First off, I know hashes are 1 way. There are an infinite number of inputs that can result in the same hash output. Why can't we take a hash and convert it to an equivalent string that can be hashed back to the original hash output?  eg:  string: "Hello World" hashed: a591a6d40bf420404a011733cfb7b190d62c65bf0bcda32b57b277d9ad9f146e   unhash: "rtjwwm689phrw96kvo48rm64unc8oetb5kmrjiuh7h8huhi6dde5n5"         (a real string that gives the same hash as "Hello World") hashed: a591a6d40bf420404a011733cfb7b190d62c65bf0bcda32b57b277d9ad9f146e    ...

I'm going to provide “proof” why a hash function can be reversed, and I hope you can tell my why I'm wrong  So, a hash function can be implemented as a series of logic gates. All logic gates can be implemented using only NOT and OR gates. (I'm fairly sure about both of these, but please correct me if I'm wrong.)  Therefore, a hash function can be implemented as a series of NOT and OR gates.  A NOT gate can be easily reversed by going through another NOT gate.  An OR gate cannot be reversed, since it fundamentally losses information. However, a possible input can be derived from any given output.  Therefore, I should be able to construct a possible input given an output from a set of logic gates, including from a hash function.  What have I gotten wrong here?


I was upgrading ubuntu 14 LTS to 18 LTS. But it went wrong. There were many broken softwares. Now I am stuck in 16 LTS but with only the terminal. So I am planning to completely uninstall this and to get a new release ubuntu 18. Can someone help how to uninstall at first?  Thanks

I would like to see a full how-to guide on how to install Ubuntu.


I am trying to install docker on my OpenVZ VPS. I have discovered that my kernel is not up to date, as I am running 2.6.32-042stab123.9 and need to upgrade it.  I have updated to 17.04, however the kernel did not update in the process.  I also tried to update manually following   However I get the error:   /usr/sbin/grub-probe: error: failed to get canonical path of `/dev/ploop35399p1'.   How can I fix this?

I have ordered a VPS with Ubuntu 13.04 on it.  The VPS reports that the kernel is a 2.6.x-series kernel.  From what I have read, Ubuntu 13.04 has at least the 3.8.x series of kernels.  Is there a reason that my VPS is seeing a 2.6.x series kernel, and not a 3.8.x series kernel?


I'm parsing a bunch of ints from strings that were 'substring-ed' from a simpleDateFormat string. For some reason that I haven't been able to figure out the String monthString keeps coming up NULL, I dont see why.   I have created the string in another function call and when I pass it to the next function the string then becomes NULL  public class MainMenu extends JFrame implements ActionListener {     private JButton start, highscore, help, stoppen;     private int yearNumber, monthNumber, dayNumber, daysInMonth;     private String monthString, yearString, dayString;      private String timeStamp = new SimpleDateFormat("dd.MM.yyyy").format(Calendar.getInstance().getTime());    public void go(){     setMonthString();     getDayString();     getYearString();     getDayNumber(dayString);     getYearNumber(yearString);     getMonthNumber(monthString);     getDaysInMonth(monthString);     makeThisMonthFolders();     maakComponenten();     maakLayout();     toonFrame(); }  private void makeComponent() {     String timeStamp = new SimpleDateFormat("dd.MM.yyyy").format(Calendar.getInstance().getTime());      String dayString = timeStamp.substring(0,2);      System.out.println("Today is day " + dayNumber + " of the month");      String monthString = timeStamp.substring(3, 5);      System.out.println("Month string: " + monthString);       start = new JButton("Move Folders"){         {             setSize(150, 75);             setMaximumSize(getSize());         }     };     start.addActionListener(this); }  private String setMonthString(){     String monthString = timeStamp.substring(3, 5);      if(monthString.substring(0,1) == "0"){         System.out.println(monthString.substring(0,1));     }     /*if(monthString.substring(0, 1) == "0"){         monthString = monthString.substring(1);     }*/     return monthString; }   public int getMonthNumber(String monthString){     System.out.println(monthString);     monthNumber = parseInt(monthString);     return monthNumber; }   }  Here is the null return from a test and the error codes thrown:  Today is day 0 of the month Month string: 07 Exception in thread "main" java.lang.NumberFormatException: null at java.lang.Integer.parseInt(Integer.java:542) at java.lang.Integer.parseInt(Integer.java:615) at com.company.MainMenu.getMonthNumber(MainMenu.java:123) at com.company.MainMenu.go(MainMenu.java:37) at com.company.Main.main(Main.java:11) 7 null  ERROR AT 123 references: System.out.println(monthString); monthNumber = parseInt(monthString); // this line return monthNumber;

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


We toss a coin. We get $1$ point for head and $2$ points for tails (starting from 0). What is the probability that there is moment we have exactly $n$ points? ($n\ge 9$)  I can calculate it for $n=9$, but I find hard do it for any $n$. Do you have any idea how to do it?

In answering , I came across a phenomenon the likes of which I don't think I've encountered before, and I'd like to know more about it.  You draw coins, each coin independently being a $1$€ coin or a $2$€ coin with equal probability. Obviously you'd expect to draw as many $2$€ coins as $1$€ coins. In particular, the expectation of $A-B$, where $A$ is the number of $1$€ coins drawn and $B$ is the number of $2$€ coins drawn, is $0$ after any given number of draws.  However, conditional on reaching a total value of $n$ euros, the expectation of $A-B$ tends to $\frac13$ for $n\to\infty$ (in fact, it's positive for all $n\gt2$): The probability to reach $n$ euros with $k$ $2$€ coins and $n-2k$ $1$€ coins is $\binom{n-k}k2^{k-n}$, so the expectation of $B$ is  \begin{eqnarray*} &&\frac{\sum_{k=0}^n\binom{n-k}k2^{k-n}k}{\sum_{k=0}^n\binom{n-k}k2^{k-n}}=\frac{\frac2{27}(3n-1)+O\left(2^{-n}\right)}{\frac23+O\left(2^{-n}\right)}=\frac n3-\frac19+O\left(2^{-n}\right)\;,\\ \end{eqnarray*}  the expectation of $A=n-2B$ is $\frac n3+\frac29+O\left(2^{-n}\right)$, and  the expectation of $A-B$ is $\frac13+O\left(2^{-n}\right)$.  This is rather counterintuitive (to me): For any given number of coins the expectation is $0$, but for any given value of the coins it's positive. This is the stuff that paradoxes are made of if you're not careful how you talk about it, e.g.: “Someone is playing this game. What value do you expect for $A-B$?” – “$0$.” – “So far they drew $137$€. Now what do you expect?” – “$\frac13$.”  The resolution here is (as it often is) that the conditions aren't properly defined – we don't know why and when the person is telling us this amount. If they fixed a number of draws to wait for and then told us the total value at that point, the correct answer would still be $0$; if they fixed a total value to wait for and then told us when it was reached, the correct answer would be $\frac13$, but then the paradox of changing our mind just because we were told some number, no matter which one, wouldn't arise, because it's the stopping protocol that makes the difference.  Still, a certain uneasy sense of paradox remains, even if it temporarily retreats under the glare of careful analysis.  I don't have any concrete questions about this, but I'd be interested to hear about any other cases where such a phenomenon occurs, or names by which it's known, or approaches to deal with it, and perhaps also to ease that lingering sense of paradox.


In the figure given, we are given that $q_1=1 \ \mu \mathrm C$, and we have to approximate the value of $q_2$. My attempt: As the field lines are going from $q_1$ to $q_2$ then this implies that $q_2$ would have opposite charge. But after this I don't know how to proceed further.

A positive and negative charge are some distance d away from each other (Electric dipole configuration) Consider the electric field lines in between them. That is, there is a straight line electric field vector that points from (+) to (-) along the d direction. There is also an arbitrary electric field line exiting the (+) charge by some angle alpha with respect to the d direction and it enters the (-) charge by some angle beta with respect to the d direction. Assume alpha does not equal beta. What are the angles?  This was a question posed by my professor to think about. At first I thought the angles would be equal so I didn't really understand his question. I think the case that they would be equal would be when the positive charge magnitude is equal to the negative charge magnitude (I may be wrong). He did not tell us what the magnitude of the (+) and (-) charges so I think this may be the main point. Would there be a way to calculate the angle? Maybe a ratio? This is mainly for my own curiosity any insight would be appreciated!


I've added a profile recently and I want to display an extra button for that profile on the visualforce page. I've tried a couple of things but it doesn't seem to work. Here is what I've tried:   <apex:outputPanel id="loggedAtkins" layout="block"        rendered="{!AND(ISPICKVAL($User.UserType,'Atkins'), $Site.LoginEnabled)}" >      </apex:outputPanel>   I've sucessfully did it for Guest and not guest user accounts using this method   <apex:outputPanel id="notlogged" layout="block"            rendered="{!AND(ISPICKVAL($User.UserType,'Guest'), $Site.LoginEnabled)}" >  <apex:outputPanel id="logged" layout="block"                     rendered="{!NOT(ISPICKVAL($User.UserType,'Guest'))}" >         Does anyone know how to show certain information only for specific users.?

I have a controller extension and want to use the Tabbed view to get rid of the Chatter caused endless scrolling.      public class UserProfileGetter {     public UserProfileGetter(ApexPages.StandardController controller) {      String userProfileName = [select u.Profile.Name, id, UserType from User u where u.id = :Userinfo.getUserId()].Profile.Name;      system.debug('Profile===================='+userProfileName);      }    }   When I run the debug it shows my Profile as 'System Administrator' correctly.  My VF page code:  <apex:page standardController="Account" extensions="UserProfileGetter" showHeader="true" tabStyle="account" >   <apex:tab label="Opportunities" name="Opportunities" id="tabOpp" rendered="{userProfileName!='Chatter Content'}">          <apex:relatedList subject="{!account}" list="opportunities" />       </apex:tab>        </apex:tabPanel> </apex:page>   So the logic for render I want is - if the user profile name isn't Chatter Content, render. But if I have this logic in the page it won't render for anyone, including me. Ideas? Thanks  Amending - to query other variable on the user, a checkbox called "Admin Team" to display the tab for Account Teams related list, I query for both like this:  public class UserProfileGetter {     public String userProfileName {         get {             return [                     select Profile.Name                     from User                     where Id = :Userinfo.getUserId()                     ].Profile.Name;         }     }     public boolean userAdminTeam {         get {             return [                     select Admin_Team__c                     from User                     where Id = :Userinfo.getUserId()                     ].Admin_Team__c;         }     }      public UserProfileGetter(ApexPages.StandardController unused) {     }   }   And then I use like this:   <apex:tab label="Account Team" name="Account Team" id="Act" rendered="{!userAdminTeam}">   Thanks all.


I want to match all strings between custom string, so here we go:  var string = `      <!--@hello-dear:John-->     <h1>John</h1>     <!--@bye-dear:John-->  `;  var startString = ""; var endString   = "";  var regString = startString + "(.*?)" + endString; var regex     = new RegExp(regString, "i");  console.log(string.match(regex));   Returns null  Expected that matched object with the string  "
John
 "

For example, this regex  (.*)<FooBar>   will match:  abcde<FooBar>   But how do I get it to match across multiple lines?  abcde fghij<FooBar>


Disclaimer: My knowledge of the x-men franchise comes from the films, not comics or cartoons. Sorry if the answer is obvious in a different medium.  Okay, so Wolverine, of the X-men, has claws. They are shape in a knife-like way, with a sharp blade on one side, but I'm nor sure they should. Here's some known facts.   His mutation provides two powers, an ability to heal almost any wound at high speed (which also allows him to never visibly age), and retractable bone claws. The claws are comprised of multiple bones, resembling the bone structure of hands and feet. His bones were infused with an alien metal, Adamantium, at a later date by William Stryker. The rest of his bones are the same shape (we see x-rays, they're normal). We see him escape immediately after the metal is implanted, there's no time for someone to add more metal or sharpen the blades.   So why would they be bladed, and not the same shape as they used to be?

In X-Men Origins: Wolverine, he had ugly bones coming out of his hands. Assuming adamantium replaced his skeleton, the adamantium should have taken their shape, instead of being nicely-shaped blades.  So was there a different explanation for Wolverine's claws or is it just so?


I would like to replace the version of Firefox that is already installed with Firefox ESR on Ubuntu 18.04.  I have downloaded it from   But I couldn't configure it successfully as I could in Ubuntu 14.04:  sudo tar -xvjf firefox-x.x.tar.bz2 -C /opt sudo ln -s /opt/firefox/firefox /usr/bin/firefox   So I have reinstalled Ubuntu completely.  How can I achieve this?

This  asks how to install FF32 bit while keeping the 64 bit.  I want the much more simple thing: is there a canonical way to install firefox 52 ESR as "default" firefox in my 16.04?  I found this  ... but there are no packages; probably no wonder given the fact that the linked blog article dates back to 2012.  So, 2017, Ubuntu 16.04; how to install FF 52 ESR (as I simply need the java plugin to work for me).  ( my current solution: I downloaded the TAR file from mozilla, extracted that to /opt; and then changed /usr/bin/firefox to be a link to that ESR version of firefox. works, but ugly )


I wanted to show $\left(1+\frac{x}{n}\right)^n\leq\left(1+\frac{x}{n+1}\right)^{n+1}$ using binomial expansion for $n\geq 2$ and $x\geq 0$.  So my idea was to expand both using binomial expansion and try to compare term-wise. The $k^{th}$ term of $\left(1+\frac{x}{n}\right)^n$ is $n\choose k $$\left(\frac{x}{n}\right)^k$, and similar for the other expansion the $k^{th}$ term is $n+1\choose k $$\left(\frac{x}{n+1}\right)^k$. I tried to compute the difference and tried to divide one by the other, neither yields any sufficient results. How should I approach this question?

So I know that showing $\left(1+\frac{1}{n}\right)^n$ is an increasing sequence has probably appeared on this site about 100 times, but my professor said he thinks the induction step is most easily seen if you expand this out and compare the summation term by term. I tried this and I did not what see why the inequality was obvious. Can somebody help me out here? Thanks!


Is it possible for a spellcaster to ready a fireball when he is out of view, move into line of sight and release it in the same turn , without giving the opposing spellcaster the chance to counterspell it since he didn't see it being cast?

Suppose I am within counterspell range of an enemy mage (who has counterspell) and want to guarantee that my spell won't be countered.   Could I do so entirely on my turn by moving behind full cover, then casting the spell with the ready action using a trigger of "when I have an unobstructed line of effect to the enemy mage", and then moving out from cover and releasing my spell?   Using my reaction seems like a fairly (or even unfairly) low cost to be able to deny a counterspell, but maybe the requirement for full cover is enough to make it a justifiable reward for making good use of the environment.


Consider two real valued sequences $\{x_n\} $ and $\{y_n\} $ satisfying the condition $x_n^3-y_n^3\rightarrow 0$ as $n\rightarrow \infty $. Then as $n\rightarrow \infty$, (A) $x_n - y_n \rightarrow 0$ always (B) $x_n - y_n \rightarrow 0$ only if $\{x_n\}$ converges. (C) $x_n - y_n \rightarrow 0$ only if $\{|x_n|-|y_n|\}$ converges. (D) $x_n - y_n \rightarrow 0$ only if $\{|x_n^2 +x_ny_n+y_n^2|\}$ converges $\bf{Try:}$ Take $x_n=(-1) ^n$ and $y_n=(-1) ^n+\frac 1n$. Then option(B) is discarded. For the other options I don't have clear idea. But I tried to proceed like this- Since $x_n^3-y_n^3\rightarrow 0$ hence for some $n>N$ we have $|x_n^3 - y_n^3|<\epsilon \implies |(x_n-y_n) (x_n^2 +x_ny_n+y_n^2) |<\epsilon$ How to conclude?

Given, $\{x_n\}$ and $\{y_n\}$ are two real valued sequences such that $\lim_{n\to\infty} (x_{n}^{3}-y_{n}^{3})=0 $ Then is it always true that $\lim_{n\to\infty} (x_n-y_n) =0 $ ? I tried by splitting $ (x_{n}^{3}-y_{n}^{3}) $, but that didn't help as $\lim_{n\to \infty} (x_{n}^{2}+x_{n}y_{n}+y_{n}^{2}) $ can be $0$ or non zero or doesn't exist.


I was trying to define a unary operator+ for a certain type. I was hoping this operator could be used only within the scope of a class, but even if that's not possible, I'm still confused by this:  struct X {};  struct Foo {     friend const char* operator+(X x) { return "hi"; }      void foo() {         +X{};   // error: invalid argument type 'X' to unary expression     } }; int main() {     +X{};   // error: invalid argument type 'X' to unary expression     return 0; }   If the operator isn't callable inside the class, and it's not callable outside the class, is it callable at all? Where did it go?  (Note that +(X{}) behaves the same way, and if the operator+ is moved outside of struct Foo, both calls are valid.)

I see in a header that I didn't write myself the following:   class MonitorObjectString: public MonitorObject {    // some other declarations    friend inline bool operator==(MonitorObjectString& lhs, MonitorObjectString& rhs) { return(lhs.fVal==rhs.fVal); }   I can't understand why this method is declared as friend. I thought it would make sense if the function is defined in another place and needs to access the internal member of the class, but this is not the case here as it is inline and doesn't even need to have access to the members.  What do you think? Is the "friend" useless?


We were asked in class to use a physics simulator beforehand to test the conditions of an experiment we are going to do and save it to use in our report. The experiment involves the dropping of a ball and measuring its efficiency afterwards Is there any configurable simulator that would allow us to change the height and spin on the ball being dropped, while taking into account air resistance, natural forces, etc? And is it able to give values of kinetic and gravitational energy as well as outputs of the set configuration at any point the ball may be at? Something like  would be good I know an experiment like this doesn't typically need a simulator and the math can be figured out by hand but our teacher has asked us to develop one and share it with him all the same

I'm a physics teacher and I would like to find a simulation software that could be used to give exact numerical answers to high school level problems in Newtonian mechanics.  I want the students to first calcultate a numerical answer to a physics problem and then use the simulator to visualize the problem in order to understand it better and verify that the simlator gives the same answer that they got when doing the calculation themselves.  Here are some examples of what kind of problems I want the students to be able to solve with the simulator:   A slope with a specific angle of inclination and a ball starts rolling at a certain point. Determine the speed, angular momentum and total mechanical energy of the ball after a specific time t. A ladder of known mass and length is leaning against the wall at a specific angle. The contact between the ladder and the wall is frictionless. Calcultate the x and y components of the force between the floor and the ladder.   I would like the software to have the following features:  - Simulation in 2D. No 3D simulations are necessary and the software should at least have the option of doing simulations only in 2D.  - Position all objects exactly by writing numbers (just positioning the objects using the mouse is not precise enough).  - Show animations of the time evolution of the system.  - Show forces, velocities and accelerations as arrows.  - Give exact numerical results so that the students can use the software to verify their calculation.  Ideally the software would have a graphical user interface, but if no suitable software with graphical interface exixts, I could also consider a software with text-based inputs. I would consider both free and commercial software.  My question is: Is there any software that would meet these requirements and if there is, where could I get it?


For $1\leq p \leq \infty$ , let $\| \cdot \|_p $ be the $\mathcal{\ell_p}$ norm on $\mathbb{R}^n$. I need to show that if $1\leq p < r \leq \infty$ , then $\| x \|_p \geq \| x \|_r $.  I have tried Holder's inequality and Minkowski inequality here but they didn't solve my purpose. I am completely stuck at this point.

The $p$-norm on $\mathbb R^n$ is given by $\|x\|_{p}=\big(\sum_{k=1}^n |x_{k}|^p\big)^{1/p}$. For $0 < p < q$ it can be shown that $\|x\|_p\geq\|x\|_q$ (, ). It appears that in $\mathbb{R}^n$ a number of opposite inequalities can also be obtained. In fact, since all norms in a finite-dimensional vector space are equivalent, this must be the case. So far, I only found the following: $\|x\|_{1} \leq\sqrt n\,\|x\|_{2}$(),  $\|x\|_{2} \leq \sqrt n\,\|x\|_\infty$ (). Geometrically, it is easy to see that opposite inequalities must hold in $\mathbb R^n$. For instance, for $n=2$ and $n=3$ one can see that for $0 < p < q$, the spheres with radius $\sqrt n$ with $\|\cdot\|_p$ inscribe spheres with radius $1$ with $\|\cdot\|_q$. It is not hard to prove the inequality (4). According to Wikipedia, inequality (3) follows directly from Cauchy-Schwarz, but I don't see how. For $n=2$ it is easily proven (see below), but not for $n>2$. So my questions are:  How can relation (3) be proven for arbitrary $n\,$? Can this be generalized into something of the form $\|x\|_{p} \leq C \|x\|_{q}$ for arbitrary $0<p < q\,$? Do any of the relations also hold for infinite-dimensional spaces, i.e. in $l^p$ spaces?   Notes: $\|x\|_{1}^{2} = |x_{1}|^2 + |x_{2}|^2 + 2|x_{1}||x_{2}| \leq |x_{1}|^2 + |x_{2}|^2 + \big(|x_{1}|^2 + |x_{2}|^2\big) = 2|x_{1}|^2 + 2|x_{2}|^2$, hence  $=2\|x\|_{2}^{2}$ $\|x\|_{1} \leq \sqrt 2 \|x\|_{2}$. This works because $|x_{1}|^2 + |x_{2}|^2 \geq 2|x_{1}\|x_{2}|$, but only because $(|x_{1}| - |x_{2}|)^2 \geq 0$, while for more than two terms $\big(|x_{1}| \pm |x_{2}| \pm \dotsb \pm |x_{n}|\big)^2 \geq 0$ gives an inequality that never gives the right signs for the cross terms.


Voldemort has horcruxes to grant him "immortality" (more like regeneration). But if his body is destroyed, why wouldn't destroying the other horcruxes afterwards not kill him just as easily? Why does the order matter?

In Half Blood Prince, Dumbledore tells Harry that:     "The seventh part of his soul, however maimed, resides inside his   regenerated body. That was the part of him that lived a spectral   existence for so many years during his exile; without that, he has no   self at all. That seventh piece of soul will be the last that anybody   wishing to kill Voldemort must attack — the piece that lives in his   body.”      — Half Blood Prince, Chapter 23, Horcruxes.   Why does the master piece that lives in Voldemort have to be the last?  If Voldemort was killed*  in the usual way (as he was in 1981), i.e., this master piece was ripped of his body and then all his Horcruxes were destroyed, would he not be finished for ever, and meet the same fate in eternal limbo as he did at the end of Deathly Hallows?  The natural answer seems to be affirmative, if not for the fact that Dumbledore explicitly uses the word 'last'.  If no, what would happen in the alternate scenario described above?  I vaguely remember some mention of this problem in this site, but it could have been in the comments.  *I must clarify that 'kill' here must refer to ripping the (part of his) soul in his body, allowing for the possibility that he might regenerate, as opposed to the ordinary usage of the word 'kill', which leads to death for unhorcruxed people.


If $R$ is a ring, J is an ideal in $R$, and $I$ is an ideal of $J$ (with $J$ considered as a ring), does it follow that $I$ is an ideal of $R$?  That is, is $I$ necessarily closed under multiplication by elements of $R$?  Surely $I$ is closed under multiplication by elements of $J$ (since $I$ is an ideal of $J$).  The "obvious" approach to proof fails so quickly that it must be false, that "an ideal of an ideal is not necessarily an ideal of the big ring".  Please provide a counterexample.  (Or a proof?)


At the moment it seems impossible to show somone, in a chat, a simple example of a few lines of code, because you can't indent it properly.  Since we're all here to discuss code, for the most part, this seems to be rather a problem.  The issue I'm referring to can be seen by typing  `test` `   indented test`   in a chat room.  The result is  test `  indented test`   I can see that blocks of code would be discouraged, by not allowing multiline code blocks to be recognised, but a single indented line seems really necessary...

I would like to be able to post code in chat. I know that I can post inline snippets of code by using backticks, but I don't know how to post blocks of code, with the entire chat message formatted as code, and indentation respected. I am aware of . After reading the comments, I found out that I could format in "fixed width", but I can't see a "fixed width" button anywhere. What should I do?


Suppose $f: \mathbb{R} \to \mathbb{R}$ is a function. For $k \in \mathbb{Z}^+$, let $$G_k = \{a\in\mathbb{R}: \textrm{there exists $\delta > 0$ such that $|f(b) - f(c)| < \frac{1}{k}$ for all $b,c, \in (a-\delta, a+\delta)$}\}.$$ Prove that $G_k$ is an open subset of $\mathbb{R}$ for each $k \in \mathbb{Z}^+$.  I've observed that each $a \in G_k$ is contained in an open interval $(a-\delta, a+\delta)$ for some $\delta$, but I am not sure how to show that $G_k$ is an open subset for EACH $k \in \mathbb{Z}^+$. I am trying to show that each $a$ is contained in an open cube contained in $G_k$ which is sufficient enough to conclude that $G_k$ is open, but how can I connect all of this together? Am I on the right track or am I overlooking something?

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function.  Show that the points at which $f$ is continuous is a $G_{\delta}$ set.  $$A_n = \{ x \in \mathbb{R} | x \in B(x,r) \text{ open }, f(x'')-f(x')<\frac{1}{n}, \forall x',x'' \in B(x)\}$$  I saw that this proof was already on here, but I wanted to confirm and flesh out more details.  "$\Rightarrow$" If f is continuous at $x$, then $f(x'')-f(x')<\frac{1}{n}$ for $x'',x' \in B(x, r_{n})$.  That is, there is a ball of radius $r$ where $r$ depends on $n$.  Then $x \in A_n$ and thus $x \in \cap A_n$.  "$\Leftarrow$" If $x \in \cap A_n$, then there is an $\epsilon > 0$ and a $\delta > 0$ such that $x' , x'' \in B(x, \delta_n)$ for all $n$ and $$|f(x'')-f(x')|<\epsilon.$$ Take $\epsilon = \frac{1}{n}$.


I have a aura map attribute defined in my component file as below  < aura:attribute name="FilesNameMap" type="Map" />   But i am not able to understand how to iterate this in the component file as we know that the <aura:iteration> will work on List but not for Map.  Below is the code which i tried to iterate the Map but couldn't succeed.  < aura:iteration items="{!v.FilesNameMap}" indexVar="key" var="item" > //- logic </ aura:iteration >

Is it possible to iterate over a Map in an aura:iteration. It doesn't give me a compile or runtime error but it doesn't appear to work.   My thought is that it works similarly to $.each in jquery.  <aura:attribute type="Map" name="myMap"  default="{key1: 'item1', key2: 'item2'}" />        <aura:iteration items="{!myMap}" indexVar="key" var="item">       {!key} : {!item}  </aura:iteration>


I was again watching the good old Endgame and noticed this, when the Avengers facility is struck by Thanos's missiles, Rhodes is found struggling to move even in his War-Machine suit to save Rocket and has to get out of this suit to help him. But when the portals are opening and Ant-Man becomes big and helps Hulk, Rocket and Rhodes out of debris, Rhodes has a brand new suit (or maybe just the old one). How is this possible?

In Avengers: Endgame,       After the Avengers HQ gets leveled   War Machine exits his suit and leaves it behind. Later that same scene, he shows up in what seems like a bigger suit with different coloring.   Where'd it come from and when? I don't recall any other scenes that might've explained it.       Except possibly Tony's opening scene but that suit is clearly being worn by Pepper at the same time as War Machine has his new armor.


In Captain America: The First Avenger, Peggy is mad at Steve so she pulls the trigger on her gun three times and the shield dents. Why is that? Also, in Captain America: The Winter Soldier, Steve gets shot at like, a million times and his shield doesn't dent. I just wanted to point that out.

Just after Captain America's shield was introduced in Captain America: The First Avenger, Peggy Carter shot few bullets at it which created few minor distortions on it.                                  From  page of Marvel.Wikia,     Proto-Adamantium   This is the original Adamantium created by Dr. MacLain. Proto-Adamantium is the official name for the metal that makes up Captain America's Shield. It has never been recreated and is the absolute most invulnerable item in all of existence.    From  page of Marvel.Wikia:     The true shield was once slightly dented by an enraged Odinforce empowered Thor, using Mjolnir, but he later reconciled and pounded out the small dent.    How were few bullets able to dent Captain America's shield then?


Let's try a standard calculus formula, here the code  \documentclass[12pt]{article} \begin{document} $$ \int_0^\infty \frac{dx}{1+x^2} = \frac{\pi}{2} $$ \end{document}   Here is the result of the integral of rational function. Notice there is a polynomial and a fraction.    Is there a way to see an "annotated" version of this formula with the boxes.  Here is what I found on a  page using their program opentype.      What are all the rectangles for?  Is there any way to get a similar picture in LaTeX?

This question led to a new package:      Some of you may know the Web Developer Toolbar for Firefox that can outline the block level elements of a page like this:  Is there a way to do something similar with TeX boxes for a complete document?


This is not "The Road Not Taken" by Harry Turtledove. Similar story idea, but I read Turtledove's story before posting this and it's not it. Probably a short story. (Can't think how it might be stretched to a novel's length.) In English, written at least 20-30 years ago. The one I am trying to remember had slightly more advanced aliens. But their weapons were still primitive compared to Earths weapons. (Still single shot but probably not muzzle loaders.) I recall the fight not being quite so one-sided. (In Turtledove's story the "ground battle" was over in just a few minutes, most aliens not even getting off a second shot.) I seem to recall the ground forces having time to report back to their commanders of the battle's progress. (i.e. They had radio communications.) The main thing I recall is the aliens describing humans' full auto weapons as "stitching guns" or "stitching weapons." (Because when their troops would be hit by them they would get 4-5-6 holes appearing side by side across the body in a line.) I seeming to recall the invasion lasted days or weeks before the aliens were defeated. (Maybe because the aliens didn't want to give up thinking the humans "stitching guns" had to run out of ammo soon. No way the humans could have that much ammo.)

Trying to identify a science fiction short story from an anthology likely published before 1991.  Aliens invade during a nuclear war (which would be World War III, WWIII, WW3). The warring nations then turn their nukes on the landing sites, but the invasion succeeds.  Believe the setting is in the U.S., possibly Pacific Northwest, but definitely a mountainous region.  Based on negative inference from the aliens' description of humans as fur-less, no-tail, bipeds (or similar), the aliens are apes or monkeys.  The aliens describe Earth as worse than the Hell planet they previously conquered. They see our tanks and think that we can't have more than a few of those to fight with.  Yet the aliens are somewhat benign, as they take some children back to their parents for a stern talking-to after the children run an alien convoy off the road into a chasm by stringing a rope across the road.


I'm trying to repair my headphones with a broken jack. I just purchased a replacement TRRS jack, and now my problem is knowing the function of the five different wires in my earbuds. How can I use a multimeter to do this? Thank you in advance.

I'm trying to fix my TRRS type headphones but I can't tell the difference between these five wires.  -Blue -Red -Green -Copper (red-ish?) -Black


We want to prove that $ \forall t, \dfrac{e^t + e^{-t}}{2} \leq e^{ \frac{t^2}{2}  } $  I thought to a convexity inequality. If $\psi$ is convex, $\dfrac{ \psi(a)+\psi(b) }{2} \leq \psi( \frac{ a+b }{2}  )$ or it may be the arithmetic-geometric inequality.

Prove the following inequality:   $$\dfrac{e^x + e^{-x}}2 \le e^{\frac{x^2}{2}}$$   This should be solved using Taylor series.  I tried expanding the left to the 5th degree and the right site to the 3rd degree, but it didn't help.  Any tips?


In my bibliography, I have an author named 'R de Jong'.  Using the apacite package, in my reference list the author is sorted under 'd' and is displayed as  de Jong, R. (year). article name etc.   However, as it concerns only one author, I would like to manually change this into  Jong, R. de (year). article name etc.    and sort this author under 'j'. How should I do that?  I am currently using Jabref for managing my references.

Can someone please explain in a clear and concise way how am I supposed to enter the names of authors in a BibTeX file? I have entries with something like   @article{someid,    author = {Juan A. Navarro P\'erez, Ra\'ul de la Garza and Andr\'es Espinoza},    ...   but somehow the output seems kind of wrong!


Now that   Eren has died  will each of his three Titan powers randomly go to three different Eldian babies? And what happened the spine creature?

It's told in the story that if a titan shifter dies without transferring his power, this power will go to an eldian person who just was born. If Eren Jaeger dies without transferring his titan powers, will the attack titan and the founding titan go to different persons?  Note that his is not a duplicate of  as this is not about what happens when a titan shifter dies. But what happens if a titan shifter with 2 powers dies, which is not answered in the answer.


Many people seem to want to keep /var/cache/apt/archives as empty as possible automatically.  Unsurprisingly, there is plenty of information out there about how to accomplish that goal.    My question is just the opposite: How can I prevent anything/everything from being deleted from that directory automatically?  If you can't answer the above question, then maybe you can answer this question: "What process(es) is/are emptying that directory, when, and on account of what system configuration specification(s)?"  (These days I'm running both 16.04 and 18.04 servers.)

I know that packages installed with apt-get are stored in /var/cache/apt/archives.  I just installed mariadb server in Ubuntu 16.04 with following command:  sudo apt install mariadb-server   When I tried to find packages in /var/cache/apt/archives, there are no packages. Where are they stored if it's not in this directory?


The issue is quite simple, I've got a form which targets an iframe. When the form is submitted the load event fires off, so I can use it as a ajax fallback for upload picture functionality for IE8/IE9.  $('#iframe').load(function () {     // do something });   This works ok, however the load event fires off even if I get 415 http code back and no response.  How can I retrieve the HTTP status code from the loaded iframe? A solution that doesn't need any server-side adjustments would be really helpful.

I used the jQuery Form plugin for asynchronous form submission. For forms that contain files, it copies the form to a hidden iframe, submits it, and copies back the iframe's contents. The problem is that I can't figure out how to find what HTTP status code was returned by the server. For example, if the server returns 404, the data from the iframe will be copied as normal and treated as a regular response.  I've tried poking around in the iframe objects looking for some sort of status_code attribute, but haven't been able to find anything like that.    The $.ajax() function can't be used, because it does not support uploading files. The only way to asynchronously upload files that I know of is using the hidden iframe method.


I learn the command at schedule to run a script at a specified time  at -f -m ./test.sh now + 10 minutes   How could I use at to schedule a command?  Suppose the situation,  I search all the musics but running silently on background  find / -name *.mp3 1> ~/desktop/all_musics.md 2>/dev/null &  I intent to open all_musics.md ten minutes later automatically.  open all_music.md at now + 10 minutes  Is it possible to get it done?

I tried to schedule a command to execute 2 minutes later  at -c "ls -l" now + 2 minutes  It fails with multiple ways  $ echo "open 'Google Chrome' " | at now + 2 minutes job 15 at Mon Oct 29 13:31:42 2018   How could I enable it working?  run "open 'Google Chrome' "  at now + 2 minutes   I tried, it is not working  $ at now  at>ls -l at>^D at> <EOT>  job 18 at Mon Oct 29 15:55:00 2018


First of all, let me explain my project. I want users to place orders of products using webforms and then create a node with a link/reference to the submission and others custom fields.  It looks like this :  CONTENT TYPE PRODUCT : - Field name / Field image / Field category / Field description  Webform is enabled for PRODUCT content type. So I've created products examples and each of these products have their own CUSTOM webform (all the forms are differents)  For example :  PRODUCT A (product content type) - fields values + custom webform fields  So what I want this kind of node beeing created after webform submission :  CONTENT TYPE ORDER NODE : - webform sid reference (linking to the submission results) - Some fields which will be the same for every product  Do you think is possible with a custom module or should I find another way to achieve this ? (I suppose replacing webform by a content type, but the problem is webform, in my case, is very usefull)  I have to point out that I'm a beginner in Drupal module's developpment.  Thank you ;-)

I'm using Drupal 7 and created a content type 'NewArticle' with the fields 'Title', 'Text' and 'Image'. Users have the permission to create a 'NewArticle', but I don't like the way of displaying the administration bar in order to let them create a 'NewArticle'.  Instead, I'd like to work with . My goal is to create a Webform with exactly the same fields as the content type 'NewArticle'. So what I want is: when users filled in the form and submit it, a new node 'NewArticle' is created with the submitted information.  How can I do this? Are there modules that make this possible? I can't find any...


I am failing to start MySQL on Ubuntu 18.04 LTS mysql -u root mysql don't work and when I use mysql -u root -p , password is required but I didn't set a password.

I used apt install mysql-server to install MySQL on Ubuntu 16.04 but during the installation, it did not ask for root password.  After installation I got ERROR 1045 when I tried to login as root and mysql_secure_installation threw the same error. I purged and autoremoved then reinstalled but it does not work.  How could i fix this? Can I set the root password if I didn't set it during installation?  This is my installation log:   The following additional packages will be installed:   libaio1 mysql-client-5.7 mysql-client-core-5.7 mysql-server-5.7   mysql-server-core-5.7 Suggested packages:   mailx tinyca The following NEW packages will be installed:   libaio1 mysql-client-5.7 mysql-client-core-5.7 mysql-server mysql-server-5.7   mysql-server-core-5.7 0 upgraded, 6 newly installed, 0 to remove and 0 not upgraded. Need to get 0 B/17,9 MB of archives. After this operation, 160 MB of additional disk space will be used. Do you want to continue? [Y/n] y Preconfiguring packages ... Selecting previously unselected package libaio1:amd64. (Reading database ... 227144 files and directories currently installed.) Preparing to unpack .../libaio1_0.3.110-2_amd64.deb ... Unpacking libaio1:amd64 (0.3.110-2) ... Selecting previously unselected package mysql-client-core-5.7. Preparing to unpack .../mysql-client-core-5.7_5.7.12-0ubuntu1_amd64.deb ... Unpacking mysql-client-core-5.7 (5.7.12-0ubuntu1) ... Selecting previously unselected package mysql-client-5.7. Preparing to unpack .../mysql-client-5.7_5.7.12-0ubuntu1_amd64.deb ... Unpacking mysql-client-5.7 (5.7.12-0ubuntu1) ... Selecting previously unselected package mysql-server-core-5.7. Preparing to unpack .../mysql-server-core-5.7_5.7.12-0ubuntu1_amd64.deb ... Unpacking mysql-server-core-5.7 (5.7.12-0ubuntu1) ... Selecting previously unselected package mysql-server-5.7. Preparing to unpack .../mysql-server-5.7_5.7.12-0ubuntu1_amd64.deb ... Unpacking mysql-server-5.7 (5.7.12-0ubuntu1) ... Selecting previously unselected package mysql-server. Preparing to unpack .../mysql-server_5.7.12-0ubuntu1_all.deb ... Unpacking mysql-server (5.7.12-0ubuntu1) ... Processing triggers for libc-bin (2.23-0ubuntu3) ... Processing triggers for man-db (2.7.5-1) ... Processing triggers for systemd (229-4ubuntu4) ... Processing triggers for ureadahead (0.100.0-19) ... Setting up libaio1:amd64 (0.3.110-2) ... Setting up mysql-client-core-5.7 (5.7.12-0ubuntu1) ... Setting up mysql-client-5.7 (5.7.12-0ubuntu1) ... Setting up mysql-server-core-5.7 (5.7.12-0ubuntu1) ... Setting up mysql-server-5.7 (5.7.12-0ubuntu1) ... update-alternatives: using /etc/mysql/mysql.cnf to provide /etc/mysql/my.cnf (my.cnf) in auto mode Checking if update is needed. This installation of MySQL is already upgraded to 5.7.12, use --force if you still need to run mysql_upgrade Setting up mysql-server (5.7.12-0ubuntu1) ... Processing triggers for libc-bin (2.23-0ubuntu3) ...


In some calculations, I am expecting to receive a value out to 15 decimal places but I am only getting it out to 6 decimal places. In the example below, For @ProRata I am getting the value 0.8871340000000 when I expect 0.887134492110339. DECLARE @EligiblePurchase DECIMAL(38,15) = 0    ,@ProRata DECIMAL(38,15) = 0                 --Percent of total purchase    ,@Reduction DECIMAL(38,15) = 0    ,@Denominator DECIMAL(38,15) = 355302907.06  --Total amount across all purchases    ,@InitialValue DECIMAL(38,15) = 315201464.00 --Specific purchase  --Sometimes @Reduction will be a reduction % like 16.677777777777777, but in this case it's 0 SET @EligiblePurchase = @InitialValue * ((100.00 - @Reduction) / 100) SET @ProRata = @EligiblePurchase / @Denominator SELECT @ProRata  My google-fu is failing me. SqlServer is doing something I am not expecting. Thanks in advance!!

Does anyone know why, using SQLServer 2005  SELECT CONVERT(DECIMAL(30,15),146804871.212533)/CONVERT(DECIMAL (38,9),12499999.9999)   gives me 11.74438969709659,  but when I increase the decimal places on the denominator to 15, I get a less accurate answer:  SELECT CONVERT(DECIMAL(30,15),146804871.212533)/CONVERT(DECIMAL (38,15),12499999.9999)   give me 11.74438969


Here are my queries..   What is the exact number of reputation required to vote in a moderator election?  Is it like I should have the same amount of reputation on all the sites where I am a member. Or if I have sufficient reputation on one of the Stack Exchange sites, is that sufficient to cast votes? What are the badges that one should possess in order to cast votes?  Just like the candidates who are competing for the moderator election, should the voters need some basic badges in order to participate in the election?

The  says that there is a moderator election occurring.   How does the election work and how can I get involved?


In Star Wars: Attacks of the Clones, why did Dooku tell Obi-wan about the Senate being under the control of a Sith Lord? Was it because Dooku had a back-stab plan for Sidious or just because Sidious had wanted him to do it?

Wasn't it a risk for Dooku to tell Obi-Wan the truth about Darth Sidious?  Count Dooku: What if I told you that the Republic was now under the control of a Dark Lord of the Sith? Obi-Wan: No, that's not possible. The Jedi would be aware of it. Count Dooku: The dark side has clouded their vision. Hundreds of senators are now under the influence of a Sith Lord called Darth Sidious.  Did Dooku tell Obi-Wan the truth simply because he knew the Jedi wouldn't believe him anyway? Why tell Obi-Wan? Note: this question was inspired by the question at


I am also facing same problem. I have already installed opensuse, fedora17(facing some problems so deleted). But 12.04 is giving me issues. I was able to install 10.04 on my machine by wubi. Later on I have tried all the versions of Ubuntu but unable to get it worked. Please help me I am starving here, I want to use Unity :'(  Or help me installing UNITY on my OPENSUSE12.01.  I tried same copy  on Dell Inspiron by my USB and it's booted in few seconds but my laptop doesn't.  One more thing I would like to mention. My all OS's(except Windows :P) freezes after installtion till the installation of graphics driver of 'nVidia 8200m' by command line.

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


i'd like to use ajax to reload only part of my webpage. The problem after reload is that i lose the 'click' event on the link element  code:
     //html/php code to get the action     if ($action==1)          echo 'activate';     else echo 'desactivate';     //...
   i had the js script in separate js file and removed it in the html to add the click event every time i reload "#content1". The event works the first time, but doesn't exist after #content1# reload. Any help for this ?  BTW, is there important browser issues when using this instead of usual reloading of the page?

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Question is as follows :   Suppose that $f:\mathbb{C}\rightarrow \mathbb{C}$ is continuous such that $f^3,f^4$ are analytic in $\mathbb{C}$ then prove that $f$ is analytic in  $\mathbb{C}$..  Choose $z_0\in \mathbb{C}$. Suppose that $f(z_0)\neq 0$. As $f$ is continuous, in a nbd around $z_0$ the value of $f$ is nonzero.  So, $f^4(z)/f^3(z)=f(z)$ in a small open ball centered at $z_0$.. So, $f$ is analytic at $z_0$.  Suppose $z_0$ is such that $f(z_0)=0$ then we can not say that $f^4(z)/f^3(z)=f(z)$ for all $z$ in a small open ball around $z_0$ as $f(z_0)=0$ we can not cancel.  But then we can certainly say that there is a ball where $f(z)$ is non zero except at $z_0$. Then in this ball we do have that $f^4(z)/f^3(z)=f(z)$. So, $f(z)$ is analytic in punctured disk around $z_0$.  I some how feel that function being analytic on punctured disk and function being continuous imply that function is analytic..  Could not figure out the proof for my supposedly correct statement.  As $f$ is analytic on punctured disk around $z_0$ we have laurent expansion for $f(z)$ as   $$f(z)=\cdots+\frac{a_{-2}}{(z-z_0)^2}+\frac{a_{-1}}{z-z_0}+a_0+a_1(z-z_0)+a_2(z-z_0)^2+\cdots$$  Suppose there is atleast one coefficient of $\dfrac{1}{z-z_0}$ that is non zero, then $|f(z)|\rightarrow \infty$ as $z\rightarrow z_0$..  But then, it is given that $f(z)$ is continuous.. continuous function on compact set is bounded so $f(z)$ has to be bounded on the disk where as we have $|f(z)|\rightarrow \infty$ if atleast one coefficient of negative powers of $(z-z_0)$ is non zero. So, this says all negative powers coefficients are zero..  So, we have $f(z)=a_0+a_1(z-z_0)+a_2(z-z_0)^2+\cdots$ in a nbd around $z_0$.  Could not deduce anything from here.  I think i am very close to final answer but could not see it immediately.

Suppose $f$ is a continuous complex valued function on a domain $\Omega$. Suppose $f^2$ and $f^3$ are holomorphic in $\Omega$. Show that $f$ is also holomorphic in $\Omega$.   Assume $f=u+iv$. I see that if $u,v$ are in $C^1$ then $f^2$ is holomorphic can imply $f$ is holomorphic considering Cauchy-Riemann equations. But I don't know how to get $u,v$ are in $C^1$ by the adding condition $f^3$ is holomorphic. (I can't get $u,v$ from some combinations of real and imaginary part of $f^2$ and $f^3$). Do someone know how to do this?


I want to split a string in Java with the following format: "value^1" so that I get the initial part, "value" in a string.  I wanted to use split instead of substring, so I tried this:  string.split("^")[0]   but unfortunately ^ is a special character and I guess it has to be escaped. I tried split("\^") but no luck.  Anybody knows how to achieve this using split?  Thanks!

I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps?


I start with a cube, then go into top view. I'd like to change its shape into something else but when I press G, only the top vertex is grabbed, and it changes my square into some weird triangle. I'd like to know if there is a way, without leaving top view, to grab both the top and bottom vertices of the square. It seems like a common problem and I can't figure it out. Should I instead be starting with a plane then adding thickness later?

I'd like to select vertices that are directly beneath the one I am selecting to save me the trouble from moving out of ortho view. It's mostly on simple shapes like the cube below.  Notice how the first image has two vertices selected. However, if the other side is not.    I want to be able to select vertices like so without coming out of ortho mode:    Is there a way to do this?


Natural numbers can be represented  by defining them to contain every number that is smaller than them. Arithmetic can be performed on them using the . Are there any similar definitions for integers, rationals and reals?  For example, I could define a rational to be an ordered pair of dividend and divisor. But that would leave the two rationals $\frac{1}{2}$ and $\frac{2}{4}$ not equal to each other, and it would be based on ordered things rather than pure sets.

In set theory, if natural numbers are represented by nested sets that include the empty set, how are the rest of the real numbers represented as sets?    Thanks for the answers. Several answers basically said for irrational numbers that  A Dedekind cut is a pair of sets of rational numbers $\{L, R\}$. The set of real numbers is defined to be the set of all Dedekind cuts, where a Dedekind cut is a pair of sets of rational numbers $\{L, R\}$ which have no elements in common, and where all the elements of $L$ are less than any element of $R$.  Each Dedekind cut is a real number. This is where I have a problem - surely that can’t be correct. The set $L$ is a set of all rationals, and there must be a rational in the set $L$ that is greater than all other rationals in that set, even if we have no method of determining it. And similarly, there must be a rational in the set $R$ that is less than all other rationals in that set, even if we have no method of determining it. If every irrational number has a corresponding set $L$, then each irrational number has some such corresponding largest element of that set $L$, and then each irrational number has some corresponding rational number. And that would mean that the irrational numbers are countable. So, with Dedekind cuts,  the only conclusion is that there must be irrational numbers $x$ which are either greater or lesser than some irrational cut $y$ of the rationals, and between $x$ and $y$ there is no rational number.  But that is impossible, so that the Dedekind cuts cannot be the correct representation of the real numbers.  Surely the problem with Dedekind cuts is in using sets of rationals that include all rationals up to a certain rational. But there is an alternative method of representing irrationals can be defined in terms of infinite sets of rational numbers. For example, in binary notation, the non-integer part of $\pi$ is $.00100100\ 00111111\ 01101010\ 10001$. You define a set by: if the nth digit is a $1$, then  the natural number $n$ is in the set. And then we have that, for the real numbers between $0$ and $1$, that the set of real numbers is simply the set of all subsets of natural numbers. Each subset corresponds to some real number between $0$ and $1$.  And in this way, all real numbers can be considered to be some set based only on nested sets of the empty set.  But I still haven’t got a satisfactory answer for how negative numbers can be represented in terms only of sets containing the empty set. Any ideas?


Can anyone please tell what are the steps to installing libxml2 on a server without root privileges? In a manner so it can be seen by other packages? I have installed it but do not know what is the correct location for it and what variable should be set to make it visible. Please help! I have to install a large number of dependencies and I am stuck at the first step!

Assume I have ssh access to some Ubuntu server as user and I need some not system tools to be installed for convenience (mc, rtorrent, mcedit). I do not want to bother admins for these small programs.   Is there a way to install them (make them run) without using something like sudo apt-get install?


I have this if else statement which is assigned to compare results from a text box to a list of context. I am wondering how do i make it such that it is case insensitive ?  value = textbox1.Text;  if (article.contains(value)) {        label = qwerty;  } else {       break; {

Is there a way to make the following return true?  string title = "ASTRINGTOTEST"; title.Contains("string");   There doesn't seem to be an overload that allows me to set the case sensitivity.. Currently I UPPERCASE them both, but that's just silly (by which I am referring to the  issues that come with up- and down casing).  UPDATE This question is ancient and since then I have realized I asked for a simple answer for a really vast and difficult topic if you care to investigate it fully. For most cases, in mono-lingual, English code bases  answer will suffice. I'm suspecting because most people coming here fall in this category this is the most popular answer.  answer however brings up the inherent problem that we can't compare text case insensitive until we know both texts are the same culture and we know  what that culture is. This is maybe a less popular answer, but I think it is more correct and that's why I marked it as such.


I just downloaded Ubuntu 13.04 earlier and was trying it out.  At least I know you can surf all installed applications with the dash home if you click the icons at the bottom, you're not forced to memorize all the names of everything.  Anyway...  I'm used to Windows, where programs have their own ways of storing passwords--and they do, and I've never had a hard time.  It makes me comfortable.  I'm very *un*comfortable with the idea of something storing pretty much ALL my passwords, I prefer them to be separate entities.  Is a keyring really necessary for programs like Chrome and Firefox?  Can I just disable the keyring altogether and still have Chrome remember my passwords, or when I use Ubuntu, will I forever have to type a password for it to automatically type a password?  To me, typing a password so I don't have to type a password just doesn't make any sense.  I'm confused.  I never remember having to do this when I installed Linux before.  And yes, I have the login password the same as the keyring password but I still have to log into both each time.

I want to disable GNOME keyring globally on my machine. So I deleted the lines  auth    optional        pam_gnome_keyring.so session optional        pam_gnome_keyring.so auto_start   in /etc/pam.d/gdm. It seems to me that this has no effect. When I lock in the syslog writes  Aug 24 18:37:03 foobar gnome-screensaver-dialog: gkr-pam: unlocked login keyring   and another user sees a menu window where he hs to enter his credentials. So what is the correct way to disable keyring for every user on that machine?


I have a piano keyboard that uses 12V 1A adapter . The adapter was not working anymore so i used another one which was 12V 2.5A but after 45 minutes of usage the keyboard got little heated up in the area where the adapter is plugged in.Now my question is :1) have it caused some damage to the keyboard?? Although its working fine. 2) Is it okay to use that adapter?

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


I read this , and at the end of page 841 there is this sentence:   demonstrating that state transitions exert a differential  effect across the firing rate spectrum (slope, 95% confidence interval 0.66–0.71)   What really means the value 0.66–0.71? How it is obtained? I couldn't find more detail in the article...   Thanks a lot  EDIT : Extract from the paper:   (B) Differential effect of brain state on neurons of different firing rates. Comparison of the firing rates (log scale) of the same pyramidal neurons during WAKE and nonREM—each point is the same neuron in two states. During nonREM, neurons at the right end of the distribution are decreased, but neurons at the left end of the distribution increase their rates compared to WAKE (arrows).

I am trying to understand the confidence interval for linear regression parameters. At this link  an answer is provided. However, I did not understand in the derivation fully. Do we consider the regression parameters as random variables?   That is what are the random variables in the following regression: $$ y=\beta_1 x+\beta_0 + \epsilon $$ From what I understand is that just the $\epsilon$ is random variable with mean 0 and variance $\sigma^2$. Considering $\beta_1, x, \beta_0$ as constants $y$ also becomes random variable with mean $\beta_1 x+\beta_0$ and variance  $\sigma^2$, from which confidence interval can be calculated.  However,for regression coefficients confidence intervals are also calculated. Can you please clarify the random variables in regression please?  Thanks.


The question reads:  Let $U$ be an open subset in the compact metric space $X$.  If $\{ F_{k} : k \in \mathbb{N} \}$ is a collection of closed subsets of $X$ such that $F_{k+1} \subset F_{k}$, for all $k \in \mathbb{N}$, and $\bigcap_{k=1}^{\infty} F_{k} \subset U$, then show that $F_{n} \subset U$, for some $n \in \mathbb{N}$.  I think I have a proof for this but it seems way too easy considering how much information I am given.  I should add that my definition of compact means that every open covering has a finite subcovering.  $\cap_{k=1}^{\infty} F_{k} \subset U \Rightarrow \forall k \in \mathbb{N}, \exists \ x_{0} \in U$ such that $x_{0} \in F_{k} $  Let $F_{n} = \{x_{0}\}$, $n  \in \mathbb{N}$  $F_{n} \subset U\ \ \ $  Q.E.D.

I am trying to prove the following:  "Let $U$ be an open subset in the compact metric space $X$. If $\{S_k : k\in\mathbb{N}\}$ is a collection of closed subsets of $X$ such that $S_{k+1}\subset S_k$ for all $k\in\mathbb{N}$, and $\bigcap_{k=1}^{\infty} S_k \subset U$, then $S_n\subset U$ for some $n\in\mathbb{N}$."  Here is what I have so far:   Being closed subsets of a compact set, each $S_k$ is compact.   Additionally, I have a theorem which states that an infinite collection of nested compact subsets of $X$ has a nonempty intersection. Therefore, $\bigcap_{k=1}^{\infty} S_k \subset U$ implies that there exists an element $p$ such that $p\in\bigcap_{k=1}^{\infty} S_k \subset U$, i.e., each $S_n$ contains at least one point which is an element of $U$. Being open, there exists some $\epsilon >0$ such that $B(p,\epsilon)\subset U$ (I'm not sure if that is important).  I haven't been able to get any further. This problem is given not long after first being introduced to compact sets, so I don't expect the completion of the proof will require much theory. Any hints or a solution or a point in the right direction would be greatly appreciated. Thank you.   Also, I am sorry if this is a duplicate, I haven't been able to find anything like it. I am also not sure if the (analysis) tag is appropriate, I don't know of a more specific tag which is relevant.


I want to install Oracle Java (JRE) from the .And set it as default.

I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7?


Do I need a transit visa if I'm a Jordanian citizen traveling to Istanbul but have a connection in Athens (athletes) for 3 hours?

I found many related questions on this site but I am still not sure about the rules. How can I decide if I need a visa to transit? Schengen members as of May 2021 are as follows:  Austria Belgium Czech Republic Denmark (excluding Greenland and the Faroe Islands - but an open border with the Schengen Area is maintained) Estonia Finland France (excluding overseas departments and collectivities) Germany Greece Hungary Iceland Italy Latvia Liechtenstein Lithuania Luxembourg Malta Netherlands (excluding Aruba, Curaçao, Sint Maarten and the Caribbean Netherlands) Norway (excluding Svalbard) Poland Portugal Slovakia Slovenia Spain (except Ceuta and Melilla) Sweden Switzerland


I'd like to change the font in the colorbox, i.e. the font for the chapter number, e.g. with \changefont{phv}{b}{n} but unfortunately when I add this command the size of the color box changes, too. Is there a way to prevent this form happening?  \documentclass[             fontsize=12pt,                              a4paper,                                                numbers=noenddot,                              headings=big]                             {scrreprt}  \usepackage[english]{babel} \usepackage[utf8]{inputenc} \newcommand{\changefont}[3]{ \fontfamily{#1} \fontseries{#2} \fontshape{#3} \selectfont}  \usepackage{color} %\usepackage{blindtext}   \usepackage[minionint,mathlf]{MinionPro}  \renewcommand{\sfdefault}{Myriad-LF}  % Define own Chapter style % Pretty chapter pages %------------------------------------------ \usepackage{soul} \usepackage{pdfpages} \usepackage{etoolbox}   \makeatletter \newsavebox{\feline@chapter} \newcommand\feline@chapter@marker[1][4cm]{% \sbox\feline@chapter{% \resizebox{!}{#1}{\fboxsep=0pt% \colorbox{red}{\color{black}\bfseries\sffamily\thechapter}% %--> \changefont{phv}{b}{n} }}% \rotatebox{90}{% \resizebox{% \heightof{\usebox{\feline@chapter}}+\depthof{\usebox{\feline@chapter}}}% {!}{\scshape\so\@chapapp}}\hspace{.4mm}% \raisebox{\depthof{\usebox{\feline@chapter}}}{\usebox{\feline@chapter}}% } \newcommand\feline@chm[1][4cm]{% \sbox\feline@chapter{\feline@chapter@marker[#1]}% \makebox[0pt][l]{% aka \rlap \makebox[1.07cm][r]{\usebox\feline@chapter}% }}     \renewcommand*{\chapterformat}{% \hspace{\leftmargin} \feline@chm[2.5cm] % Height of the colored box \hspace{1.0cm} }  \patchcmd{\@@makechapterhead}   {\size@chapter{#1}}   {\size@chapter{\parbox[b]{\dimexpr\textwidth-2.8cm\relax}{\raggedright#1}}}   {}   {}  \makeatother %------------------------------------------  \begin{document}   \chapter{Lorem ipsum dolor sit amet, consectetuer adipiscing elit} Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum. \end{document}

When trying to typeset a table of contents with KOMAscriptand tocstyle(alpha 0.2d), I finally managed to change the font of the pagenumbers (like the rest of the document to CMSS) with \settocfeature{pagenumberhook}{\changefont{cmss}{m}{n}}, however now the page numbers are aligned at the left and not at the right side!   So how can I change that back to an alignment on the right side of the page numbers like that, but with the sans serif font?   Example:  \documentclass[11pt, a4paper]{scrartcl} \usepackage[ngerman]{babel} \usepackage{blindtext}  \newcommand{\changefont}[3]{ \fontfamily{#1} \fontseries{#2} \fontshape{#3} \selectfont}  \usepackage[]{tocstyle} \usetocstyle{classic} %\settocstylefeature[1]{entryvskip}{10pt} %\settocstylefeature[2]{entryvskip}{3pt} %\settocstylefeature[1]{entryhook}{\bfseries} \settocfeature{pagenumberhook}{\changefont{cmss}{m}{n}}  \begin{document}  \changefont{cmss}{m}{n}  \tableofcontents  \newpage  \blinddocument \blinddocument \blinddocument  \end{document}


I have a windows server that I created a BAT file that basically goes into a network sharefolder and copies a file to a different location. When I run the BAT file manually it works perfectly. When I schedule the file nothing happens. Is there something scheduler doesn't like about sharefolders?

I'm trying to run a BAT script from Task Scheduler in Windows 2008 R2 and it runs for 3 seconds and then stops.  It says it successfully completes but I know it doesn't.  I can run this script from the command line directly, and it runs just fine.  The bat file I'm running actually deletes files older than 7 days using "forfiles" then I'm mapping a network drive, moving the files across the network using robocopy, and then closing the network connection.  I have taken the network and copy options out of the file and it still does the same thing.  Here is how my file looks:  rem This will delete the files from BBLEARN_stats forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_stats" -m *.* -d -17 -c "cmd /c del @file"  rem This will delete the files from BBLEARN_cms_doc forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_cms_doc" -m *.* -d -14 -c "cmd /c del @path"  rem This will delete the files from BBLEARN_admin forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_admin" -m *.* -d -10 -c "cmd /c del @path"  rem This will delete the files from BBLEARN_cms forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN_cms" -m *.* -d -10 -c "cmd /c del @path"  rem This will delete the files from attendance_bb forfiles -p "E:\BB_Maintenance_Data\DB_Backups\attendance_bb" -m *.* -d -10 -c "cmd /c del @path"  rem This will delete the files from BBLearn forfiles -p "E:\BB_Maintenance_Data\DB_Backups\BBLEARN" -m *.* -d -18 -c "cmd /c del @path"  rem This will delete the files from Logs forfiles -p "E:\BB_Maintenance_Data\logs" -m *.* -d -10 -c "cmd /c del @path"  NET USE Z: \\10.20.102.225\coursebackups\BB_DB_Backups /user:cie oly2008  ROBOCOPY E:\BB_Maintenance_Data Z: /e /XO /FFT /PURGE /NP /LOG:BB_DB_Backups.txt  openfiles /disconnect /id *  NET USE Z: /delete /y   This is happening on 2 servers when trying to run commands from inside a BAT file.  The other server is giving an error if (0xFFFFFFFF) but that file is running a CALL C:\dir\dir\file.bat -options and I've used commands like that before in Server 2003.  Here is the file for this file:  call C:\blackboard\apps\content-exchange\bin\batch_ImportExport.bat -f backup_batch_file.txt -l 1 -t archive  NET USE Z: \\10.20.102.225\coursebackups\BB_Course_Backups /user:cie oly2008  ROBOCOPY E:\ Z: /move /e /LOG+:BB_Move_Course_Backups.txt  openfiles /disconnect /id *  NET USE Z: /delete /y


My mother's visa is expiring soon. I am intending to take her to USA on a one month trip but I am fearful, her entry into USA when her visa is expiring that soon may cause problems?  Note that I have done that before, she last entered USA when her visa was expiring in about 20 days. She then got another 5 year multiple visa, but now that visa is expiring soon too.   My concern is, would it be ok for my mother to enter USA just 3 days before her visa expires. She will have a return ticket.

I'm a bit surprised from my US Visa. I plan to go to a conference on 3rd of April. Amazingly though, the visa expiration date is written as April 3rd.  So what does that mean. Can I enter the US on April 3rd? or should I enter one day earlier?


I want to create a random generator of math operations. I'm trying with ASCII codes but what happens is that it just concatenate the operands and operators as a String. Anyone has a suggestion for this?    let a = Math.floor(Math.random()*100) let b =  Math.floor(Math.random()*100) let ascCode = Math.floor(Math.random()* (46 - 42)) + 42 let op = String.fromCharCode(ascCode) let c = a + `${op}` + b;   console.log(c)

I'm writing some JavaScript code to parse user-entered functions (for spreadsheet-like functionality). Having parsed the formula I could convert it into JavaScript and run eval() on it to yield the result.  However, I've always shied away from using eval() if I can avoid it because it's evil (and, rightly or wrongly, I've always thought it is even more evil in JavaScript, because the code to be evaluated might be changed by the user).  So, when it is OK to use it?


Suppose I have two parallel hyperplanes: $\{x \in \mathbb{R}^n|a^Tx=b_1\}$ and $\{x \in \mathbb{R}^n|a^Tx=b_2\}$. How would I find the distance between these two hyperplanes?

I have two parallel hyper planes $$a^Tx=b_1,a^Tx=b_2$$ where $a \in \mathbb{R}^n, x \in \mathbb{R}^n ,b \in \mathbb{R}$ and I want to find the distance between the two. I have read that the distance between the two hyperplanes is also the distance between the two points $x_1$ and $x_2$ where the hyperplane intersects the line through the origin and parallel to the normal vector $\vec a$. These points are given by $$x_1=\frac{b_1}{\|a\|^2_2}a$$ and $$x_2=\frac{b_2}{\|a\|^2_2}a$$ Then the distance is $|x_1-x_2|$ but I don't really understand how we got $x_1$ and $x_2$.


Is there an easy way in python to format a number with commas ie 11222.33 would print as: $11,222.33.  Currently I'm doing something like:  def formatMoney(number):     res = str(number)      # Number of digits before decimal     n = res.find('.')     n = n if (n >= 0) else len(res)     if n < 4:         return res[:n+3]      # Location of first comma     start = n % 3     start = start if (start > 0) else 3      # Break into parts     parts = [res[:start]]     parts += [res[i:i+3] for i in range(start, n - 3, 3)]     # Last part includes 3 digits before decimal and 2 after     parts += [res[n-3:n+3]]      return ",".join(parts)   But I feel like I must be reinventing the wheel here. Have I missed a package in the standard library, or a more obvious way of doing this?

I am looking to format a number like 188518982.18 to £188,518,982.18 using Python.  How can I do this?


I have a custom query where I need a JOIN because I want to COUNT all the posts of a specific category.  So I checked the tables and I found out that table wp_term_relationships contains a reference to the wp_term_taxonomy table. The term_taxonomy_id.  However when I looked into the wp_term_taxonomy table again I found out that term_taxonomy_id and term_id are having the exact same values.  So are they always the same? Can I filter the results by category with only joining wp_term_relationships and using term_taxonomy_id?

The title says it all. At the moment in my custom taxonomies I'm getting the terms using the term id and taxonomy name.  Thought this question would've been asked before but can't find it anywhere! So just thought I'd ask and see if anyone has any answers.


I don't understand why this is happening even though I have classified $verified as a boolean on my bind_param.     $sql = "INSERT INTO users (user_name, email, verified, token, password) VALUES (?, ?, ?, ?, ?)";     $stmt = $conn->prepare($sql);     $stmt->bind_param('ssbss', $username, $email, $verified, $token, $password);

I have a problem binding booleans using mysqli_stmt::bind_param in PHP5. The SQL query is the following: insert into `nvp_notes` (subject,messageid,receivedate,read) values (?,?,?,?)  Where 'read' is a tinyint, either 0 or 1, as I've had issues with bit using mysqli. So the types that I list in bind_param are: $stmt->bind_param('sdsd', ...);  I've also tried 'sdsb' and 'sdss' but nothing seems to work, and I always get the message:  Warning: mysqli_stmt::bind_param(): Number of variables doesn't match number of parameters in prepared statement  When I remove the read field in the statement everything works fine. I've run out of ideas with this one. Surely bind_param works with booleans?


I can make live boot usb drives, but I want to know if/how it is possible to install a full version of Linux onto a 32 GB flash drive that i have. I have been trying to no avail so was wondering if I am even doing it correctly.

If you are hurrying to reply, System → Administration → StartUp Disk Creator -- no, that's not what I'm talking about.   I want to try Ubuntu 11.04's Unity without touching my existing Ubuntu install.  To do this, I need to install the nVidia drivers first (sigh).  To do this, I need changes to persist a reboot.  To do this, I need to really install Ubuntu on a USB key.  How do you do that?    What I tried   I tried to make a USB key from , then boot from it, then choose "Install Ubuntu." The installer refused to install to the installation media itself. I tried, from my installed copy of Ubuntu:  sudo kvm /dev/sdb --cdrom .cache/testdrive/iso/ubuntu_natty-desktop-i386.iso   ...but the installer didn't detect the disk properly.


I am waiting for someone to fly in this week, but have no idea when they are arriving and can't contact them. I looked online and found flight trackers, but they only show flights already "en route" or that have recently arrived. I know both airports, but there's no way I can narrow down when the person would be leaving to know when they are arriving.  I know it's not possible to get flight info using someone's name as that is a breach of privacy, but is there any way to get a list of booked flights and their departures from and to airports to get a better idea of arrival/departure times between travels? Obviously not by name though.  This should help me figure when my friend would be arriving if I knew a list of booked flights so I could figure which ones they'd be getting on based on the time differences from where we are.   Thanks ahead of time!

Is there a search engine to find regular service flights between cities ? Given two cities, airline optional, I'd like to see a list of flight numbers and their departure/arrival times. Unlike regular searches, I'm not interested in prices/purchasing and I'd like to see all flights available even if the earliest departure has already past.    Context: A friend is flying into town today from Calgary, but I don't know when. I happen to know it's Air Canada so I found the routes and flight numbers on their website, but assuming I didn't, where would I find this information (besides asking her for the flight number obviously :) ?


If a light incident on a smooth surface ,then light reflects. Why does the reflected light goes in a direction such that angle of incidence and angle of reflection  to be equal and reflected ray be in the plane of incidence?  In short , why does the law of reflection hold true?  (I mean the plane of incidence here as the plane containing the incident ray and perpendicular to the surface of incidence)

In the Law of Reflection, the angle of incidence is equal to angle of reflection. Why is this true? This is clearly true experimentally, but how does one prove this true mathematically?


Why does this script give error?  #!/bin/bash # This script checks whether  # the current user is root or  # not. if [ $UID -ne 0 ] then     echo "Non-root user." else     echo "Root user." Fi         Output  myuser@kali:~$ ./user.sh ./user.sh: line 7: syntax error near unexpected token `else' ./user.sh: line 7: `else' myuser@kali:~$

With the following shell script, why I am getting errors   syntax error near unexpected token `else'   Shell Script   echo "please enter username" read user_name echo "please enter password" read -s pass echo ${ORACLE_SID} SID=${ORACLE_SID} if ["${ORACLE_SID}" != 'Test'] then sqlplus -s -l $USER_NAME/$PASS@$SID <<EOF copy from scott/tiger@orcl insert EMP using select * from EMP exit EOF else echo "Cannot copy" fi


I was reading  recommending setting the TZ variable in order to avoid unnecessary stat system calls in programs using localtime, and it uses the following syntax:  TZ=:/etc/localtime   The trick described in the document works, but it also works without the colon: TZ=/etc/localtime.  What might be the purpose of the : here?

I have been looking at a few scripts other people wrote (specifically Red Hat), and a lot of their variables are assigned using the following notation VARIABLE1="${VARIABLE1:-some_val}" or some expand other variables VARIABLE2="${VARIABLE2:-`echo $VARIABLE1`}"  What is the point of using this notation instead of just declaring the values directly (e.g., VARIABLE1=some_val)?  Are there benefits to this notation or possible errors that would be prevented?  Does the :- have specific meaning in this context?


echo './2d41d907b7cb558db6f3ca49e992ad8/rendering/02.png' | xargs -I {} cp {} `echo {} | sed s'/\///g' `   This gives me an error saying   cp: './2d41d907b7cb558db6f3ca49e992ad8/rendering/02.png' and './2d41d907b7cb558db6f3ca49e992ad8/rendering/02.png' are the same file   It is as if the sed is not working..  I ultimately want to do something like this   find . -name "*.png" | xargs -I {} cp {} ../`echo {} | sed s'/\///g' `   without using for loop or exec.

The statement below should print afc abc but it prints abc abc instead. I tried many times but every time same result Don't know why this happens could anyone explain and help me?  echo abc|xargs -i{} echo $(echo {}|sed 's/b/f/g') {}


The problem is created several process and start them using process.start() and now i have to move these processes between states.  but the thing is I cant use the Thread.Suspend() i think.   So how can I suspend these processes and then resume them?  private void button1_Click(object sender, EventArgs e) {     var process1 = new Process();     var process2 = new Process();     var process3 = new Process();     process1.StartInfo.FileName = "proc1";     process2.StartInfo.FileName = "proc2";     process3.StartInfo.FileName = "proc3";     process1.Start();     process2.Start();     process3.Start(); }   these 3 processes are C# programs (.exe) that I created to read and write into different files.

How do I suspend a whole process (like the Process Explorer does when I click Suspend) in C#.  I'm starting the Process with Process.Start, and on a certain event, I want to suspend the process to be able to do some investigation on a "snapshot" of it.


I have noticed that the two routes to getting unanswered questions show different counts.    For example on Academia.SE, if I click "Unanswered" on the top banner, it says there are 109 unanswered questions.  If, on the other hand, I click "Questions" and go to the "Unanswered" sub-set, it says there are 118 unanswered questions.  This seems wrong, that there should be two conflicting numbers for what the site leads me to believe should be identical queries.    Further investigation reveals the exact difference, which leads me to believe that we are definitely dealing with a bug.  Because apparently I have nothing better to do with my time, I ran a diff by hand on the two sets of Academia unanswered questions.  The 9 questions in the "Questions --> Unanswered" that are not in "Unanswered --> Votes" break down as follows:   Two are negatively voted questions with no answers, e.g.  Seven are positively voted questions with negatively voted answers, e.g.,    The first might be a desired behavior, but if so it should be documented.  The second is clearly a problem because the most highly voted unanswered question on the site is not listed, just because somebody gave it a crappy answer!

On , I notice that if I use the lower "unanswered" tab (the one in line with "All Questions"), the count is 1,432 questions. If I use the upper "Unanswered" tab (in line with the site title), I get 1,383 "questions with no upvoted or accepted answers".  This changes the options in the lower tab, one of which is "no answers".  Clicking here, I now get 1,083 "questions with no answers". If I run select Id from Posts where PostTypeId=1 and AnswerCount=0;  in the , I get 1158 rows back. Which of these is correct, and why is the first one (1,432) so much higher than the others?  I understand that the numbers may only be updated periodically, but that difference in particular seems much too great for this to be the reason. To clarify:  1,432 is the number of "unanswered questions". 1,383 is the number of "questions with no upvoted or accepted answers". 1,083 is the number of "questions with no answer" 1,158 is the number of questions with no answer in the data explorer.  This is not live data, but that means it should be smaller, not larger, than 1,083.  I promise we did not offset this with answers to the tune of 80 questions this week.  The first three are obviously live because they fluctuate. The difference between the first two is ~50, implying they actually don't refer to the same thing, and the difference between the last two seems too great (and in the wrong direction) to be explained by the a live vs. data explorer source.


Over the years I have slowly developed a  that validates MOST email addresses correctly, assuming they don't use an IP address as the server part.  I use it in several PHP programs, and it works most of the time.  However, from time to time I get contacted by someone that is having trouble with a site that uses it, and I end up having to make some adjustment (most recently I realized that I wasn't allowing 4-character TLDs).  What is the best regular expression you have or have seen for validating emails?  I've seen several solutions that use functions that use several shorter expressions, but I'd rather have one long complex expression in a simple function instead of several short expression in a more complex function.


I have a csv file that contains the following:   "N","n","M" 200,100,50   How can I read it with LaTeX such that \N, \n_trees and \M then returns respectively 200, 100 and 50 ? Or some other internal name, like \myarray{N}, \myarray{n}, \myarray{M} or any other syntax that would allow me to use these values in my text.

I would like to create some name badges using a loop. I have a spreadsheet with names and affiliations that I save in names.csv file as follows  "Name1","Surname1","Affiliation1", "Name2","Surname2","Affiliation2", "Name3","Surname3","Affiliation3"   I can copy the content of names.csv in a string array and use a loop to recover the entries. The following is an example of working code producing the output Surname2:    \documentclass{article} \usepackage{tikz} \usepackage{pgf} \usepackage{array}  \def\names{{"Name1","Surname1","Affiliation1", "Name2","Surname2","Affiliation2", "Name3","Surname3","Affiliation3"}}  \begin{document}  \pgfmathparse{\names[4]}\pgfmathresult  \end{document}   I can use this idea to create hundreds of name badges in a loop. But instead of writing the whole list in the .tex file I would like to call directly my names.csv file. I used the modified code  \documentclass{article} \usepackage{tikz} \usepackage{pgf} \usepackage{array}  \def\names{{\input{names.csv}}}  \begin{document}  \pgfmathparse{\names[4]}\pgfmathresult  \end{document}   which apparently enters in an endless loop. I understood that \input{} works just as copy-pastying, but it doesn't seem the case. Of course I can work in the spreadsheet and then copy paste the names.csv file content, but I would like to understand what happens. Any clues?  PS edit: The suggested solution is enough for my case. But still I would like to be able to define macros with \input'. It seems that\input{}' inside a macro is not expanded immediately. I mean if I have some code in file.tex', that I want to plugin in a new macro,\def\mymacro{\input{file}}' will save \mymacro' as '\input{file}' and will only look what's inside the file when I call the macro in the document. That's why in the previous example\names' is not understood as an array. In the same way  \begin{filecontent*}{newfile.tex} \input{file} \end{filecontent*}   will save the code \input{file}' innewfile.tex', but not the content in `file.tex'. Anyone has any idea how to force input to expand?


I am new to ubuntu server and I cannot find this information online.  When I login via SSH I am in:  root@Ubunutu ~ #   I used mkdir mydir to create a folder, but I cannot find it anywhere (using filezilla).  I also do not understand what ~ means, where am I?  I can use cd .. then it will show root@Ubunutu / #, which I understand. From here I can use ls to see folders.  To summarize:  What does ~ mean, which location is it?  Where is my folder?

I'm new to Linux and Ubuntu. People keep using ~/filename in their answers to my questions. What does ~/ mean?


Usually I just use TikZ for plots but was hoping Pgfplots would simplify life (axis, labels, etc...) but I can not find what is the right syntax to pass parameters to the function. Here is the MWE:  \documentclass[12pt]{article} \usepackage{tikz} \usepackage{pgfplots} \begin{document}    \pgfplotsset{compat=1.10}    \begin{tikzpicture}       \begin{axis}[        title=Test,        xlabel=$x$,        ylabel=$f$,        ]           \foreach \y in {0,1,2,3}              {\addplot[              red,              domain=0:1,              samples=4,               ]               {x+\y};              }      \end{axis}   \end{tikzpicture} \end{document}

How can I say sum multiple columns of a table using y expr while also using \foreach  I was hoping something like this would work but apparently it requires some sort of expression evaluation I can't get to work:  \documentclass{article} \usepackage{pgfplots} \pgfplotsset{compat=1.9}  \begin{document} \begin{tikzpicture} \begin{axis}     \foreach \y in {1,3,5,7}         \addplot table[x=Foo, y expr={\thisrowno{\y} + \thisrowno{\y+1}}] {data.csv}; \end{axis} \end{tikzpicture} \end{document}   The data:  Foo John John_a Paul Paul_a George George_a Ringo Ringo_a 1 0.0 37.0 0.00 9.00 0.0 4.0 0.0 12.80 2 16.0 5.0 4.0 1.0 0.6 2.80 0.0 12.80 4 8.0 5.0 2.0 1.0 0.3 2.8 0.0 12.80 8 4.0 5.0 1.0 1.0 0.4 2.8 0.0 12.80 16 2.0 5.0 1.2 1.0 0.4 2.8 0.0 12.80 32 1.0 5.0 1.3 1.0 0.5 2.8 0.0 12.80


I'm writing documentation for a computer script I wrote. I'm wondering which I should say:   The script should run at the 1st of every month.  The script should run on the 1st of every month.

I’m often confused when I speak about times and dates. What is the rule for using on, in, and at in the following sentences?   I will do it ___ Tuesday. We married ___ March. He returned ___ the same day. Every day ___ the same time, I walk the dog.


I've always used them interchangeably according to my mood.  But are there any rare cases where they aren't interchangeable or have a slightly different meaning?

As per google meaning I understood like,  Anyone - any person or any people  Anybody - anyone  It seems both are relevant. I am trying to understand the proper place for using these words. Please help me.  Thanks in Advance.


I have Battlefield 3 and went to browse games on my Xbox 360 and clicked on it and it gave me the option of install and did not know what that meant. Does that mean I can put the game on my hard drive and forget about the disk?

Are there any benefits/downsides to installing an Xbox 360 game to my hard drive before playing it?


I'm using C# .NET Framework console application. I'm creating my own interface but I am getting a stack overflow exception. Can someone explain to me why it is happening? Here is my code:  namespace Interfaces {     interface IWorker     {         string name { get; set; }         string surname { get; set; }         uint age { get; set; }     }     class TeamLeader : IWorker     {         public string name { get => name; set => name = value; }          public string surname { get => surname; set => surname = value; }          public uint age { get => age; set => age = value; }         public override string ToString()         {              return $"Name: {name} Surname: {surname} Age: {age}";         }     }      class Program     {         static void Main(string[] args)         {             TeamLeader tm = new TeamLeader();             tm.name = "John";             tm.surname = "Wick";             tm.age = 22;             Console.WriteLine( tm.ToString() );          }     } }    I'm new to this short ways to write get and set stuff. My background is C++, it's my first time using these syntax. In my opinion they are the ones that making the error.

I know java and would normally put in getter/setter methods. I am interested in doing it in C# with the following code, but it throws a StackOverflow exception. What am I doing wrong?  Calling Code  c.firstName = "a";   Property Code    public String firstName; {     get     {         return firstName;     }     set     {         firstName = value;     } }


In Windows 10 the Network panel shows mobile devices I never connected to either my network or my computer. See image (just an example, could be Sony, LG, ...). They change from time to time.  My computer has only wired Ethernet and no wireless capabilities (BT, WiFi).  The WiFi home network is based on a OpenWRT install plus a Netgear extender they are protected with WPA2-PSK and firewall to the outside (very few ports open). No additional devices are listed as connected.  The modem by the provider offers a private Wired+WiFi for me plus a WiFi public for all his other customers. My OpenWRT is connected to the wired private network and not reachable by the other customers.  Where are they coming from?

Yesterday, Network listing on Windows 10 file explorer showed me one external phone. Thus, I changed my router WiFi password just in case.  Nevertheless, I checked this today and I found 5 new phones appearing randomly for a few seconds.  I've found a similar question , but no solution.  Here is an screenshot:    If I double click that I see: Model: LG-E465g, MAC: 48:59:29:b4:8d:87.  This happens on two PCs that were recently upgraded to Windows 10:   one is connected through Ethernet (desktop PC) the other through WiFi (and I disabled Bluetooth)   I hadn't seen this issue before. I guess these are phones trying to connect to my network, I just don't understand why Windows shows them if they are not connected to my router.  Update: If I hide my SSID this issue stops. As soon as my router SSID is visible, phones start appearing again.  Update 2: I tried MAC filtering but is useless.


I am new to Java and have just beginning doing some exercises a friend sent me. The exercise in question asks us to create a class Term for the terms of a polynomial, and another the class Polynomial itself, where the polynomial is represented as a fixed size array and the values of its fields are provided. I have written the following code:  class Term {     int coeff;     int exponent; }  public class Polynomial {      static int size=5;       Term[] poly;      public Polynomial()     {         poly = new Term[size];          for(int i=0;i<size;i++)         {             poly[i].coeff=0;             poly[i].exponent=0;         }     }      public static void main(String args[]) throws Exception     {         Polynomial p = new Polynomial();     } }   And I keep getting the following exception:  Exception in thread "main" java.lang.NullPointerException at prac.polynomial.<init>(polynomial.java:25) at prac.polynomial.main(polynomial.java:34)   Please help me with what I am doing wrong here.

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


In an euclidean vector space $E$ how can I prove that a projection $p$ is orthogonal if and only if $$||p(x)||\leq ||x||\quad \forall x\in E$$  I can prove that if $p$ is an orthogonal projection then we have the inequality but I'm stuck in the other implication. Any suggestion is welcome.

Seems like I , I think I am missing something important.     Let $V$ be an $n$ dimensional inner product space ($n \geq 1$), and $T\colon\mathbf{V}\to\mathbf{V}$ be a linear transformation such that:         $T^2 = T$   $||T(a)|| \leq ||a||$ for every vector $a$ in $\mathbf{V}$;         Prove that a subspace $U \subseteq V$ exist, such that $T$ is the orthogonal projection on $U$.   Now, I know these things:   The fact hat $T^2 = T$ guarantees that $T$ is indeed a projection, so I need to prove that T is an orthogonal projection (I guess this is where $||T(a)|| \leq ||a||$ kicks in). To do this I can prove that:   For every $v$ in $ImT^{\perp}$, $T(v) = 0$ Alternatively, I can prove that for every $v$ in $ImT$ and $u$ in $KerT$, $(v,u)=0$. $T$ is  (according to Wikipedia) The matrix $A = [T]_{E}$ when $E$ is an orthonormal basis, is hermitian (this is equivalent to the previous point). What else?    I've been thinking about it for quite some time now, and I'm pretty sure there is something big I'm missing, again. I just don't know how to use the data to prove any of these things.  Thanks!


I have to prove the following part, but I can not. Please help me.  Let $n$ be a positive integer and $p=4n+1$, a prime number. Show that:  $((p-1)/2)!$ is a root of $x^2+1=0$ equation over $\mathbb{Z}_p$.

$$\text{ If } p \neq 2 \text{ is a prime, we know that: }$$ $$\left(\left(\frac{p-1}{2}\right)!\right)^2 \equiv (-1)^{\frac{p+1}{2}} \pmod p$$  According to this,prove that: $$p \equiv 1 \pmod 4 \Rightarrow x^2+1\equiv 0 \pmod p \text{ has a solution}$$ $$\text{Which is the solution?}$$ Solve: $\displaystyle{ x^2+1 \equiv 0 \pmod{29} \text{ , } x^2+1 \equiv 0 \pmod{37}}$  Inversely,prove that $x^2+1 \equiv 0 \pmod p \text{ has a solution } \Rightarrow p \equiv 1 \pmod 4$  I have thought the following:   $$\left(\left(\frac{p-1}{2}\right)!\right)^2-(-1)^{\frac{p+1}{2}} \equiv 0 \pmod p \Rightarrow \left(\left(\frac{p-1}{2}\right)!\right)^2+(-1)^{\frac{p+3}{2}} \equiv 0 \pmod p $$   As $p=4k+1$, $(-1)^{\frac{p+3}{2}}=(-1)^{\frac{4k+4}{2}}=1$  So,we have: $$\left(\left(\frac{p-1}{2}\right)!\right)^2+1 \equiv 0 \pmod p$$  So,we conclude that $x^2+1 \equiv 0 \pmod p \text{ has a solution , this one: } (\frac{p-1}{2})!$  Is it right or have I done something wrong?   So,are the solutions of $x^2+1 \equiv 0 \pmod{29} \text{ and } x^2+1 \equiv 0 \pmod{37}$,these one: $\displaystyle{(14)! \text{ and } (18)! \text{ respectively}}$ ? Are these the only solutions?? How can I show the inverse?


In a strange twist of events, I got this error that said that my edits couldn't be submitted because I needed the moderator tag . I'm not a moderator, so I just decided to humor the system.  And now there's this random old FAQ that's featured on SFF meta as a result (). It's even showing up in the sidebar:    Here is a screenshot of , which don't show me adding the tag, but I did:        I'm not sure why this happened, but I will note that it's a community wiki  question and the previous revisions were all done by an ex-moderator whose account is now deleted.  I can't add any red tags here on MSE though.

Look at  edit. I didn't really expect that I would able to suggest adding  tag, but I could!  How is it possible? (seems that usual users can add mod-only tags without moderator help!)  Edit  Oded removed  back :-(


How to rename the last number-string it finds with a zero-padded version and leave the rest of the filename alone?  AAA 2000-01-03 bbb 2001-03-04 page_1.pdf   To:  AAA 2000-01-03 bbb 2001-03-04 page_0001.pdf   See:     (on Stack Overflow)

I have a situation where I have the following:  file01.ext . . . file99.ext file100.ext . . .   And I want to (using rename ) insert the '0' for the files 01-99 (so that they become 000-099) but not modify files larger than 100. Which expression should I use and what is a good source on learning regular expressions such as these?   On Windows I would have used Total Commander's multi rename function which has a very simple renaming syntax. Are there some good alternatives for that tool (multi-rename) for Ubuntu?