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# Let $u \in C^3(\mathbb{R}^n)$ and harmonic such that $u(x) = o(|x|)$ when $|x| \rightarrow \infty$. Show that $\nabla u(0) = 0$ and u is constant

Let $$u \in C^3(\mathbb{R}^n)$$ and harmonic such that $$u(x) = o(|x|)$$ when $$|x| \rightarrow \infty$$.
1. Show that $$\nabla u(0) = 0$$
2. Show that u is a constant function.

To show that $$\nabla u(0) = 0$$, I tried to show that $$\frac{\partial u}{\partial x_i}(0) = 0, \forall i$$, but came up with nothing.
For example, I know that the partial derivatives are also harmonic functions, so using the mean value theorem i get that:

$$\frac{\partial u}{\partial x_i} = \frac{1}{\operatorname{Vol}(r \cdot B^n)}\int_{r \cdot B^n}\frac{\partial u}{\partial x_i}(x) dx$$

and then I tried to use the divergence theorem on the vector field $$F = (0,\ldots,0,u,0,\ldots,0)$$ where the $$u$$ is in the i-th coordinate, so I get: (sorry about the strange formatting of that vector)

$$= \frac{1}{\operatorname{Vol}(r \cdot B^n)} \int_{r \cdot S^{n-1}} \left< \left(\matrix{0\\ \vdots\\u\\ \vdots \\ 0}\right),\frac{x}{r}\right> dS =\frac{1}{\operatorname{Vol}(r \cdot B^n)} \int_{r \cdot S^{n-1}}u \cdot \frac{x_i}{r}dS$$

and if $$u \cdot x_i$$ was harmonic, I would've finished here by using the mean value theorem again because obviously $$u \cdot x_i = 0$$ at $$x=0$$, but it isn't harmonic for sure.

Any help will be very appreciated.
Do note that this is a question from a past exam in an advanced multivariate calculus class, so we don't have so much claims about harmonic functions and that's why I thought I could find a solution with the divergence theorem.
I did find this answer, which somehow answers both questions together, but seems like a complete overkill, and probably this is not close to the solution the professor thought of when he wrote the questions and the solution to the second question somehow involves the first question.

If you take the Poisson integral formula and differentiate under the integral sign it follows that there exists $$C$$ such that $$|\nabla u(0)|\le C\sup_{|x|=1}|u(x)|.$$
Now for $$r>0$$ let $$u_r(x)=u(rx)$$. Then $$|\nabla u_r(0)|=r|\nabla u(0)|$$, so $$r|\nabla u(0)|\le C\sup_{|x|=r}|u(x)|=o(r);$$that can't happen unless $$\nabla u(0)=0$$.
Now if you let $$v(x)=u(x+p)$$ this shows that $$\nabla u(p)=\nabla v(0)=0.$$
Details added on request. The Poisson kernel can be found for example here; for $$r=1$$ it's $$P(x,\zeta)=\frac{1-|x|^2}{\omega_{n-1}|x-\zeta|^n}.$$So above if $$|x|<1$$ we have $$u(x)=\int_{|\zeta|=1}P(x,\zeta)u(\zeta)\,d\sigma(\zeta).$$Since $$P(x,\zeta)$$ depends smoothly on $$x$$ it follows that $$\nabla u(0)=\int_{|\zeta|=1}\nabla_x P(0,\zeta)u(\zeta)\,d\sigma(\zeta),$$hence $$|\nabla u(0)|\le c\max_{|x|=1|}|u(x)|,$$with $$c=\int_{|\zeta|=1}|\nabla_x P(0,\zeta)|\,d\sigma(\zeta).$$


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# Copy and Paste: what is copied to the clipboard?

Copy and Paste is so familiar and works so well that I never wondered what is really happening. My simple idea is that when I select something in the notebook and press [ControlKey]C, then my selection is placed on the on the clipboard. Then, when I go to another position in my notebook and press [ControlKey]V, the contents of the clipboard, i.e. what I selected, is placed at that position in the notebook.

What exactly is placed on the clipboard? I know we have a menu for that, Copy As, but I am considering the straightforward Copy. Since everything in the notebook is typesetted in boxes, I expect that it will be some or other box structure, similar to cell expressions, or a string.

Evaluate:

DynamicModule[{x}, Dynamic[x]]

The output looks like FE'x$$37, but in fact is a DynamicModule. I select the output cell and copy it. Then I paste it into a text editor, e.g. Notepad++, and I see \!$$DynamicBox[ToBoxes[CellContextx, StandardForm], ImageSizeCache->{88., {2., 15.}}]$$  That is more or less as expected. Almost identical: DynamicModule[{x}, x]  It shows x$$, but just as before, it is a DynamicModule. When I copy the output cell and paste it into Notepad++, I see only

x$$ Nevertheless, when I paste it into the notebook, I find a DynamicModule. Even stronger, when I start a fresh Mathematica session and paste the clipboard into a new notebook, the result is a cell containing the DynamicModule as above. So the clipboard contains enough information that Mathematica can construct the DynamicModule, but Notepad++ (and Ditto) are unable to show the complete information from the clipboard. Is there a way to see what exactly Mathematica has placed on the clipboard? It is not important at all, I am just curious. • NotebookGet[FrontEndClipboardNotebook[]]? – kglr Jun 19 '18 at 10:20 • On some operating systems (definitely on Windows) the clipboard can hold data in multiple formats at the same time. I do not know if this is what happens in Mathematica, but it could work like this: when you copy a Graphics, it may be copied in vector format (EMF), as a bitmap, as a Mathematica expression (i.e. text) simultaneously. As I remember, MS Word on Windows even has a special Paste command that allows choosing the format to paste. – Szabolcs Jun 19 '18 at 10:20 • Normally, what gets pasted depends on what application you are pasting into, and what formats that application can handle. E.g. when copying rich text, the plain text version would get pasted into Notepad, but the rich text version into WordPad. Here's a screenshot of the 6 different formats Mathematica seems to produce on OS X when copying a graph: i.stack.imgur.com/YoS5M.png They seem to come in pairs, so only 3 are distinct: a Cell expression, a bitmap in TIFF format, and vector graphics in PDF format. On Windows, this might be different. – Szabolcs Jun 19 '18 at 10:24 • Even on OS X, if I copy a different symbolic expression, e.g. 1+x^2, I see a different collection of formats on the clipboard: a Cell expression, MathML and plain text in 3 different character encodings. – Szabolcs Jun 19 '18 at 10:27 ## 1 Answer This answer is specifically for the Windows platform, but should be similar in other OS as well. Whenever you copy something to the clipboard the OS attempts to save it to a temporary cache in as many formats as possible. Then when you paste it, the program chooses which format is most appropriate. In your question you mentioned pasting into Mathematica sessions as well as a text editor. If you had tried posting it into an graphics program, you would have seen FE'x$$37as an image. You can see this functionality easily in Word where it allows you to select the paste format.

In older versions of Windows, there was something called Clipboard Viewer. It doesn't come standard since XP, but you can download it and it works fine. The program gives you a sneak peak at what is in your clipboard. If you use the View menu, it shows you all the formats available. If the program can show it nativity, it will, otherwise it shows the type of data included but the option is greyed out.

As per your question, I am attaching a screenshot of all the formats your particular result in Mathematica puts into the clipboard for the output FE'x$$37: I did some testing and confirmed that depending on the nature of the object, Mathematica puts different formats in the clipboard. You can download the clipboard viewer and explore some more if you are interested. • Your answer came in when I was already studying the clear comments of @Szabolcs. Thanks to both of you. I was not aware of a clipboard viewer in Windows, so I found it highly interesting to see the one in OS X. Moreover, it was completely new to me that when you copy something to the clipboard, it could be stored in more than one format. That explains quite well that in my x$$ example, there must be at least two formats and when pasting into a text editor, only the text format is used. That answers my question. – Fred Simons Jun 19 '18 at 12:59
• I also looked at three clipboard viewers for Windows. The original Windows Clipboard Viewer mentioned by Ben shows the format Mathematica Cells, but it is grayed out and indeed does not work. I also found InsideClipboard and Free Clipboard Viewer. Both show the Mathematica Cells format correctly, but with a Plot result in the clipboard, InsideClipboard was unable to show the picture, Clipboard Viewer showed the picture in in the format Picture (inclusive the cell label) and Free Clipboard Viewer in the format RTF (without the cell label). – Fred Simons Jun 19 '18 at 13:04
• It really is impressive that so much is going on in the background with just a few simple key strokes that we use all the time. Amazing that programs can output so many formats and then other programs can (usually) correctly choose how to bring the info back in. I ended up playing around with a few other programs (Word, Paintshop, Audacity) and it is cool to see all the formats they automatically cache. – kickert Jun 19 '18 at 13:22
• I used ClipView (peterbuettner.de/develop/tools/clipview) when developing a solution for mathematica.stackexchange.com/questions/158117/… – Gustavo Delfino Jun 19 '18 at 14:23

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# 1d Kinematics, missing something.

1. Oct 7, 2006

### Kildars

A person who walks for exercise produces the position-time graph given with this problem.

(b) Calculate the average velocity for each segment to verify your answers to part (a).
A
m/s
B
m/s
C
m/s
D
m/s

B is obviously 0

For A I did .20 of an hour is 300 seconds.
And 1km = 1000m

So 1000/300 =3.33 and that is wrong..

What am I doing wrong here I used:
$$v_{ave} = \Delta x / \Delta t$$

2. Oct 7, 2006


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# Can one show that $\frac{\vec{u}\cdot \vec{v}}{||\vec{u}||*||\vec{v}||}$ is always on the range of $\cos \theta$?

A basic property of the dot product of two vectors is that

$$\frac{\vec{u}\cdot \vec{v}}{||\vec{u}||*||\vec{v}||} = \cos \theta$$

Where $\theta$ is the angle between the two vectors. Since there is obviously always an angle between two vectors, this means that the quotient of the dot product and the magnitudes of the two vectors will always be on the range of the cosine function:

$$-1 \leq \frac{\vec{u}\cdot \vec{v}}{||\vec{u}||*||\vec{v}||} \leq 1$$

Square the quotient to make it non-negative and get the inequality

$$\frac {(\vec{u}\cdot \vec{v})^2}{||\vec{u}||^2*||\vec{v}||^2} \leq 1$$

For the quotient to be less than one, the denominator must be greater than the numerator:

$$||\vec{u}||^2*||\vec{v}||^2 \geq (\vec{u}\cdot\vec{v})^2$$

And rewrite using the property $\vec{u}\cdot\vec{u} = ||\vec{u}||^2$ :

$$(\vec{u}\cdot\vec{u})*(\vec{v}\cdot\vec{v}) \geq (\vec{u}\cdot\vec{v})^2$$

The above inequality is the claim I want to prove. Is there a way to show why the inequality holds for arbitrarily many dimensions, and using general vector operations instead of components?

I have found a way to show that the inequality holds for two-dimensional vectors using components, but it bugs me that I have to use components instead of more general vector notation and operations. And of course I want to be able to show it in more dimensions.

Proof:

Let $\vec{u} = <u_1, u_2>$ and $\vec{v} = <v_1, v_2>$ with real components. The inequality becomes

$$(u_1^2+u_2^2)*(v_1^2+v_2^2) \geq (u_1v_1 + u_2v_2)^2$$

Multiply it out.

$$u_1^2v_1^2 + u_2^2v_2^2 + u_1^2v_2^2 + u_2^2v_1^2 \geq u_1^2v_1^2+u_2^2v_2^2 + 2u_1u_2v_1v_2$$

Subtract the quantity $u_1^2v_1^2 + u_2^2v_2^2$ from both sides.

$$u_1^2v_2^2 + u_2^2v_1^2 \geq 2u_1u_2v_1v_2$$

Observe that the right side can be rewritten

$$(u_1v_2-u_2v_1)^2 + 2u_1u_2v_1v_2 \geq 2u_1u_2v_1v_2$$

And subtract the long term

$$(u_1v_2-u_2v_1)^2 \geq 0$$

And the left side will be a non-negative number because it is squared and $x^2 \geq 0$ for all real numbers $x$. Since the components of the vectors are real, $u_1v_2- u_2v_1$ is real and the inequality holds for all real vectors $\vec{u}$ and $\vec{v}$.

• Heard of Cauchy Swartz inequality? Just check out its Wikipedia page. – G-man Jan 16 '16 at 4:04

This is called the Cauchy-Schwarz inequality.

If $\vec{v}$ or $\vec{w}$ is the zero vector, the result is trivial. So assume $\vec{v} \neq \vec{0}$ and $\vec{w} \neq \vec{0}$ Start by noting that $\langle v-w,v-w\rangle \geq 0$. Expanding this out, we have: \begin{align*} \langle v,v \rangle - 2 \langle v,w \rangle +\langle w,w\rangle &\geq 0 \\ 2\langle v,w \rangle &\leq \langle v,v \rangle + \langle w,w\rangle \end{align*}

Now, if $\vec{v}$ and $\vec{w}$ are unit vectors, this says that

\begin{align*} 2\langle \vec{v}, \vec{w} \rangle &\leq 2 \\ \langle \vec{v},\vec{w}\rangle &\leq 1 \end{align*}

Now to prove the result for any pair of nonzero vectors, simply scale them to make them unit vectors:

\begin{align*} \langle \frac{1}{|\vec{v}|}\vec{v},\frac{1}{|\vec{w}|}\vec{w}\rangle &\leq 1\\ \langle v,w\rangle &\leq |v||w| \end{align*}

This proves one half of the inequality. Can you prove the other half?

• For some reason, this proof does not seem to appear in most standard sources, but I find it to be the easiest to understand. – Steven Gubkin Jan 16 '16 at 4:18
• Thank you for your answer. It is a bit difficult for me to read the Wikipedia article and this answer because the notation is different from what I learned in class. Is it correct that $\langle \vec{v}, \vec{w} \rangle$ is the dot product of $\vec{v}$ and $\vec{w}$, and only one vertical bar is used to indicate the magnitude of a vector? – Apoapsis Jan 16 '16 at 4:24
• My textbook is Calculus: Early Transcendentals by Jon Rogawski. – Apoapsis Jan 16 '16 at 4:24
• @Apoapsis Yes, you are correct in both of your presumptions about the notation. I personally find the inner product notation to be easier to work with than the dot notation, because it is harder to confuse scalar multiplication with the inner product. – Steven Gubkin Jan 16 '16 at 4:38

Yes, this is the Cauchy-Schwarz inequality.

After scaling, you can assume that $u$ and $v$ are both unit vectors. Let $t = u \cdot v$. The goal is to show that $|t| \leq 1$.

Write $u = tv + (u - tv)$. (The vector $tv$ is the projection of $u$ along $v$.) We have $(tv) \cdot (u - tv) = t^2 - t^2 = 0$, so $1 = u \cdot u = |tv|^2 + |u - tv|^2 \geq |tv|^2 = t^2$.


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# asymptotic variance of bernoulli

In Example 2.34, σ2 X(n) Lindeberg-Feller allows for heterogeneity in the drawing of the observations --through different variances. Read more. is the number of times we get heads when we flip a coin a specified number of times. Asymptotic Distribution Theory ... the same mean and same variance. Lecture Notes 10 36-705 Let Fbe a set of functions and recall that n(F) = sup f2F 1 n Xn i=1 f(X i) E[f] Let us also recall the Rademacher complexity measures R(x 1;:::;x n) = E sup For nonlinear processes, however, many important problems on their asymptotic behaviors are still unanswered. From Bernoulli(p). ???\sigma^2=(0.25)(0-0.75)^2+(0.75)(1-0.75)^2??? Therefore, since ???75\%??? ?, and ???p+(1-p)=p+1-p=1???). Our results are applied to the test of correlations. 1.4 Asymptotic Distribution of the MLE The “large sample” or “asymptotic” approximation of the sampling distri-bution of the MLE θˆ x is multivariate normal with mean θ (the unknown true parameter value) and variance I(θ)−1. We say that ϕˆis asymptotically normal if ≥ n(ϕˆ− ϕ 0) 2 d N(0,π 0) where π 2 0 is called the asymptotic variance of the estimate ϕˆ. In this case, the central limit theorem states that √ n(X n −µ) →d σZ, (5.1) where µ = E X 1 and Z is a standard normal random variable. How do we get around this? What is asymptotic normality? Realize too that, even though we found a mean of ???\mu=0.75?? C. Obtain The Asymptotic Variance Of Vnp. 1 Department of Mathematical Sciences, Augustine University Ilara-Epe, Nigeria. The first integer-valued random variable one studies is the Bernoulli trial. 11 0 obj Finding the mean of a Bernoulli random variable is a little counter-intuitive. The variance of the asymptotic distribution is 2V4, same as in the normal case. 1 Department of Mathematical Sciences, Augustine University Ilara-Epe, Nigeria. I find that ???75\%??? A Bernoulli random variable is a special category of binomial random variables. I ask them whether or not they like peanut butter, and I define “liking peanut butter” as a success with a value of ???1??? In Example 2.33, amseX¯2(P) = σ 2 X¯2(P) = 4µ 2σ2/n. and the mean, square that distance, and then multiply by the “weight.”. Notice how the value we found for the mean is equal to the percentage of “successes.” We said that “liking peanut butter” was a “success,” and then we found that ???75\%??? This is accompanied with a universality result which allows us to replace the Bernoulli distribution with a large class of other discrete distributions. There is a well-developed asymptotic theory for sample covariances of linear processes. ML for Bernoulli trials. A Note On The Asymptotic Convergence of Bernoulli Distribution. to the success category of “like peanut butter.” Then we can take the probability weighted sum of the values in our Bernoulli distribution. asked Oct 14 '16 at 11:44. hazard hazard. As discussed in the introduction, asymptotic normality immediately implies As our finite sample size $n$ increases, the MLE becomes more concentrated or its variance becomes smaller and smaller. and success represented by ???1?? A Bernoulli random variable is a special category of binomial random variables. %�쏢 2. Well, we mentioned it before, but we assign a value of ???0??? If we want to create a general formula for finding the mean of a Bernoulli random variable, we could call the probability of success ???p?? Asymptotic Distribution Theory ... the same mean and same variance. of our class liked peanut butter, so the mean of the distribution was going to be ???\mu=0.75???. with a Bernoulli random variable, we have exactly one trial only (binomial random variables can have multiple trials), and we define “success” as a 1 and “failure” as a 0. I will show an asymptotic approximation derived using the central limit theorem to approximate the true distribution function for the estimator. If our experiment is a single Bernoulli trial and we observe X = 1 (success) then the likelihood function is L(p; x) = p. This function reaches its maximum at $$\hat{p}=1$$. The cost of this more general case: More assumptions about how the {xn} vary. ?, and then call the probability of failure ???1-p??? from Bernoulli(p). 2. Normality: as n !1, the distribution of our ML estimate, ^ ML;n, tends to the normal distribution (with what mean and variance? <> Title: Asymptotic Distribution of Bernoulli Quadratic Forms. ???\sigma^2=(0.25)(0-\mu)^2+(0.75)(1-\mu)^2??? A Note On The Asymptotic Convergence of Bernoulli Distribution. In the limit, MLE achieves the lowest possible variance, the Cramér–Rao lower bound. There is a well-developed asymptotic theory for sample covariances of linear processes. It seems like we have discreet categories of “dislike peanut butter” and “like peanut butter,” and it doesn’t make much sense to try to find a mean and get a “number” that’s somewhere “in the middle” and means “somewhat likes peanut butter?” It’s all just a little bizarre. Bernoulli | Citations: 1,327 | Bernoulli is the quarterly journal of the Bernoulli Society, covering all aspects of mathematical statistics and probability. u�����+l�1l"�� B�T��d��m� ��[��0���N=|^rz[���Ũ)�����6�P"Z�N�"�p�;�PY�m39,����� PwJ��J��6ڸ��ڠ��"�������$X�*���E�߆�Yۼj2w��hkV��f=(��2���$;�v��l���bp�R��d��ns�f0a��6��̀� On top of this histogram, we plot the density of the theoretical asymptotic sampling distribution as a solid line. for, respectively, the mean, variance and standard deviation of X. Specifically, with a Bernoulli random variable, we have exactly one trial only (binomial random variables can have multiple trials), and we define “success” as a ???1??? Say we’re trying to make a binary guess on where the stock market is going to close tomorrow (like a Bernoulli trial): how does the sampling distribution change if we ask 10, 20, 50 or even 1 billion experts? (2) Note that the main term of this asymptotic … The exact and limiting distribution of the random variable E n, k denoting the number of success runs of a fixed length k, 1 ≤ k ≤ n, is derived along with its mean and variance.An associated waiting time is examined as well. In this chapter, we wish to consider the asymptotic distribution of, say, some function of X n. In the simplest case, the answer depends on results already known: Consider a linear The study of asymptotic distributions looks to understand how the distribution of a phenomena changes as the number of samples taken into account goes from n → ∞. We compute the MLE separately for each sample and plot a histogram of these 7000 MLEs. We can estimate the asymptotic variance consistently by Y n 1 Y n: The 1 asymptotic con–dence interval for can be constructed as follows: 2 4Y n z 1 =2 s Y n 1 Y n 3 5: The Bernoulli trials is a univariate model. ). 6). MLE: Asymptotic results It turns out that the MLE has some very nice asymptotic results 1. B. The Bernoulli numbers of the second kind bn have an asymptotic expansion of the form bn ∼ (−1)n+1 nlog2 n X k≥0 βk logk n (1) as n→ +∞, where βk = (−1) k dk+1 dsk+1 1 Γ(s) s=0. %PDF-1.2 Question: A. If our experiment is a single Bernoulli trial and we observe X = 1 (success) then the likelihood function is L(p; x) = p. This function reaches its maximum at $$\hat{p}=1$$. I create online courses to help you rock your math class. Lehmann & Casella 1998 , ch. In this chapter, we wish to consider the asymptotic distribution of, say, some function of X n. In the simplest case, the answer depends on results already known: Consider a linear variance maximum-likelihood. Under some regularity conditions the score itself has an asymptotic nor-mal distribution with mean 0 and variance-covariance matrix equal to the information matrix, so that u(θ) ∼ N It means that the estimator b nand its target parameter has the following elegant relation: p n b n !D N(0;I 1( )); (3.2) where ˙2( ) is called the asymptotic variance; it is a quantity depending only on (and the form of the density function). where ???X??? I can’t survey the entire school, so I survey only the students in my class, using them as a sample. No one in the population is going to take on a value of ???\mu=0.75??? ����l�P�0Y]s��8r�ޱD6��r(T�0 x��]Y��q�_�^����#m��>l�A'K�xW�Y�Kkf�%��Z���㋈x0�+�3##2�ά��vf�;������g6U�Ժ�1֥��̀���v�!�su}��ſ�n/������ِ�w�{��J�;ę�$�s��&ﲥ�+;[�[|o^]�\��h+��Ao�WbXl�u�ڱ� ���N� :�:z���ų�\�ɧ��R���O&��^��B�%&Cƾ:�#zg��,3�g�b��u)Զ6-y��M"����ށ�j �#�m�K��23�0�������J�B:���o�U�Ӈ�*o+�qu5��2Ö����$�R=�A�x��@��TGm� Vj'���68�ī�z�Ȧ�chm�#��y�����cmc�R�zt*Æ���]��a�Aݳ��C�umq���:8���6π� asymptotic normality and asymptotic variance. The cost of this more general case: More assumptions about how the {xn} vary. stream share | cite | improve this question | follow | edited Oct 14 '16 at 13:44. hazard. Adeniran Adefemi T 1 *, Ojo J. F. 2 and Olilima J. O 1. And we see again that the mean is the same as the probability of success, ???p???. Therefore, standard deviation of the Bernoulli random variable is always given by. and the mean and ???1??? Consider a sequence of n Bernoulli (Success–Failure or 1–0) trials. Let X1, ..., Xn Be I.i.d. Example with Bernoulli distribution b. ?? This is the mean of the Bernoulli distribution. 2 The asymptotic expansion Theorem 1. The paper presents a systematic asymptotic theory for sample covariances of nonlinear time series. Next, we extend it to the case where the probability of Y i taking on 1 is a function of some exogenous explanatory variables. We’ll use a similar weighting technique to calculate the variance for a Bernoulli random variable. Fundamentals of probability theory. and “failure” as a ???0???. The exact and limiting distribution of the random variable E n, k denoting the number of success runs of a fixed length k, 1 ≤ k ≤ n, is derived along with its mean and variance.An associated waiting time is examined as well. Normality: as n !1, the distribution of our ML estimate, ^ ML;n, tends to the normal distribution (with what mean and variance… For nonlinear processes, however, many important problems on their asymptotic behaviors are still unanswered. Then with failure represented by ???0??? Authors: Bhaswar B. Bhattacharya, Somabha Mukherjee, Sumit Mukherjee. Let’s say I want to know how many students in my school like peanut butter. of the students in my class like peanut butter. Adeniran Adefemi T 1 *, Ojo J. F. 2 and Olilima J. O 1. multiplied by the probability of failure ???1-p???. Browse other questions tagged poisson-distribution variance bernoulli-numbers delta-method or ask your own question. Asymptotic normality says that the estimator not only converges to the unknown parameter, but it converges fast … by Marco Taboga, PhD. The advantage of using mean absolute deviation rather than variance as a measure of dispersion is that mean absolute deviation:-is less sensitive to extreme deviations.-requires fewer observations to be a valid measure.-considers only unfavorable (negative) deviations from the mean.-is a relative measure rather than an absolute measure of risk. ?, the distribution is still discrete. In this case, the central limit theorem states that √ n(X n −µ) →d σZ, (5.1) where µ = E X 1 and Z is a standard normal random variable. Specifically, with a Bernoulli random variable, we have exactly one trial only (binomial random variables can have multiple trials), and we define “success” as a 1 and “failure” as a 0. k 1.5 Example: Approximate Mean and Variance Suppose X is a random variable with EX = 6= 0. series of independent Bernoulli trials with common probability of success π. MLE: Asymptotic results It turns out that the MLE has some very nice asymptotic results 1. series of independent Bernoulli trials with common probability of success π. As for 2 and 3, what is the difference between exact variance and asymptotic variance? Maximum Likelihood Estimation Eric Zivot May 14, 2001 This version: November 15, 2009 1 Maximum Likelihood Estimation 1.1 The Likelihood Function Let X1,...,Xn be an iid sample with probability density function (pdf) f(xi;θ), where θis a (k× 1) vector of parameters that characterize f(xi;θ).For example, if Xi˜N(μ,σ2) then f(xi;θ)=(2πσ2)−1/2 exp(−1 Consistency: as n !1, our ML estimate, ^ ML;n, gets closer and closer to the true value 0. 307 3 3 silver badges 18 18 bronze badges $\endgroup$ Earlier we defined a binomial random variable as a variable that takes on the discreet values of “success” or “failure.” For example, if we want heads when we flip a coin, we could define heads as a success and tails as a failure. Suppose that $$\bs X = (X_1, X_2, \ldots, X_n)$$ is a random sample from the Bernoulli distribution with unknown parameter $$p \in [0, 1]$$. ML for Bernoulli trials. The paper presents a systematic asymptotic theory for sample covariances of nonlinear time series. (20 Pts.) Suppose you perform an experiment with two possible outcomes: either success or failure. We could model this scenario with a binomial random variable ???X??? 2 Department of Statistics, University of Ibadan, Ibadan, Nigeria *Corresponding Author: Adeniran Adefemi T Department of Mathematical Sciences, Augustine University Ilara-Epe, Nigeria. In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability = −.Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. to the failure category of “dislike peanut butter,” and a value of ???1??? 2 Department of Statistics, University of Ibadan, Ibadan, Nigeria *Corresponding Author: Adeniran Adefemi T Department of Mathematical Sciences, Augustine University Ilara-Epe, Nigeria. of the students dislike peanut butter. If we observe X = 0 (failure) then the likelihood is L(p; x) = 1 − p, which reaches its maximum at $$\hat{p}=0$$.


text:
# Matrix times its transpose equals original matrix

I have a 6x6 matrix that equals the original matrix when multiplied by its transpose. What does this say about this matrix? What unique conditions does this matrix satisfy, since this property doesn't seem to hold in general?

-
I don't follow. This means that the matrix is the identity. Did you mean to say something else? – Qiaochu Yuan Oct 14 '12 at 2:08
Sorry, I made a mistake. I meant matrix times its transpose, not matrix times its inverse. – metrix Oct 14 '12 at 2:09
In the case of a symmetric matrix, this property is called idempotence. – Max Oct 14 '12 at 2:11
The math working out is a reason. Is there anything in particular you're after? – EuYu Oct 14 '12 at 2:13
This certainly doesn't seem like a lucky coincidence to me. Perhaps you should include more details of the context of the problem. – EuYu Oct 14 '12 at 2:17

• They are symmetric: $M^T = M$.
• They are idempotent: $M^2 = M$.


text:
Abstract view

Indecomposable Higher Chow Cycles

Published:2005-06-01
Printed: Jun 2005
• Kenichiro Kimura
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: HTML LaTeX MathJax PDF PostScript

Abstract

Let $X$ be a projective smooth variety over a field $k$. In the first part we show that an indecomposable element in $CH^2(X,1)$ can be lifted to an indecomposable element in $CH^3(X_K,2)$ where $K$ is the function field of 1 variable over $k$. We also show that if $X$ is the self-product of an elliptic curve over $\Q$ then the $\Q$-vector space of indecomposable cycles $CH^3_{ind}(X_\C,2)_\Q$ is infinite dimensional. In the second part we give a new definition of the group of indecomposable cycles of $CH^3(X,2)$ and give an example of non-torsion cycle in this group.
 MSC Classifications: 14C25 - Algebraic cycles 19D45 - Higher symbols, Milnor $K$-theory


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# Random Linux/Latex tricks

This is a collection of various tips and tricks I’ve found useful in my interaction with the standard geek tools I use often. They’re mainly posted here as a reference for me, so don’t blame me if you don’t find it useful… :)

### Using custom labels with the alpha BibTeX stylePosted 2017-12-08

The alpha BibTeX style produces citation labels of the form [Ken90] or [XYZ94]. While it usually does the right thing, sometimes it doesn’t get the label right (e.g. the label is too long when the authors have multiple / hyphenated last names). Here is how you can provide a custom label with the alpha style.More »

### Swapping control/caps lock, and using Apple keyboards on LinuxPosted 2017-12-07

I rarely use caps lock and often use control. Since the caps lock key is located on the home row, I find typing more efficient if I swap control and the left caps lock. I also like to swap the command and option modifiers when I use Apple keyboards, and make the funciton keys work without having to use the FN modifier. Here are instructions on each of these.More »

### Getting DOI / arXiv links with BibTeX.Posted 2017-11-14

Many bibliography databases supply a DOI (Digital Object Identifier) or arXiv eprint number with BibTeX entries. However, the standard BiBTeX style files either ignore this information or print it without hyperlinking it correctly. Here’s how you can get working clickable links to both DOI and arXiv eprints.More »

Tags: bibtex

### Static Jinja2 Site GeneratorPosted 2017-10-21

I recently rewrote my website using staticjinja, a static site generator. This is what my website looks like and here is the source code. The features / setup-instructions are described below.More »

### Using git and DropboxPosted 2016-04-06

Dropbox isn’t version control. If you use git to version control your files, and have co-authors that use Dropbox then here is a way to use the two systems together.More »

Tags: linux, git

### Using Box.com cloud storage on LinuxPosted 2015-08-07

Recently CMU announced all users will have 1TB of space of cloud storage at Box.com. This motivated me to set it up on my Linux box, and this post describes the setup instructions to mount it as a local folder and copy files back and forth. (Note, no syncing instructions are here, since I’m perfectly happy with my unison set up and haven’t tired to set it up yet.)More »

Tags: linux

### Reverse chronological sorting with BibTeXPosted 2015-03-24

How to sort references chronologically, reverse chronologically or change the references title.More »

Tags: latex

### Using UTF-8 in mrxvt, even though mrxvt doesn't support itPosted 2014-09-14

I use mrxvt (see also the SourceForge page) as my terminal emulator. Unfortunately it lacks utf8 support. (We have an experimental utf8 branch, but never managed to make it usable.) Here are a few things I’ve done that allows me to keep using mrxvt and interact correctly with UTF-8.More »

Tags: linux

### Transfering files to Android Devices in LinuxPosted 2014-08-10

Transfering files to/from a android device to a Linux box via mtp-tools, FTP over USB, or ssh.More »

Tags: linux, android

### De-Uglyfying ikiWiki and other horror stories.Posted 2014-07-20

These are old instructions on how to theme ikiWiki and might not be relelvant anymore. I no longer use ikiWiki to maintain my website. This site is generated using staticjinja and a custom build script.More »

Tags: linux, ikiwiki

### Setting up a Debian/testing chroot on stable (wheezy)Posted 2014-07-16

I run Debian/wheezy on all my computers, mainly because I can’t afford the downtime. However, once in a while, I encounter programs I need that are only in testing. For instance the new (2014-07-16) Viber linux client needs glibc-2.14 or higher, and wheezy only has 2.13. Some blog posts suggest installing libc6 from testing on your wheezy system, but I think that’s playing with fire. libc6 is crucial to many packages, and I’m not sure things will work fine if you upgrade it.

I decided to set up a Debian/testing chroot, and then install whatever I needed under it.More »

Tags: linux

### Maintaining an old texlive installation.Posted 2014-07-12

How to subbornly continue using an obsolete version of texlive well after its due date.More »

Tags: latex, linux

### Adjusting the space between references in the bibliography.Posted 2014-07-12

If you use LaTeX and want to adjust the spacing between each item in your bibliography, then here are two ways to do it.More »

Tags: latex

### Expanding aliases in zshPosted 2014-06-25

I wanted to make some of my zsh aliases behave like vim abbreviations: Namely, as soon as you press space, the alias is expanded and you see the expanded command before executing it. Since I have a large number of clunky aliases, I didn’t want all aliases to be expanded by default.

Consequently, I came up with the following (based on something I first saw here.More »

Tags: linux

### LaTeX forward/inverse searches with ZathuraPosted 2014-03-10

I use zathura to view PDF files. As of version 0.2.7 it supports full forward / inverse searches with LaTeX. Namely, you can “control click” in any place on the PDF file, and it will open the TeX source file in your editor, and move to the corresponding location. Conversely, you can configure your editor so that pressing a particular key when editing your TeX file will open the PDF file and highlight the corresponding location.More »

Tags: linux, latex

### Using bibtool to fix your BibTeX databases.Posted 2014-03-04

Downloading BibTeX citations from review sites (e.g. MathSciNet, WebOfKnowledge) doesn’t always get you consistent results. Sometimes the case is messed up, there are extra braces, etc. Or there is a note field showing the number of citations (which shows up in your final PDF output). Moreover the citation keys are often of the form MR673830, which is useless unless you’re a computer. Here’s an easy way to fix most of these problems using BibTool.More »

Tags: latex

### KVM Macvtap vs bridgingPosted 2014-03-03

Switching my KVM networking from a bridged setup bridged setup to macvtap got me a huge performance improvement. Here are instructions on how to set it up.More »

Tags: linux

### Accessing Journals via an SSH proxyPosted 2014-03-03

Most universities have IP based authentication for access to Journals and index sites (MathSciNet, Web of Knowledge, etc.) If you’re off campus, they usually provide some VPN client (e.g. Cisco) which is quite painful to work with (at least on Linux). However, if you have ssh access to a machine on campus, you can access set up a proxy and access journals very easily.More »

Tags: linux

### Using Git and latexdiffPosted 2014-03-01

If you use git to manage your LaTeX documents, then you can easily integrate latexdiff to produce a PDF of the differences. Here are setup instructions.More »

Tags: git, latex, linux

### Installing older versions of Pentadactyl in FirefoxPosted 2014-02-18

The “latest” release of Pentadactyl doesn’t always run on any modern version of Firefox. Here’s how to get and install the bleeding edge version from the source tree.More »

Tags: linux, vim

### Setting up WordPress on your own serverPosted 2014-01-29

Tips I found useful when installing WordPress on my own server.More »

Tags: linux

### LaTeX headers to maximise space.Posted 2013-09-30

A few tricks to save space when writing documents (e.g. NSF proposals) that have strict font, margin and page restrictions.More »

Tags: latex

### Setting up ikiWiki and MathJAXPosted 2013-09-30

These are old instructions on how to set up ikiWiki and MathJAX, and might not be relelvant anymore. I no longer use ikiWiki to maintain my website. This site is generated using staticjinja and a custom build script.More »

Tags: ikiwiki

### A git quickstart guide for LaTeX usersPosted 2013-09-29

Git is a source control management system that you can use to track changes in any text file. Git, however, is quite complicated and learning it can be quite time consuming. This is a quick introduction to git for someone who will primarily use git to edit LaTeX/text documents (not code) and possibly collaborate with a handful of co-authors.More »

Tags: git, latex


text:
# Chapter 4. Working with the Filesystem, Drives, Data, and Search

At the heart of Windows Vista are the filesystem and the files in it; without files, there's no reason to use a computer, after all. When Windows Vista was first announced, Microsoft had big plans for a completely redone filesystem, along with powerful search tools, all built on top of a new filesystem database.

Reality intruded, and those plans had to be curtailed. Still, despite that, the ways to navigate your hard disk and find files have been dramatically upgraded compared to previous versions of Windows. Windows Explorer has gotten a face-lift, along with new capabilities for filtering and viewing files. And the new Search is one of Windows Vista's best new features. Not only is it available almost everywhere, but it's also lightning fast and includes considerable new ways to search, including the ability to save searches for future use. This chapter covers that, along with all other aspects of the filesystem, Windows Explorer, and Search.

Here is an alphabetical reference of entries in this chapter:

 Explorer Folder and Search Options OpenFiles File Compare (comp) Folder Properties Search File Compare (fc) Indexing Options Shadow Copies File Expansion Utility Label Subst File Properties NTFS Compression Utility Windows Explorer

## Explorer

See "Windows Explorer," later in this chapter.

## File Compare (comp): \windows\system32\comp.exe

Compare the contents of two files (or sets of files) byte by byte and display the differences between them.

To open

Command Prompt comp

Usage

comp [file1] [file2] [/n=number] [/c] [/offline] [/d] [/a] [/l]

Description

File Compare (comp.exe) compares two files (or more, using wildcards) and reports whether the files are identical. If the files are identical, comp.exe will report Files compare OK. If the files are the same size but have different contents, comp.exe displays the differences, character by character, by reporting Compare Error at OFFSET n (where n is the byte offset, or the location of the difference, in characters, from the beginning of the file). If the files are different sizes, comp.exe reports Files are different sizes, and the comparison stops there.

Here are the options for comp.exe:

file1, file2

Specify the filenames of the files to compare. For any files that aren't in the current directory, you'll need to include the full path. If file1 includes a wildcard, all matching files are compared to file2. Likewise, if file2 includes a wildcard, each matching file is compared to file1. If one or both of these parameters are omitted, comp.exe will prompt you for the files to be compared.

/n= number

Include the /n option to compare only the first specified number of lines in the files, or omit it to compare the files in their entirety. For example, specify /n=5 to check on the first five lines in each file.

/c

Disregard the case of ASCII characters; upper- and lowercase letters are treated as identical.

/offline

comp.exe normally skips files marked as "offline." Specify /offline (or just /off) to include offline files as well. (See "Sync Center," in Chapter 7, for more information on offline files.)

/d

Display differences in decimal format.

/a

Display differences in ASCII characters. The /a option is the default, so specifying it has no effect.

/l

Include line numbers in any output.

Notes

• Windows Vista actually comes with two file comparison utilities: comp.exe (this one) and fc.exe (discussed in the next section). comp.exe performs a character-by-character comparison, but displays differences only if the files are exactly the same size. fc.exe performs a line-by-line comparison and works regardless of the file sizes. For most users, fc.exe will be the tool of choice, as it displays the differences between the files and doesn't have any prompts, so you can use it from a WSH script or batch file.

• You can also use File Compare in interactive mode, without first typing filenames. Type comp at the command prompt, and you'll be asked for the names of files to compare, along with any options for comparing.

• Regardless of the outcome of the comparison, comp.exe will ask whether you want to perform another comparison. Although there's no way to disable this prompt, you can use the following workaround to bypass it:

echo n | comp file1 file2

## File Compare (fc): \windows\system32\fc.exe

Compare the contents of two files (or sets of files) line by line and display the differences between them.

To open

Command Prompt fc

Usage

fc file1 file2 [/a] [/c] [/lbn] [/n] [/t] [/w] [/offline] [/nnn]
[/l]
fc /b filename1 filename2

Description

File Compare (fc.exe) compares the contents of two files (or more, using wildcards) and displays the differences (if any). If the files are identical, fc.exe will report FC: no differences encountered. If the files are different, fc.exe lists the differing lines. Here's an example of how to use fc.exe.

Start with an ordinary text filesay, Bill.txt. Open it in Notepad, change one line, and save it into a new filenamesay, Marty.txt. Then open a Command Prompt window, make sure you're in the same directory as the two files, and type the following:

fc bill.txt marty.txt

The output will look something like this:

Comparing files Bill.txt and Marty.txt
***** Bill.txt
Way down Louisiana close to New Orleans
Way back up in the woods among the evergreens
There stood a log cabin made of earth and wood
***** Marty.txt
Way down Louisiana close to New Orleans
Way back up in the woods among the antihistamines
There stood a log cabin made of earth and wood
*****

For each line or sequence of lines that differs in the two files, fc.exe prints out a pair of excerpts from each file. The first and last lines in each excerpt are what the two files have in common and are included for context. The lines in between (only a single line in this example) show the differences. The report will include one pair of excerpts for each difference found; if there are three nonconsecutive differing lines, there will be six excerpts. Here are the options for fc.exe:

file1, file2

Specify the filenames of the files to compare. For any files that aren't in the current directory, you'll need to include the full path. If file1 includes a wildcard, all matching files are compared to file2. Likewise, if file2 includes a wildcard, each matching file is compared to file1. Both parameters are required.

/a

Display only the first and last lines for each set of differences, as opposed to the default of every different line. This option is applicable only if a single sequence of differing lines (resulting in a single excerpt pair) is three lines or longer; otherwise, /a has no effect.

/c

Disregard the case of ASCII characters; upper- and lowercase letters are treated as identical.

/lb n

Specify the maximum consecutive mismatches; /lb17 will list only the first 17 differing lines. If omitted, the default is 100 maximum mismatches.

/n

Include line numbers in the report.

/t

Preserve any tabs in the files being compared. By default, tabs are treated as spaces, with one tab equal to eight spaces.

/w

Compress whitespace (tabs and spaces) to a single space for comparison. This is possibly useful when comparing .html files, as web browsers will eliminate redundant tabs in spaces as well.

/offline

fc.exe normally skips files marked as "offline." Specify /offline (or simply /off) to include offline files as well. (See "Sync Center," in Chapter 7, for more information on offline files.)

/ nnn

Specify the number of consecutive lines that must match after a mismatch. For example, if you specify /4, a mismatched line followed by three matching lines, followed by one or more mismatched lines, is treated as though it were a single sequence of mismatched lines in the report.

/l

Treat the files as ASCII (plain text). Because /l is the default, it has no effect.

/u

Treat the files as Unicode text.

/b

Treat the files as binary and perform the comparison on a byte-by-byte basis (similar to comp.exe, the other file comparison utility). Differing bytes are displayed in parallel columns, instead of in the pairs of excerpts explained earlier. A binary comparison is typically appropriate only for files of the same sizes, but unlike comp.exe, the comparison will still be performed if they are different sizes. You can't use the /b option in conjunction with any of the other options.

Notes

• Windows Vista actually comes with two file comparison utilities: comp.exe (discussed in the preceding section) and fc.exe (this one). comp.exe performs a character-by-character comparison, but displays differences only if the files are exactly the same size. fc.exe performs a line-by-line comparison and works regardless of the file sizes. For most users, fc.exe will be the tool of choice, as it displays the differences between the files and doesn't have any prompts, so you can use it from a WSH script or batch file.

• fc.exe is most useful when comparing two different but similar text files. For example, you can compare two Registry patches (because .reg files are plain-text files) made at two different times to see what changes have been made. See Chapter 13 for more information on Registry patches.

• Although fc.exe can compare two binary files, if you try to compare two word processor documents (.doc and .wpd files are binary files), the results won't be terribly helpful. Try converting the documents to an ASCII-based format, such as .rtf or .html, and then perform an ASCII comparison. Naturally, most modern word processors have their own document comparison tools, but they can often be limited; although word processors may miss subtle formatting changes, fc.exe will catch every single difference.

• If you just want to see whether two files are different, you can redirect the differences to the nul: device and use the fact that fc.exe sets an ERRORLEVEL of 1 when the files differ:

fc file1 file2 > nul:
if ERRORLEVEL 1 (echo Different) ELSE (echo Same)

This will also let you compare two binary files without your command prompt beeping at you while you press Ctrl-C in a desperate attempt to halt the stream of non-ASCII characters flooding your screen.

## File Expansion Utility: \windows\system32\expand.exe

Extract one or more compressed files from a cabinet (.cab) file.

To open

Command Prompt expand

Usage

expand -d source.cab [-f:files]
expand [-r] source.cab [destination]
expand source.cab -f:files destination

Description

A cabinet file is a compressed archive commonly used to package application installation files. You use the File Expansion Utility to extract files embedded in these cabinet files. The utility takes the following options:

source.cab

The name of the cabinet (.cab) file from which to extract the files.

destination

The name of the folder in which to place the extracted files, a new filename to use for the extracted files, or a combination of the two. If using the -f option, destination is mandatory and must include a filename (with or without wildcards).

-d

Display (list) the contents of the specified cabinet file.

-r

Specify -r (recursive) without destination to extract all the files contained in the specified cabinet file. For example:

expand -r package.cab

Specify -r along with destination to rename the files according to the file specification included in destination. For example, the following extracts all the files in package.cab and renames their file extensions to .txt:

expand -r package.cab *.txt

-f: files

Use the -f option to specify one or more files to extract; use this if you don't want to extract all the files from the cabinet file. For example, the following extracts the file uno.txt from package.cab:

expand package.cab -f:uno.txt uno.txt

Note that the destination parameter is mandatory when using the -f option and is used to specify the target filename. In this example, as well as most times this program will be used, files and destination will be the same.

Notes

• The easiest method for extracting files from cabinets is to simply double-click the .cab file in Explorer and then drag the desired file(s) out. You can also use it when installing or repairing Windows Vista when Explorer isn't available.

"Cabinet (CAB) Maker," in Chapter 10

## File Properties

View and change the properties of files.

To open

Right-click a file Properties

Click a file Organize Properties

Description

The File Properties window has four tabs:

General

This tab (Figure 4-1) displays basic information about the file, including its location, type, size, and size on disk; the date it was created, modified, and last accessed; and its attributes. You can change the program that opens it by clicking the Change button, and you can change the file attributes by selecting Read-only or Hidden. The Advanced button lets you compress and/or encrypt the file, add or take away the file from the index for searching, and add or take away the Archive bit (for use in backups).

 Why are there two listings for file sizeone for size, and one for size on disk? There are two cases where the file size and size on disk are different: The cluster size of your NTFS filesystem dictates the size of the chunks that are set aside for files. On an NTFS filesystem with 4 KB clusters, a 1 KB file would use up 4 KB of disk space, and a 5 KB file would use up 8 KB.If a file has been compressed, the size listing shows its uncompressed size, and the size on disk shows its actual size on your hard disk.

##### Figure 4-1. The General tab, which shows you basic information about the file

Security

This tab (Figure 4-2) shows you who has access to read and modify the file and its attributes, and lets you change those permissions. Click each group and username and you'll be shown the rights that person or group has to the filewhether they can read the file, modify the file, and so on. You can modify the permissions for each person or group, add new groups or people and set their permissions, and delete people or groups, which means they would have no access to the file.

 The various file permission options and their meanings are quite complex, and beyond the scope of this book. However, if you want more details about the available options, go to the Microsoft Knowledge Base article at http://support.microsoft.com/kb/308419/en-us.

##### Figure 4-2. The Security tab, which lets you see what rights different people and groups have to the fileand lets you alter them

Details

This tab (Figure 4-3) displays the metatags associated with the file, as well as a wide variety of other information, including the basic file information shown in the General tab. It also has a great deal of program-specific information. For example, a Word document will display what template was used to create the file, the number of pages in the file, the word count, the character count, the line count, the paragraph count, the total length of time during which the file has been edited, and so on. You can also remove metatags and properties from the file by clicking the Remove Properties and Personal Information link. The details for each file type are quite different from one another. Graphics files, for example, include resolution, bit depth, width and height, and other similar information, as well as a quality rating that users can apply to the file.

##### Figure 4-3. The Details tab, which displays metatags and other useful information about the file

Previous Versions

This tab (Figure 4-4) lets you view, save, or restore a previous version of a file, if such a version is available. Two types of previous versions may be available: those from a backup and those from what Windows Vista calls shadow copies. A shadow copy is a copy of a file made when Windows creates a restore point. (See "System Protection and System Restore," in Chapter 11, for details.) Different files and types of folders have differing options for how you handle previous versions, but in general, you'll be able to open and save the previous version of a file to a different location, or restore it over the existing files.

##### Figure 4-4. The Previous Versions tab, which lets you restore previous versions of the file

Microsoft Office files may have another tab in addition to the standard four:

Custom

This tab (Figure 4-5) displays custom information about Microsoft Office files. You can add new values, and modify and delete existing values.

##### Figure 4-5. The Custom tab, which is for Microsoft Office files

Notes

• To restore a previous version of a file without using the File Properties screen, right-click the file in Windows Explorer and select "Restore previous versions." You'll receive a warning before you overwrite the existing folder with the previous one.

• Some file types may have other tabs in addition to the ones mentioned here, depending on whether the program that created it created those additional tabs.

• Music files include a great deal of detailed information, including the artist, album, year of release, genre, bit rate, and so on.

"Folder Properties," discussed next, "System Protection and System Restore," in Chapter 11, and "Sharing Resources and Files," in Chapter 7

## Folder Properties

View and change the properties of folders.

To open

Right-click a folder Properties

Click a folder Organize Properties

Description

The Folder Properties window has five tabs:

General

This tab (Figure 4-6) displays basic information about the folder, including its parent folder, size, size on disk, date and time created, and number of files and subfolders contained within. The Advanced button lets you compress and/or encrypt the folder, add or take away the folder from the index for searching, and add or take away the Archive bit (for use in backups).

 Why are there two listings for folder sizeone for size, and one for size on disk? If a folder has been compressed, the size listing shows its uncompressed size, and the size on disk shows its actual size on your hard disk.

##### Figure 4-6. The General tab, which shows you basic information about the folder

Sharing

This tab (Figure 4-7) lets you set sharing options for the folder. Click Share to share the folder, or change sharing options if the folder is already shared. Click Advanced Sharing if you want to give it a shared name in addition to its existing folder name. You would do this if you wanted to make it easier for someone to find the folder.

##### Figure 4-7. The Sharing tab, which lets you set sharing options for the folder

Security

This tab (Figure 4-8) shows you who has access to read and modify the folder and its attributes, and lets you change those permissions. Click each group and username and you'll be shown the rights that person or group has to the folderwhether they can read it, modify it, and so on. You can modify the permissions for each person or group, add new groups or people and set their permissions, and delete people or groups, which means they would have no access to the folder. The Advanced button gives you additional ways to edit permissions, as well as a way to change who has ownership of the folder.

 The various file permission options and their meanings are quite complex, and beyond the scope of this book. However, if you want more details about the available options, go to the Microsoft Knowledge Base article at http://support.microsoft.com/kb/308419/en-us.

##### Figure 4-8. The Security tab, which lets you see what rights different people and groups have to the folderand lets you alter them

Previous Versions

This tab (Figure 4-9) lets you view, save, or restore a previous version of a folder, if such a version is available. Two types of previous versions may be available: those from a backup and those from what Windows Vista calls shadow copies. As explained earlier, a shadow copy of a folder is a copy of a file made when Windows creates a restore point. (See "System Protection and System Restore," in Chapter 11, for details.) Different files and types of folders have differing options for how you handle previous versions, but in general, you'll be able to open and save the previous version of the folder to a different location, or restore it over the existing folder.

##### Figure 4-9. The Previous Versions tab, which lets you restore previous versions of the folder

Customize

This tab (Figure 4-10) lets you customize how the folder looks and acts. You can choose the kind of folder it is (All Items, Documents, Pictures and Videos, Music Details, or Music Icons). Based on what type of folder it is, the documents in it will be displayed differently, and different features will be available. For example, if a folder is a Pictures and Videos folder, the details it will display about each file include the date taken, tags, size, and rating, and the folder toolbar will include a Slide Show button so that you can display a slide show of the files in the folder. If the folder is a Documents folder, the details it will display are the date modified, type, size, and tags, but no Slide Show button will appear on the toolbar.

##### Figure 4-10. The Customize tab, which lets you change how the folder looks and acts

The tab also lets you choose a file that will be displayed on the folder's icon in Windows Explorer, and lets you choose a different icon than the default.

Notes

• To restore a previous version of a folder without using the Folder Properties screen, right-click the folder in Windows Explorer and select "Restore previous versions." You'll receive a warning before you overwrite the existing file with the previous one.

"File Properties," earlier in this chapter, "Sharing Resources and Files," in Chapter 7, and "System Protection and System Restore," in Chapter 11

## Folder and Search Options

Control the way folders appear in Explorer and configure Search.

To open

Control Panel [Appearance and Personalization] Folder Options

Windows Explorer Organize Folder and Search Options

Command Prompt control folders

Description

The Folder Options window has three tabs (General, View, and Search):

General

Of the three settings on this page, the one people find most confusing is the Tasks section (see Figure 4-11). If you select "Show preview and filters," the Details and Preview panes will appear in all folders. In Windows classic folders, your other choice, the Details and Preview panes, will not be displayed. It will give you more room to display files because those panes are missing, but you'll see less information about each file.

##### Figure 4-11. The General tab, which lets you turn off the Details and Preview panes in folder windows, among other options

View

After you've selected all your preferences in the General and View tabs, click Apply to Folders to make your settings the default. Otherwise, all your settings will be lost as soon as you switch to a different folder.

The Advanced settings in the View tab (Figure 4-12) here are quite important, and they give you a great deal of control over the way you work with Windows. Some of the default settings, in fact, can make Windows more difficult to use. Many of these settings are self-explanatory; some of the more interesting and useful ones follow:

##### Figure 4-12. The Folder Options' View tab, which contains many settings that affect the display of folders and files

Always show icons, never thumbnails

A thumbnail is a visual representation of a file's actual contents (for example, you'll see a thumbnail-size picture of a graphics file), and an icon is a generic, static representation of a file type. Thumbnails are more useful, but if previews slow down your system or Windows Explorer, choose this setting so that only icons will be used.

Windows Vista has done away with menus in Windows Explorersort of. In fact, the classic Windows menus are still there, waiting to be sprung into action. Press the Alt key and they'll be visible just above the toolbar. If you'd like them to be visible all the time, choose this setting.

Display simple folder view in Navigation pane

This rather oddly named option simply shows or hides the dotted lines in the collapsible folder tree (see "Trees," in Chapter 3) in Windows Explorer. The default is on, but if you turn it off, the tree appears more like it did in earlier versions of Windows. In my opinion, the lines make the tree a little clearer and easier to use, so I recommend turning this option off.

Hidden files and folders

By default, Windows doesn't show hidden files in Explorer. Change this option if you need to access them. As a general rule, if you do any kind of system customization or troubleshooting, you should show hidden files and folders.

Hide extensions for known file types

In one of Microsoft's biggest blunders, this option has been turned on, by default, since Windows 95. By hiding file extensions, Microsoft hoped to make Windows easier to usea plan that backfired for several reasons. Because only the extensions of registered files are hidden, the extensions of files that aren't yet in the File Types database are still shown. What's even more confusing is that when an application finally claims a certain file type, it can appear to the inexperienced user as though all of the old files of that type have been renamed. It also creates a "knowledge gap" between those who understand file types and those who don't. (Try telling someone whose computer still has hidden extensions to find Readme.txt in a directory full of files.) Other problems have arisen, such as trying to differentiate Excel.exe and Excel.xls in Explorer when the extensions are hidden; one file is an application and the other is a document, but they may have the same icon. The upshot is that it's not a good idea to hide extensions for known file types.

 There's another reason you should not hide file extensions: doing so can be a security hazard. Windows allows you to create files with several file extensionsfor example, you can create an executable file named kittenpictures.jpg.exe. When you hide file extensions, only the last extension is hidden. So if you hide file extensions and you are sent the file kittenpictures.jpg.exe in an email, the file will appear as kittenpictures.jpg. You would assume that the file contains pictures of kittens, but in fact it is an executable fileone that could be a Trojan or a virus. If you didn't hide file extensions, you would see the entire filename, kittenpictures.jpg.exe, and you would know that it was a potentially dangerous executable file, not a picture.

Hide protected operating system files

By default, this option is checked. It is another attempt by Microsoft to protect you against yourself so that you don't accidentally delete or harm important Windows Vista files. But hiding these files makes troubleshooting and customizing much more difficult, so consider unhiding them.

Launch folder windows in a separate process

Turn on this option to start a new instance of the Windows Explorer application every time you open a new folder window.

Remember each folder's view settings

If this option is enabled and you use Explorer's View menu to alter the display of a particular folder, those settings will be saved with that folder for the next time it's opened. If you're looking for a way to save your View settings as the default for all folders, this option won't do it; instead, use the Apply to Folders button.

Restore previous folder windows at logon

If you select this option, when you start your computer this will open the folders you were using the last time you shut down Windows.

Show encrypted or compressed NTFS files in color

If you've encrypted or compressed NTFS files, this will show them in a color to distinguish them from files that haven't been encrypted or compressed.

Show preview handlers in preview pane

Good luck translating this option into English. Here's what it means, though: if you deselect it, the contents of your files will never be shown in the Preview pane. Why use this option if displaying previews slows down your system?

Use check boxes to select items

Normally, in Windows, you can select several files at once by holding down the Ctrl key while you click the files. If you'd instead prefer that checkboxes show up next to files so that you can select them that way, use this option.

Use Sharing Wizard

Windows Vista includes a new wizard to help you share files with others on your PC. If you prefer to walk through the file-sharing process manually, uncheck this selection.

Search

This tab (Figure 4-13) controls the basic features of Search. (For more details, see "Search," later in this chapter.) It includes these sections:

##### Figure 4-13. The Search tab, where you can customize many Search functions

What to search

This section controls how Search handles filenames and file contents. In some circumstances it searches through the actual names of files, and in other circumstances it searches through the names of files as well as through their contents. By default, it searches filenames and contents in indexed locations, and filenames only in nonindexed locations. This section, however, lets you change that behavior. Keep in mind that if you choose to always search through filenames and contents of nonindexed files, it may slow your search considerably, because searching nonindexed files can be sluggish.

How to search

This controls a variety of search behavior. You can include or not include subfolders when typing in the Search box, find or not find partial matches, and choose not to use the index when searching (doing this will slow down the search process considerably, but it casts a wider net).

In addition, it lets you use what is called natural language search. Windows Vista's Search is an extremely powerful tool, but it can be confusing to use because it often requires very strict and specific syntax in order to work. If you'd prefer to use plain English commands (music by Gluck and Salieri) rather than kind: music artist: (Gluck AND Salieri), turn on natural language search. See "Search," later in this chapter, for more details about natural language search.

When searching non-indexed locations

You can choose to include or not include system directories and compressed files when searching through nonindexed areas. Including them will slow down search performance but will result in a broader search.

Notes

• Windows XP had another useful tab, File Types, but it has been taken away in Windows Vista. The File Types tab let you create and change file associations, and customize various actions associated with files. For example, in Windows XP, you could set multiple associations for files, as well as customize precisely what actions a program should take when it opens a file. You could, for example, set one program to play a file type by default, but a different program to edit the file by default. In Windows Vista, you can change file associations, but nothing else. To change file associations, you choose Start Default Programs Associate a file type or protocol with a program. See "Default Programs Control Panel," in Chapter 10, for details.

• You can add a nonindexed area, such as Universal Serial Bus (USB) flash drives, flash memory cards, network drives, and nonindexed portions of your hard disk, to your index so that you'll be able to search them faster. For details, see "Search," later in this chapter.

"Search" and "Windows Explorer," later in this chapter, and "Default Programs Control Panel," in Chapter 10

## Indexing Options

Configure and customize the index for searching.

To open

Control Panel System and Maintenance] Indexing Options

Windows Explorer Search Tools Modify Index Locations (the Search Tools icon appears when you type text into the Search box, but it is otherwise invisible)

Description

The Indexing Options screen (Figure 4-14) shows you what folders are included in your index and lets you add or remove folders. The index is used to speed up searches in Windows Vista.

##### Figure 4-14. The Indexing Options screen, where you set your indexing options

The Advanced button leads to two tabs: Index Settings and File Types. The Index Settings tab (Figure 4-15) lets you index encrypted files, control how accented characters are treated, rebuild the index, and change the location of the index. It also lets you tell the index how to handle two words that are otherwise identical, except that one has an accent mark (known as a diacritic) and the other doesn't. You can tell the index to treat them as separate words or as the same word (the default). The File Types button lets you set which file types should be indexed, and choose for each file type whether the contents and properties of the file should be indexed, or just the properties.

##### Figure 4-15. The Advanced button, where you set advanced indexing options

To remove existing folders or to add new folders, from the Indexing Options screen choose Modify Show all locations. Then expand the drives you see. Folders with checkboxes are included in the index; those without checkboxes are not included. Check or uncheck the checkboxes as appropriate.

Notes

• File properties include not only filenames, but also tags, such as date created, date modified, and so on.

• If you discover that when you search, you're not finding files that you know are in your index, the index may have been damaged. To solve the problem you'll need to rebuild the index. Select Advanced Index Settings Rebuild.

"Search"

## Label: \windows\system32\label.exe

Change the label of any hard disk, floppy disk, or removable media.

To open

Command Prompt label

Usage

label [drive:] [label]

Description

Every disk has a labelthe name shown in Explorer next to the drive letter (Explorer doesn't show the label for floppies). To change the label for any disk, right-click on its icon in Explorer (or the My Computer window), select Properties, and type a new name in the unlabeled field at the top of the Properties window. The Label tool duplicates this functionality from the command line. For example, to change the label of drive c: to "shoebox," type:

label c: shoebox

If you omit label, you will be prompted to enter a new label. If you omit drive, label will use the current drive.

Notes

• A disk's label has no effect on the operation of the disk; for hard disks, it's purely decorative. For CDs and other removable media, it's used to quickly identify what's in the drive.

• You can also set a label for a drive using the Disk and Volume Properties dialog. For details, see "Disk and Volume Properties," in Chapter 9.

## NTFS Compression Utility: \windows\system32\compact.exe

View or configure the automatic file compression on NTFS drives.

To open

Command Prompt compact

Usage

compact [/c | /u] [/s[:dir]] [/a] [/i] [/f] [/q] [filename]

Description

One of the features of the NTFS filesystem (see "FAT to NTFS Conversion Utility," in Chapter 11) is its support for automatic compression of individual files; older files can be optionally compressed to take up less disk space at the expense of speed to access them.

Right-click on any file or folder, select Properties, and then click the Advanced button. The "Compress contents to save disk space" option is used to instruct Windows to compress the selected item. If a folder is selected, all of its contents will be compressed (you'll be prompted about any subfolders); furthermore, any files added to that folder will be automatically compressed as well.

The NTFS Compression Utility is the command-line equivalent of this setting, useful for automating the compression or decompression of several files with the help of a WSH script or batch file. The NTFS Compression Utility takes the following options:

filename

Specifies a file, folder, or group of files (using wildcards) to compress or uncompress.

/c

Compresses the specified file(s). If a folder is specified for filename, the folder will be marked so that subsequent files added to the folder will be compressed automatically. Include the /s parameter to compress files already in the folder.

/u

Uncompresses the specified file(s). If a folder is specified for filename, the folder will be marked so that subsequent files added to it will not be compressed automatically. Include the /s parameter to uncompress files already in the folder.

/s

If a folder is specified for filename, the /c and /u parameters will act only on new files added to the folder. Include the /s parameter as well to compress or uncompress files already in the folder. If filename is omitted, use the /s option to act on all files in the current folder.

/a

Includes files with hidden or system attributes set; otherwise, ignored by compact.exe.

/i

Ignores errors; otherwise, compact.exe will stop when the first errors are encountered.

/f

Forces compression on all specified files; otherwise, files that are already compressed will be skipped.

/q

Quiet mode; use this option to report only the most essential information.

If you run the NTFS Compression Utility without any options, it will display the compression settings for the current directory and all of its contents.

Notes

• This type of file compression is supported on NTFS drives only.

• Go to Windows Explorer Organize Folder and Search Options View tab and turn on the "Show encrypted or compressed NTFS files in color" option to visually differentiate such files from unencrypted, uncompressed files.

• For tangible proof that a given folder or file is actually compressed, right-click on it in Explorer and select Properties. If the "Size on disk" value is less than the "Size" value, the item is compressed.

"FAT to NTFS Conversion Utility," in Chapter 11

## OpenFiles: \windows\system32\openfiles.exe

List all currently open files, either shared and accessed by other users on a network or (optionally) opened locally.

To open

Start type command into the Search field right-click on Command Prompt Run as Administrator

Usage

openfiles /local [ on | off ]
openfiles /query [/s system [/u user [/p [pass]]]]
[/fo format] [/nh] [/v]
openfiles /disconnect [/s system [/u user [/p [pass]]]]
{[/id id] [/a accessedby] [/o openmode]} [/op openfile]

Description

The OpenFiles tool lets you view a list of all the shared files that are currently open across the network and, optionally, files that are opened locally. You can use this to avoid deleting or changing a document that a remote user is working on.

Type openfiles without any options to display a report such as this:

Files Opened Remotely via local share points:
---------------------------------------------
ID Accessed By Type Open File (Path\executable)
===== ============= ========== ======================================
98 LOU Windows C:\Stuff to Eat\frittatas.txt
101 EDDIE Windows C:\Stuff to Drink\milkshakes.txt
107 CLANCY Windows C:\Stuff to Eat\pork chops.txt

OpenFiles accepts one of

 Windows Vista in a Nutshell
 Part I: The Big Picture
 Part III: Appendixes


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# A device calculates the worth of gem stones based on quality such that

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A device calculates the worth of gem stones based on quality such that [#permalink]

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Updated on: 17 Feb 2018, 07:56
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A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q - 1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p - r is how many times greater than that of a gem with a rating of p?

(A) $$p^5-r^5$$
(B) $$r^5$$
(C) $$(p-r)^5$$
(D) $$5^{(p-r)}$$
(E) $$5r$$
[Reveal] Spoiler: OA

Originally posted by itsmek80 on 14 Feb 2018, 18:12.
Last edited by chetan2u on 17 Feb 2018, 07:56, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 5774
A device calculates the worth of gem stones based on quality such that [#permalink]

### Show Tags

17 Feb 2018, 07:56
itsmek80 wrote:
A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q - 1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p - r is how many times greater than that of a gem with a rating of p?

(A) $$p^5-r^5$$
(B) $$r^5$$
(C) $$(p-r)^5$$
(D) $$5^{(p-r)}$$
(E) $$5r$$

q - 1 is worth 5 times more than a gem with a quality rating of q
the relation could be..
1) 5*1
2) 5^1

so for p-r. it can be
1) 5*r
2) 5^r

only 5r is there, so the answer is E

Otherwise
also substitute p as q and r as 1 and the ANSWER should be 5
lets see the choices
(A) $$p^5-r^5........q^5-1^5=q^5-1$$...NO
(B) $$r^5........1^5$$.... NO
(C) $$(p-r)^5.......(q-1)^5$$...NO
(D) $$5^{(p-r)}.....5^{q-1}$$...NO
(E) $$5r.....5*1=5$$....YES

E
_________________

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Don't understand Challenge Question in my Princeton Review book. [#permalink]

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12 Apr 2018, 19:30
Hi everyone,

I don't understand the following challenge question in my Princeton Review Cracking the GMAT book. I looked at the solution in the back, but the explanation is vague or not quite step by step. I personally felt like this question was missing some information in order for me to actually solve it. Please let me know your thoughts.

A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q-1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p-r is how many times greater than that of a gem with a rating of p?

(A) p^5 - r^5
(B) r^5
(C) (p-r)^5
(D) 5^(p-r)
(E) 5r

The correct answer is D, but not sure how I would start to establish a pattern in order to even solve the question. I know I'm given that
q-1 = 5q
and I'm supposed to use solely that information?

Intern
Joined: 28 Feb 2017
Posts: 1
Don't understand Challenge Question in my Princeton Review book. [#permalink]

### Show Tags

12 Apr 2018, 20:09
Hi everyone,

I don't understand the following challenge question in my Princeton Review Cracking the GMAT book. I looked at the solution in the back, but the explanation is vague or not quite step by step. I personally felt like this question was missing some information in order for me to actually solve it. Please let me know your thoughts.

A device calculates the worth of gem stones based on quality such that a gem with a quality rating of q-1 is worth 5 times more than a gem with a quality rating of q. According to this device, the worth of a gem with a quality rating of p-r is how many times greater than that of a gem with a rating of p?

(A) p^5 - r^5
(B) r^5
(C) (p-r)^5
(D) 5^(p-r)
(E) 5r

The correct answer is D, but not sure how I would start to establish a pattern in order to even solve the question. I know I'm given that
q-1 = 5q
and I'm supposed to use solely that information?

Consider 3 gems p p-1 p-2. Now using information you will see than P-2 is costlier than P-1 by 5 times P-1 is costlier than P by 5 times. So that makes P-2 costlier by 25 times compared to P. And only D satisfies.

Sent from my iPhone using GMAT Club Forum mobile app
Don't understand Challenge Question in my Princeton Review book.   [#permalink] 12 Apr 2018, 20:09
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text:
# Create Multi-Column Plot Legends3

Posted by Brett Shoelson,

Brett's Pick this week is "columnlegend," by Simon Henin.

Today's Pick is another that is an author's first submission to the File Exchange. Simon shared a nice, easy-to-use function to create multi-column figure labels.

MATLAB's built-in legend command suffices for most cases when there are few objects to differentiate. However, when the number of lines plotted, for instance, gets large, columnlegend shines. It enables one essentially to reshape the default n-by-one legend into a p-by-q one.

Consider:

nLines = 18;
legend_str = cell(nLines,1);

myColors = distinguishable_colors(nLines);

(See my previous post about distinguishable_colors, or comment out the above line, and uncomment the following one.)

%myColors = jet(nLines);
t = 0:pi/64:3*pi;
dPhi = pi/16;
lineStyles = {'-', '--', ':', '-.'};
for ii=1:nLines,
plot(t,sin(t+dPhi*ii),...
'linestyle', lineStyles{rem(ii-1,numel(lineStyles))+1},...
'color', myColors(ii,:),...
'linewidth',3);
hold on;
legend_str{ii} = num2str(ii);
end
axis([0 3*pi -1.15 1.6])
legend(legend_str,'location','NorthWest')

Now consider how columnlegend improves the situation:

for ii=1:nLines,
plot(t,sin(t+dPhi*ii),...
'linestyle', lineStyles{rem(ii-1,numel(lineStyles))+1},...
'color', myColors(ii,:),...
'linewidth',3);
hold on;
legend_str{ii} = num2str(ii);
end
axis([0 3*pi -1.15 1.6])
columnlegend(6,legend_str,'NorthWest');

That's better! columnlegend also conveniently provides a handle to the legend-containing axes, allowing you to tweak parameters (like position). Very nice first effort, Simon!

One further note: in a comment on his submission page, Simon mentioned that he had fixed an issue with plot markers. As of this writing, that modification is still pending; it should be available shortly.

Get the MATLAB code

Published with MATLAB® 7.11

Adrian Cherry replied on : 1 of 3

Congraulations to Simon for the PotW award, this was a very useful submission and a great springboard for me to develop the code. However I feel it would be remiss of me at this point not to advertise a few updates I’ve included in my submission, gridLegend, which is linked from columnlegend.

The changes I’ve made include :
* enable legend properties to be included in the call

gridLegend(hdl,8,gKey,'Orientation','Horizontal','Fontsize',8)

* The orientation parameter name allows you to change whether the legend entries are column orientated or row orientated.

* resizes the plot area so that the legend can be placed outside the axes.

* retains the boxing around the legend, although ‘box’,'off’ still works.

* works with clickableLegend, another useful PotW.

* works with bar charts and errorbar plots.

* I’ve fixed the printing problem in columnLegend, including a write up up in undocumented MATLAB http://undocumentedmatlab.com/blog/multi-column-grid-legend/
so it should be possible to print directly or export to an image file.

Regards

Roman replied on : 2 of 3

Thanks, for the submission. I am struggling with a pie chart which has too many line entries in the legend. I would like to break it into 2 columns in your spirit. Would this be possible?

Kind regards

Roman

Bill replied on : 3 of 3

I found a bug of this program. For example, when you try to change 1_by_2 legends to 2_by_1, this program will not work. Because the numpercolumn is 1, and the col is always -1.

Replace the code

if mod(i,numpercolumn)==1,
col = col+1;
end

with

if numpercolumn>1,
if mod(i,numpercolumn)==1,%列位置，隔numpercolumn+1
col = col+1;
end
else
col=i-1;
end

to kill this bug.

These postings are the author's and don't necessarily represent the opinions of MathWorks.


text:
Recent results on Central Exclusive Production with the STAR detector

Submission summary

 As Contributors: Rafał Sikora Arxiv Link: https://arxiv.org/abs/2108.00686v1 (pdf) Date submitted: 2021-08-03 06:26 Submitted by: Sikora, Rafał Submitted to: SciPost Physics Proceedings Proceedings issue: DIS2021 Academic field: Physics Specialties: High-Energy Physics - Experiment Approach: Experimental

Abstract

We present results on the Central Exclusive Production of charged particle pairs $h^{+}h^{-}$ ($h = \pi, K, p$), $pp\to p^\prime+h^{+}h^{-}+p^\prime$, obtained with the STAR experiment at RHIC in proton-proton collisions at a center-of-mass energy of $\sqrt{s} = 200$ GeV. All final-state particles were reconstructed, including forward-scattered protons detected in the Roman Pot system. As a result, the Double Pomeron Exchange (DPE) events were selected and the non-exclusive backgrounds were efficiently rejected. Differential fiducial cross sections were measured as functions of observables related to the central hadronic final state and to the forward-scattered protons. The measured cross sections were compared to phenomenological model predictions based on the DPE. We also present preliminary results on the measurement of the same physics process at higher collision energy $\sqrt{s} = 510$ GeV. The data demonstrate features similar to those observed at $\sqrt{s} = 200$ GeV.

Current status:
Editor-in-charge assigned


text:
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Problem: Numerical Differentiation, 2x^3-4x+1, [2,4], x=2.1, h=0.25 [ Calculator, Method and examples ]

Solution:
Your problem -> Numerical Differentiation, 2x^3-4x+1, [2,4], x=2.1, h=0.25

Equation is f(x) = 2x^3-4x+1.

Numerical differentiation method to find solution.
The value of table for X and Y

 X Y 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 9 14.7812 22.25 31.5938 43 56.6562 72.75 91.4688 113

Newton's forward differentiation table is as follows.
 X Y(X) DeltaY Delta^2Y Delta^3Y Delta^4Y 2 9 5.7812 2.25 14.7812 1.6875 7.4688 0.1875 2.5 22.25 1.875 0 9.3438 0.1875 2.75 31.5938 2.0625 0 11.4062 0.1875 3 43 2.25 0 13.6562 0.1875 3.25 56.6562 2.4375 0 16.0938 0.1875 3.5 72.75 2.625 0 18.7188 0.1875 3.75 91.4688 2.8125 21.5312 4 113

The value of x at you want to find f(x) : x_0 = 2.1

h = x_1 - x_0 = 2.25 - 2 = 0.25

t = (x_0 - 2)/h = (2.1 - 2)/0.25 = 0.4

[(dy)/(dx)]_(x=x_0) = 1/h * ( Delta Y_0 + (2t-1)/(2!) * Delta^2 Y_0 + (3t^2-6t+2)/(3!) * Delta^3 Y_0 + (4t^3-18t^2+22t-6)/(4!) * Delta^4 Y_0)

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text:
# At the foot of a mountain the elevation of its summit is 45º; after ascending 1000 m towards the mountain up a slope of 30º inclination is found to be 60º. Find the height of the mountain. - Mathematics

Sum

At the foot of a mountain the elevation of its summit is 45º; after ascending 1000 m towards the mountain up a slope of 30º inclination is found to be 60º. Find the height of the mountain.

#### Solution

Let F be the foot and S be the summit of the mountain FOS.

Then, ∠OFS = 45º and therefore ∠OSF = 45º. Consequently,

OF = OS = h km(say).

Let FP = 1000 m = 1 km be the slope so that

∠OFP = 30º. Draw PM ⊥OS and PL ⊥OF.

Join PS. It is given that ∠MPS = 60º.

In ∆FPL, We have

\text{sin }30^\text{o}=\frac{PL}{PF}

\Rightarrow PL=PF\text{ sin }30^\text{o}=( 1\times \frac{1}{2})=\frac{1}{2}km.

\therefore OM=PL=\frac{1}{2}km

\Rightarrow MS=OS-OM=( h-\frac{1}{2})km

\text{Also, cos }30^\text{o}=\frac{FL}{PF}

\Rightarrow FL=PF\text{ cos }30^{o}=( 1\times\frac{\sqrt{3}}{2})=\frac{\sqrt{3}}{2}km

Now, h = OS = OF = OL + LF

\Rightarrow h=OL+\frac{\sqrt{3}}{2}

\Rightarrow OL=( h-\frac{\sqrt{3}}{2})km

\Rightarrow PM=( h-\frac{\sqrt{3}}{2})km

In ∆PSM, we have

\text{tan }60^\text{o}=\frac{SM}{PM}

⇒ SM = PM. tan 60º …..(ii)

\Rightarrow ( h-\frac{1}{2})=( h-\frac{\sqrt{3}}{2})\sqrt{3}

[Using equations (i) and (ii)]

\Rightarrow h-\frac{1}{2}=h\sqrt{3}-\frac{3}{2}

⇒ h(√3 – 1) = 1

\Rightarrow h=\frac{1}{\sqrt{3}-1}

\Rightarrowh=\frac{\sqrt{3}+1}{(\sqrt{3}-1)(\sqrt{3}+1)}=\frac{\sqrt{3}+1}{2}

=\frac{2.732}{2}=1.336km

Hence, the height of the mountain is 1.366 km.

Concept: Heights and Distances
Is there an error in this question or solution?


text:
# Smooth mixing Anosov flows in dimension three are exponentially mixing

### Abstract

We show that a topologically mixing $C^\infty$ Anosov flow on a 3-dimensional compact manifold is exponentially mixing with respect to any equilibrium measure with Hölder potential.

## Authors

Masato Tsujii

Kyushu University, Fukuoka, Japan

Zhiyuan Zhang

Institut Galilée, Université Paris 13, CNRS UMR 7539, Villetaneuse, France