text:
# Steganography for images

For a school project I'm working on a small library to do steganography. I've just finished the first method of steganography and thought I'd get some feedback.

This steganography method works by changing the last bit of each channel of each pixel to a bit of the file. Reading the file from the image does the reverse operation.

The first point I'm unsure about, is my parameter and return types. The user will be able to hide any file in an image, so I'm currently asking for a Bitmap and a String with the file location. Should I ask for two file paths? Or should I ask for a Bitmap and a Path? I'm not sure. And what about the return types? Should I be giving back a byte[], or should I give back a file?

Besides that, general comments are welcome as well. Should anyone need it, the entire project is on GitHub.

public class SteganoBMP
{
//Embed a file in an image. Because Bitmap is an abstract representation of an image,
//it can then be saved in any image format. Though the file will not be retrievable from
//a lossy format.
public static Bitmap Embed(Bitmap target, String inputFilePath)
{
BitmapData bmpData = PrepareImage(target);

//Math.Abs because Stride can be negative if the image is saved upside down
//i.e. The first pixel in memory is the bottom right one.
int imageSize = Math.Abs(bmpData.Stride) * bmpData.Height;

//Get all the bytes from the file we want to embed, and save it in a byte array

//If the file we want to embed is larger than 8 times the size of the image, we can't store it.
//This is because We need one byte in the image to store each bit of the file
if (fileBytes.Length * 8 > imageSize)
throw new FileTooLargeException("The file you are trying to embed needs an image of at least" + fileBytes.Length * 8 +  "bytes large");

bool fileWritten = false;
int lastByte = 0;

unsafe
{
byte* ptr = (byte*)bmpData.Scan0;

for (int i = 0; i < imageSize; i++)
{
//We need to do this step 8 times per iteration because we need to access 8 bytes
//in the image for each byte in the file.
for (int j = 0; j < 8; j++)
{
//Go out of the loop once we've written the entire file.
if (i >= fileBytes.Length)
{
fileWritten = true;
break;
}
//AND the current value with ~1 (inverse of 1: 11111110).
//This wil set the last bit to 0.
//Then OR with the new bit
//Helper.GetBitAsByte extracts a single bit from a byte.
//And converts it to a byte, so we can do boolean arithmetic with it.
ptr[i * 8 + j] = (byte)(ptr[i * 8 + j] & ~1 | Helper.GetBitAsByte(fileBytes[i], 7 - j));
}

//We've now written all bytes, remember position so we can write EOF there.
if (fileWritten)
{
lastByte = i;
break;
}
}

//Write an EOF character (0xff) after our data.
//This is the last byte in our file, so we've used 8 times as many in our image, hence times 8
for (int i = lastByte * 8; i < lastByte * 8 + 8; i++)
{
ptr[i] = (byte)(ptr[i] | 1);
}
}

target.UnlockBits(bmpData);

return target;
}

//Extract an embedded file from an image.
//Returns a byte[], so the consumer can do with the data whatever he likes.
public static byte[] Extract(Bitmap source)
{
BitmapData bmpData = PrepareImage(source);

int imageSize = Math.Abs(bmpData.Stride) * bmpData.Height;

//We use a List, because we don't know in advance how big the enbedded file is.
List<byte> fileBytes = new List<byte>();

unsafe
{
//Get a pointer to the first pixel;
byte* ptr = (byte*)bmpData.Scan0;

for (int i = 0; i < imageSize; i++)
{
for (int j = 0; j < 8; j++)
{
//Set the last bit of the current file byte to the last bit of the image byte.
//Then shift it one spot to the left.
//This allows us to do this:
//0000 0001
//0000 0011
//0000 0110
//0000 1101
//etc.
fileBytes[i] <<= 1;
fileBytes[i] = (byte)(fileBytes[i] & ~1 | Helper.GetBitAsByte(ptr[i * 8 + j], 0));

if (fileBytes[i] == 0xff)
{
break;
}
}

break;
}
}

//Remove our last byte, this is the EOF byte.
fileBytes.RemoveAt(fileBytes.Count - 1);

//Convert it to a byte array
byte[] byteArray = fileBytes.ToArray<byte>();

return byteArray;
}

//This is some boilerplate code to prepare our image for unmanaged access.
private static BitmapData PrepareImage(Bitmap image)
{
//We don't require a specific area to be locked, but we still need to specify one
//So we choose to lock the entire image.
Rectangle lockArea = new Rectangle(0, 0, image.Width, image.Height);

//We use LockBits instead of GetPixel, because it is much faster.
//As a consequence we need to work with unmanaged data.
BitmapData bmpData = image.LockBits(lockArea,
image.PixelFormat);

return bmpData;
}
}

Helper class:

static class Helper
{
//Does a bitshift, but wraps the overflow
public static byte RotateLeft(byte value, int count)
{
return (byte)((value << count) | (value >> (8 - count)));
}

//Does a bitshift, but wraps the overflow
public static byte RotateRight(byte value, int count)
{
return (byte)((value >> count) | (value << (8 - count)));
}

//Gets the bit at a certain position in a byte
public static bool GetBit(byte b, int bitNumber)
{
return (b & (1 << bitNumber)) != 0;
}

//Gets the bit at a certain position in a byte,
//And presents it as a byte: 00000000 or 00000001
public static byte GetBitAsByte(byte b, int bitNumber)
{
//This is the same function as GetBit, but we add a conversion to Byte.
//This is possible because a boolean also takes a byte of memory.
return Convert.ToByte((b & (1 << bitNumber)) != 0);
}

• Can you provide the Helper.GetBitAsByte() method also ? – Heslacher Sep 24 '14 at 11:01
• @Heslacher Done. I didn't include my Helper class because I got those functions from some very popular SO questions on the topic. – Simon Verbeke Sep 24 '14 at 11:03
• TIL steganography is not a typo for stenography... – ANeves Sep 24 '14 at 11:24

Good

• Most of the comments are telling why something is done.
• The input and local used parameter are named good
• The method- and parameternames fit the naming guidlines

• Some of the comments are useless, as they tell what is done like e.g
//Get all the bytes from the file we want to embed, and save it in a byte array byte[] fileBytes = File.ReadAllBytes(inputFilePath); instead of why something is done.
• ifstatement without brackets {}
• The Extract() method does not call UnlockBits()

As you are unsure which inputparameters and which retuntypes to use, why don't you add some overloads of your methods?

public static Bitmap Embed(string imageFilePath, string inputFilePath)
{
}
public static Bitmap Embed(Bitmap target, string inputFilePath)
{
}
public static Bitmap Embed(Bitmap target, byte[] content)
{
return InternalEmbed(target, content);
}

and rename your former public Embed() method to the private InternalEmbed() method

private  static Bitmap InternalEmbed(Bitmap target, byte[] fileBytes)
{
}

After thinking about the overloads and looking at the signature of the methods I realized that if we return a Bitmap and also take a Bitmap as input parameter one would not assume that the passed Bitmap would be altered. As we have the overloads taking also a string we can't change the return type to void, therefor we need to call the InternalEmbed() method differently.

public static Bitmap Embed(Bitmap target, String inputFilePath)
{

now we don't alter the passed Bitmap anymore.

format: plain


text:
# Why this equality must holds for minimal surfaces?

When minimizing a surface area with respect to a fixed volume $V$, I found in some notes that the parametrization $X: U \longrightarrow \mathbb{R}^3$ must satisfy the equality $\iint_U (2H - \lambda) \langle \varphi, N \rangle du dv = 0$ for all variations $\varphi$, where $N$ is the normal, $\lambda$ is some constant and $H$ is the mean curvature. I know that it's related to some constraint, so there's the Lagrange multiplier $\lambda$, however I didn't understand this well.

-
I like to think of this in physical terms as a bubble enclosing a fixed amount of air. The forces on any patch of the bubble are $-2H\mathbf N$ due to the surface tension of the bubble, and $\lambda\mathbf N$ due to the pressure of the air inside. Then your equation merely states that the bubble is in equilibrium. Of course, this is not a rigorous mathematical explanation. –  Rahul Feb 3 '13 at 21:16
Yes, the physical picture is so nicely fits in with the mathematical counter parts. –  Narasimham Aug 14 '14 at 18:18

This is correct: the constraint is that the surface must enclose volume $V$. The test function $\varphi$ describes a variation of the surface: we compare the original parametrization $X:U\to\mathbb R^3$ again the perturbed $X+\epsilon\varphi$. We are interested in the first derivative with respect to $\epsilon$, evaluated at $\epsilon=0$. For the surface area this derivative turns out to be $\iint_U 2H\langle \varphi, N\rangle$, and for the volume it is simply $\iint_U \langle \varphi, N\rangle$. At a critical point the gradient of the objective (surface area) is a multiple of the gradient of the constraint (volume). Hence, $\iint_U (2H-\lambda)\langle \varphi, N\rangle =0$.
It is not surprising that only the normal component of $\varphi$ matters. It should be geometrically intuitive that variation in tangential directions has $o(\epsilon)$ effect on both surface area and the enclosed volume. For this reason, it is convenient to consider only normal variations: that is, $\varphi=\psi N$ where $\psi$ is a scalar function.


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# Brans-Dicke gravity and the fifth force

In Brans-Dicke gravity, we have the following gravitational action:

$$S_{BD} = \frac{1}{16\pi}\int d^4 x \sqrt{-g} [\phi R - \frac{\omega}{\phi}(\nabla \phi)^2] + S_m[g_{\mu \nu}; \Psi_n]$$,

with $$S_m$$ the matter action for fields $$\Psi_n$$, and $$\phi$$ the long range scalar field.

In Misner, Thorne and Wheeler's "Gravitation" (section 39.1), they observe that "the scalar field does not exert any direct influence on matter; its only role is that of participant in the field equations that determine the geometry of spacetime". This is clear.

However, if one undergoes the conformal transformation

$$g_{\mu \nu} = e^{2\alpha \phi}\tilde{g}_{\mu \nu}, \quad \phi = e^{-2 \alpha \psi}, \quad \alpha = \sqrt{\frac{4\pi}{2\omega + 3}}$$,

the action then takes the form

$$S_{BD} = \frac{1}{16\pi}\int d^4 x \sqrt{-\tilde{g}} [\tilde{R} - \frac{1}{2}(\nabla \psi)^2] + S_m[e^{2\alpha \psi}\tilde{g}_{\mu \nu}; \Psi_n]$$.

In this Einstein frame then we explicitly see that matter now couples to both the scalar field as well as the new metric. Hence we have some form of fifth force being mediated by $$\phi$$, resulting in a violation of the strong equivalence principle. However, the comments from Gravitation seem to contradict this. But since classically all physical observables are independent of the choice of frame, then this fifth force should still emerge regardless. How then do we see this effect in the Jordan (initial) frame of reference, where the coupling of $$\phi$$ to matter is not explicit?


text:
# The latex file coding is not there but the pdf file is there

I wrote all my coding in the .tex file. The next day when I opened it the coding is all gone and the pdf file is opening with it and is displayed as an output. How do I bring back my coding?

• This is going to be an editor or PC issue: TeX itself won't delete the content of input files. We'll do our best to help if you can give us more detail, but the first question has to be 'Do you have a backup'? – Joseph Wright Sep 15 '16 at 5:57
• I don't have the backup of the coding. Like I opened the latex file and along with it the pdf version is also opened with all the text, but the latex file has no coding. Is there a way to retrieve back the coding because the pdf file is opening. – Zainab Saeed Sep 15 '16 at 6:02
• Possible duplicate: How to convert PDF to (La)TeX? – Werner Sep 15 '16 at 6:06
• also yesterday's tex.stackexchange.com/questions/329566/… – David Carlisle Sep 15 '16 at 6:53
• Pro-tip: LaTeX source files are small, unlike DOCX or similar stuff. Always store them in Dropbox or another cloud service. :) – Andrea Lazzarotto Sep 15 '16 at 13:56

As the question pops up rather regularly I will try to answer.

1. It is possible to destroy files and content when running LaTeX. LaTeX has to write a lot of files (.log, .aux, .toc, etc) and it must be able to overwrite them, so it needs the rights to overwrite existing files. This here e.g. will "destroy" testoverwrite.tex -- even if this is the name of the running file:

\documentclass{article}
\usepackage{filecontents}
\begin{filecontents}{testoverwrite.tex}

\end{filecontents}
\begin{document}
blblb
\end{document}

2. Other applications can destroy files too - by accident or by (evil) purpose.

3. Errors can destroy files, e.g. some synchronization going bad, failure of power, failure of your hard disk, or too fast typing (ctrl+A + delete).

This all means that backups are important. If you spent hours on a document you should regularly store a copy in some other place.

The pdf output of LaTeX is not a good backup: At first it misses all the important coding. At second it changes at every compilation and so can be destroyed very fast.

If you don't have a backup (which happens once in a while to everyone) and you suddenly miss a file or some content it is important to do nothing rash: Most editors have a temporary backup somewhere (often with the ending .bak) but if you change something it can be lost. Copy all files that could be helpful to some usb stick or some other place. Check where your editor perhaps stores its backups and copy them too. If you are using some cloud space: They often have a version control system so check if you can retrieve an older version of the file from there.

I just encountered this issue, using Texmaker on Linux, and the problem turned out to be that I was out of hard drive space. There wasn't enough room to save the new file, so Texmaker saved a blank file in its place.

• Wow that's pretty awful design. Are the Texmaker developers aware of this bug, does anyone know? – ShreevatsaR May 9 '17 at 16:46


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# reverse chain rule calculator

A free online chain rule calculator to differentiate a function based on the chain rule of derivatives. Displaying the steps of calculation is a bit more involved, because the Derivative Calculator can't completely depend on Maxima for this task. Chain Rule in Derivatives: Double Integral Calculator Added Apr 29, 2011 by scottynumbers in Mathematics Computes the value of a double integral; allows for function endpoints and changes to order of integration. Instead of using the reverse power rule, you should just memorize that the antiderivative of (rule 3 in the table). This problem has been solved! The Power Rule of Derivatives applies to find the power of more than two functions. The following chain rule examples show you how to differentiate (find the derivative of) many functions that have an “inner function” and an “outer function.”For an example, take the function y = √ (x 2 – 3). Advanced Math Solutions – Limits Calculator, The Chain Rule In our previous post, we talked about how to find the limit of a function using L'Hopital's rule. The Chain rule states that the derivative of f (g (x)) is f' (g (x)).g' (x). The Power Rule of Derivatives applies to find the power of more than two functions. Use this Chain rule derivatives calculator to find the derivative of a function that is the composition of two functions for which derivatives exist with ease. Up Next. Our mission is to provide a free, world-class education to anyone, anywhere. After teaching my classes how to integrate using "reverse chain rule" and giving them enough practice to feel confident about the method, I have used this worksheet to try to encourage them to use less time and steps. Well, U-Sub is nothing more than the reverse of the chain rule! Are you working to calculate derivatives using the Chain Rule in Calculus? Now suppose that I pick a random day, but I also tell you that it is cloudy on the c… The derivative of cos(2x) is -2sin(2x). The above Calculator computes a derivative of a given function with respect to a variable x using analytical differentiation. The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. Reverse chain rule integration Related articles A-level Mathematics help Making the most of your Casio fx-991ES calculator GCSE Maths help A-level Maths: how to avoid silly mistakes Q: e^(3x^4 − 5x + 2) How do I integrate this. This is because, according to the chain rule, the derivative of a composite function is the product of the derivatives of the outer and inner functions. Chain rule for conditional probability: Let us write the formula for conditional probability in the following format $$\hspace{100pt} P(A \cap B)=P(A)P(B|A)=P(B)P(A|B) \hspace{100pt} (1.5)$$ This format is particularly useful in situations when we know the conditional probability, but we are interested in the probability of the intersection. U substitution (also called integration by substitution or u substitution) takes a rather complicated integral and turns it—using algebra—into integrals you can recognize and easily integrate. Let u = 5x (therefore, y = sin u) so using the chain rule. We can rewrite this, we can also rewrite this as, this is going to be equal to one. The reverse chain rule is really just u-substitution with some minor manipulation of the. ³5(1 5 ) x dx3 4. The problem is recognizing those functions that you can differentiate using the rule. Just enter the cost and markup, and the price you should charge will be computed instantly. Type in your sum to see how to solve it step by step. ( ) ( ) 3 1 12 24 53 10 Free inflation calculator that runs on U.S. CPI data or a custom inflation rate. 0. using chain rule and logarithms to differentiate a function. In this section, we discuss one of the most fundamental concepts in probability theory. Why? In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. You can specify any order of integration. Show Instructions. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7 th edition in print. That material is here. 84 Lesson 4-1 Reverse Chain Rule, u-substitution Warm-up Examples: Differentiate 1. d (1 5 )4 dx x 2. d sin 1 5 dx Now, integrate 3. The most common expressions to substitute are the objects by themselves, for example, in the denominator, in the exponent, under the radical, or as an argument to another function. Find Derivatives Using Chain Rules: Use this Chain rule derivatives calculator to find the derivative of a function that is the composition of two functions for which derivatives exist with ease. In the previous post we covered the basic integration rules (click here). Find more Mathematics widgets in Wolfram|Alpha. Free antiderivative calculator - solve integrals with all the steps. ... Another useful way to find the limit is the chain rule. Just type in sums like these (see Order of Operations for more detail): The Chain rule states that the derivative of f(g(x)) is f'(g(x)).g'(x). Integration by Substitution "Integration by Substitution" (also called "u-Substitution" or "The Reverse Chain Rule") is a method to find an integral, but only when it can be set up in a special way.. What we did with that clever substitution was to use the chain rule in reverse. The answer to this is simple: you just need to use a factor of … When evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integration. Test your antiderivatives by differentiating them. Then raise the “X” figure obtained above by (1/ Investment’s term in years. Show Instructions. Chain Rule: d d x [f (g (x))] = f ' (g (x)) g ' … Order of Operations Calculator. The chain rule states dy dx = dy du × du dx In what follows it will be convenient to reverse the order of the terms on the right: dy dx = du dx × dy du which, in terms of f and g we can write as dy dx = d dx (g(x))× d du (f(g((x))) This gives us a simple technique which, with some practice, enables us to apply the chain rule directly Key Point Derivative calculator is an equation simplifier which uses derivative quotient rule & derivative formula to find derivative of trig functions. let t = 1 + x² therefore, y = t³ dy/dt = 3t² dt/dx = 2x by the Chain Rule, dy/dx = dy/dt × dt/dx so dy/dx = 3t² × 2x = 3(1 + x²)² × 2x = 6x(1 + x²)² Derivative Calculator Use our simple online Derivative Calculator to find derivatives with step-by-step explanation. Message received. The big problem is that reverse chain rule is right at the start of the integration chapter of the most popular textbook so most teachers teach it first. For example, suppose that in a certain city, 23 percent of the days are rainy. The reverse power rule works for all powers (including negative and decimal powers) except for a power of negative one. Example. So all we need to do is to multiply dy /du by du/ dx. No ads, popups or nonsense, just a hex number reverser. Find more Mathematics widgets in Wolfram|Alpha. Maths is challenging; so is finding the right book. • Fill in the boxes at the top of this page with your name. It helps to differentiate composite functions. If y = (1 + x²)³ , find dy/dx . You will find it extremely handy here b/c substitution is all about simplification, transforming the function into something more familiar. Reverse chain rule introduction More free lessons at: http://www.khanacademy.org/video?v=X36GTLhw3Gw 1. This becomes especially handy when multiple substitutions are used. 84 Lesson 4-1 Reverse Chain Rule, u-substitution Warm-up Examples: Differentiate 1. d (1 5 )4 dx x 2. d sin 1 5 dx Now, integrate 3. Before we continue with more advanced... Advanced Math Solutions – Integral Calculator, the basics. We must restrict the domain of the squaring function to [0,) in order to pass the horizontal line test. • Answer all questions and ensure that your answers to … As u = 3x − 2, du/ dx = 3, so. The Reverse Chain Rule. Advanced Math Solutions – Integral Calculator, common functions. With the chain rule in hand we will be able to differentiate a much wider variety of functions. It helps to differentiate composite functions. Not all of them will be proved here and some will only be proved for special cases, but at least you’ll see that some of them aren’t just pulled out of the air. Sub can be a product of 2 expressions BUT there's a link between function "in" and the outside function where 1 is derivative of the other, while no such link in parts. Integral of tan x. Load hex, reverse its digits. Even though derivatives are fairly straight forward, integrals are... To create your new password, just click the link in the email we sent you. $\begingroup$ yeah but I am supposed to use some kind of substitution to apply the chain rule, but I don't feel the need to specify substitutes. Examples: 2+3*4 or 3/4*3 Description . The process of finding this derivative uses the chain rule. Substitution reverses the chain rule; Parts reverses the product rule! This rule allows us to differentiate a vast range of functions. Like always, pause the video and see if you can figure it out on your own and I will give you a hint, think reverse chain rule. The backpropagation algorithm works by computing the gradient of the loss function with respect to each weight by the chain rule, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this is an example of dynamic programming. Free online calculator that allows you to dynamically calculate the differential equation. But how do we do this? We saw that the integral was probably a composite function. first I go for the power if any, then I go for the rest bit, etc. Example problem #1: Integrate ∫sin 3x dx. This is because, according to the chain rule, the derivative of a composite function is the product of the derivatives of the outer and inner functions. Also, find the historical U.S. inflation data, learn more about inflation, experiment with other financial calculators, or explore hundreds of calculators addressing other topics such as math, fitness, health, and many more. Building graphs and using Quotient, Chain or Product rules are available. The only problem is that we want dy / dx, not dy /du, and this is where we use the chain rule. We can use integrals to check our work when finding derivatives. Next lesson. Type in any integral to get the solution, steps and graph (reverse chain rule) 0. This rule of thumb works in the majority of anchorages relatively close to the shore where the water is quite shallow, but for deeper anchorages (of around 10-15m) you obviously need more chain. Integration is the inverse of differentiation. We saw that the integral was probably a composite function. A key trend surrounding the need for more insight and know-how into supply chain functions and their costs involves real-time analytics. Using the reverse chain for (x/2)sin(2x^2 + 2) ... then this business right over here is f prime of x, which is a good signal to us that, hey, the reverse chain rule is applicable over here. Partial fraction expansion. Test your antiderivatives by differentiating them. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. Chain Rule: Problems and Solutions. Question: Solve Using The Reverse Chain Rule, Upload Your We Legible. Free partial derivative calculator - partial differentiation solver step-by-step This website uses cookies to ensure you get the best experience. 0. The square root function is the inverse of the squaring function f(x)=x 2. A short tutorial on integrating using the "antichain rule". Show transcribed image text. This website uses cookies to ensure you get the best experience. This is the currently selected item. Double Integral Calculator Added Apr 29, 2011 by scottynumbers in Mathematics Computes the value of a double integral; allows for function endpoints and changes to order of integration. Logic calculator: Server-side Processing Help on syntax - Help on tasks - Other programs - Feedback - Deutsche Fassung Examples and information on the input syntax Please note that the letters "W" and "F" denote the constant values truth and falsehood and that the lower-case letter "v" denotes the disjunction. Here is the question: as you obtain additional information, how should you update probabilities of events? What we did with that clever substitution was to use the chain rule in reverse. All functions are functions of real numbers that return real values. We can … The markup calculator (alternatively spelled as "mark up calculator") is a business tool most often used to calculate your sale price. BY REVERSE CHAIN RULE . We will need to make a change of variables. You can also get a better visual and understanding of the function by using our graphing tool. Stratonovich integral and chain rule. We explain Reverse Chain Rule with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. Strong algebra skills and knowledge of rules of differentiation, y = ( 1 rating ) previous Next... Step by step can skip the multiplication sign, so  5x  is equivalent .... a triangular transaction is a chain transaction calculator:... a triangular transaction is a direct of... Function is the question: solve using the reverse of the function into more... And markup, and the price you should charge will be computed instantly just! With step-by-step explanation: Select a term for “ u. ” Look substitution. On integrating using the chain rule in reverse when finding derivatives as antiderivatives ease! Each of the function, with steps shown blog, Wordpress, Blogger, or iGoogle problem. This question... another useful way to find the indefinite integral ( antiderivative ) of squaring... Saw that the antiderivative of ( rule 3 in the chain rule reverse. Problem is recognizing those functions that you can skip the multiplication sign, so  5x  is to... Power of more than the reverse chain rule and logarithms to differentiate a much wider of! Of calculation is a direct consequence of differentiation must restrict the domain of the function by using this website cookies... ( if possible ) steps of calculation is a rule in reverse those functions you... Madas question 1 Carry out each of the recognizing those functions that you can differentiate using the rule another way. Can also get a better visual and understanding of the days are rainy dx = 3 so. ( 2x ) a given function with respect to a variable x using analytical differentiation to solve them for. Two functions visual and understanding of the given point if needed ), steps... Reverse when finding an anti-derivative is discussed here we use the chain in!, or iGoogle derivative uses the chain rule in reverse this online calculator find! Our Cookie Policy ( 1 + x² ) ³, find dy/dx derivative uses the chain rule calculator '' for... I integrate this instead, the derivatives have to be equal to one U.S. CPI or... Your Calculus courses a great many of derivatives applies to find the gradient the..., common functions your Calculus courses a great many of derivatives applies to find the limit the. Using the chain rule makes it easy to learn & solve equations popups. Function ( at the top of this page with your reverse chain rule calculator...., fourth derivatives as well as differentiation. Much wider variety of functions of integration finding an anti-derivative is discussed here third, fourth derivatives, as as! Ease and for free a derivative of a function based on the chain of. Probability theory here b/c substitution is one way you can skip the multiplication sign, so step-by-step so you calculate... Data or a custom inflation rate ) so using the chain rule to  *. Needed ), with steps shown ( if possible ) well as antiderivatives with ease and for free of. Chain functions and their costs involves real-time analytics composite function tool that reverses hex numbers functions real... Simplifies it are available sin 5x, chain or Product rules are available differentiation solver step-by-step this website blog. Many of derivatives is a chain transaction calculator:... a triangular is! Antiderivative before applying the boundaries of integration power of more than the reverse power rule, you agree our. The boxes at the given function, ie of cos ( 2x ) is -2sin ( 2x is... Just solve it step by step parentheses: x 2-3.The outer function is the question: as obtain! Our simple online derivative calculator to [ 0, ) in order pass. And this is going to be calculated manually step by step ’ s term in years ( +... 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text:
Volume 9 (2013) Article 10 pp. 403-411
On the Real $\tau$-Conjecture and the Distribution of Complex Roots
Revised: April 11, 2013
Published: May 21, 2013
$\newcommand{\eee}{\mathrm{e}}$
Koiran's real $\tau$-conjecture asserts that if a non-zero real polynomial can be written as $f=\sum_{i=1}^{p}\prod_{j=1}^{q}f_{ij}$, where each $f_{ij}$ contains at most $k$ monomials, then the number of distinct real roots of $f$ is polynomially bounded in $pqk$. We show that the conjecture implies quite a strong property of the complex roots of $f$: their arguments are uniformly distributed except for an error which is polynomially bounded in $pqk$. That is, if the conjecture is true, $f$ has degree $n$ and $f(0)\not=0$, then for every $0<\alpha-\beta< 2\pi$ $\Big|N_{\alpha,\beta}(f)- \frac{(\alpha-\beta)}{2\pi} n \Big|\leq (pqk)^c\,,$where $c$ is an absolute constant and $N_{\alpha,\beta}(f)$ is the number of roots of $f$ of the form $r\eee^{i\phi }$, with $r>0$ and $\beta<\phi <\alpha$, counted with multiplicities. In particular, if the real $\tau$-conjecture is true, it is also true when multiplicities of non-zero real roots are included.


text:
## Tuesday, June 26, 2012

### Summary of research paper "Simple EnglishWikipedia: A New Text Simplification Task" by William Coster and David Kauchak

This is a summary of the research paper http://www.aclweb.org/anthology-new/P/P11/P11-2117.pdf. This paper describes a way to automatically create a parallel corpus that pairs sentences with a simpler version of the sentences which will be useful for training text simplification systems. The sentences for the corpus come from articles in Wikipedia and Simple English Wikipedia. Simple English Wikipedia is a version of Wikipedia which is edited with the aim of being understandable by children and English learners by encouraging the use of simple vocabulary and grammar. By pairing up equivalent sentences in Wikipedia and Simple English Wikipedia, it was possible to build a 137,000 sentence parallel corpus.

In order to build such a corpus, both Wikipedia sites were downloaded, the articles were paired by title, all pairs that contained an unusable article (e.g. stubs, disambiguation pages, etc.) were removed, the equivalent paragraphs in the article pairs were paired up and finally the equivalent sentences in the paragraph pairs were paired up.

To align paragraphs in the article pairs, where a single paragraph in Simple English Wikipedia could correspond to multiple paragraphs in Wikipedia but not the other way round, the words in each paragraph from the Simple English Wikipedia article were used as a set of keywords to search for all corresponding paragraphs in the Wikipedia article. This was done by using TF-IDF and keeping only those paragraphs which resulted in a vector with cosine similarity to the Simple English Wikipedia paragraph of 0.5 or more. In this way, each paragraph in the Simple English Wikipedia article is paired up with a list of paragraphs in the Wikipedia article which are similar to it.

Once the paragraph pairs were found in each article pair, the next step was to pair up the sentences in the paragraph pairs such that in each pair you get a Wikipedia sentence and its simplified counterpart from Simple English Wikipedia. Such a pairing of sentences is called an "alignment". This was less simple than how the paragraphs were paired because now there could be multiple sentences in Simple English Wikipedia that correspond to multiple sentences in Wikipedia. Instead, the sentences in the paragraph pairs are paired up in many different ways and the alignment which gives the maximum sum of similarities in each sentence pair was used. The similarity of two sentences in a pair is found by using TF-IDF with cosine similarity. The paragraph pairing was important in order to limit the number of different ways to attempt to align the sentences.

Following some clarifications via email with the author, here is how the sentence alignment algorithm works:

Let "n" be the number of Wikipedia sentences in a paragraph pair
Let "m" be the number of Simple English Wikipedia sentences in a paragraph pair
Let "sim(i,j)" be a function which measures the similarity between the "i"th Wikipedia sentence and the "j"th Simple English Wikipedia sentence (using TF-IDF with cosine similarity) in a paragraph pair

I shall now introduce a new function "align(n,m)" which is not mentioned in the paper but which will help explain the whole sentence alignment concept.

The function "align(n,m)" gives the best sentence alignment such that the sum of the similarity between each sentence pair is maximized. In order to align the sentences, 6 operations are successively applied to the sentences in the paired paragraphs. The operations are:
• Skip the next sentence in the Wikipedia paragraph (it does not correspond to any of the sentences in the Simple English Wikipedia paragraph)
• Skip the next sentence in the Simple English Wikipedia paragraph (it does not correspond to any of the sentences in the Wikipedia paragraph)
• Pairing the next Wikipedia sentence to the next Simple English Wikipedia sentence
• Pairing the next Wikipedia sentence to the next two Simple English Wikipedia sentences
• Pairing the next two Wikipedia sentences to the next Simple English Wikipedia sentence
• Pairing the next two Wikipedia sentences to the next two Simple English Wikipedia sentences crossed up (for example, if the Wikipedia sentences are [a, b] and the Simple English Wikipedia sentences are [x, y] then the pairing would be [(a,y), (b,x)])

These operations are applied successively using dynamic programming in order to find the alignment with the maximum sum of similarities.

We shall first see the function "a(n,m)" which calculates this maximal similarity and then we shall see "align(n,m)". "a(n,m)" will also be applying the operations using dynamic programming, but it will only be calculating the sum of the similarities of the sentence pairs rather then the actual pairs. Having initial arguments being the number of sentences in each paragraph in the paragraph pair, "a(n,m)" will recursively call itself on less and less sentences until it reaches a base case of having no sentences to align. In accordance with the paper, the "i"th sentence is not 0 based like in arrays but 1 based. So the first sentence is in position 1, the second is in position 2, etc.

This is "a(i,j)" in Python without using dynamic programming (for simplicity):

def a(i, j):
if i == 0 or j == 0: #Base case: if there are no more sentences to align in the paragraphs then the similarity is 0
return 0

else: #Recursive case: if there are sentences to align then check what the maximum similarity achieved will be after applying each operation and return the maximum of the similarities
alternatives = []

#Max similarity after skipping next Simple English Wikipedia sentence
alternatives.append(a(i, j-1) - skip_penalty)

#Max similarity after skippin next Wikipedia sentence
alternatives.append(a(i-1, j) - skip_penalty)

#Max similarity after pairing next Wikipedia sentence with next Simple English Wikipedia sentence
alternatives.append(a(i-1, j-1) + sim(i, j))

if j >= 2: #If there are more than one Simple English Wikipedia sentences then try pairing up two such sentences
#Max similarity after pairing next Wikipedia sentence with next two Simple English Wikipedia sentences
alternatives.append(a(i-1, j-2) + sim(i, j-1) + sim(i, j))

if i >= 2: #If there are more than one Wikipedia sentences then try pairing up two such sentences
#Max similarity after pairing next two Wikipedia sentences with next Simple English Wikipedia sentence
alternatives.append(a(i-2, j-1) + sim(i-1, j) + sim(i, j))

if i >= 2 and j >= 2: #If there are more than one sentences in both paragraphs then try pairing up two of each
#Max similarity after pairing next two Wikipedia sentences with next two Simple English Wikipedia sentences crossed up
alternatives.append(a(i-2, j-2) + sim(i-1, j) + sim(i, j-1))

return max(alternatives) #Return the maximum of the similarities

"skip_penalty" is a constant (the authors set it to 0.0001) which is used to reduce the total similarity every time a sentence is skipped. This is to discourage skipping too many sentences.

Now "align(n,m)" would be very similar to "a(n,m)". Every "sim(x,y)" there is in "a(n,m)" represents a pairing of the "x"th Wikipedia sentence with the "y"th Simple English Wikipedia sentence. So in "align(n,m)", every time we compute "sim(x,y)" we would add the pair "(x,y)" to our alignment. We still need to know what the maximum similarity of the alignment will be after applying each operation so "align(n,m)" needs to return both the similarity and the alignment.

This is "align(i,j)" in Python without using dynamic programming (for simplicity):

def align(i, j):
if i == 0 or j == 0: #Base case: if there are no more sentences to align in the paragraphs then the similarity is 0
return (0, [])

else: #Recursive case: if there are sentences to align then check what the maximum similarity achieved will be after applying each operation and return the maximum of the similarities
alternatives = []

#Best alignment after skipping next Simple English Wikipedia sentence
(similarity, alignment) = align(i, j-1)
alternatives.append((similarity - skip_penalty, alignment))

#Best alignment after skippin next Wikipedia sentence
(similarity, alignment) = align(i-1, j)
alternatives.append((similarity - skip_penalty, alignment))

#Best alignment after pairing next Wikipedia sentence with next Simple English Wikipedia sentence
(similarity, alignment) = align(i-1, j-1)
alternatives.append((similarity + sim(i, j), alignment + [(i, j)]))

if j >= 2: #If there are more than one Simple English Wikipedia sentences then try pairing up two such sentences
#Best alignment after pairing next Wikipedia sentence with next two Simple English Wikipedia sentences
(similarity, alignment) = align(i-1, j-2)
alternatives.append((similarity + sim(i, j-1) + sim(i, j), alignment + [(i, j-1), (i, j)]))

if i >= 2: #If there are more than one Wikipedia sentences then try pairing up two such sentences
#Best alignment after pairing next two Wikipedia sentences with next Simple English Wikipedia sentence
(similarity, alignment) = align(i-2, j-1)
alternatives.append((similarity + sim(i-1, j) + sim(i, j), alignment + [(i-1, j), (i, j)]))

if i >= 2 and j >= 2: #If there are more than one sentences in both paragraphs then try pairing up two of each
#Best alignment after pairing next two Wikipedia sentences with next two Simple English Wikipedia sentences crossed up
(similarity, alignment) = align(i-2, j-2)
alternatives.append((similarity + sim(i-1, j) + sim(i, j-1), alignment + [(i-1, j), (i, j-1)]))

return max(alternatives, key=lambda p:p[0]) #Return the maximum of the similarities (the similarity is the first element of each similarity/alignment pair)

And here is the same algorithm using dynamic programming:
def align(i, j):
memo = dict()

for x in range(0, i+1):
memo[(x, 0)] = (0.0, [])
for y in range(0, j+1):
memo[(0, y)] = (0.0, [])

for y in range(1, j+1):
for x in range(1, i+1):
alternatives = []

#Best alignment after skipping next Simple English Wikipedia sentence
(similarity, alignment) = memo[(x, y-1)]
alternatives.append((similarity - skip_penalty, alignment))

#Best alignment after skippin next Wikipedia sentence
(similarity, alignment) = memo[(x-1, y)]
alternatives.append((similarity - skip_penalty, alignment))

#Best alignment after pairing next Wikipedia sentence with next Simple English Wikipedia sentence
(similarity, alignment) = memo[(x-1, y-1)]
alternatives.append((similarity + sim(x, y), alignment + [(x, y)]))

if y >= 2: #If there are more than one Simple English Wikipedia sentences then try pairing up two such sentences
#Best alignment after pairing next Wikipedia sentence with next two Simple English Wikipedia sentences
(similarity, alignment) = memo[(x-1, y-2)]
alternatives.append((similarity + sim(x, y-1) + sim(x, y), alignment + [(x, y-1), (x, y)]))

if x >= 2: #If there are more than one Wikipedia sentences then try pairing up two such sentences
#Best alignment after pairing next two Wikipedia sentences with next Simple English Wikipedia sentence
(similarity, alignment) = memo[(x-2, y-1)]
alternatives.append((similarity + sim(x-1, y) + sim(x, y), alignment + [(x-1, y), (x, y)]))

if x >= 2 and y >= 2: #If there are more than one sentences in both paragraphs then try pairing up two of each
#Best alignment after pairing next two Wikipedia sentences with next two Simple English Wikipedia sentences crossed up
(similarity, alignment) = memo[(x-2, y-2)]
alternatives.append((similarity + sim(x-1, y) + sim(x, y-1), alignment + [(x-1, y), (x, y-1)]))

memo[(x,y)] = max(alternatives, key=lambda p:p[0]) #Return the maximum of the similarities (the similarity is the first element of each similarity/alignment pair)
return memo[(i,j)]

This function will return the best alignment and its total similarity. The alignment will be a list of sentence position pairs and not the sentence pairs themselves.

Once the sentences in each paragraph were aligned, the sentence pairs were then filtered such that if any sentence pairs were less similar than 0.5 then they would be discarded. The filtering went from 10,000 article pairs to 75,000 paragraph pairs to 137,000 sentence pairs. Out of a sample of 100 sentence pairs, human judges determined that 91 of them were correct sentence simplifications. They were also tested on a phrase based translation system called Moses which simplified test sentences with statistically significant improvement.

The final parallel corpus is available at http://www.cs.pomona.edu/~dkauchak/simplification/.

## Saturday, June 23, 2012

### Summary of research paper "Readability Assessment for Text Simplification" by Sandra Aluisio, Lucia Specia, Caroline Gasperin and Carolina Scarton

This is a summary of the research paper http://aclweb.org/anthology-new/W/W10/W10-1001.pdf. This paper is about a program which classifies text into one of three difficulty of reading levels: "rudimentary", "basic" and "advanced". These difficulty levels are defined by INAF (Portuguese document at http://www.ibope.com.br/ipm/relatorios/relatorio_inaf_2009.pdf), the National Indicator of Functional Literacy. The aim is to use this program to assist authors to detect parts of their writing which can be simplified. The program is designed to work with Portuguese rather than English.

The following list of features is extracted from the Portuguese text to assess using various tools and resources described in the paper (copied directly from the paper):
1. Number of words
2. Number of sentences
3. Number of paragraphs
4. Number of verbs
5. Number of nouns
8. Number of pronouns
9. Average number of words per sentence
10. Average number of sentences per paragraph
11. Average number of syllables per word
12. Flesch index for Portuguese
13. Incidence of content words
14. Incidence of functional words
15. Raw Frequency of content words
16. Minimal frequency of content words
17. Average number of verb hypernyms
18. Incidence of NPs
19. Number of NP modifiers
20. Number of words before the main verb
21. Number of high level constituents
22. Number of personal pronouns
23. Type-token ratio
24. Pronoun-NP ratio
25. Number of “e” (and)
26. Number of “ou” (or)
27. Number of “se” (if)
28. Number of negations
29. Number of logic operators
30. Number of connectives
31. Number of positive additive connectives
32. Number of negative additive connectives
33. Number of positive temporal connectives
34. Number of negative temporal connectives
35. Number of positive causal connectives
36. Number of negative causal connectives
37. Number of positive logic connectives
38. Number of negative logic connectives
39. Verb ambiguity ratio
40. Noun ambiguity ratio
43. Incidence of clauses
45. Incidence of apposition
46. Incidence of passive voice
47. Incidence of relative clauses
48. Incidence of coordination
49. Incidence of subordination
50. Out-of-vocabulary words
51. LM probability of unigrams
52. LM perplexity of unigrams
53. LM perplexity of unigrams, without line break
54. LM probability of bigrams
55. LM perplexity of bigrams
56. LM perplexity of bigrams, without line break
57. LM probability of trigrams
58. LM perplexity of trigrams
59. LM perplexity of trigrams, without line break

The features from 1 to 42 are the "Coh-Metix PORT" feature group and were derived from the Coh-Metrix-PORT tool, which is a Portuguese adaptation of the Coh-Metrix.

The features from 43 to 49 are the "Syntactic" feature group and were added to analyse syntactic constructions which are useful for automatic simplification.

The features from 50 to 59 are the "Language model" feature group and are derived by comparing n-grams in the input text to n-gram frequencies in the language (Portuguese) as well as their perplexity and scores for any words which are not listed in the system's vocabulary.

The features from 1 to 3 and 9 to 11 are also called the "Basic" feature group because they require no linguistic knowledge. Feature 12 is also put into a feature group on its own called "Flesch".

Experiments were performed to check if it is possible to use machine learning techniques to learn to detect the INAF difficulty of reading levels and to discover which features are best to use for complexity detection.

Three types of machine learning algorithms in Weka were evaluated:
• "Standard classification" (SMO): A standard classifier (support vector machines) which assumes that there is no relation between the difficulty levels
• "Ordinal classification" (OrdinalClassClassifier): An ordinal classifier which assumes that the difficulty levels are ordered
• "Regression" (SMO-reg): A regressor which assumes that the difficulty levels are continuous

Manually simplified corpora were used as training data for the algorithms. The corpora were simplified into each of the difficulty levels. Using these simplified corpora it was possible to check if the system could predict that the original corpora are of "advanced" difficulty level, the lightly simplified corpora are of "basic" difficulty level and the heavily simplified corpora are of "rudimentary" difficulty level.

In order to determine the importance of each feature described, the absolute Pearson correlation between each feature of each corpora and how well it predicts the corpora's difficulty level is computed. The results for the best features below are copied from the paper (1=highly correlated, 0=not correlated):
• Words per sentence: 0.693
• Incidence of apposition: 0.688
• Incidence of clauses: 0.614
• Flesch index: 0.580
• Words before main verb: 0.516
• Sentences per paragraph: 0.509

In order to determine which machine learning algorithm is better at classifying the corpora into correct difficulty levels using the features mentioned earlier, the Pearson correlation with true score was used on how the corpora were classified. The experiments were also run using the sub-groups of features which were mentioned to see how important each group was. Here are the results, summarized from the paper:

Standard classification
Feature groupPearson correlation
All0.84
Language model0.25
Basic0.76
Syntactic0.82
Coh-Metrix-PORT0.79
Flesch0.52

Ordinal classification
Feature groupPearson correlation
All0.83
Language model0.49
Basic0.73
Syntactic0.81
Coh-Metrix-PORT0.8
Flesch0.56

Regression
Feature groupPearson correlation
All0.8502
Language model0.6245
Basic0.7266
Syntactic0.8063
Coh-Metrix-PORT0.8051
Flesch0.5772

It is clear that it is better to use all the features together than any sub-group of them, but the syntactic features, followed by the Coh-Metrix-PORT features are the most useful feature groups and the language model feature group was the worst.

The simple classification algorithm was chosen as the best because although it is the simplest algorithm, its results are comparable to the other algorithms' results.

## Sunday, June 17, 2012

### Rummy and the most probable sequence in a probability tree

Rummy
Lately I was trying to program a game of Rummy, which is a card game where you have to replace one of your cards with the card on the deck until you have grouped your cards into sequences, where each sequence is 3 or more cards. The challenge with programming such a game seemed to be with writing code which determines which of your cards should be discarded to be replaced with the one on the deck.

The way this was done was by giving each card in the deck a probability of being available. Cards in the player's hand are given a probability of 1 and cards which are lost in the graveyard or taken by the opponent are given a probability of 0. The other cards will be given a probability depending on how likely the opponent has them given the cards they have taken.

Once each card has a probability of being obtained we can then calculate the probability of every legal sequence of cards in a group and of each possible arrangement of groups. The probability of each group is calculated and the groups with the maximum probability, containing both cards in the player's hand and cards which are likely to be available, is to be pursued. Any cards in the player's hand which are not in the most likely groups to arrange can be discarded to be replaced.

Examples of legal sequences of cards which can be used as a group in Rummy are
• ace of diamonds, ace of hearts, ace of spades
• two of hearts, two of clubs, two of diamonds
• two of hearts, two of clubs, two of diamonds, two of spades
• ace of diamonds, two of diamonds, three of diamonds
• etc.

A number of groups needs to be arranged such that the total number of cards equals 10 and no two groups have the same cards. The probability of a card group is the product of the probabilities of each card in the group. The aim is to find an arrangement of card groups that have the maximum probability of being obtained. Obviously since only cards that are already in the player's hand have a probability of 1, the more cards used which are already in the player's hand, the better.

Since a group cannot contain any cards in another group, we need to treat the choosing of groups as a probability tree, where each node in the tree is a new legal group. As we choose more groups, we have less groups to choose from for the next choice. Since there are so many cards to choose from, an algorithm which quickly chooses the most probable sequence in the probability tree was needed.

The probability tree would look something like this:

Most probable sequence in a probability tree
I'll be expressing the algorithm using Python. I'll be using this Node class to represent a node in the probability tree:
class Node:
def __init__(self, prob, children):
self.prob = prob
self.children = children

Where "prob" is the probability of choosing that node and "children" is a list of child nodes to follow next. Obviously in practice both of these properties can be dynamically generated with callback functions.

After having a tree, we need to represent a root path in the tree which is a list of nodes from the root to one of the leaves. We also need to calculate the probability of the path which is done using this function:
def path_prob(path):
prob = 1.0
for node in path:
prob *= node.prob
return prob

The probability of nodes in sequence in a probability tree is the product of each node's probability.

We'll start from a simple algorithm, one which generates the paths from the root to every leaf node.
def all_root_paths_nonacc(node):
if node.children == []:
yield [node]
else:
for child in node.children:
for subpath in all_root_paths_nonacc(child):
yield [node] + subpath

It's a naturally recursive generator function which doesn't use an accumulator. It starts from the root and attaches that root node to the front of every path from its children to a leaf. When a leaf is reached, a list consisting of only that leaf is returned.

Once we have this function, we can generate every root path in our probability tree and then find which path has the greatest probability using some code such as:
#comment to make code longer than one line
max(all_root_paths_nonacc(root), key=lambda path:path_prob(path))
#comment to make code longer than one line

However this would be inefficient to use. We need to be able to choose the most probable path during the recursion in such a way that we can stop recurring mid-way through the paths in order to avoid wasting time. I'll explain how this will work in a minute. First we need to know what path we are building during recursion and to do that we need to use an accumulator, like this:
def all_root_paths(node, prev_path=[]):
curr_path = prev_path + [node]
if node.children == []:
yield curr_path
else:
for child in node.children:
for path in all_root_paths(child, curr_path):
yield path

This is a modified version of the previous algorithm. It keeps an extra accumulator parameter which starts off being an empty list and then start adding the current node to the end of it every time a new recursion is made. That way at any point in the recursion you can know what path is being built from the root node to the current node. When a leaf is reached, the path is returned.

This algorithm still returns all the root paths in the probability tree which we then have to choose from. Now we shall use an algorithm which returns the most probable path without returning any other path.
def naive_max_root_path(node, prev_path=[], curr_max_path=None):
curr_path = prev_path + [node]
if node.children == []:
if curr_max_path == None or path_prob(curr_path) > path_prob(curr_max_path):
return curr_path
else:
return curr_max_path
else:
for child in node.children:
curr_max_path = naive_max_root_path(child, curr_path, curr_max_path)
return curr_max_path

Again this is a modification of the previous algorithm. This time we keep two accumulators, one with the path that has been built up to now and one with the path which is the most probable up to now. Every time a full path is built (by reaching a leaf) a choice is made between returning the newly built path and the best current path. The returned path is then used as the current best path. Obviously if the current best path is "None" (null), then it means that we are still generating the first path and so this should be considered the best path.

Even if only the best path is returned, the algorithm checks each and every possible path there is, so this algorithm will not be faster than the other algorithms. We shall now instead use to our advantage the fact that when a probability is multiplied by another probability, the product will be smaller than or equal to both probabilities. What this means is that as we multiply the probabilities of the nodes in a path from first to last, the product will never grow but will either remain the same (if there is a probability sequence of 1s) or will become smaller. So if at any point the probability of a partially built path becomes smaller than the probability of the best path, we can immediately stop building that path and try some other path since its probability will only get even smaller.
def quick_max_root_path(node, prev_path=[], curr_max_path=None):
curr_path = prev_path + [node]
if node.children == []:
if curr_max_path == None or path_prob(curr_path) > path_prob(curr_max_path):
return curr_path
else:
return curr_max_path
else:
for child in node.children:
if curr_max_path == None or path_prob(curr_path + [child]) > path_prob(curr_max_path):
curr_max_path = quick_max_root_path(child, curr_path, curr_max_path)
return curr_max_path

As you can see, the only difference between this and the previous algorithm is that a decision is also made in the recursive case when the path is still being built. This algorithm can probably be even faster by avoiding the calls to "path_prob" and passing the probabilities as parameters too. Then with every recursive call, the probability of the current path is the probability of the previous path times the probability of the new node.

Many times, especially in the Rummy case, there is more than one best sequence in a probability tree, all of which have an equal probability. In such cases we might want an algorithm which returns all such paths and not just the first one. Here is a naive version of the algorithm which checks every possible root path:
def naive_max_root_paths(node, prev_path=[], curr_max_paths=[]):
curr_path = prev_path + [node]
if node.children == []:
if curr_max_paths == [] or path_prob(curr_path) > path_prob(curr_max_paths[0]):
return [curr_path]
elif path_prob(curr_path) == path_prob(curr_max_paths[0]):
return curr_max_paths + [curr_path]
else:
return curr_max_paths
else:
for child in node.children:
curr_max_paths = naive_max_root_paths(child, curr_path, curr_max_paths)
return curr_max_paths

Obviously we now need to return a list and so the parameter which keeps the current best path needs to be a list of paths. As can be seen, there are now three cases to consider in the base case which are:
• If the current path is better than any of the best paths (all paths in "curr_max_paths" have an equal probability), return a list consisting of only the current path.
• If the current path is equal to any of the best path, return a list of the best paths together with the current path/
• If the best paths are better than the current path, return the best paths only.
So the only difference between this and "naive_max_root_path" is that the path is considered if it is of equal probability to the best and added to a list if so.

We now use the previous trick to make the algorithm quick by skipping paths which are worse than the best mid-way through. However we now need to consider paths which are of equal probability to the best too in the recursive case.
def quick_max_root_paths(node, prev_path=[], curr_max_paths=[]):
curr_path = prev_path + [node]
if node.children == []:
if curr_max_paths == [] or path_prob(curr_path) > path_prob(curr_max_paths[0]):
return [curr_path]
elif path_prob(curr_path) == path_prob(curr_max_paths[0]):
return curr_max_paths + [curr_path]
else:
return curr_max_paths
else:
for child in node.children:
if curr_max_paths == [] or path_prob(curr_path + [child]) >= path_prob(curr_max_paths[0]):
curr_max_paths = quick_max_root_paths(child, curr_path, curr_max_paths)
return curr_max_paths

Conclusion
As already explained, the probability tree path in Rummy will be the card groups chosen and we need to find which arrangement of card groups is the most likely to be available and thus that the player should aim for. Now that we can find which arrangement of card groups is the most probable, we know which cards we can discard, and since, using the last algorithm, we can know all the arrangements that give the best probability, we can even narrow down the cards to discard to the ones which are needed the least in all the alternative best arrangements.


text:
# Undetermined coefficient method

1. Oct 17, 2015

### masterchiefo

1. The problem statement, all variables and given/known data
y''+10y'+25y=x+2+3e-5*x

2. Relevant equations

3. The attempt at a solution
F(D) = D2+10D+25 zeroes: -5
yc= C1*e-5*x + C2*e-5*x *x

yp = ax+b + C*e-5*x
yp = ax+b + C*e-5*x*x2

I just want to know if my yc and yp is correct, after that I know how to do it.

2. Oct 17, 2015

### HallsofIvy

yc is correct, yp is not. The SECOND yp, $ax+ b+ cx^2e^{-5x}$ is correct. Since $e^{-5x}$ and $xe^{-5x}$ satisfy the associated homogenous equation you need the "$x^2$".


text:
×

I am very weak at Combinatorics!

Can anyone give me the list of all topics covered in combinatorics like PHP,IEP etc, so that I can work on them....?

Note by Alpha Beta
4 years, 9 months ago

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Look up the Combinatorics section of the Brilliant Blog. I've been designing a series of posts on basic combinatorics topics since most students do not get exposed to such basic ideas.

Staff - 4 years, 9 months ago

Permutations,Combinations and Probability

- 4 years, 9 months ago


text:
MAT334-2018F > Quiz-5

Q5 TUT 0301

(1/1)

Victor Ivrii:
Use Morera's Theorem to show
that the following function is analytic on the indicated domain; find a
power-series expansion for the function by using the known power series for
the integrand and interchanging the summation and integration.
$$\int_{0}^{1} \frac{dt}{1-tz}\qquad\text{on}\; |z|<1.$$

Meerna Habeeb:


text:
# Definition:Linear Differential Operator

Jump to navigation Jump to search

## Definition

A linear differential operator is a differential operator $\mathscr L$ with the property that:

$\map {\mathscr L} {\alpha \phi_1 + \beta \phi_2} = \alpha \map {\mathscr L} {\phi_1} + \beta \map {\mathscr L} {\phi_2}$

Thus if $\phi_1$ and $\phi_2$ are solutions to the differential equation $\map {\mathscr L} {\phi_i} = 0$, then so is any linear combination of $\phi_1$ and $\phi_2$.


text:
# Thread: HSC 2012-2015 Chemistry Marathon (archive)

1. ## Re: HSC 2012 Chemistry Marathon

This is from Independent 09 Trial Exam

Multiple Choice Q3:

3. The molar heat of combustion of ethanol is 1367kJ/mol
What mass of ethanol is required to heat 1.0 moles of water by 10 degrees.

a - 136.7g
b - 46.0g
c - 25.3g
d - 0.025g

2. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by nightweaver066
Question:

A. Amphiprotic species are those that can act as proton donors as well as proton acceptors. For example when HCl is added, HCO3- + H+ -> H2CO3. In this case the bicarbonate ion has accepted a proton thus act as a proton acceptor. However when titrated against NaOH, HCO3- + OH- -> H2O(l) + CO32-, where the bicaronate ion act as a proton donor, donating a hydrogen ion to the hydroxide. HCO3-, able to donate as well as accept hydrogen ions is thus amphiprotic.
B. 8

QUESTIOn
Explain the process of filtration by microscopic membrane filters with reference to their design and composition.

3. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by EazyEEE
A. Amphiprotic species are those that can act as proton donors as well as proton acceptors. For example when HCl is added, HCO3- + H+ -> H2CO3. In this case the bicarbonate ion has accepted a proton thus act as a proton acceptor. However when titrated against NaOH, HCO3- + OH- -> H2O(l) + CO32-, where the bicaronate ion act as a proton donor, donating a hydrogen ion to the hydroxide. HCO3-, able to donate as well as accept hydrogen ions is thus amphiprotic.
B. 8

QUESTIOn
Explain the process of filtration by microscopic membrane filters with reference to their design and composition.
Microscopic membrane filters have microscopic pores and the use of appropriate sized filters can avoid the need to chemically treat the water. The filters can be classified as microfiltration, ultrafiltration, nanofiltration or reverse osmosis membranes depending on the size of the pore.
The membrane is made from synthetic polymers dissolved in a mixture of solvents.

Semi-permeable membranes used in reverse osmosis are either made of cellulose acetate or a layer of polyamide attached to another polymer. Under pressure these polymers allow the passage of water molecules but not that of most atoms, ions or other molecules.

Water is made to flow across the membrane not through it. This reduces the blockage of the pores and contaminants are carried away as waste. The membrane is housed in a pressure vessel and is either made as a wound spiral or hollow fibres.

Microfiltration removes protozoans, bacteria, colloids, some colouration and some viruses. The size of the pore determines which sized particle or organism may pass through the membrane. The finer the pore size the smaller the particles trapped and the more expensive the membrane.

Question- explain, with an example, how oxidation states allow chemists to decide whether or not a reaction involves electron transfer. (assume 3 marks for this quest)

4. ## Re: HSC 2012 Chemistry Marathon

bump
explain, with an example, how oxidation states allow chemists to decide whether or not a reaction involves electron transfer. (assume 3 marks for this quest)

5. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by VJ30
bump
explain, with an example, how oxidation states allow chemists to decide whether or not a reaction involves electron transfer. (assume 3 marks for this quest)
Your response to that membrane filter was great.

Of course, in an exam, diagram!

If oxidation state increases, oxidation has occured and an electron has been released.

If oxidation state decreases, reduction has occured and an electron has been captured.

In redox reactions, if oxidation occurs, a reduction reaction must occur.

If the oxidation state of one reactant increases, and decreases for another reactant in the same reaction, this means an electron has been released by one of the reactants the same electron was captured by the other revealing that the reaction involves an electron transfer.

Therefore, by monitoring the oxidation states of reactants in a reaction, if one increases and another decreases of the same magnitude, a reaction involving an electron transfer has occured.

Now,

Assess the effectiveness of monitoring and managing CFC & halon production & usage. (5)

6. ## Re: HSC 2012 Chemistry Marathon

In this option you studies one natural product that was not a fossil fuel. Describe the issues associated with shrinking world supplies of this natural product, and evaluate progress being made to solve the problems identified.

Marks : 10

Criteria
Identifies an appropriate natural product
Provides a judgement
Provides characteristics and features of at least TWO issues associated with shrinking world supplies of the natural product
Provides characteristics and features of progress being made to find replacement materials
Provides a response that demonstrate coherence and logical progression and includes correct use of scientific principles and idea

7. ## Re: HSC 2012 Chemistry Marathon

Industrial Chemistry Question ^

8. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by nightweaver066

- Ethene is usually produced from the cracking of large hydrocarbons.
- The cracking of a large alkane always produces a small alkene, usually ethene and occasionally propene, and a large alkane.
- The cracking process involves heating the hydrocarbons to 500C with a zeolite catalyst in the absence of oxygen to prevent combustion.
--> Example: C8H18 --> C2H4 + C6H14
- The zeolite catalyst adsorb alkanes, weakening their bonds is required because the activation energy of cracking without a catalyst is very high, requiring immensely high temperatures making it uneconomical.
- Ethene can then be separated from the hydrocarbons by cooling the gas where 5-carbon alkyl chains will condense into liquids.
- Ethene can be separated from small the other smaller hydrocarbons such as propene by fractional distillation, if necessary.

9. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by someth1ng
- Ethene is usually produced from the cracking of large hydrocarbons.
- The cracking of a large alkane always produces a small alkene, usually ethene and occasionally propene, and a large alkane.
- The cracking process involves heating the hydrocarbons to 500C with a zeolite catalyst in the absence of oxygen to prevent combustion.
--> Example: C8H18 --> C2H4 + C6H14
- The zeolite catalyst adsorb alkanes, weakening their bonds is required because the activation energy of cracking without a catalyst is very high, requiring immensely high temperatures making it uneconomical.
- Ethene can then be separated from the hydrocarbons by cooling the gas where 5-carbon alkyl chains will condense into liquids.
- Ethene can be separated from small the other smaller hydrocarbons such as propene by fractional distillation, if necessary.
Great response

10. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by nightweaver066
Great response

- There are many ways a radioisotope can be produced.
- Two such methods include neutron bombardment and nuclear fission.
--> Both of these methods are frequent used as induced nuclear transformations.
- Neutron bombardment usually involves bombarding a certain nuclei with a neutron but does not necessarily involve the product to undergo fission to produce smaller products, as seen in the case of Technetium-99m.
[Equation] Mo-98+neutron-->Mo-99
[Equation] Mo-99-->Tc-99m+electron+gamma
- Nuclear fission often involves the bombardment of a certain nuclei or particle (including neutrons) causing it to spontaneously undergo fission to produce smaller products, as seen in the case of Strontium-90.
[Equation] U-235+neutron-->Xe-138+Sr-90+8neutrons+gamma
- Evidently, although both methods are different, they are both used to produce radioisotopes.

Fairly plain response but I think it'd get 3/4, not exactly a 4/4 response, in my opinion.

Assess the impact of atomic absorption spectroscopy (AAS) on our understanding of trace elements. (3 marks)

11. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by someth1ng
- There are many ways a radioisotope can be produced.
- Two such methods include neutron bombardment and nuclear fission.
--> Both of these methods are frequent used as induced nuclear transformations.
- Neutron bombardment usually involves bombarding a certain nuclei with a neutron but does not necessarily involve the product to undergo fission to produce smaller products, as seen in the case of Technetium-99m.
[Equation] Mo-98+neutron-->Mo-99
[Equation] Mo-99-->Tc-99m+electron+gamma
- Nuclear fission often involves the bombardment of a certain nuclei or particle (including neutrons) causing it to spontaneously undergo fission to produce smaller products, as seen in the case of Strontium-90.
[Equation] U-235+neutron-->Xe-138+Sr-90+8neutrons+gamma
- Evidently, although both methods are different, they are both used to produce radioisotopes.

Fairly plain response but I think it'd get 3/4, not exactly a 4/4 response, in my opinion.
I think you should include the technology/machinery involved or comparing something else to get 4/4

Assess the impact of atomic absorption spectroscopy (AAS) on our understanding of trace elements. (3 marks)
- AAS is a quantitative analysis technique for determining small concentrations of metals in samples.
- Using AAS, scientists have been able to monitor and understand the effect of certain concentrations of trace elements such as cobalt and copper in agricultural land for optimum crop growth
- However, AAS has detection limits in determining concentrations (e.g. detection limit of 1ppb for lead in water samples) and so cannot monitor the effects of such small concentrations
- Overall, AAS has made a profound impact on our understanding of trace elements as farmers are able to optimise plant growth as [Pb] < 1 ppb does not greatly effect plant growth (made this part up, is it fine? lol)

Question:

12. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by nightweaver066
I think you should include the technology/machinery involved or comparing something else to get 4/4

- AAS is a quantitative analysis technique for determining small concentrations of metals in samples.
- Using AAS, scientists have been able to monitor and understand the effect of certain concentrations of trace elements such as cobalt and copper in agricultural land for optimum crop growth
- However, AAS has detection limits in determining concentrations (e.g. detection limit of 1ppb for lead in water samples) and so cannot monitor the effects of such small concentrations
- Overall, AAS has made a profound impact on our understanding of trace elements as farmers are able to optimise plant growth as [Pb] < 1 ppb does not greatly effect plant growth (made this part up, is it fine? lol)
Yeah, I know...I felt that the marking scheme would expect at least two valid comparisons (2 marks, 1 mark for each comparison), identifying two methods (1 mark), identifying two examples (1 mark).

1. Another comparison could be:
Neutron bombardment usually does not require acceleration as neutrons hold no electrical charge, as it is not repelled by the positive nuclei by electrostatic repulsion, it won't need to be forces into the nucleus.
Nuclear fission can often require bombardment of a positively charged nuclei, this means that it must be accelerated to very high speeds to overcome electrostatic repulsion and allowing a new nucleus to be formed which could spontaneously decay into smaller molecules.

2. How? Give an example such as in South Australia, what appeared to be land very suitable for agriculture did not thrive and it was found that cobalt deficiency did not allow grass to grow for grazing.

3. Never make information up, you get 0 marks for it. If you said "extremely miniscule amounts of many heavy metals (eg lead) such that it is undetectable by AAS usually does not have a significant adverse effect on plant growth", you could have gotten a good mark for it and being general but "academic" makes your work more favourable.

13. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by someth1ng
Yeah, I know...I felt that the marking scheme would expect at least two valid comparisons (2 marks, 1 mark for each comparison), identifying two methods (1 mark), identifying two examples (1 mark).

1. Another comparison could be:
Neutron bombardment usually does not require acceleration as neutrons hold no electrical charge, as it is not repelled by the positive nuclei by electrostatic repulsion, it won't need to be forces into the nucleus.
Nuclear fission can often require bombardment of a positively charged nuclei, this means that it must be accelerated to very high speeds to overcome electrostatic repulsion and allowing a new nucleus to be formed which could spontaneously decay into smaller molecules.

2. How? Give an example such as in South Australia, what appeared to be land very suitable for agriculture did not thrive and it was found that cobalt deficiency did not allow grass to grow for grazing.

3. Never make information up, you get 0 marks for it. If you said "extremely miniscule amounts of many heavy metals (eg lead) such that it is undetectable by AAS usually does not have a significant adverse effect on plant growth", you could have gotten a good mark for it and being general but "academic" makes your work more favourable.
Didn't think i needed to be very specific with the example.

Thanks for the feedback

14. ## Re: HSC 2012 Chemistry Marathon

Originally Posted by nightweaver066
Didn't think i needed to be very specific with the example.

Thanks for the feedback
I just thought it wasn't detailed enough, how have they understood it? Those sort of questions, in a way, undermine your answer to some extent since it doesn't fully address all aspects of the question. It's probably better to do too much than too little.

That's my thoughts, at least. But otherwise, you're doing well.

15. ## HSC Chemistry Marathon

The HSC Chemistry Marathon is an open chain of questions between students. It works by answering a question then posting another question and allowing the cycle to repeat itself.

Rules:
- After answering a question, always provide a new one - this is what keeps the thread alive.
- Allocate a number of marks for any question that you post.
- Do not cheat, if you cannot answer a question, do not search how to answer the question but rather, allow other students to answer the question.
- No copyrighted questions (eg CSSA and Independent) should be posted.

Tips:
- You may post more than one question.
- When possible, after questions have been answered, you can peer mark using the marking scheme.

16. ## re: HSC Chemistry Marathon Archive

$HCl \rightarrow H^+ + Cl^-$

$n(HCl) = CV = 0.1 \cdot 0.005 = 0.0005 \ mol$

There is a one to one ratio between HCl and H+

Hence

$n(H^+)= 0.0005$

$\therefore [H^+]= \frac{0.0005}{0.105} =0.0047...$

We get 0.105 from the Volume of the soln which is 105 ml
We now have conecntration of Hydrogen ions, so we take -log of it

$pH = -\log 0.0047 = 2.32$

I hope I'm right lol

=======================

How is it possible to have NEUTRAL water at ph6?

(just brief and straight to the point)

17. ## re: HSC Chemistry Marathon Archive

Correct.

Isn't neutral water defined with pH 7?

18. ## re: HSC Chemistry Marathon Archive

Originally Posted by bleakarcher
Correct.

Isn't neutral water defined with pH 7?
I would tell you why this is not the case, but it would give the answer away haha.

EDIT: I didn't want to kill the thread this early, here is another question in the mean time while people think about it

Upon analysis of mass of a hydrocarbon was found to contain 82.6% Carbon and 17.4% Hydrogen. Calculate its empirical formula

19. ## re: HSC Chemistry Marathon Archive

Originally Posted by Sy123
Upon analysis a hydrocarbon was found to contain 82.6% Carbon and 17.4% Hydrogen. Calculate its empirical formula
What sort of analysis?

Without knowing the type of analysis you don't know whether it is mol% or mass%

20. ## re: HSC Chemistry Marathon Archive

Originally Posted by Riproot
What sort of analysis?

Without knowing the type of analysis you don't know whether it is mol% or mass%
Fixed. But as far as I know it is impossible for there to be those numerical percentages and it meaning mol%, the Carbon - Hydrogen ratio is too high for it to be mol.

21. ## re: HSC Chemistry Marathon Archive

Umm just curious coz I'm kinda wtf-ing, but are both of your questions HSC level?

22. ## re: HSC Chemistry Marathon Archive

Originally Posted by Sy123
Fixed. But as far as I know it is impossible for there to be those numerical percentages and it meaning mol%, the Carbon - Hydrogen ratio is too high for it to be mol.
But still! It's the principle of the thing.

(It's gravimetric analysis or something, right?)

23. ## re: HSC Chemistry Marathon Archive

Originally Posted by theind1996
Umm just curious coz I'm kinda wtf-ing, but are both of your questions HSC level?
The pH 6 one would be one of the tricky ones but the percentage one is fine. I think we did more of that stuff in year 11 though iirc.

24. ## re: HSC Chemistry Marathon Archive

Originally Posted by theind1996
Umm just curious coz I'm kinda wtf-ing, but are both of your questions HSC level?
They are both within syllabus standards not sure what you mean by HSC level.

25. ## re: HSC Chemistry Marathon Archive

Originally Posted by Riproot
The pH 6 one would be one of the tricky ones but the percentage one is fine. I think we did more of that stuff in year 11 though iirc.
Oh yeah shit.

The empirical formula is from moles shit in Yr 11.

Post some more Production questions guys? I think most people haven't done Acidic in great depth.

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text:
Atmospheric Pressure

Atmospheric pressure of a hydraulic network

 Description The Atmospheric Pressure component provides a connection to atmospheric pressure in a hydraulic circuit. Every hydraulics network should contain a connection to this component.
 Equations $p={p}_{A}=P$ $q={q}_{A}$

Variables

 Name Units Description Modelica ID $p$ $\mathrm{Pa}$ Pressure at component p $q$ $\frac{{m}^{3}}{s}$ Flow-rate into component q

Connections

 Name Description Modelica ID $\mathrm{portA}$ Hydraulic port portA

Parameters

 Name Default Units Description Modelica ID $P$ $0$ $\mathrm{Pa}$ Gage pressure P


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 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2008, Volume 262, Pages 16–31 (Mi tm762)

On a Class of Optimal Control Problems Arising in Mathematical Economics

S. M. Aseevab, A. V. Kryazhimskiiab

a Steklov Mathematical Institute, Russian Academy of Sciences
b International Institute for Applied Systems Analysis

Abstract: This paper is devoted to the study of the properties of the adjoint variable in the relations of the Pontryagin maximum principle for a class of optimal control problems that arise in mathematical economics. This class is characterized by an infinite time interval on which a control process is considered and by a special goal functional defined by an improper integral with a discounting factor. Under a dominating discount condition, we discuss a variant of the Pontryagin maximum principle that was obtained recently by the authors and contains a description of the adjoint variable by a formula analogous to the well-known Cauchy formula for the solutions of linear differential equations. In a number of important cases, this description of the adjoint variable leads to standard transversality conditions at infinity that are usually applied when solving optimal control problems in economics. As an illustration, we analyze a conventionalized model of optimal investment policy of an enterprise.

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References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 262, 10–25

Bibliographic databases:

Document Type: Article
UDC: 517.977

Citation: S. M. Aseev, A. V. Kryazhimskii, “On a Class of Optimal Control Problems Arising in Mathematical Economics”, Optimal control, Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday, Tr. Mat. Inst. Steklova, 262, MAIK Nauka/Interperiodica, Moscow, 2008, 16–31; Proc. Steklov Inst. Math., 262 (2008), 10–25

Citation in format AMSBIB
\Bibitem{AseKry08} \by S.~M.~Aseev, A.~V.~Kryazhimskii \paper On a~Class of Optimal Control Problems Arising in Mathematical Economics \inbook Optimal control \bookinfo Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday \serial Tr. Mat. Inst. Steklova \yr 2008 \vol 262 \pages 16--31 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm762} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2489724} \zmath{https://zbmath.org/?q=an:1162.49027} \transl \jour Proc. Steklov Inst. Math. \yr 2008 \vol 262 \pages 10--25 \crossref{https://doi.org/10.1134/S0081543808030036} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000262228000002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53849114662}

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, “Infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 67:2 (2012), 195–253
2. Hespeler F., “On Boundary Conditions Within the Solution of Macroeconomic Dynamic Models with Rational Expectations”, Comput. Econ., 40:3 (2012), 265–291
3. Cruz-Rivera E. Vasilieva O., “Optimal Policies Aimed at Stabilization of Populations with Logistic Growth Under Human Intervention”, Theor. Popul. Biol., 83 (2013), 123–135
4. S. M. Aseev, “On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 11–21
5. Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 22–39
6. Derev'yanko T.O., Kyrylych V.M., “Problem of Optimal Control For a Semilinear Hyperbolic System of Equations of the First Order With Infinite Horizon Planning”, Ukr. Math. J., 67:2 (2015), 211–229
7. Rokhlin D.B., Usov A., “Rational taxation in an open access fishery model”, Arch. Control Sci., 27:1 (2017), 5–27
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# Accelerometer raw data output to measure vibration,and do a frequency spectrum/ amplitude spectrum?

Ive used an Arduino to measure vibration on a washing machine and have up to 100 raw data out putvalues. I want to present an amplitude/frequency spectrum with these values, i have matlab and simulink , but dont know how to start?

And example of how i think

Ax=[1 0 6 25 1 51 51 81 81 51 1 51 51 511 1 551 51 1 1 51 51 10 51 05 1510 15 5 8 0 8 0...]

time= 0-100 seconds.

plot(freq/amp specturm).

Regards,

Volkan

• en.wikipedia.org/wiki/Fast_Fourier_transform – jippie May 4 '14 at 19:04
• Well thats not gonna be helpful if you think that.. – draaknar May 4 '14 at 19:26
• Dude, jippie's comment is helpful, and the answer. The FFT is such a common function that MathWorks builds it into the main package, no add-ons required. Now go into Matlab's documentation and figure out how to use the FFT function. – Matt Young May 4 '14 at 20:49
• I think this is more related to signal processing, Fourrier math or Matlab programming than electronics design. – Blup1980 May 5 '14 at 10:42

• @draaknar I can't give you FFT formulas but if you wanted to "test" the presence for say 0.1Hz, you multiply and integrate the samples you have with a 0.1Hz sinewave and 0.1Hz cosinewave. This gives you two numbers (A and B) and the measure of 0.1Hz in your samples is $\sqrt{A^2 + B^2}$. That's standard numerical fourier analysis – Andy aka May 4 '14 at 20:58


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# Re: Installing SVN

From: Andy Levy <andy.levy_at_gmail.com>
Date: 2005-12-07 18:00:36 CET

On 12/7/05, Najar, Monica J (GE Energy) <monica.najar@ge.com> wrote:
> I don't think this is a bug, but I can't find where can I ask for some help... maybe you can guide me
>
> I'm trying to install SVN in my computer, I have Windows 2000.
>
> I'm following the steps that are in the INSTALL file
>
> D. Installing from a Zip or Installer File under Windows
>
> Of all the ways of getting a Subversion client, this is the
> (*-setup.exe) file from:
> http://subversion.tigris.org/servlets/ProjectDocumentList?folderID=91
>
> For a Zip file, run your unzipping utility (WinZIP, ZipGenius,
> UltimateZIP, FreeZIP, whatever) and extract the DLLs and EXEs to
>
> To test the installation, open a DOS box (run either "cmd" or
> the directory you installed the executables into, and run:
> C:\test>svn co http://svn.collab.net/repos/svn/trunk svn
>
> This will get the latest Subversion sources and put them into the
> "svn" subdirectory.
>
> If using a self-extracting .exe file, just run it instead of
> unzipping it, to install Subversion.
>
> But when I test the installation in the DOS box, this error appears:
>
> 'svn' is not recognized as an internal or external command,
> operable program or batch file.
>
> Am I missing something? Do I need to do something before this?

The directory you unzipped Subversion into is not in your path.
You'll need to update the PATH environment variable and append the svn
directory, or specify c:\path\to\svn.exe on the command line.

However, the installer I used was a regular Windows install package
and it did all this for me automagically.

---------------------------------------------------------------------
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# Quiz | Chemical Calculations for Solutions

1

Which of the following factors affects the solubility of a particular substance?

Solubility is the maximum quantity of solute dissolvable in a solvent at a particular temperature. A solid is more soluble at higher temperatures and in a solvent with similar types of intermolecular forces

2

What is the molarity of a solution that contains 8 moles of solute in 2 liters of solution?

Molarity M  =  $\frac{{\mathrm{n}}_{\mathrm{solute}}}{{\mathrm{V}}_{\mathrm{solution}}}$  =  $\frac{8}{2}$ =  4M

3

What is the mass of NaCl in 250 mL of a 0.4 M solution?

number of moles nNaCl  =  M x Vsolution  =  $\frac{{\mathrm{m}}_{\mathrm{NaCl}}}{{\mathrm{M}}_{\mathrm{NaCl}}}$

⇒ mNaCl  = M x Vsolution x MNaCl   with MNaCl = molar mass of NaCl = MNa + MCl = 23.0 + 35.4 = 58.4 g.mol-1

⇒ mNaCl  = 0.4 x 0.250 x 58.4 = 5.84 g

4

What does not change when a solution is diluted by the addition of solvent?

In dilution, the amount of solute does not change: the number of moles are the same before and after dilution

5

How many mL of a 2.0 M NaBr solution are needed to make 300.0 mL of 0.5 M NaBr?

In dilution, the amount of solute does not change: n1 = n2 ⇒ M1 x V1 = M2 x V2
2.0 x V1 = 0.5 x 0.300 ⇒ V1 = 0.075 L = 75 mL

6

What is the endpoint of a titration?