the other catalogs, which do not include themselves, such as the catalog of all the plays of Shakespeare, have blue covers. Now is there a catalog of all the catalogs with blue covers?

I wasn't sure she would get this, but it succeeded much better than I expected. After I prompted her to consider what color cover it would have, she thought it out, first ruling out one color, and then, when she got to the second color, she just started laughing.

A couple of days ago she asked me if I could think of anything that was like that but with three different colors. Put on the spot, I suggested she consider what would happen if there could be green catalogs that might or might not include themselves. This is somewhat interesting, because you now can have a catalog of all the blue catalogs; it can have a green cover. But I soon thought of a much better extension.

I gave it to Iris like this: say you have a catalog, let's call it X. If X mentions a catalog that mentions X, it has a gold stripe on the spine. Otherwise, it has a silver stripe. Now:

1. Could there be a red catalog with a gold stripe?
2. Could there be a red catalog with a silver stripe?
3. Could there be a blue catalog with a gold stripe?
4. Could there be a blue catalog with a silver stripe?
And more interesting:

1. Is there a catalog of all the catalogs with gold stripes?
2. Is there a catalog of all the catalogs with silver stripes?
I knew that early 20th century logicians, trying to repair the Russell paradox, first tried a very small patch: since comprehension over the predicate XX causes problems, just forbid that predicate. This unfortunately doesn't solve the problem at all; there are an infinite number of equally problematic predicates. (Whitehead and Russell's theory of types is an attempt to fix this; Quine's New Foundations is a different attempt.) One of these predicates is ¬∃Y.X∈Y and Y∈X. You can't construct the set of all X such that ¬∃Y.X∈Y and Y∈X because there is no such set, for reasons similar to the reason why there's no set of all X such that XX, so that's where I got the silver stripe predicate.

Translating this into barber language is left as an exercise for the reader.

Wed, 04 Jan 2012

Mental astronomical calculations
As you can see from the following graph, the daylight length starts increasing after the winter solstice (last week) but it does so quite slowly at first, picking up speed, and reaching a maximum rate of increase at the vernal equinox.

The other day I was musing on this, and it is a nice mental calculation to compute the rate of increase.

The day length is given by a sinusoid with amplitude that depends on your latitude (and also on the axial tilt of the Earth, which is a constant that we can disregard for this problem.) That is, it is a function of the form a + k sin 2πt/p, where a is the average day length (12 hours), k is the amplitude, p is the period, which is exactly one year, and t is amount of time since the vernal equinox. For Philadelphia, where I live, k is pretty close to 3 hours because the shortest day is about 3 hours shorter than average, and the longest day is about 3 hours longer than average. So we have:

day length = 12 hours + 3 hours · sin(2πt / 1 year)
Now let's compute the rate of change on the equinox. The derivative of the day length function is:

rate of change = 3h · (2π / 1y) · cos(2πt / 1y)
At the vernal equinox, t=0, and cos(…) = 1, so we have simply:

rate of change = 6πh / 1 year = 18.9 h / 365.25 days
The numerator and the denominator match pretty well. If you're in a hurry, you might say "Well, 360 = 18·20, so 365.25 / 18.9 is probably about 20," and you would be right. If you're in slightly less of a hurry, you might say "Well, 361 = 192, so 365.25 / 18.9 is pretty close to 19, maybe around 19.2." Then you'd be even righter.

So the change in day length around the equinox (in Philadelphia) is around 1/20 or 1/19 of an hour per day—three minutes, in other words.

The exact answer, which I just looked up, is 2m38s. Not too bad. Most of the error came from my estimation of k as 3h. I guessed that the sun had been going down around 4:30, as indeed it had—it had been going down around 4:40, so the correct value is not 3h but only 2h40m. Had I used the correct k, my final result would have been within a couple of seconds of the right answer.

Exercise: The full moon appears about the same size as a U.S. quarter (1 inch diameter circle) held nine feet away (!) and also the same size as the sun, as demonstrated by solar eclipses. The moon is a quarter million miles away and the sun is 93 million miles away. What is the actual diameter of the sun?

[ Addendum 20120104: An earlier version of this article falsely claimed that the full moon appears the same size as a quarter held at arm's length. This was a momentary brain fart, not a calculational error. Thanks to Eric Roode for pointing out this mistake. ]

Tue, 03 Jan 2012

The other day Iris and I were putting together a model, and she asked what a certain small green part was for. I said "It's a thing for connecting a thing to another thing."

Iris objected that this was a completely unhelpful explanation, but I disagreed. I would have agreed that it was an excessively verbose explanation, but she didn't argue that point.

Later, it occurred to me that Haskell has a syntax for eliding unnecessary variables in cases like this. In Haskell, one can abbreviate the expression

        λx → λy → x + y

to just (+). (Perl users may find it helpful to know that the Perl equivalent of the expression above is sub { my ($x) = @_; return sub { my ($y) = @_; return $x +$y } }.) This is an example of a general transformation called η-reduction. In general, for any function f, λxf x is a function that takes an argument x and returns f x. But that's exactly what f does. So we can replace the longer version with the shorter version, and that's η-reduction, or we can go the other way, which is η-expansion.

Anyway, once I thought of this it occurred to me that, just like the longer expression could be reduced to (+), my original explanation that the small green part was "a thing for connecting a thing to another thing" could be η-reduced to "a connector".

Perhaps if I had said that in the first place Iris would not have complained.


text:
# Can you build an interferometer between the stars?

We're getting some very good results here on Earth using interferometers, 'virtual' telescopes with dishes hundreds or thousands of kilometers across that are 'built' by combining the data from multiple sites in a computer. This got me to wondering. I know the theory behind such devices, but I'm a little fuzzy on the details of exactly how it is done - specifically, whether the data needs to be combined in real time, or whether recorded observations can be compiled and combined after the fact.

The Colonisation Program - an autonomous, non-governmental organisation that exists to train people as colonists and send them to new planets - has access to six of the twelve Faster-Than-Light starships in the human galaxy. One of their primary missions is to search for potentially habitable planets, gather as much information as they can about them, and then send missions to colonise them. To this end, they want to build a really big interferometer and I, as the God of their universe, have to decide whether they can or not.

So, here's the question: Given access to an FTL starship to courier data back and forth, is it theoretically possible to build an interferometer array from telescopes in multiple different star systems, with a baseline measured in light years? If it's possible, how much detail would such a telescope be able to see in a star system hundreds of light years away? If it's not possible, what would be the maximum practical size of an interferometer?

• To the question of how it is done: the data must be coherent, meaning the exact time delays between the signals can be measured and analyzed (to within a fraction of a wavelength). Often this is implemented by combining the data in real time, but it can be done by other means that guarantee the data remains coherent and then post processed later. – Cort Ammon Jan 2 '17 at 1:28
• I think you are mixing the ideas of interferometer and synthetic aperture. See How big can we make a telescope? for hard-science numbers. Also, I've seen other posts (here and on Physics) calculate the resolution and seeing ability — the same issues apply here, just scaled up. – JDługosz May 31 '17 at 21:00
• Aperture synthesis is a type of interferometry. They're the same thing. See the accepted answer's definition of Very Long Baseline Interferometry. – Werrf Jun 1 '17 at 17:07

What is the maximum practical size of an interferometer? Apart from the obvious fact that this depends on the maximum practical technological capacity any given technological society has at any given time, then the correct answer is it depends.

However, it worth considering what constitutes Very Long Baseline Interferometry (VLBI) and try to dtermine whether it is workable in the OP's scenario.

VLBI is an acronym for Very Long Baseline Interferometry and associated with radio astronomy and geodesy. Typically VLBI refers to experiments that do not process their data in real time, but record it for later correlation. In the world of increasing network connectivity, we are entering the realm of eVLBI (electronic VLBI), in which data are cross correlated in virtually real time. VLBI experiments have baselines of usually 100s or 1000s of km.

VLBI falls into several categories:

Continental – baselines of 100s to 1000s of km,
Global – Baselines of 1000s of km,
Space VLBI – involving the use of satellites, like VSOP.

VLBI is used in measuring pulsar parallaxes and proper motions, resolving the cores of radio galaxies and jets from supermassive black holes, among others.

Source: VLBI

The real question is whether "data are cross correlated in virtually real time" means that if data can be cross correlated using FTL spacecraft to transport data sets to combined and analyzed at a given node in the system, then this interstellar baseline interferometer is a practical working system.

Having multiple telescopes located in multiple planetary systems, while this might be convenient, doesn't seem like a good idea. The various interferometer component dishes would be better located in space, outside planetary systems to minimize gravitational perturbations, and with this elements are relative rest to each other. This is basically how space-based VBLI systems currently work. The same principles should apply not over interstellar distances.

Essentially the cross correlation centre should be located at the midpoint of the various interferometer telescopes, so that the data are analyzed as if it was part of the one single array. This won't be analyzing the data in "true" real time, but in a "time-shifted" virtual real-time.

Referring back to the basic principles of radio astronomy interferometry and this give a reasonable idea of the practically of an interferometer VLBI and its effective resolution of stars hundreds of light years distant.

A radio interferometer is an array of radio antennas or ‘elements’ that are used in astronomical observations simultaneously to simulate a discretely-sampled single telescope of very large aperture. To put it another way, a radio interferometer can be thought of as a single telescope with a very large and incompletely-filled aperture, of maximum size equivalent to the maximum spacing, or baseline, between any two of its component elements. This large ‘synthesized’ aperture is only sampled at the locations at which an element exists, and this is aided by the rotation of the Earth which effectively moves the elements within it, hence increasing the sampling. This is known as ‘Earth rotation aperture synthesis’. The size of the synthesized aperture dictates the resolution or ‘beam size’ of the array; the larger the aperture, the smaller the resolution.

If the aperture size is light years, then the resolution of stars hundreds of light years away should be extremely good. Certainly, enough to map the surfaces of any planets.

• You also need time synchronyzation. For correlation you have to measure time delay in 0.001 nanoseconds. It's hard since even for close space you need not only precise clocks but take into account relativistic effects and solve math task. Interstellar equations could be too complex because of gravity from any planet between them. 0.001 nanosecond is reality for today. On Earth orbit it's enough but for interstellar - maybe no. It could be solved in far future but possibly could NOT. – ADS Jun 1 '17 at 21:18
• @ADS Quite so. "It could be solved in far future but possibly could NOT." I assumed that in future it might be, but I didn't think that would be trivial. I remain amazed by the technological sophistication in the engineering of gravitational wave detectors. My proposal is an extrapolation of similar technological developments for interferometers. – a4android Jun 2 '17 at 4:41
• I agree it could be solved. Especially in its own world :) Just because of reality-check tag I added comment to note that something is hard enough (even with FTL) and something is just impossible (like Heisenberg's uncertainty principle) – ADS Jun 2 '17 at 6:17