I'm having a hard time proving the following $$\int_0^{\infty} \frac{x^8 - 4x^6 + 9x^4 - 5x^2 + 1}{x^{12} - 10 x^{10} + 37x^8 - 42x^6 + 26x^4 - 8x^2 + 1} \, dx = \frac{\pi}{2}.$$  Mathematica has no problem evaluating it while I haven't the slightest idea how to approach it. Of course, I would like to prove it without the use of a computer. Is this an explicit form of a special function I fail to recognize?


Intrinsic topology and metrics... (looking for name of a method)

Suppose I have an n-dimensional dataset and its points are roughly in the shape of an n-dimensional horseshoe or something along those lines. Using euclidian distance might be a bad idea, since points on the tip of the horseshoe would the appear close, although this wouldnt make any sense given the shape of the data.  It should be possible to find something like a (lower dimensional) topology and a meaningful metric on it, that uses the intrinsic topology of the data.  A couple of years ago, I had a longer discussion about that sort of thing, but i can't remember what it was called...


Get TEXT value of a CLOB OID in Postgresql

I have a database table that looks like:   create table answers(    id int not null,    question_id int not null,    answer text null )   This table was originally build by Hibernate using the @Lob attribute for the "answer" column.  I did not realize it at the time, but when setup that way, Hibernate stores an OID in the column instead of the actual text.  Everything works fine when I use Hibernate to retrieve the values since it automatically converts the OID to the CLOB string, however it is becoming a performance problem and I'd like to get rid of the OID.   select * from answers ID     QUESTION_ID     ANSWER =============================== 1       123             55123 2       234             51614 3       345             56127 should be ID     QUESTION_ID     ANSWER =============================== 1       123             Male 2       234             203-555-1212 3       345             555 Main St. New York, NY    My desire is to add an extra column to the table "ANSWER_VALUE TEXT" and do something like below to get the actual value into the table, then change Hibernate around to not use the @Lob designator   update answers set ANSWER_VALUE= getValueFromOID(ANSWER)   Does that "getValueFromOID" function exist?  If not, could I get some pointers on how to create one or at least how to fetch the actual value of an OID?  Thanks


How to get the mean and standard deviation from several individuals each with their own mean and standard deviation?

A simple question has led to much confusion via searching for the correct way to obtain the answer: Individual 1: mean = 20, standard deviation = 3, number of measures = 80; Individual 2: mean = 25, standard deviation = 5, number of measures = 120; Individual 3: mean = 22, standard deviation = 7, number of measures = 20; Individual 4: mean = 18, standard deviation = 4, number of measures = 67; Individual 5: mean = 28, standard deviation = 3, number of measures = 92 Mean of all individuals = (20 + 25 + 22 + 18 + 28) / 5 = 22.6, is this correct? standard deviation of all individuals = ???, how do I calculate this?? Thank you.


What is the function(s) of the hidden Debug menu in Disk Utility?

What is the function(s) of the Debug menu and why is it hidden by default?


How to get Custom Object Metadata CreatedBy

I need to get list of Custom Objects in a Salesforce org and find Created By User of each of them (Created By of object, not the records) .  Is it possible? I can get string list of custom objects as follows:  List<String> CustomObjectsList  = new List<String>(); List<Schema.SObjectType> gd = Schema.getGlobalDescribe().Values();   for(Schema.SObjectType f : gd) {     if (f.getDescribe().isCustom()){         CustomObjectsList.add(f.getDescribe().getName());     } }   Now I need to find object creator of each (not record creator).


Since I upgraded to 17.04, my mouse has become a lot slower. I had set it to max fast, which I like, but now it feels like less than half as fast. I have to move my hand a lot further to reach the other end of the screen, while before, a short twist of my wrist would do the job.  How can I make my mouse pointer a lot faster, if in the settings menu it's already at maximum? I'm looking for increasing pointer acceleration in particular.  Please, Ubuntu developers, make increasing mouse speed and acceleration easy.


Proving that a function must be constant using Complex Analysis

Fix nonzero ω1,ω2 ∈R. Suppose that f is an entire function which satisﬁes $$f(z + ω1) = f(z + iω2) = f(z)$$ for all $z ∈\Bbb C$. Prove that f must be constant.   My first and immediate thought upon seeing this problem is to use Liouville's theorem somehow, because if I can prove that the function's $n$th derivative is entire and bounded for some fixed positive integer $c ∈\Bbb C$, then the function is constant throughout the plane.   So can I say, by the Cauchy Integral formula, that since we know that f is entire, all of its derivatives are entire? Thus, by the conditions of Liouville, everything follows from there?


If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$

Prove that for a prime $p>2$, if $p \mid m^p+n^p$, prove $p^2\mid m^p+n^p$  From Fermats theorem I concluded $p \mid m+n$, so $p^2\mid (m+n)^p$. How do I proceed next? Any hints are welcomed.


Let $R$ be a unital ring (not necessarily commutative) and $x,y\in R$ be non-invertible elements. Then is $xy$ non-invertible? And how about the case $xy=yx$?  (postsclipt)  : This page gives a counterexample of the case $xy\neq yx$.


Im asked to prove that a polynomial of an odd degree has a root. Im going to use IVT to prove this, but I'm wondering if I can use the assumption that an odd degree polynomial has either two cases:  $$ \lim_{x\to\infty}h(x)=+\infty \\ \lim_{x\to-\infty}h(x)=-\infty \\ $$ $$and$$ $$ \lim_{x\to\infty}h(x)=-\infty \\ \lim_{x\to-\infty}h(x)=+\infty \\ $$ Then by this there exists numbers $a,b$ such that $$ h(a)<0<h(b) $$ $$or$$ $$ h(b)<0<h(a) $$ Which I think would prove that odd degreed $h(x)$ has at least a root. Or is there a more convincing way to show that there are numbers in $h(X)$ greater than zero and less than zero?  edit: (sorry about the bad limit notation)


Is there a general way extend Siri on iOS 8 to use other apps?  For instance, I am not using the apple E-Mail app but "". I'd like to make Siri use this app when telling her to write an e-mail?   By extension, can non-apple apps for sending instant messages, listening to music be plugged into Siri?


Missing icons with CKEditor for Drupal 7

I've recently installed CKEditor 4 for Drupal 7 module and some of the toolbar's icons don't seem to show up.  They are: Add Media Media Teaser Break and YouTube (to name a few).  I've cleared the Drupal and Browser cache, but that hasn't helped. I've also ensured that I've got the right skins (reuploaded just in case). I tried multiple skins and these same buttons don't seem to want to appear.  Does anyone have any ideas for how to resolve this issue? Test thread is here.    (Note, I installed CKEditor because I needed an easy solution for users to upload multiple images when created a post so I'm not really attached to CKEditor if someone has a better idea. I was using TinyMCE with the WYSIWYG module)


We know that in $\mathbb Q[x]$ that two cyclotomic polynomials $\Phi_n(x),\Phi_m(x)$ are relatively prime when $m\neq n$. This means that there are integer polynomials $a(x),b(x)$ and a positive integer $D$ such that:  $$a(x)\Phi_n(x)+b(x)\Phi_m(x)=D$$  The smallest such $D$ can be thought of as some kind of integer $GCD$ of the polynomials. I'm wondering if there is a good general formula for this?  Lets write $\langle m,n\rangle$ to be this $D$.  If $m=1$ then $$\langle 1,n\rangle=\Phi_n(1)=\begin{cases}p&n=p^k\\1&\text{otherwise}\end{cases}$$  If $m,n>1$ and $\gcd(m,n)=1$ then we easily get that $\langle m,n\rangle = 1$, by the same argument that $\gcd(x^n-1,x^m-1)=x^{\gcd(m,n)}-1$, since the proof of that is entirely in $\mathbb Z[x]$.  When $m=p,n=2p$ with $p$ prime, you get $\langle m,n\rangle = 2$, since we get $\Phi_{p}(x)(1-x)+\Phi_{2p}(x)(1+x)=2$.    A related question is, given distinct integers $m,n$, what is the smallest $D$ such that for all integers $k$:  $$\gcd(\Phi_m(k),\Phi_n(k))\mid D$$  In general, this $D\mid\langle m,n\rangle$ but is not necessarily equal. For example, when $m=p,n=2p$ where $p$ is an odd prime, then $\Phi_m(k)$ is never even, so $D=1$ when $\langle m,n\rangle = 2$.


Is there a term for this concept involving functions?

If $f_1:X_1\to Y_1$, $\ldots$, $f_n:X_n\to Y_n$ are maps, is there a term for the map $\left(x_1,\ldots,x_n\right)\mapsto\left(f_1\left(x_1\right),\ldots,f_n\left(x_n\right)\right)$ from $X_1\times\cdots\times X_n$ to $Y_1\times\cdots\times Y_n$? Thanks.


For the last 1.5 years I've tended to put my laptop in sleep mode rather than turn it off. Recently I started to feel it's not as fast as it was when I bought it, even if I restore a fresh Windows 7 image (I made it 1 week after installing the system for the first time).  Maybe it's just an impression, I'm not sure...   Can it be a result of putting my laptop in sleep mode? What computer parts get worn down over time? Is there software to test if these parts are worn?


Is $\sum_{r=1}^nrx^{r-1}$ always irreducible (over the integers)?

Is $$\sum_{r=1}^nrx^{r-1}$$ always irreducible (over the integers)? For example, the polynomial $1+2x+3x^2+4x^3+5x^4+6x^5+7x^6$ is of the requred form. I have no idea how to approach this. I have simply experimented with these polynomials and so far they seem to be irreducible for small values of $n$. Thanks for your help.


Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?

For injective side, in my opinion, we can find two square matrices $A, B$ with each injective but $AB$ has a zero row ($\dim\ker(AB)\ne 0$), so $TS$ is not injective. But I don't know how to find such matrices.  For surjective side, I have no idea how to start.  I feel my idea is very confusing, could someone give me a clear way to solve the problem?


Intuitively, I would expect the change in kinetic energy of a particle to be frame independent. It just doesn't "feel" right that between two points in time-space, one frame should measure a change in kinetic energy of a particle different to another frame.  Is my intuition right? Is the change in kinetic energy of a particle frame independent?


I am unsure about this question using hermite polynomials and satifying recurrence relations

How would I answer a question like this? It is in a practise question for a test.


Prove that the subsequence of a convergent series with nonnegative terms converges

Let $\sum_{k=1}^\infty a_k$ be a convergent series with nonnegative terms and let $a_{n_k}$ be a subsequence of {$a_k$}. Prove that the series $\sum_{k=1}^\infty a_{n_k}$ converges.  I am having trouble figuring out how to prove this and am pretty lost.  My very first idea was to try and prove that it is increasing but don't know where I would take it from there. Any help would be appreciated!


Are there any good alternatives to Nautilus? I'm looking for something lightweight, with a cleaner interface, but the ability to manually enter file paths is still important. Any suggestions?


How to use wp.hooks.addAction() in React JS

I am able to successfully use wp.hooks.applyFilters() and wp.hooks.addFilter(), but I'm not able to render a React Component using wp.hooks.addAction(). However, the console.log() runs just fine within the callback for an action. This is my code:  import { createHooks } from '@wordpress/hooks';  let globalHooks = createHooks();  const Header = () => {     return (
Header Component
     ); }  const RevisedHeader = () => {     return (
Revised Header Component
     ) }  export default class App extends Component {      constructor( props ) {         super();          globalHooks.addFilter( 'replace_header', 'revisedHeaderCallback', this.revisedHeaderCallback );         globalHooks.addAction( 'after_replace_header', 'afterRevisedHeaderCallback', this.afterRevisedHeaderCallback );     };      revisedHeaderCallback( header ) {         return <RevisedHeader />;     }      afterRevisedHeaderCallback() {         return <RevisedHeader />;     }      render() {          return(
                 { globalHooks.applyFilters( 'replace_header',  ) }                 { globalHooks.doAction( 'after_replace_header' ) }
         );     } }


How to set Firefox to open as a maximized window?

Whenever I open Firefox it doesn't open as a maximized window, just a rectangle. At first I didn't care but after some use it's been getting annoying and now I'm trying to fix it. I tried following  but to no avail.  (Ubuntu 18.04.3 LTS - Firefox 69.0 64-bit)


I use the usepackage \theoremstyle{plain} \newtheorem{proposition}{Proposition}  Then I write normally \begin{proposition} [Put name of proposition here] ... \end{proposition}  If the name of your proposition is for example "Euler [1750] and Fermat", then TexStudio  will close the name after the first ] bracket and not the last one!! Something strange will be the output. I saw that mistake, when I tried to cite like this: "\cite[][p. 99]{Serrebook}" TexStudio showed a mistake because after "\cite[]" was a cut... Am I wrong or is that really a mistake of Texstudio?


Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.

Let $f$ be a real-valued function continuous on $[a,b]$ and differentiable on $(a,b)$. Suppose that $\lim_{x\rightarrow a}f'(x)$ exists. Then, prove that $f$ is differentiable at $a$ and $f'(a)=\lim_{x\rightarrow a}f'(x)$.    It seems like an easy example, but a little bit tricky. I'm not sure which theorems should be used in here.    ==============================================================  Using @David Mitra's advice and @Pete L. Clark's notes I tried to solve this proof. I want to know my proof is correct or not.  By MVT, for $h>0$ and $c_h \in (a,a+h)$ $$\frac{f(a+h)-f(a)}{h}=f'(c_h)$$ and $\lim_{h \rightarrow 0^+}c_h=a$.    Then $$\lim_{h \rightarrow 0^+}\frac{f(a+h)-f(a)}{h}=\lim_{h \rightarrow 0^+}f'(c_h)=\lim_{h \rightarrow 0^+}f'(a)$$   But that's enough? I think I should show something more, but don't know what it is.


npm commands not working on WSL with zsh

I've recently started using , I've installed  and done some config.  I am however unable to use npm commands in the WSL bash window. I can happily use npm in Git Bash Cygwin, Command Prompt, etc. But if I try the command within Bash for Ubuntu on Windows I get the following error:  $ npm init zsh: command not found: npm   Is this a zsh config error or how do I go about solving this?  EDIT (Fixed): I received the below feedback from a Bash on Windows Github contributor. Essentially what this means is that you must install certain runtimes(such as NodeJs) on WSL, even if they already exist on Windows, in order to use those runtimes within Bash on Windows. I've installed Node on WSL and it's working perfectly.        You should think of WSL as a light weight Linux subsystem that runs on   Windows similar to a container. The runtimes on Windows and WSL should   be considered independent, but with interop between the two the lines   can start to blur. For example, if you have perl installed in both   environments you could either run with the WinPE perl.exe or the elf64   perl.


I'm, Syrian Citizen, travelling from Dubai to Turks and Caicos. The plane transit by NY JFK, do I need transit Visa.


How to perform partial PIT Recovery without using a staging database in MySQL?

I have a full physical backup and binlogs available for my MySQL instance. Is there a way to perform a partial point in time recovery (meaning restoring in time a subpart of the whole database, i.e. some specific tables) without mean of a staging database, by simply selecting the desired binlogs?


Is there a command or program can add line number to display by pipe?

I always need to find some key words in thousands of feedback and locate it in which line. I used to redirect feedback to a file, and open file wiith vim, and execute vim command :set nu to do this. But it is pretty inconvenient and cause some unnecessary disk IO. So I wonder if there is a command can achive below results: $ sudo my-command | line-number-command | grep 'foo\|bar' 114  bla bla bla foo 514  bla bar bla bla 810  foo bla bla bla 1919 bla bla bar bla


How does PKCS 1.5 solve the insecureness of Textbook RSA?

As we know, Textbook RSA is not enough safe to use because of the following issues;   Guessable plaintext problem  Small $e$ issue   I want to know how PKCS 1.5 solved these problems.


Is it legal to throw an alley-oop to yourself in a real game?

In this video, a college basketball player steals the ball, races down court, and avoids the defender by throwing a pass to himself off the backboard.    In all the (disorganized) basketball games I've played in, a shot had to hit the rim before the shooter was allowed to rebound. And that looks like a shot to me.  Obviously the officials allowed it, but I couldn't find an explicit mention in the . Is this ruled as a shot, and if so, why is it legal? I'd be interested in the answer for any level of basketball, though NCAA is the most relevant.


I would like to know how to use this command , and what is its benefits for a user .  I know its for speech and can read documents , but how to use it ?


I am a math undergrad, I know some basics of algebraic geometry and hence, elliptic curves. I was attending a talk today which was about Poncelet's theorem. In the end of the talk, the speaker discussed complex elliptic curves and wrote     $$\Bbb{C}/\Lambda \simeq \text{torus}$$ i.e. complex elliptic curves   are tori. Where $\Lambda$ is a lattice in $\Bbb{C}$.   Is there an intuitive explanation to this? I know some basics of quotient topology and elliptic curves.


Transparent textured planes produce black artifacts

Having problems with hair transparency using cycles. I ported over a model from daz studio (have done this a few times before with no issues).   Using a simple mix shader, transparent top, diffuse bottom, black/white texture in the fac.  Heres the blend  with images packed.


Words about words: When an old word describes a new thing

I'm wondering if there is a name for words which describe a function where the thing described doesn't relate to the reality of the function anymore. Examples:   dial, as a verb. "Dial the phone". Dial phones are largely unused now. footage, used to describe a video recording. Large digital now. filming, used to describe the act of making a video recording.   This is almost like a retronym, but is kind of the other side of that coin. An important aspect here is that there is an etymological disconnect. If in some distant future "dial" is still being used, someone studying the word itself might be completely baffled as to why it was being used unless told that phones used to have them.   "Holdover" is close. However, the definition of holdover as      "a person or thing surviving from an earlier time, especially someone   surviving in office or remaining on a sports team"   suggests that entity doing a job in the ways of those times. Consider the difference between "Karl" and "Karen" who are typesetters. Karl still sets brass sorts into lines and turns them into lead slugs, he's a holdover. Karen used to do that, but now she flows the text into InDesign. She's still called a typesetter, but she's not exactly a holdover, since she's moved forward with the technology.  I'll admit it's a fine point I'm making here.  Any ideas?  This might be a duplicate of


How can I type to "All chat" in Heroes of the Storm?  And if you can't, are there ways to say GG/WP? I noticed someone on the enemy team did this the other day, but I don't know how.


I have installed Kali Linux on my T100 Transformer Book (laptop). And have not been able to connect to wifi. I am brand new at Kali and don't know much at all about it. Also I have Windows 8.1 but it got deleted in the installation of Kali. So just Kali Installed. No VM. And I have no ethernet port.  Things I have tried:   Going to icon at the top right. It has no WiFi option or anything like it. ifconfig in terminal shows only lo. And yes I am administrator. Downloading drivers. Using an external USB dongle. On other computers it works and lights up green but nothing when I plug it into Kali. Not even the green light. And the USB port works with other devices. A lot of other things I have tried online. Just commands and things. Nothing works.   Device information:      Laptop - Asus T100 Transformer book   Wireless Protocol - 802.11a/b/g/n   External USB WiFi Dongle - TP-LINK AC1200 Wireless Dual Band USB   Adapter Model: T4U   Edit: I just tried on another external USB wireless dongle and it worked. However, I transport this laptop around all the time and the Dongle is huge.


I frequently login to a server, then cd into a specific directory. Is it possible to simplify these two commands into one?   ssh bob@foo   cd /home/guest   I'd like to avoid changing anything on 'foo' if possible, as I'll have to clear it with the server administrator. I use bash, but I am open to answers in other shells.


Is centripetal acceleration mandatory for circular motion?

If we consider a case where a closed circular wall is present, and inside the boundary, just adjacent to the inner wall, two particles are placed touching the surface of inner boundary such that the distance between both particles tends to 0. Particle A and B have identical masses, shapes and physical properties. Particle B applies a constant force on particle A and particle B is in uniform circular motion. Thus, particle A also moves in a circle. And here, centripetal force is not required to make particle A move in a circle.   What's going on?


How to prove the monotonicity of nth root of n (natural numbers)

I am currently practicing series and I have come across this problem many times. I know how to prove that $$\large n^{\frac{1}{n}}$$ is bounded by $1$ and by $2$. What I don't know is how to prove its monotonicity for natural numbers without using derivatives and expansions. Can anyone help?


I have written this code. All right for the figure. The question is about the references to the subfigures.  \begin{figure*}[!t] \normalsize     \begin{subfigure}[b]{0.48\textwidth}         \includegraphics[width=\textwidth]{img/sigma-v} \label{fig:Pv-sigma}         \caption{$P(v)$ trend to the vary of pole $p$.}         \label{fig:sigma}     \end{subfigure}%     ~     \begin{subfigure}[b]{0.48\textwidth}         \includegraphics[width=\textwidth]{img/gamma-v} \label{fig:Pv-gamma}         \caption{$\gamma(v)$ trend to the vary of pole $p$.}         \label{fig:gamma}     \end{subfigure} \vspace*{-2em} \caption{Trend of model $P(v) = \hat{q} v^\gamma$ to the vary of pole $p$ and speed $v$.}\label{fig:Pv} \vspace*{-8pt} \hrulefill \vspace*{-8pt} \end{figure*}  The results is in Fig.~\ref{fig:Pv-sigma}, Fig.~\ref{fig:Pv-gamma} e Fig.~\ref{fig:Pv}.   I obtain:    There is a way for refereeing directly the figure and subfigures without refer only figure and add, by hand, a, b, c...?  NOTE I use this packages:  \documentclass[conference,a4paper]{IEEEtran} \usepackage{spconf,amsmath,graphicx,cite} \usepackage{epstopdf,epsfig,mathtools,caption,subcaption,amsfonts}   MISTAKES I have used a double label (as you can see in the answer).  So, the problem is not in cross-references, but in this part of code:          \includegraphics[width=\textwidth]{img/sigma-v} %\label{fig:Pv-sigma}         \caption{$P(v)$ trend to the vary of pole $p$.}         \label{fig:sigma}   Where the code remarked solve the problem.


One Selenium framework to rule them all (or an actively maintained collection of frameworks)

I am looking for most universal, up to date, open source, selenium framework for test automation. Or at least a number of frameworks for different languages. I am surprised as how every company and every test automation developer is building his own framework. It feels like  over and over again. Even Dave Haeffner  about how everyone wants to build their own. Yet in the links provided in the video by him, the framework collection seems poor (one framework per language) and, at least for java, out of date (2 years old), only with 6 contributors, and seems to be copyrighted. In test automation community so many things seem to be de facto standard. Why not pull it all together and have a repository, actvively maintained by test automation developers. As for this question to not seem too much opinion based: Please provide links for Java-Selenium-JUnit frameworks you know and use and believe in.


Can someone explain why if two random variables, X and Y, are uncorrelated, it does not necessarily mean they are independent?

I understand that two independent random variables are by definition uncorrelated as their covariance is equivalent to 0: $Cov(x,y) = E(xy)- E(x)E(y)$ $E(x)*E(y) = E(xy)$, when x and y are two random independent variables. Therefore, $Cov(x,y) = 0$. However, I am having trouble understanding if two random variables, X and Y, are uncorrelated, it does not necessarily mean they are independent. Could someone also give me a real world example of when two random variables are neither independent nor casually connected? I believe it will help me understand this concept better.


Concatenate rows into columns (NO FOR XML PATH('') and recursive CTEs) - SQL Server 2012

I have a very particular problem at hand.  Brief introduction: I have two columns at a database that I need to "group concatenate", in MySQL I would simply use GROUP_CONCAT to get the desired result, in SQL Server 2017 and on I would use STRING_AGG, the problem that I have is in the SQL Server 2012, which doesn't have this function.  Now, under normal circumstances I would use FOR XML PATH('') to get the solution, this is not viable since I'm running the query from the editor inside a third source application, the error that I get is      FOR XML PATH('') can't be used inside a cursor   For the sake of the argument let's assume that it's completely out of question to use this function.   I have tried using recursive CTE, however, it's not viable due to execution time, UNION ALL takes too much resources and can't execute properly (I  am using the data for reporting).  I will no post the screenshots of the data due to the sensitivity of the same, imagine just having two columns, one with an id (multiple same id's), and a column with the data that needs to be concatenated (some string). The goal is to concatenate the second columns for all of the same id's in the first columns, obviously make it distinct in the process.  Example:  Input:  col1  col2  1     a 1     b 2     a 3     c   Output:   col1  col2  1     a/b 2     a 3     c   Does anyone have a creative idea on how to do this?


Why I got 'unable to resolve host' when I do 'sudo'?

Whenever I do 'sudo' I get an error saying 'sudo: unable to resolve host HP-Pavilion'. I recently change my hostname to "HP-Pavilion". I wonder if I screw up something.  $ sudo mkdir SourceCodePro sudo: unable to resolve host HP-Pavilion [sudo] password for mike:   Thank you for your help.


Could some one tell me how I increase the weight of an order total using  and  module?


difference between 'class[] arrayname' and 'class arrayname[]'

I don't understand the difference between String[] arrayName = {/*some data here*/}; and String arrayName[] = {/*some data here*/}; Is there any difference between placing square brackets after the type (String[]) and after the array name (String arrayName[])? If so, what?


How to push the data into database using javafx

I am editing the question that i added yesterday because i solved that issue. Now i want to know that, is there any specific way to push the data into database?  I am using sqlite database ( firefox plugin ) and eclipse for coding.   Thank you


I have studied the following theorems on inequality: the QAGH (quadratic-arithmetic-geometric-harmonic) mean inequality, the triangle inequality, Cauchy Schwarz inequality, Weierstrass inequality and Chebycheff's sum inequality which states that  If $a_1,a_2,\ldots a_n$ are real numbers such that (i) $$a_1\le a_2\le\ldots \le a_n$$ and $$b_1\le b_2 \le \ldots \le b_n$$, then: $$n(a_1b_1 + a_2b_2 +\ldots + a_nb_n) \ge (a_1 + a_2 + \cdots + a_n)$$  (ii) $$a_1\ge a_2\ge\ldots\ge a_n$$ and $$b_1\le b_2 \le \ldots \le b_n$$, then: $$n(a_1b_1 + a_2b_2 +\ldots + a_nb_n) \le (a_1 + a_2 + \cdots + a_n)$$  One question from my assignment for which I need help is: If $$0\le x_1\le x_2\le\ldots\le x_n,$$ and it is given that $$\frac{1}{1+x_1} +\frac{1}{1+x_2}+\ldots+\frac{1}{1+x_n} = 1$$ Prove that: $$ (\sqrt{x_1} + \sqrt{x_2} +\cdots + \sqrt{x_n}) \ge (n - 1) \left(\frac{1}{\sqrt {x_1} } +\frac{1}{\sqrt{x_2} } + \cdots + \frac{1}{\sqrt{x_n} }\right) $$ Where n is a natural number, $ n\ge 2$ I have tried in many ways to prove this statement using the theorems I know, without any success. Could you please help me?


How to show the maximum likelihood of $\theta$?

Let $x$ have a uniform density  $f_x(x\mid\theta) \sim U(0,\theta)=\left\{     \begin{array}{ll}         \frac{1}{\theta} & 0 \leq x \leq \theta \\         0 & \text{otherwise}     \end{array} \right.$  If there are $n$ samples $D=\{x_1,x_2,...,x_n\}$ drawn independently according to $f_x(x\mid\theta)$; then:  How can I show that the maximum likelihood of $\theta$ is $\max[D]$?


I have a rather basic question but I couldn't find a straight answer anywhere. Consider $C \subset [0,1]$ a Cantor set, that is a closed, nowhere dense and perfect subset of $[0,1]$.  Is the Hausdorff dimension of $C$ necessarily positive?  And even more basic: is it possible to find $A$ an uncountable subset of $[0,1]$ whose Hausdorff dimension is $0$? Obviously a negative answer to the former question would provide such an example.  I'd be very satisfied with dry answers with references if that's all you can provide :)


I’m currently working on this page:  with an embedded javascript form called infusionsoft (iframe form) and my client asks me to make it responsive.  Is there a possible way to override the css or inject custom style inside the iframe form?  Thanks!


Oneboxing should take into account whether the source uses MathJax

While it's reasonable to not add MathJax to chat (), one-boxing does all the heavy-lifting once, on the server, so those reasons don't apply. And currently all posts making use of MathJax look severly broken when oneboxed. So, could oneboxing please consider whether the source uses MathJax or something else similarly exotic and apply it on the server? A chat-message trying to onebox a post on  ():


I’m stuck with a and the. What is the mental process to choose between them?

If the word isn’t specific, so need ’a’. Or If the word isn’t common, so need ’the’.  Which way your mental process works?


I have a question that is the opposite of : since upgrading to Windows 10 version 1809 on my machine, the "Run" box has stopped caching the commands I type.  Previously, and on other machines, I hit Windows+R to open the "Run" box, where I type a command to execute. The next time I open the Run box, previous commands appear there and can be found by scrolling or starting to type.  Now, on this machine, the Run box always comes up empty and I have to type all commands completely each time.  Does anyone know how to re-enable that cache?  In my searches, I have found many pages talking about how to clear this cache, but none to help me enable it.


Procuring both F-1 and B-1 at the same time

I'm an Indian citizen, and I need to attend a business meeting from 13th of July in the US sponsored by my company. Hence I will require a B-1 visa for 10 days in mid July.   However, soon after the meeting, I'll be moving for studies and hence will need an F-1 visa from 10th of August for staying at an institute in the US for the next few years. The college will be sending me the I-20 this week.  How should I proceed to book slots with the consulate? Will there be any effect on either of the visas? I cannot seem to find information on such a case. Any help would be greatly appreciated.


Is a convex function defined on a convex open subset of $\mathbb R^n$ continuous?

Let $K$ be a convex open set in $\mathbb R^n$ and $f$ a convex function defined on $K$; how to show that $f$ is continuous?


What is the standard limit on senses (vision, hearing)?

Just as the title asks, what is the normal limit on how far a character can see/hear under normal conditions (normal lighting, no fog or other weather interference)?   Under the  section all I can find are rules for decreased light, light sources and low-light/darkvision.  I've been told as a general rule to treat normal senses as double the limit of things like low-light/darkvision, so they would extend out to 120 ft. While this seems reasonable as a distance over which to see/hear something clearly, I'd like to know if there is a RAW mention of an actual range that I've simply overlooked.


I got the application of version 1.1.2 in the playstore. I am checking the update of the playstore in the application but I got the error. I researched but couldnot get any solution. I got stuck with the error NumberFormatException.I have implemented as follows:   try {         currentVersion = context.getPackageManager().getPackageInfo(context.getPackageName(), 0).versionName;     } catch (PackageManager.NameNotFoundException e) {         e.printStackTrace();     }   I have tried to fetch the version number of the application from playstore.  private class GetVersionCode extends AsyncTask<Void, String, String> {      @Override      protected String doInBackground(Void... voids) {          String newVersion = null;          try {             Document document = Jsoup.connect("https://play.google.com/store/apps/details?id="+context.getPackageName()+"&hl=en" )                     .timeout(30000)                     .userAgent("Mozilla/5.0 (Windows; U; WindowsNT 5.1; en-US; rv1.8.1.6) Gecko/20070725 Firefox/2.0.0.6")                     .referrer("http://www.google.com")                     .get();             if (document != null) {                 Elements element = document.getElementsContainingOwnText("Current Version");                 for (Element ele : element) {                     if (ele.siblingElements() != null) {                         Elements sibElemets = ele.siblingElements();                         for (Element sibElemet : sibElemets) {                             newVersion = sibElemet.text();                         }                     }                 }             }         } catch (IOException e) {             e.printStackTrace();         }         return newVersion;      }       @Override      protected void onPostExecute(String onlineVersion) {          super.onPostExecute(onlineVersion);          if (onlineVersion != null && !onlineVersion.isEmpty()) {              if (Float.valueOf(currentVersion) < Float.valueOf(onlineVersion)) {                 //show anything             }          }          Log.d("update", "Current version " + currentVersion + "playstore version " + onlineVersion);      } }


Inbox notifications should clear when I view/reply to a comment/answer

I think it only makes sense that if you get a notification for say, a comment on your answer. When reading it (by clicking the "show all comments" link, or by replying to it), it should clear the notification automatically.  For notifications on answers for your questions, leaving a comment, editing, voting or accepting should all clear the notification.


Why do I get blurry pictures when I take a lens attachment off?

I bought a Canon D3300 bundle. This is my first dSLR. It came with a couple lenses. On Easter, I decided to use a wide angle lens to get all the action. Now I can't use my camera without this lens because it is so blurry. I have tried putting it on Auto, and restarting it. For now I'm just not getting it. I want to use my 18-55mm lens. Please help.


Let $ w \in \Bbb C $, and let $ \gamma, \delta : [0,1] \rightarrow \Bbb C $ be closed curves such that for all $ t \in [0,1], |\gamma(t) - \delta(t)| < |\gamma(t) - w| $. By computing the winding number $n_\sigma(0)$ about the origin for the closed curve $\sigma(t) = (\delta(t) - w)/(\gamma(t) - w) $, show that $n_\gamma(w) = n_\delta(w)$.  This seems intuitively clear to me. (Informally, the inequality tells us that $\delta$ and $\gamma$ can never be on "opposite sides" of $w$, and hence their winding numbers must be equal. Making this rigorous isn't enough, however, since I need to use the winding number of $\sigma$ about 0.  I can also show that $n_\sigma(0) = n_\gamma(w) - n_\delta(w)$ (fairly elementarily), so it remains to show that $n_\sigma(0) = 0$. This is the bit that I'm stuck on.  Can someone give me a (small) hint (not a major hint)? If I still can't get anywhere, then I'll probably ask for a larger hint!  There is also a second part to this question - dependent on whether I'm able to do the first part with a hint, I may well update this question to include the second part.  (This is an example sheet question - completely non-examinable.)  Thanks! :)


Forgotten the pattern and phone not showing the "forgot pattern" button.

I upgraded my Moto G2 to Android Lollipop using over-the-air upgrade. It was awesome but I set a pattern lock which I forgot. Usually after 5 wrong attempts it shows the "forgot password" button but it is not showing that button even after 100 wrong attempts. How to unlock the phone?


Problem with Ubuntu install onto secondary HDD, no GRUB

I have two drives in my Dell Inspiron N5010 laptop. One Samsung SSD and one Hitachi HDD via HDD frame. I tried to install Ubuntu onto my HDD. I made a partition for Ubuntu. In the beginning of the install I didn’t see the partitions just the hard drive. I thought it’s not a big deal I install it alongside Windows 7. According to my searching the installer would have to ask the size of Ubuntu partition. It did not. The installer began. It was strange but I did not care. After the installer finished and the laptop rebooted the grub rescure booted. Great. I started the Ubuntu in Try mode and I saw the HDD drive was formatted and the Ubuntu istalled on this drive. WHAT? – I thought.  The Ubuntu istaller formatted my HDD with all datas on it.  Could you please help me? I really would like to use Ubuntu. Unfortunately I can’t shrink my SSD drive (C:) because only 5GB allowed. I would like to make two partitions on my HDD drive and install the Ubuntu  onto one partition.  I am sorry about my english if there’s any mistake.


It is known that HIV is usually transmitted by direct blood or body fluid contact between an infected individual and a healthy person (like blood transfusion or needle sharing):  Suppose a mosquito bites an individual suffering from AIDS and in the process sucks up some T cells infected with HIV along with RBCs. Then it bites another person not suffering from the disease, and transfers these infected T cells. Isn't there a high probability of the second individual contracting HIV?


Partial Differential Equation equal to a function

Hi the question I have to solve is:  $u_x + u_y + u = e^{x+2y} \ $  where $ u(x,0) = 0$  First, I tried to solve the question of the form:  $$ u_x + u_y + u = 0$$  We know that $\dot x = 1 \ $ and $\dot y = 1 \ $. From that we can introduce s where $$x(s) = s +x_0$$ and $$y(s) = s$$. Then if $z = u(x(s), y(s))$ we have that $\dot z + z = 0$.   By setting $s = y$ we have then that $x_0 = y-x$.   Then we can get that $u(x,y) = e^{-y} \ g(y-x)$.  Now, to get $\dot z + z = e^{x+2y}$ I am completely stuck


How does focal length determine lens quality?

What does an 18 - 50 mm lens mean? Are those numbers the first focal length and second focal length? How do you use this parameter to judge what kind of lens to buy? Does more equal better?


How can I use controllers with FIFA 13 on the PC?

I just bought a controller because I am tired of not to being able to do any tricks with keyboard controls. The problem is I am can't configure controls as FIFA 13 PC version  doesn't consider a controller in their settings.  Does anyone know how to do this?


Do not show file paths of build machine in stack trace

I am currently developing a C# application which has got it's own logging. When exceptions are thrown, the exception is saved into a list which can be viewed by the user via a list view.  When the user clicks on a exception in the list view, the stack trace of the exception is shown in a text box. But even when I am executing the program on a remote machine, the stack trace shows the file paths to the original source files from the machine where the application was compiled.   e.g.:  at C:\Folder1\Folder2\Class1.cs:81 at C:\Folder1\Folder2\Class2.cs:65 at C:\Folder1\Folder1\Class3.cs:21   Only displaying the source files without folders would be nice...  How can I change this behaviour?  Is there any native solution? Or do I have to simply do some string manipulation?


my 4 week old daughter will not stop crying. We've tried everything from sucking, both on pacifiers and fingers to breastfeeding, white noise, movement, diaper is clean she doesn't seem to have a fever.   We've tried everything we can read about and think of.  We are both a little bit ill, the common cold and the baby may have gotten it and be upset but we are just at the end of our nerves when nothing helps our poor little one!   Does anyone know anything we can do to help?


Remove occurrence of a pattern from string everywhere

I want to remove occurrence of a string from a given string. Like /hello: from a string like /yo:/sup:/hello:/yo:/hello:/yup. And one thing for sure if string contains a colon in end then it must be removed.  There can be anything between /hello and colon (:) so I want to strip all from /hello to first colon (:).


Your invoice has been modified [to reflect vs reflecting in] the change to this month's order. Which is correct?

I'm wondering how to select between "to infinitive or -ing" in sentence properly.  Your invoice has been modified [to reflect vs reflecting in] the change to this month's order  In this sentence, right answer is "to reflect". But I'm wondering why "reflecting in" cannot be selected.  What if just "reflecting (without "in")"? this can be right answer in that sentence?  I would thank you for your help.  This is a whole paragrah.  Dear Mr.Mulgrew,  As you requested over the phone on 5 November, we checked the monthly order of food supplies you submitted through our Web site on 2 November. As you had noted, the order did indeed include ten jars of mayonnaise more than you had specified. As a result, on 8 November, we addressed this issue, which we acknowledge was our fault. On that date, we deducted ten units from your order. Your invoice has been modified [to reflect vs reflecting in] the change to this month's order, and this has been enclosed with this letter. Please accept our apologies for the error. Your item should arrive by 15 November as you requested.


Direct connecting to PostgreSQL from ArcGIS Desktop?

I am trying to connect to Postgresql database that I just installed on my server machine. As instructed by Esri I have download from postgres and installed psqlodbc. However, when I tried to add the database connection using "Add OLE DBconnection" I could not find it listed under OLE DB provider(s). More over I do not understand the connection parameters. I could the see driver installed in the control panel (under add/delete programs). However I could not see it listed in the OLE DB connection. Can you help me understand my problem? Thanks.  Additional information: I just install postgresql. It has a default database. I have not install ArcSDE on top of it.


Can I Modify Ubuntu 16.04.03 and sell it for Profit?

I am a software developer. I have been using Ubuntu 16.04.03 from several weeks, I had well modified it, thanks to the open source who had allowed me to do so.IT is modified to a level which can beat its' competitors even it could bring a revolution in OS world specially for Linux distros, if the authority will allow me to sell my modified Ubuntu then a huge profit could be earned and no matter if shares will be divided among me and authority involved, well I had googled it but there were lots of confusing links I want its' sure answer.


I am having trouble creating a buffer around a polygon of a county in QGIS. When I run the "fixed distance buffer" geoprocessing tool, no features are returned in the 'buffer' shapefile that is created. Has anyone had trouble with this as well? Or does anyone have suggestions of what I may be doing wrong?  Here is the polygon I am attempting to buffer:


How to remove all white spaces just between brackets [] using Unix tools?

Input  testing on Linux [Remove white space] testing on Linux   Output  testing on Linux [Removewhitespace] testing on Linux   So, how can we just remove all the white space between the brackets and achieve output as given?


How do I create a shared folder after virtualization Windows 10 with VirtualBox on Ubuntu 18.04 LTS?

I have installed Ubuntu on my computer(moving from Mint). Everything is fast, secure and outright amazing.  But, I still need to use Windows for a few custom-built work applications. I tried using Wine but it doesn't work properly.  So, I had to install VirtualBox and install Windows 10 home on it.  I have installed all the necessary applications and everything seems to be working like a charm.  Now, I have to share a folder with both of these OS to optimize my workflow.   I am tired of using Dropbox.  Please, help me.  Any help would be greatly appreciated.  PS: Linux Ubuntu is the host and Windows 10 is the guest operating system.


If humans can be shrunk down to the quantum level, does this mean that the shrunk human will experience time slower as they have smaller mass?

I am doing some research about "time travelling" by shrinking humans to the quantum level. It's something based on the delayed choice quantum experiment, so that we can go back to the past and travel to another parallel universe or to another universe in another timeline. So I just want to make sure if smaller mass changes the way the smaller object experiences time. But do note that I am only 16 so I do wish that it can be simple haha so that I don't end up being more confused.


What is the difference between order of base point and curve order in EC?

When I was read about the elliptic curve cryptography I found some definition about domain parameter of  elliptic curve like the follow. But I did not understand something $p$: prime number. $a, b$: field elements, they specify the equation of the elliptic curve $ E$ over $F_P$, $y^2  ≡ x^3+a • x+b  $ $G$: A base point represented by $G= (xg, yg)$ on $E (F_P)$ $n$: Order of point $G$ , that is $n$ is the smallest positive integer such that $nG = O$. $h$: cofactor, and is equal to the ratio #E($F_P$)/$n$, where #E($F_P$) is the curve order. My question What's diffrence between  $n$ & #E($F_P$)? also I think two are same value. because #E($F_P$) is Curve Order where The number of points on the elliptic curve is called its curve order. and when we do #E * $G$ = $O$. Is this right or not right?


Linux programs that can edit and program PDF

If this is the wrong place, sorry. It's the best place I could think of to ask.  Goal:  I want to create a PDF with viewable data onscreen. If anyone trys to print it, I want the paper to be blank, have a different message (Thou shall not steal.), all black, whatever.  I don't know how to do this, but firstly I need to know what opensource  software is the best, and robust in features, for attempting this.  I do not want to edit content or drag-and-drop.  I need something that effectively lets me manipulate the actual code of the PDF file.  I will have to muddle through learning PDF programming later.   I know I could use standard security features to protect the PDF from printing.


why does my audit ban increase despite passing dozens of audits since my last failure?

Ask Ubuntu user here.  Recently I was banned for 7 days from reviewing. I know that particular post was audit and I clicked on Edit   ( I know it was better to use delete than edit- but I thought I can use  Edit button for such audits to pass )     Previously I was banned for 2 days. After that till today I am sure I passsed dozens of audits and no single audit fail  My question:  Why the ban has increased from 2d to 7d, even I passed  dozens of audits since my last failure ?   Ban for only single audit fail ?


systemd cannot find PID file after YAJSW wrapper startup

I have a systemd startup script for a forking service (let's call it foo) based on . The relevant part of the .service file looks like this:  ExecStart=/opt/foo/startup.sh ExecStop=/opt/foo/shutdown.sh Restart=always     Type=forking PIDFile=/opt/foo/wrapper.pid   The startup.sh script is responsible for starting the YAJSW wrapper. The YAJSW configuration file is set so that its PID is written to a file during startup:   wrapper.pidfile = /opt/foo/wrapper.pid   This way if the wrapper process dies (for any reason), systemd should bring it up, which is the desired behaviour. I have verified that this configuration works correctly, yet a strange line shows in journalctl:  foo.service: PID file /opt/foo/wrapper.pid not readable (yet?) after start: No such file or directory   Strangely, the systemctl status foo shows the main PID correctly:  foo.service ... Main PID: 12313 (java)   Am I doing something wrong or is this a bug in one of the software components? I am running Ubuntu 16.04.3 LTS, kernel version 4.4.0, systemd version 229.4. Any help will be appreciated.


Chrome refused to run a java app unless i upgraded to .45, which I did my dling the installer from oracle.  Java 7 u45.  Installer said it worked.  Chrome still won't start java.    $ which java /usr/bin/java  $ java -version java version "1.7.0_06" Java(TM) SE Runtime Environment (build 1.7.0_06-b24) Java HotSpot(TM) 64-Bit Server VM (build 23.2-b09, mixed mode) ~/private/WDI/git🍔     I may be easily fooled, but that doesn't say "45" anywhere.  (Yes, "06", and "24" and "23.2-b09", but nary a 45.  Such numbers!)  Anybody know if this is u45, or where the installer placed it?  UPDATE: there is a Java System Preference Panel that says "Your system has the recommended version of Java: Java 7 Update 45."  Still, Chrome doesn't appear to see it.


How do I get past the Sea Snake in Candy Box 2? It won't die. I've even tried killing it with the enchanted Monkey Staff.


Merge LUKS-partition with partition on another HDD

I just bought a 2 TB hard disk because the home partition on the old one is almost full.  What I want to do is to extend the home partition on hard disk 1 (sda2) to also include all the space on the new hard disk (sdb1). This seemed rather straight forward at first, however there's one issue. My home-partition is LUKS-encrypted.  How do I extend sda2 to also span over sdb1 and act as one single partition? My initial thought was to create a logical volume (merging sda2 and sdb1), however I wasn't able to find a guide with a scenario like my own. Any ideas?  fdisk -l output:  Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders, total 1953525168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x0c000236     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048   204802047   102400000    7  HPFS/NTFS/exFAT /dev/sda2       204802048  1953525167   874361560   83  Linux   Disk /dev/sdd: 2000.4 GB, 2000398934016 bytes 81 heads, 63 sectors/track, 765633 cylinders, total 3907029168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x12e102fd     Device Boot      Start         End      Blocks   Id  System /dev/sdb1            2048  3907029167  1953513560   83  Linux  Disk /dev/mapper/sda2_crypt: 895.3 GB, 895345184768 bytes 255 heads, 63 sectors/track, 108852 cylinders, total 1748721064 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x00000000  Disk /dev/mapper/sda2_crypt doesn't contain a valid partition table


Displaying a Tree Structure in Crystal Reports

Does anyone know of a way to represent a tree structure in Crystal Reports? My big issue is that I don't know the depth of the tree.  It is represented in a database table with a simple "childId -> parentId" relationship.  A perfect example would be to open Windows Explorer, and look at the directory tree on the left side.  If anyone knows a way to represent that tree, then it'll work for what I need to do too.  My initial attempts have been:  1) to programatically (in C#) add Groups to the report. Unfortunately, you can't create a new instance of the Group class and add it to the Groups collection.  2) recursively nest the same report into itself for each level. In other words:  mainReport   subReport     subReport     subReport   subReport   subReport     subReport   etc...  Unfortunately, SubReports can't contain SubReports.  I really don't want to just add X number of groups into a report and hide the ones I don't need, because I'd have to add a fixed number of nested groups, but technically the data design can support an infinite depth, even though in practice we see up to about 5 levels of depth.  So, any other ideas?


How to run a program or file that the user has entered in C#?

I have a program with a simple text box and button (at the moment).  The user will either enter/select the file from a dialog.  The user will enter a given file path, and when you press the 'EXECUTE' button, the program will attempt to open/run this file/executable?  what is the best way about achieving this? I'm fairly novice and so am not entirely sure what all the 'lingo' is?   PS. I have looked at google for examples, but the code never seemed to actually 'DO' anything?  Any help much appreciated.  btnExecute   string myFile = MyfilePath.Text   Also, is there anyway of checking if the file exists/lets them select it instead of typing it into the textbox?  Is there anyway of ensuring the file is 'openable'?


how to install drivers for wifi adaptor Ralink 148f:7601 on ubuntu?

Recently, i bought a wifi adaptor,but as a result of new to ubuntu , i have no idea about how to  install drivers to run the wifi adaptor. Following some instructions from others, i used   lsusbto check out the chips id of the wifi adaptor.Here it is:ID 148f:7601,and i dont' know   what to do next,hope someone could help fix this problem.Thanks!


Show $E(X)= \int_{[0, \infty)} P[X>t] dt$, without using density argument

For $X$, a positive random variable, use Fubini's theorem applied to $\sigma$-finite measure to prove   \begin{align*} E(X)= \int_{[0, \infty)} P[X>t] dt \end{align*}  I found several references on the the site like this:        but all of them assume that $X$ has density or discrete is the are different proof that does not use this assumption.   This is what I tried  \begin{align*} \int_{[0, \infty)} P[X>t] dt&= \int_{[0, \infty)} E(\mathsf{1}_{[X>t]}) dt=\int_{[0, \infty)} \int_{\Omega} \mathsf{1}_{[X>t]}dP dt\\  &=\int_{\Omega} \int_{[0, \infty)} \mathsf{1}_{[X>t]} dt dP=\int_{\Omega} \int_{[0, X)} 1 dt dP=\int_{\Omega} X dP=E[X] \end{align*} where the first step in second line is due to Fubinni's theorem


It is easy to see that in an atomic domain (where every element factors into irreducibles), we have that all irreducibles are prime iff the domain in question is an UFD.  I think it is not true for a general (commutative, unital) ring: if we consider the ring of eventually constant sequences of integers, we can find there elements which do not decompose (in fact, any sequence which is not eventually $0,1$ or $-1$ will be like that), and irreducible elements are those which have one prime coordinate, and all others $0,1$ or $-1$.  But what about domains? Can there be a domain where all irreducibles are prime, but which is not a unique factorisation domain? Better yet, is there a domain where there are no irreducible elements?


How do IVs affect a Pokemon's combat in Pokemon Go?

Just found out there are hidden Individual Values (Attack, Defense and Stamina) for a pokemon in Pokemon Go. How do these value affect the combat performance in gym?  Attack Value: A Vaporeon with a Water Gun has 6 attack points, does a higher attack value makes this Vaporeon's Water Gun more powerful so the Water Gun will get rid of more than 6 HP of the opponent's HP? Or does a higher attack value make this Vaporeon to response faster when you click the screen to attack or swipe to dodge?  Defense Value: Does a higher defense value gives more HP or simply better defense so a 6 point Water Gun attack can only get rid of half or less of the HP?  Stamina Value: Does a stamina value gives more HP or it makes the stamina bar to fill up quicker in gym battle?


in some textbook i read that one can describe wave displacement by y(t)=Asin(ωt+ϕ) and y(t)=Acos(ωt+ϕ) . i know both these terms are periodic but how one can use any of these equations in numericals and get the correct answer because both these terms have different trigonometric values ???


What can I use to typeset MATLAB code in my document?

This question led to a new package:      Does anybody have a quick and easy way to typeset some relatively long MATLAB code in the appendix? I looked up a few methods, and the mcode package emerged as a possibility, but it seems to be unmaintained...  I have a ton of equations in my code, so I'd prefer a solution that avoids having to use $ to denote equations.  Also, if possible, if there's a way to keep all of MATLAB's "natural" coding colors (e.g. green for comments), that would be great...  Any idea?


Why is the absolute gradient of the metric tensor $\nabla_{\alpha} g_{\mu \nu} = 0$ in every coordinate system?

Is there any intuitive explanation for why the absolute gradient of the metric tensor $\nabla_{\alpha} g_{\mu \nu} = 0$ in every coordinate system?


Is Dark Energy Pushing Us Or Pulling Us?

This may seem silly, but how do they know that the effects we are seeing from , (which we only assume must be there due to observed acceleration), are not from gravity pulling us out from the other side?  Say there's all of this fast moving energy like light, and it extends further out than slower moving galaxies in the sphere of the entire universe.   Would the gravity of all those particles be enough to produce the observations that we assume are due to a pushing effect?


Google chrome wants to use the keychain password frequently in my mac system(OSX version 10.9.2).  Before updating the OS to new version, the applications like Textedit, Preview are used to ask the password while accessing them. If I click the cancel button twice, the popup will be disappeared. But, after updating to new OS version, a popup saying Google chrome wants to use the keychain password without any reason.    I need to click the cancel button for eight to twenty times to disappear the popup. While writing this question that dialog box appears three times. Sometimes, I keep that alert box to the bottom like below.    I tried deleting the password for Chrome in keychain, as suggested in  link. But, no use.


Consider a heat reservoir which gains heat $Q$ irreversibly at temperature $T$ from the surroundings which is at temperature $T_0$. The entropy change of reservoir is then given by $\frac{Q}{T}$, while that of the surroundings is $-\frac{Q}{T_0}$.  My question is, how is this possible? According to the Clausius inequality, the entropy change of a irreversible process is greater than that due to heat transfer. Please help, thank you!


I need to add the log file to my code in order to convert the exception into text document

My code stops automatically and I am not getting the cause behind it. So I need to add the log file in order to capture the exception message and save it in text document format in my machine.  public void objInsurityTimer_Elapsed(object sender, ElapsedEventArgs e)     {         try         {             if (IsTimeActive())             {                 clsTextComparison clsCallTextComaprison = new clsTextComparison();                 clsCallTextComaprison.GetActivityLog();              }             clsInsurityWorkFlow.GetInstance().ProcessXML();             clsInsurityWorkFlow.DestroyInstance();         }         catch (Exception )         {          }   Please let me know what to write in the Catch part in order to get the log file in text format and it to save it in my machine folder.


If I have a fire damage weapon, but primary is cold based, which element am I?

I'm a Demon Hunter with  which does up to 1423 Fire damage, however for my primary resource generator , I'm using the Focus rune which makes it Cold damage.  So when I shoot with Evasive fire, do I do fire, cold or both damage at the same time?


If $d(n)$ is the sum of digits of n, find $d(d(d(n)))$ of $n=4444^{4444}$


Can you treat a prepositional phrase as the subject?

I just recently read this paragraph: "Think of an ad campaign that you still remember long after viewing it. Consider a book that might have inspired you. Behind those memories are solid writing."  I would say grammatically, the subject of that bolded sentence is "writing," and "behind those memories" is a prepositional phrase modifying "writing." Therefore, the verb would be "is" not "are" since it needs to agree with the subject. (solid writing, which is singular).  But even if it were changed to "Behind those memories is solid writing," I still find the sentence awkward. I am trying to figure out how I would reword, but perhaps, I am wrong, and it is fine as is.


Is there a name for matrices that are symmetric along the cross diagonal?

Something like  $$ A= \begin{bmatrix}     a & b & c\\     b & d & e\\     c & e & f \end{bmatrix} $$  would be a symmetric matrix because the values are reflected along the diagonal, and $A=A^\intercal$  Is there a name for a matrix that's symmetric along the cross diagonal? Something like  $$ B= \begin{bmatrix}     c & b & a\\     e & d & b\\     f & e & c \end{bmatrix} $$


Show that only one prime can be expressed as $n^3-1$ for some positive integer $n$   $n^3-1=(n-1)(n^2+n+1)$. If  $n^3-1$ is prime then $n-1=1$ or $n=2$ so $n^3-1=7$. But I need a concrete proof of it, not from intuition.


I have a string that I want to use as a filename, so I want to remove all characters that wouldn't be allowed in filenames, using Python.  I'd rather be strict than otherwise, so let's say I want to retain only letters, digits, and a small set of other characters like "_-.() ". What's the most elegant solution?  The filename needs to be valid on multiple operating systems (Windows, Linux and Mac OS) - it's an MP3 file in my library with the song title as the filename, and is shared and backed up between 3 machines.


I am getting the following error on my terminal   E: The package libllvm3.8 needs to be reinstalled, but I can't find an archive for it.  when I try to run apt-get install or apt-get upgrade. Please help. Thanks in advance.


Is It possible to use passive voice in the infinitive form without "to"?

I have read in a book sentence: "operation first requires that a permit be obtained"  As I understand this sentence is a passive voice in the infinitive form but why here "be" is used without "to"?  Thanks!


How to explain implicit time dependence to someone?

I am trying to explain what implicit time dependence is and how it differs from explicit time dependence, but I'm unsure how "sound" my explanation is. Here is what I said:  Suppose I have a function $T(x,y,z,t)$ which is a temperature field of a room. If $T$ has explicit time-dependence, then even though I may stay at a fixed point, $(x,y,z)$, in the room, the value of $T$ at that point can change over time, the temperature may increase or decrease over time. Now, suppose for simplicity that the temperature at each point in the room doesn't change in time, i.e. $T$ has no explicit time dependence such that $T=T(x,y,z)$.   Then, suppose that I start walking around the room, now the temperature at each point remains fixed, but now my position $(x(t),y(t),z(t))$ is time dependent, i.e. it changes in time due to me walking around the room. As such, the temperature function $T$, that I use to measure the temperature at each point, is said to have implicit time dependence since its value changes over time, not due to the value at each given point changing over time, but because the position, $(x(t),y(t),z(t))$, at which it is evaluated, is changing over time.  Hence, for explicit time dependence, we have that $\frac{\partial T}{\partial t}\neq 0$, since even if my position remains fixed, the temperature at that point is changing over time. For implicit time dependence (and no explicit time dependence), we have that $\frac{\partial T}{\partial t}= 0$, since the value of the temperature at each point is fixed in time, however, $\frac{dT}{dt}\neq 0$, since my position is changing over time and so the temperature will implicitly change over time due to my movement around the room.  Would this be a correct explanation at all, or would something else be better?


Is there a \urlstyle{tt} (or something else) for \href to make it the same font as \url links?

Is there a \urlstyle{tt} (or something else to that effect) for \href to make it the same font as \url links? I'm happy with any monospace font, as long as they both (\url and \href) show up the same.


Is it possible to turn off a specific USB port so it doesn't accept any device?

I have a lot of ports on my computer. I would like to turn off one of them, so when I connect my phone to that port, it only charges. I do want my phone to work with my computer in some occasions though, so I hope other ports are not affected.  I would just like to know how possible this is.


I bought an entry-level DSLR at Christmas time (Nikon D3000 with 18-55mm and 55-200mm lenses) and have been figuring my way around the camera.  I know the very basics, but want to take a class and can't logistically take one offered in my area.  Are there good online classes for learning about lighting, exposure, composition, etc.?  Or maybe sites with good exercises for beginners?


Crash with input/out error and swap unmounting

I am looking for hints on this problem. I've searched around, but can't find something exactly similar.  I am running Debian 8 stable, updated, very minimal install (i3wm, small number of apps running) on a 4yr laptop. While doing some web browsing it crashed - black screen showing swap partition errors (I did not make a note and could not take a picture unfortunately). It stayed like that for a while, and I left the computer be, but after a few minutes I tried switching TTYs and was able to come back to the window manager (other TTYs were black). I could open a new tab in a terminal and tried running some commands like dmesg and tried to look in /var/ and /run/. But every command would result in a seg fault without running. lsblk, mount, dmesg grep - everything was seg faulting OR giving input/output error. For example, lsblk would give input/out error. I could not reboot without pressing the power key.  It seemed like (just a guess) that almost everything that was already in memory at the time (like the terminal, WM, wireless, htop) was able to run, but any IO to disk and some memory accesses failed. That potentially brings up several levels of issues, but I can only guess from theory and not sure if they are possible (maybe even invalid read to a single memory plank/block - guesses along those lines). I am thinking memory issues because of the seg faults on common applications, but that could also mean multiple things.  It is a long shot, but maybe someone has seen something like this. I've had a very similar problem with input/out error sometime ago on the same machine, but it happened only once, and I did not think of it much. I ran badblocks with 0 bad blocks found.  I am a comp sci student, but troubleshooting Linux errors like this is not something I got to do a lot. I can get technical, but I don't know where to look. I can post the right logs (still looking through syslog to find something) on demand. I would really appreciate some help/hints.   Thanks in advance.


I have some trouble to understand what is happening here:  [guido@localhost 9]$ ls -1 Star\ Wars\ Episode\ * Star Wars Episode II Attack of the Clones.avi Star Wars Episode III Revenge of the Sith.avi Star Wars Episode I The Phantom Menace.avi Star Wars Episode IV A New Hope.avi Star Wars Episode VI Return of the Jedi.avi Star Wars Episode V The Empire Strikes Back.avi   III\b before I\b, but II\b before III\b? Whatever is causing this, it is not behaving consistently. This is also the same sorting result I get in the GUI. I checked all the blanks are actually blanks, and there are no case difference among the filenames. How can it be? Is it skipping the roman numeral, and trying to sort after it?  Other tests:  [guido@localhost 9]$ find -name "Star Wars *" -print ./Star Wars Episode I The Phantom Menace.avi ./Star Wars Episode II Attack of the Clones.avi ./Star Wars Episode III Revenge of the Sith.avi ./Star Wars Episode IV A New Hope.avi ./Star Wars Episode V The Empire Strikes Back.avi ./Star Wars Episode VI Return of the Jedi.avi   But:  [guido@localhost 9]$ find -name "Star Wars *" -print | sort ./Star Wars Episode II Attack of the Clones.avi ./Star Wars Episode III Revenge of the Sith.avi ./Star Wars Episode I The Phantom Menace.avi ./Star Wars Episode IV A New Hope.avi ./Star Wars Episode VI Return of the Jedi.avi ./Star Wars Episode V The Empire Strikes Back.avi   While:  [guido@localhost 9]$ find -name "Star Wars *" -print | sort -f ./Star Wars Episode I The Phantom Menace.avi ./Star Wars Episode II Attack of the Clones.avi ./Star Wars Episode III Revenge of the Sith.avi ./Star Wars Episode IV A New Hope.avi ./Star Wars Episode V The Empire Strikes Back.avi ./Star Wars Episode VI Return of the Jedi.avi   I don't think my locale may be affecting this (I also set it to en_US.utf8 anyway) as the doc suggests. What am I missing?  [guido@localhost 9]$ sort --version sort (GNU coreutils) 8.22


Is the 'w' in 'cow' a vowel or a consonant?

Is the w in cow a vowel or a consonant? Assuming it is considered a vowel, would it likewise be so in how?  I learned that the vowels are "a, e, i, o, u, and sometimes y."  If w can be a vowel, what other letters can be vowels? What is the definition of a vowel?  By the way, I know w can be a vowel, for example in the word cwm, described in the OED as:     A valley; in Physical Geogr., a bowl-shaped hollow partly enclosed by steep walls   lying at the head of a valley or on a mountain slope and formed originally by a   glacier; a cirque.


Suppose that $f : E \rightarrow F$.  What is $f(f^{-1}(A))$? Is it always $A$? $f^{-1}$ is the inverse function.  This is not a homework, I'm confused by this statement.


My stats background is not very strong so I was hoping I'd be able to get some help. In my MSc thesis I am using R to test for significant differences in means between populations. My data is not normally distributed (based on QQplots, Shapiro-Wilk's and histograms), therefore I cannot use parametric tests. So I am using a Mann Whitney Wilcoxon test instead (wilcox.test in R).   Now from my understanding Mann Whitney Wilcoxon test for significant differences in medians, not means. I have a table with my data reported as means, but I report significance testing results in my thesis based on medians as calculated by R. Is this an appropriate approach? Or do I need to convert the means to medians in my table?   Thanks.


Well, it's been , but it's been 8 months and it hasn't got any easier. Epic is by far the hardest silver badge. Only 103 of them have been awarded so far. The majority of gold badges have a higher count; except Copy Editor (80), Reversal (49) and duh - Legendary (30).* Should the requirements be lowered? (Disclosure of interest: I have 38 "exceeded" days). * (Not counting the new badges Announcer, Booster and Publicist).


Splitting layer with many polygons into independent shapefilles?

Is there any way to save many shapefile, which are not multipolygons, into shapefile, and then iterate over them?  I have shapefile with plot polygons and I want to have each one independent in order to build a grid for each one of them and to use rotate in order to make the grid look good inside the polygon.  This is what I have right now    My end goal is to use the Model builder to iterate those polygons and to create for each one of them a grid.


Was this epic answer from Scifi & Fantasy SE manually added to the Hot Network Questions?

According to  and  answer, it becomes exceedingly difficult/impossible for a question to hit the HNQ once it gets older. When this  appeared on Science Fiction & Fantasy SE, it was over four years after the question had originally been asked. In spite of the epicness of the answer and overwhelming response (possibly the best ever on that SE), it should have been totally impossible for the question/answer to hit the HNQ, since the HNQ formula  However, SF&F SE moderator Rand al'Thor  due to the epic answer. Rand notes  by   I thought of the story as soon as I saw the post in hot network questions. Now I am lamenting not having seen it in the unanswered section.  The user has   Here's the data I can provide: When I saw the question in HNQ, I was on Win7 and using Internet Explorer 11 (only browser allowed on work computer at the time). I saw the question in the HNQ section on the right-hand side. At the moment, that section looks  for me. It's right underneath the Linked and Related questions lists. I was probably on either Puzzling or SuperUser since those are the two I frequent the most. I was definitely not on the root  site.  So:  Was this question really in the HNQ after the answer was posted? If yes, was it manually added* to celebrate the epic answer? If yes to #1 but no to #2, how was it possible?  I have tried to , but the records seem incomplete for the relevant time period. The problem seems to be that the the second, third, fourth page etc. of the front page aren't cached frequently enough to give detailed results. I've also gotten  saying "No questions found", further complicating research. * = I have never heard of a question being manually added to the HNQ, but if this question was actually there after the answer, I can't really think of any other explanation. Unless I have misunderstood the math somehow.


I have a trouble with this limit of the infinite product: $$\lim _{n \to\infty}\left(1-\frac{1}{1 \cdot 2}\right)\left(1-\frac{1}{2 \cdot 3}\right) \cdots\left(1-\frac{1}{n(n+1)}\right)$$ My attempt:  We have  $$\prod_{n=1}^{\infty}\left(1-\frac{1}{n(n+1)}\right)=\prod_{n=1}^{\infty}\left(\frac{n^{2}+n-1}{n^{2}+n}\right)=\prod_{n=1}^{\infty} \frac{\left(n-a_{1}\right)\left(n-a_{2}\right)}{n \left(n+1\right)},$$ where $a_{1}=\dfrac{-1+\sqrt{5}}{2}$, $a_{2}=\dfrac{-1-\sqrt{5}}{2}$.  So I would just like a hint as to how to proceed. Any help would be appreciated.


In Star Wars: The Force Awakens we learn that Kylo Ren is >! a member of "Knight of Ren". We also learn that this is the team that       slaughtered Luke's Jedi students.   So we have a group of fighters, and one of them(Kylo Ren) is a Dark Side of the force user.   They take orders from Snoke, who seems to be a Force user.  So this team are Sith? Or is a new order , calling themselves "Knight of Ren", who continue the "legacy" of Sith and what the difference between them? Are they something like Inquisitorius? And what Ren could possibly mean?


Where I could report a bug in Python? or Someone could tell me what's going on?

I was doing a program in Python a little puzzle where the user only have to order the numbers, whatever in the program I create a list of lists. The main list it's empty, I create a method where the program fill the list with another 4 lists using a for with an enumerate and when the account comes every 4 times save the secondary list inside the main list and here comes where need someone explain me or if it's a bug. I clean the secondary list but the main list cleaning to and I don't know what's going on only when I create a new list works but with the other method doesn't. class Puzzle:          def __init__(self, array):         self.array = array         self.account = 0          def fillPuzzle(self):         """Method that fill the list of lists"""         # account = self.account         newlist = list()         for account, number in enumerate(range(1,17),start=1):             number = str(number) if number != 16 else 'X'             newlist.append(number)             if account in (4,8,12,16):                 self.array.append(newlist)                 newlist.clear()# here it's the problem, if i use newlist = list() works         return self.array     def showArray(self):         print(f"\nLista : {self.array}")  emptylist = list() newpuzzle = Puzzle(emptylist) #  newpuzzle.showArray() newpuzzle.fillPuzzle() newpuzzle.showArray()


Is it a bad idea to use \begin{section} ... \end{section} in LaTeX?

In several discussions about relatives merits of LaTeX v. xml, a xml supporter complained that in LaTeX sections, subsections etc are not properly closed, so it is hard to tell where a section ends.  Of course it is typically possible to recognize an end of a section, but there is actually a number of ways how a section can end: start of another section, start of the next chapter or part, start of \endmatter, bibliograpy, index, etc, or the end of document.  That makes it hard if you want to write a script that would in some way manipulate sections (change their order, write each of them into a separate file, ...).  The same is of course true for subsections, paragraphs etc.   One answer to that is that it is actually possible in LaTeX2e to use sectioning commands as environments, and write   \begin{section}{Blah blah}    ... \end{section}   and because of the way environments are handled in LaTeX2e, it will work.  I he recently seen several comments discouraging such use of regular commands as environments, and it seems that in LaTeX3 it will no longer be possible (on the other hand, it seems that you will be able to define a section environment without causing a conflict with the \section command).   I wanted to know what people think about using sectioning commands as environments.  Is it a good idea, is it OK, or should it not be done?


Global maximum and minimum of $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ with Lagrange multipliers?

The global maximum and the global minimum of the function $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ can be found using Lagrange multipliers.  $\nabla f = \lambda \nabla g$  $g(x,y,z)=x^2+2y^2+3z^2-6=0$  This results into:  $$yz = \lambda 2x$$ $$xz = \lambda 4y$$ $$xy=\lambda6z $$  When looking at the equation $x^2+2y^2+3z^2-6=0$, it can be seen that there are six solutions $(x,y,z)$ with two coordinates equal to zero: $(0,0,\pm \sqrt 2 ),  (0, \pm \sqrt 3, 0 ) ,  (\pm \sqrt 6, 0, 0 ) $  But I got stuck here. Could someone help me with this?


Should I add @Override annotation when overriding doGet() and doPost() methods from javax.servlet.http.HttpServlet?  For example:  @WebServlet("/") public class MyServlet extends HttpServlet {     @Override     protected void doGet(HttpServletRequest req, HttpServletResponse res) throws ServletException, IOException {         /* my code */     } }   I've never seen code that adds @Override annotation to servlet code.


Difference between "ten years old" and "ten-year-olds"

They are all 10 years old. They are all ten-year-olds  What is the difference between these? And, what is the reason why we must add s to the following?"  They are all ten-year-olds


Can I copy prepared Cleric spells that are also on the Wizard spell list into my spellbook?

I'm multiclassing as a Wizard2/Cleric3. I'm wondering if it's possible to prepare a spell from the cleric spell list and then if it's also found in the Wizard spell list, would I be able to write it down in my wizard spellbook? I'm confused by this as the PHB states that if I find a scroll or a book, I can decipher it and boom, it's in my own book. I'm essentially my own walking book book. I've found this in the sidebar in the PHB under wizard regarding spellbooks.  Replacing the Book. You can copy a spell form your own spellbook into another book-for example, if you want too make a backup copy of your spellbook. This is just like copying a new spell into your spellbook, but faster and easier since you understand your own notation and already know how to cast the spell. You spend only 1 hour and 10gp for each level of the copied spell. If you lose your spellbook, you can use the same procedure to transcribe the spells that you have prepared into a new spellbook. Filling out the remainder of yourspellbook requires you to find new spells to do so, as normal. For this reason, many wizards keep backup spellbooks in a safe place.  Now, lets say that I prepare Protection from Evil and Good, which is a 1st level spell and can both be found in the Cleric spells list and in the Wizard spell list. Shouldn't it be possible for me to write it down into my spellbook by following the given formula in the "Replacing the Book"; 10gp + 1hour for each level of the copied spell. I understand that it  would have been very different if the holder of the spell I want to copy is another creature (party member or not) but now it's all me. I know the spells, I own the book, I am the Wizard.


Obviously the first tester group would be your own group. But beyond that? It would seem to make sense to have at least more than one group test out your game, as different groups want different things and play differently. Fresh eyes find different bugs, etc. etc.  Are there resources out there to help aspiring game designers without a lot of contacts find people willing and eager to test out their game?  Or is this in essence a "" issue?  To clarify my own situation:  I have the mechanics finished. The setting is still under development, but in accordance with the motto "fail faster" I want to go ahead and test the mechanics (in a different setting for now) to see if they work and are fun or if I need to go back to the drawing board. I have a sort-of group, but I don't know them very well and they don't meet often, and so I'm not excited about the prospect of presenting the mechanics to them right now (as I'm sure there are a dozen issues I've overlooked). Also, I'd like to test the game (including the setting, later) on more than one group, as mentioned above. I've put out some feelers among my current friends and acquaintances, but nobody's really been excited about playtesting or even really giving in-depth feedback, and I don't want to be that person who's always shoving their project in your face. I'm willing to run something online as well. I'm also interested in having others run a game without me present, and giving me their feedback.  Also, I'm looking for something of a guide-type answer that might help someone besides just me.


sorry I am a new guy here and in illustrator, I am gonna make a low opacity and blur object that effects on every object behind itself. like below finally


Proving that $\sum_{j=0}^n {n \choose j} = {n \choose 0} + ... + {n \choose n} = 2^n$

I'm looking for a proof verification, precisely at the end of the proof. We proceed by induction on $n$.  Pf. Base case $n = 1$,$$\sum_{j=0}^1 {1 \choose j} = {1 \choose 0} + {1 \choose 1} = 1 + 1 = 2^1$$ Notice also for $n=2$, $$\sum_{j=0}^2 {2 \choose j} = {2 \choose 0} + {2 \choose 1} + {2 \choose 2} = 1 + 2 + 1 = 2^2$$ Now, suppose that for $k\in\mathbb{N}$ it is true that $$\sum^k_{j=0} {k \choose j} = 2^k$$  Then, by Pascal's identity,  $$\sum^k_{j=0} {k \choose j} + \sum^k_{j=0} {k \choose j-1} = \sum^{k+1}_{j=0} {k+1 \choose j} = 2^{k+1}$$ Since $k$ is any natural number, it should then also work for $k+1$.  My reservations are that I'm using the assumption incorrectly or misusing the assumption by not starting with the assumption. Any clarity is appreciated.  Edit: It seems that changing the bound on the second sum in this equation     Then, by Pascal's identity,    $$\sum^k_{j=0} {k \choose j} + \sum^k_{j=0} {k \choose j-1} = \sum^{k+1}_{j=0} {k+1 \choose j} = 2^{k+1}$$   to $k+1$ yielded the quickest fix to the original proof, with the convention that, as Brian M. Scott pointed out: ${n \choose k}$ is 0 if $k$ is a negative integer.


In the Temple of Eothas there are 3 bells that you have to ring to (presumably) open the door to the next level.  I've found one clue, that the large bell is to be rang second, where can I find the other clues (or what is the actual order).


Can I use two possessive nouns in a sentence?

I'm writing a very brief description for a job duty. Is it grammatically correct to use two possessive nouns in a sentence (e.g., Administration's and company's)?  Full sentence is... They support, strategize, and promote  the Administration's and company's programs, initiatives, and campaigns.


Solutions of the equations of the degree 5 and more

I know that there is a precise solution of the equations:  \begin{align}     x + a & = 0 \\     x^2 + a\cdot x + b & = 0 \\     x^3 + a\cdot x^2 + b\cdot x + c & = 0 \\     x^4 + a\cdot x^3 + b\cdot x^2 + c\cdot x + d & = 0 \end{align}  Why there is no solutions for equation of degree $\ge 5$?


Finding & correcting missing layer in MXD using ArcPy?

Am struggling with ArcPy.  Can someone help with a script to identify missing layers (red arrow in TOC) and then to search for the correct file locations & then update the mxd.


How to remove/desolder very minute smd chips safely?

This is the component I'm trying to remove: BU48xx voltage detector VSOF package (attached pic)


Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$

I have had big problems finding the limit of the sequence $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$. So far I've only succeeded in proving that for $n\geq2$: $x_n>0\Rightarrow x_{n+1}>0$  (Hopefully that much is correct: It is true for $n=2$, and for $x_{n+1}>0$ exactly when $\frac{1}{1+x_n}>0$, which leads to the inequality $x_n>-1$ which is true by the induction assumption that $x_n>0$.)  On everything else I failed to come up with answers that make sense (such as proving that $x_{n+1}>x_n \forall n\geq1$). I'm new to recursive sequences, so it all seems like a world behind the mirror right now. I'd appreciate any help, thanks!


3 variable diophantine equation word problem: coins

When Mr. Smith returned from Europe in 1966, he found that he had in his possession 35 British sixpence coins, 55 French ten-centime pieces, and 77 Greek drachmas. Mr. Smith converted each of these coins to its value in American money (rounded off to the nearest cent) and found that the total was worth $5.86. How much was each coin worth in 1966 (to the nearest cent)?  I started by setting up the equation 35B+55F+77G=586, but I was not sure how to solve a three-variable diophantine equation.


Is it possible to set Allocation Unit Size with GParted when formating an external hard drive?

I want to format and set a single partition in an external hard drive with GParted (Ubuntu 12.04) and would like to set the Allocation Unit Size. I don't see any options to do this with GParted. Is there a way to set AUS in Ubuntu?


Difficult variation of the committee problem

It is a trivial exercise in the pigeonhole principle to show that if an organization contains $m$ people and forms disjoint committees of $n$ members each, then at most $$\bigg \lfloor \frac{m}{n} \bigg\rfloor$$ committees can be formed.  However, I have recently attempted a seemingly simple variation on this problem: what if the committees need not be disjoint, but no two committees can share more than one member.  It seems like another easy exercise in the pigeonhole principle, but I have been unable to come up with a formula for the largest possible number of committees in terms of $m$ and $n$. Does anyone know of such a formula?


Is there a formal spelling for the English letter names?

The English alphabet has a common pronunciation. For example, the letter b is pronounced like the word bee, the letter c like the word see, and the letter i like the word aye.  Is there a formal spelling for the letter names?


How can PCB trace have 50 ohm impedance regardless of length and signal frequency?

Hmm, this seems to be just another question on line impedances.  I understand that when we say "transmission line" effects we talk about things like cross talk, reflections and ringing (I guess that is just about it). These effects are not present at low frequencies where the PCB trace behaves like an "ideal" transmission medium, more like we expect a wire to behave in our early school days.  I also understand that the 50 ohm value comes not from the line resistance which is going to be very small and less than 1 ohm. This value comes from the ratio of L and C on the line. Changing C by changing the trace height above ground plane or changing L by changing the trace width shall change the impedance of the line.  We all know that the reactance of L and C is dependant on the signal frequency as well. Now my questions:   Why should we not call this as line reactance only rather than line impedance? How can it be just 50 ohm? It has to be signal frequency dependent right?  E.g 50 ohm at 1 MHz  Will the world end if I chose to do a 100 ohm or 25 ohm trace instead?  I know that while we like to say 50 ohm as a magic number, it will be within some range around 50 ohm and not 50.0000 ohm exactly.  Is there any time when the actual resistance of a PCB trace may matter?


Lemma : If $(G,\times)$ is a cyclic group and $g \in G$ has order $n$,then $g^m=1$ if and only if $n$ divides m. $\Longleftarrow$ If $n$ divides $m$ then there exist an integer $r$ such that $nq=m$,and $g^{m}=g^{nq}=(g^{n})^q=1$ $\Longrightarrow$ Suppose $g^m=1$,by the division algorithm there is unique integers $r,q$ such that $$m=nq+r \;\;\;\;\;\;\;\;\;\;0\le r<n$$ $$g^m=(g^{n})^q\cdot g^r \;\;\;\text{so}\;\;\;\;\;\; 1=g^r$$ Since $n$ is the least such positive $n$ and $0\le r<n$,easily follows $=0$ and hence $n$ divides $m$.   If $(G, \times)$ is a cylic group and of order $n$,then for $m<n$ the order of $g^m$ is $\frac{n}{\gcd\left(n,m\right)}$.   ${\gcd\left(n,m\right)}$ divides $m$ and hence  $\frac{m}{\gcd\left(n,m\right)}$ is an integer and $n$ divides  $\frac{nm}{\gcd\left(n,m\right)}$,from the last lemma $$g^{\frac{nm}{\gcd\left(n,m\right)}}=\left(g^{n}\right)^{\frac{m}{\gcd\left(n,m\right)}}=1$$   Suppose $(g^m)^k=1$ ,by the lemma $n$ divides $mk$,so:   $$\frac{n}{\gcd\left(m,n\right)} \mid  k\cdot\frac{m}{\gcd\left(m,n\right)}$$   However $\gcd\left(\frac{n}{\gcd\left(m,n\right)},\frac{m}{\gcd\left(m,n\right)}\right)=1$,so $\frac{n}{\gcd\left(m,n\right)}$ divides $k$,and thus it divides any integer power of $g^m$ which is one,and so  the order of $g^m$ is $\frac{n}{\gcd\left(n,m\right)}$.  I don't understand why $\frac{n}{\gcd\left(m,n\right)} \mid  k\cdot\frac{m}{\gcd\left(m,n\right)}$ and why $$\gcd\left(\frac{n}{\gcd\left(m,n\right)},\frac{m}{\gcd\left(m,n\right)}\right)=1$$ Can someone help me?


Make desktop entry for app that requires root privileges

I used gksu before but it seems that it is no longer available. So how can I make something with the same functionality? Obviously I can still run app through the terminal but I don't want to do that.  [Desktop Entry] Name=Xampp GenericName=Localhost Server Exec=gksu /opt/lampp/manager-linux-x64.run Terminal=false Icon=/opt/lampp/XAMPP.png Type=Application Categories=Programming;Development;


What is the number of different partitions of the set N of integers? My reasoning thus far goes as follows: the number must be at least as big as ω because any given integer can be matched with any other integer in a single partition cell. The number must be greater than ω (the first infinite cardinal), because diagonalization kicks in as soon as you try to enumerate the set. But it can be no bigger than ω(2), because each partition is a collection of subsets of N and thus a subset of P(N) (the power set of N). Hence, the set of all partitions is a subset of P(P(N)). Therefore, given the continuum hypothesis, the number I am looking is either the first or the second uncountable ordinal. Any ideas?


Do faculty at Harvard, Princeton, Stanford, etc. only want to hire people from those universities?

This is what I have heard from someone who did his PhD at Princeton. Harvard, Stanford, Berkeley, Princeton, MIT, etc. are biased towards accepting candidates who got their degrees from those schools.


I insert   \begin{figure}[ht!] \begin{center} \includegraphics{figure 1.png} \end{center} \caption{First question} \label{fig1} \end{figure}   and the figure and title are appeared correctly but above the figure is appeared 1.png.  How can i omit this?


What is the meaning of Base* p = new(buf) Base;

I recently came across some C++ Code that is supposed to illustrate the many different types of errors that are possible to be caught in valgrind, gdb, insure, and such...  One of the examples is as follows:  // ============================================================================= // A base class without a virtual destructor class Base {     public:         ~Base() { std::cout << "Base" << std::endl; } };  // Derived should not be deleted through Base* class Derived : public Base {     public:         ~Derived() { std::cout << "Derived" << std::endl; } };  // A class that isn't Base class NotBase {     public:         ~NotBase() { std::cout << "NotBase" << std::endl; } };  // ============================================================================= // Wrong delete is called. Should call ~Base, then // delete[] buf void placement_new() {     char* buf = new char[sizeof(Base)];     Base* p = new(buf) Base;     delete p; }   My question pertains to the line:  Base* p = new(buf) Base;   I have never seen this syntax before and after much Googling I am not sure what to even search for in finding an explanation.  Can anyone point me in the right direction? Much apologies if this is redundant or simple, but I'm very curious what is going on in this example.  Thank you.


ConTeXt: Suppress blank page in asymmetrical multicolumn layout

Background  Creating a custom multi-column layout having columns that differ in width.  Problem  This question's problem is mentioned but not addressed in a previous :     Setting page=yes causes an unfortunate side-effect: the book is interwoven with blank pages in between chapters. These can be eliminated using Ghostscript to post-process...   In other words, without the page=yes option, ConTeXt is unable to format the text as desired. With the page=yes option, ConTeXt formats as expected but exports an undesired blank page between major sections.  Code  Minimum working example that illustrates the problem:  \definepapersize[BookPaperSize][width=24in, height=12in,] \setuppapersize[BookPaperSize]  \definelayout[BookTextLayout][   topspace=.5in,   backspace=.5in,   header=\zeropoint,   footer=\zeropoint,   grid=yes, ] \setuplayout[BookTextLayout]  \definecolumnset[BookColumns][n=4,distance=.25in] \setupcolumnset[BookColumns:1][width=11.75in] \setupcolumnset[BookColumns:2][width=3.46in] \setupcolumnset[BookColumns:3][width=3.46in] \setupcolumnset[BookColumns:4][width=3.46in]  \setuphead[section][   page=yes,   beforesection={\startcolumnset[BookColumns]},   aftersection={\stopcolumnset}, ]  \setuphead[subsection][   after={\column}, ]  \setuphead[subsubsection][   after={\blank[small]}, ]  \starttext \startsection[title={Section Title}] \startsubsection[title={Subtitle}] \dorecurse{2}{\input knuth}  \dorecurse{2}{%   \startsubsubsection[title={Subsubtitle}]     \dorecurse{1}{\input ward}     \dorecurse{2}{\input lorem}     \dorecurse{1}{\input bryson}   \stopsubsubsection }  \stopsubsection \stopsection \stoptext   Actual Output  The page before each section is blank:    Output Without Page  When the page=yes option is removed, the output has issues:    The \column command no longer appears to respect the column widths and the text bunches up at the bottom of the first column.  Expected Output  The desired output would not have a blank page between major sections:    Work Around  The  contains multiple pages. Using  works to delete every other page (e.g., using gs -sPageList=even), which produces the desired result:     Theory of Inflation by  Stars by    However, the extra blank page causes knock-on problems: extra image processing steps, PDF pages need reordering, and increased compile time due to needing two passes.  Question  What needs to change so that the blank pages are eradicated from the document?  Ideas  Adding page=yes to the \definecolumnset and removing page=yes from the setuphead resolves the issue of blank pages; however, the first page columnset is scrunched to the left. I've attempted to address the issue using:  \definecounter[BookPageNumber][   way=bychapter,   prefix=no, ]  \definecolumnset[BookColumns][n=4,distance=.25in,page={\doifelse{\rawcountervalue[BookPageNumber]}{1}{}{yes}}] \setupcolumnset[BookColumns:1][width=11.75in] \setupcolumnset[BookColumns:2][width=3.46in] \setupcolumnset[BookColumns:3][width=3.46in] \setupcolumnset[BookColumns:4][width=3.46in]  \setuphead[section][   before={%     \doif{\rawcountervalue[BookPageNumber]}{1}{\page}     \incrementcounter[BookPageNumber]   },   beforesection={\startcolumnset[BookColumns]},   aftersection={\stopcolumnset}, ]   However, this does not produce the desired output.