This is probably a trivial question however i cannot find the correct information online.   When simplifying mappings from $\mathbb{R}$ to $\mathbb{R}$ such as:  $$\frac{x(x-1)}{(x-1)}$$  Why is it okay to simplify this to simply just $x$? if $x=1$ do we not have the singularity $$\frac{0(1)}{0}$$ Thank you


I'm trying to get the text values of all of my div elements.  My expected output is:  Menu 1 Abc  Def Menu 2 Ghi  Jkl Menu 3 Mno  Pqr   But I get  Menu 1 Abc  Def Ghi  Jkl Mno  Pqr Menu 2 Abc  Def ...   HTML

     <input type="text" value="Menu 1">
     Abc
     Def

     <input type="text" value="Menu 2">
     Ghi
     Jkl
   ...
   JS  $("#output div").each(function() {   console.log($(this).find("input").val());   $("a").each(function() {     console.log($(this).text() + "\n");   }); });   .


Show that an integral domain with every strictly decreasing chain of ideals $I_1 \supset I_2\supset \cdots $ finite in length is a field.

Show that an integral domain with the property that every strictly decreasing chain of ideals $I_1 \supset I_2\supset \cdots $ must be finite in length is a field.  Attempt: We need to show that every element in the integral domain $D$ is invertible. Let us suppose $\exists~ a \in D$ such that $a$ is not invertible.  Clearly, $ \langle a \rangle \supset \langle a^2 \rangle \supset\cdots \supset\langle a^n \rangle $ where $\langle a^{n } \rangle $ is the last ideal in the chain.  Now,   $\langle a^{n+1} \rangle $ should be equal to one of the  $\langle a^i \rangle ;~ 1 \leq i \leq n$  But $\langle a^{n+1} \rangle $ also satisfies $\langle a^n \rangle \supseteq \langle a^{n+1} \rangle $ and $\langle a^i \rangle \supset\langle a^n \rangle $  $\implies \langle a^j \rangle =\langle a^n \rangle ~~\forall~~j \geq n$  Now, since $a$ is not a unit, $\langle a  \rangle $ does not contain the unity and hence, $\langle a  \rangle \neq D$  How do I move forward and have I interpreted the problem correctly?  Thank you for your help..


How do saving throws for half combine with damage resistance?

Let's say a player has to make a saving throw or take 20 cold damage. If they succeed on the save, they take half damage (10).  Resistance also halves damage. What happens if they have cold resistance and succeed on said saving throw? Do they take half damage (10) or quarter damage (5)?


Why do not we ask negative questions without a contraction on the not after the verb?

I have found multiple questions touching on this but not a single one that has a comprehensive answer. The information is all there but in little bits.     etc.   Exactly why is "Do not you sleep?" ungrammatical (except in poetry/with artistic license)? I understand that not can't contract after you: "Do you not sleep?" because not can only contract after a verb, and that it always does after do: "Don't you sleep?" but why does it (why must it) contract if it's placed after the verb in a question?   Don't you sleep? (common form) Do not you sleep? (ungrammatical) Do you not sleep? (less common form)


How can I install Ubuntu on a new computer without any OS and without a cd drive?

I bought a new computer and I want to install Ubuntu on it. The computer doesn't have a CD drive or OS. I want Ubuntu to be the only OS on the computer. So how can I install Ubuntu on a brand new computer? Until now I was using a dual boot and I installed Ubuntu with a flash drive.


Use mathematical induction to prove the following $n! < n^n$

So I'm reviewing some problems but I can't seem to understand the part below, doesn't really have to do with induction but just so you guys understand whats going on.  Use mathematical induction to prove the following statement is true for integers $n > 1:$  $n! < n^n$  Solution  Base Case: $n = 2$  LHS: $2! = 2$  RHS: $2^2 = 4$  Because the LHS is less than the RHS the base case is shown to be true.  Inductive Hypothesis: Assume for an arbitrary positive integer $n = k$ s.t $k! < k^k$  Inductive Step: Prove for $n = k+1$ that $(k+1)! < (k+1)^{k+1}$  (starting with the IH)  $k! < k^k$  $(k+1)k! < (k+1)k^k$  $(k+1)! < (k+1)k^k$ <--  $(k+1)! < (k+1)(k+1)^k$ <--  $(k+1)! < (k+1)^{k+1}$  (starting with k+1)  (k+1)! = (k+1)k!  $(k+1)! < (k+1)k^k$ by the IH  $(k+1)! < (k+1)(k+1)^k$  $(k+1)! < (k+1)^{k+1}$  Now what I'm lost on is how did he go from $(k+1)k^k$ to $(k+1)(k+1)^k$ ?


Private beta markdown shows ** instead of bold

Private beta  shows **private beta** instead of making the text bold. Based on this question the  on the login page (however 4 years ago it was shown in italics).


The easiest way to write TeX in MS Word?

Is there some way I can use MS Word with the TeX formulas? On  I've learned the syntax $\frac{\partial u}{\partial x}$ etc.. But I do not know how to create a LaTeX document. Is there some way I can use this syntax in MS Word?


Elevate a running program to administrator (Windows 7)

Sometimes you may open a program that you want to run as an administrator, but you may already have opened it not as an administrator. Is it possible to elevate the privileges of an already running program in Windows 7 or do I have to close and restart as admin?


When a spontaneous radioactive reaction happens, there is an emission of gamma rays (in most cases) What causes this emission?


How does the derivative with respect to the complex conjugate even make sense?

I came across this the other day: $$ \frac{\partial f}{\partial \bar{z}} = \frac12\left(\frac{\partial f}{\partial x}+i\frac{\partial f}{\partial y}\right) $$ I decided to attempt to work it out myself to better understand it. I know $2x = z + \bar{z}$, and $2iy = z - \bar{z}$, and using the total derivative we have $$ \frac{\partial f}{\partial \bar{z}} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial \bar{z}} + \frac{\partial f}{\partial y}\frac{\partial y}{\partial \bar{z}} $$ and this is about where I got stuck. How exactly am I supposed to calculate $\frac{\partial x}{\partial \bar{z}}$? My confusion doesn't lie in the notation, but in the mechanics of the very thing I'm being asked to differentiate. Look at $x$: $$ x(\bar{z}) = \frac{\bar{z} + z}{2} = \frac{\bar{z}+\bar{\bar{z}}}{2} $$ if we label $Z = \bar{z}$, then $\frac{\partial x}{\partial \bar{z}} = \frac{\partial x}{\partial Z}$, and $x(Z) = \frac{Z+\bar{Z}}2$. However, as far as I can tell, $\frac{Z+\bar{Z}}{2}$ isn't even complex differentiable, because $\bar{Z}$ isn't complex differentiable with respect to $Z$. $x(Z)$ doesn't satisfy the CR equations: $$ x(X+iY) = X + i0 = u(X, Y) + iv(X, Y) \\ u_X = 1 \neq 0 = v_Y \\ v_X = 0 \neq -1 = -u_Y $$  so how could I possibly take the complex derivative of it? That doesn't make any sense.  What exactly am I missing here? Is the derivative $\frac{\partial x}{\partial \bar{z}}$ a different kind of derivative? Are we not supposed to do the complex derivative but instead something else?


Why is the genus 2 canonical map of degree 2 ?

Let $C$ be a smooth genus 2 curve, with canonical divisor W. From Riemann-Roch's theorem, we know that $l(K)=2$ so there exist two functions $g_1,g_2$ that span $L(W)$.  Since $g_1$and $g_2$ are linearly independent, the map $\varphi:C⟶\mathbb P^1$ defined by $[g1(P):g2(P)]$ is a non-constant morphism of smooth curves, so it is surjective.  We also know that $\deg \varphi\geq 2$, else $C$ would be birrational to $\mathbb P^1$, contradicting the assumption on its genus.  I want to show with elementary arguments that $\deg\varphi=2$. Using that $\deg\varphi$ is either the degree of the zero part of a $g_i$ or its pole part, I tried to write $W$ as $D_0+Q_1+Q_2$, with $D_0\in\mbox{Pic}^0(C)$ and the $Q_i$ possibly equal to obtain a contradiction with the numbers of poles/zeros that $g_1$ or $g_2$ should have, but it seems it does not work.  If $D_0=0$, then as $\mbox{div}(g_i)+K=\mbox{div}(g_i)+Q_1+Q_2≥0$ and that $g_i$ has poles at $Q_1$ and $Q_2$, then this means the $g_i$ has 2 zeroes and poles and I get the result. But I fail to see why $D_0$ would be 0 be zero.  So my questions are: is my reasoning correct ? Why would $D_0$ be zero ? For my curiosity also, is there a more elegant way using elementary arguments ?  I am not familiar with sheaves and linear bundles, etc, and sadly I cannot find any proof of this well-known result with the most elementary language. Also, I do not want to consider a possible equation for $C$.  Thanks in advance !


I have this cron:  00 0 * * * root /home/bitnami/backup.sh > /home/bitnami/backup.log   The Backup script contains:  #!/bin/bash  cd /tmp file=$(date +%Y-%m-%d).sql mysqldump \   --host localhost \   --port 3306 \   -u user \   --password="123" \   bitnami > ${file} if [ "${?}" -eq 0 ]; then   gzip ${file}   aws --region us-west-2 s3 cp ${file}.gz s3://backups/fc-wiki/   rm ${file}.gz else   echo "Error backing up mysql"   exit 255 fi   Which works fine when executing it by hand (sudo .\backup.sh)  When the crontab runs it only logs the following error in backup.log: Error backing up mysql  Is there a problem how I'm setting up the cron tab with the piping to log perhaps? Even without the piping it doesn't work.


Finding the PGF of $Z$ using conditional expectation.

I am working on this problem, where I am required to write down the pgf of $X$, as well as the pgf of $Y$ given $X=j$, and then using conditional expectation find the pgf of $Z$.  So far, I have \begin{align*} G_{X}(z)&=(pz+(1-p))^{n}\\ G_{Y|X=j}(z)&=(qz+(1-q))^{n+j} \end{align*}  I'm new to generating functions and am having difficulty finding the pgf of $Z$. I thought I had a breakthrough when I wrote down \begin{align*} G_{Z}(z)&=\mathbb{E}\left(z^{Z}\right)\\ &=\mathbb{E}\left(z^{n+j-Y}\right)\\ &=\frac{z^{n+j}}{G_{Y}(z)} \end{align*}  But I'm quite sure this isn't correct as I am then required to deduce that $Z$ has the same distribution as the sum of two independent Binomial random variables. I don't know how to apply conditional expectation here. I'm sure this is a very simple problem, and I just want to understand it. Thanks for your patience and time.


How to create a node with submissions of a webform?

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 just installed Android 5.0 on my Nexus 7 and now it is 5x slower but it doesn't connect to WiFi. I don`t like this update and I wish I hadn't done it. Now I can't even use my tablet. Is there anything to do?


what's the key sequence when enumerating an object in javascript?

I already know . My question is what's the key sequence while enumerating.Is it by A-Z or time ordered?  code  var a = {            "a":""          ,"b":""          ,"c":""}; for (var k in a) {     console.log(k); }    output  a,b,c   code   var a = {            "b":""          ,"a":""          ,"c":""}; for (var k in a) {     console.log(k); }    output  b,a,c   code   var a = {            "b":""          ,"a":""          ,"c":""}; a.d = ""; for (var k in a) {     console.log(k); }    output  b,a,c,d


Is it possible to delete files in a .zip file without unzipping it Python?

I have a .zip file with around 26k image files. I have a list of files that I want to keep in the .zip I was wondering if it was possible for me to remove files within that .zip that aren't in my file list without unzipping the actual folder (because it would take up way too much space on my computer) using Python 3. I couldn't find anything on this and was wondering if anyone knows a way I can do this Thank you!


How can we go to chat profile of user from main site profile?

When I click on a user's name or gravatar in the chat interface, I get a popup with a number of options like:   user profile user profile on (chat user's parent site)   Like from which we can go to user's profile on main site. So I was thinking is there any link given on main site for chat user's profile. I have searched it but didn't got any.  If this option is present currently how can I do?


I have gone through tonnes of online resources (other stackexchange postings as well) and textbooks but still have not been able to grasp the concept. Most of them have vague explanations like "if you want a mean fixed, only n-1 observations can vary and not n". Does anyone have a better explanation to it? For standard deviation alone, the n-1 is also explained as a Bessel's correction which does make sense. But what about degrees of freedom in general or in other statistics?


Get an error when deploying a webpage because my java code is faulty

I wrote an array but it crashes once I try to access a certain webpage. I'm also using a tomcat server and Servlets. I backtracked it and found it at line 114 which is a piece of Java code.   I'm trying to print certain info that people give when they register in my webapp as an overview on another webpage which it does when I press the register button. But what a navigate manually to it crashes.  Can someone help me figure out what I did wrong in that piece of code? Thanks in advance.  114:ArrayList<Registratie> leden = (ArrayList) request.getAttribute("leden");     String result="";     for(Registratie Registratie:leden){         result = result +  "
 " + Registratie.getNaam() +"	 \n" + "" + Registratie.getAchternaam() + "	 \n" + ""                 + Registratie.getLoginnaam() + "	 \n" + "" + Registratie.getEmail() + "	 \n" + "" + Registratie.getNiveau()+"	" +"
" + "\n";     }   photo of register process:   photo of database:   When I click on "leden overzicht" which should show an overview of all those that registered:


$|\sin(nx)| ≤ n|\sin x|$ Proof by induction

Using induction, prove $|\sin(nx)| \le n|\sin x|$ for $n\in \mathbb{N}$.    How I can show that with induction? Normally , When I make a induction I know for $n$, and I prove for $n+1$. But I can't write $n+1$ in this question. If I write $n+1$, formula change like this: $|\sin((n+1)x)| \le (n+1)|\sin x|$ for $n+1$, This new formula doesn't include $n$.   What should I do in such cases?


Is there a way to configure (with or without an app) an Android phone to forward calls from only certain numbers/callers to another number?  I'm not interested in call screening; I'm looking for a way for this to happen silently in the background.


What the difference is here? Are you seeing ? VS Do you see?

Are you seening family members arriving at the hospital to find some of the miners? ( exact quote from BBC presenter asking someone over the phone )  Do you see .......  Difference in meaning not grammar.


QGIS CRS does not have correct coordinates

I'm using QGIS to extract centroid coordinates in a multi-shape object from a project I was given. I want the coordinates to be regular latitude an longitude, but they're coming out huge (see below).     These locations are in New York City, so x and y should be somewhere around 74 longitude and 41 latitude. I tried to use this:     where I set the CRS layer for my shapefile and centroids to be EPSG:3628 but it doesn't appear to have worked. I have the same results using the CRS found originally in the project folder. I think these are not the problem as adding an OpenStreetMap layer using either CRS displays New York City.


Is it acceptable to drop the comma in "Thanks, John"?

I grew up learning that the comma must be placed there, but it seems like an unnecessary interruption in a phrase that isn't ever spoken that way.


How to check file types of uploaded files in PHP?

On the PHP website, the only real checking they suggest is using is_uploaded_file() or move_uploaded_file(), . Of course you usually don't want user's uploading any type of file, for a variety of reasons.  Because of this, I have often used some "strict" mime type checking. Of course this is very flawed because often mime types are wrong and users can't upload their file. It is also very easy to fake and/or change. And along with all of that, each browser and OS deals with them differently.  Another method is to check the extension, which of course is even easier to change than mime type.  If you only want images, using something like getimagesize() will work.  What about other types of files? PDFs, Word documents or Excel files? Or even text only files?  Edit: If you don't have  or  and system("file -bi $uploadedfile") gives you the wrong file type, what other options are there?


Best way to implement friends list into a database? MySQL

So my project has a "friends list" and in the MySQL database I have created a table:  nameA  nameB  Primary Key (nameA, nameB)  This will lead to a lot of entries, but to ensure that my database is normalised I'm not sure how else to achieve this?  My project also uses Redis.. I could store them there.   When a person joins the server, I would then have to search for all of the entries to see if their name is nameA or nameB, and then put those two names together as friends, this may also be inefficient.  Cheers.


Using "and" in a list with an element already containing "and"

I'm struggling with the following sentence in an APA format paper. I don't like the double usage of and here, but 'supply and demand' is one thing in this context. Is this correct or do I need to make a change?     Riggs (2011) argues that tuition prices can be explained by the basic principles of supply and demand and perceived quality.   To clarify: My intent is for the term "basic principles" to apply to both "supply and demand" (as a single principle) and "perceived quality" as the other. As this sentence is paraphrasing Riggs, this must be the meaning conveyed whether or not we agree with his over-simplification of S&D.


For any positive integer $n$, prove the following inequality.

Prove that for any positive integer n, the following inequality is true. $$\left(1+ \frac{1}{n}\right)^n < \left(1+\frac{1}{n+1}\right)^{n+1}$$  Attempt  Not a good attempt but this is my thinking  It will not be a problem when checking whether this is true for smaller integers. Only for larger integers, it will be difficult to prove. So, I took the equation LHS-RHS < $0$. I took limit for n tending to infinity and then applied L'Hospital Rule( though the equation was difficult to handle) & therefore could not do anything further.         Edit: I, now, want to know about @Rebellos' last equation and his answer (though at first my intention was to know about the question). Please see the comments of @Rebellos ' answer.  Adding graph for @Rebellos 's last equation


Which is correct to say... are you not tired of being in pain because of football or are you not tired from being in pain because of football?


How to install moonlight in Ubuntu 12.0.4?

I tried to open this  in Ubuntu 12.0.4. but it suggested to install silverlight.   I searched in Google for this, finally I got Ubuntu not supported to SilverLight, so we need to install MoonLight.  For this, I run the following command:  sudo apt-get install mono-complete   after installing, I refresh the above page. Still it's not working.  How can I fix this?


Compact subset of a compact topological space

Let $X$ be a compact topological space and $K$ be a compact subset of $X$. I want to prove that $K$ is a closed subset of $X$, or not. I tried to show that the complement of $K$ in $X$, is open. But, I am not able prove that. I also tried to show that $K$ contains all its limit points. If $K$ is not closed in $X$, please give an example.


$az+b\overline{z}+c=0$ represents a line

When does $az+b\overline{z}+c=0$ represent a line?   All of $a,b,c$ are complex numbers.  I know that a line in the complex plane is usually represented by $z=a+bt$, where the parameter $t$ runs through all real values.   So suppose we're given the equation $az+b\overline{z}+c=0$. If $z$ represents a line $d+et$, we must have $a(d+et)+b(\overline{d}+\overline{e}t)+c=0$. Since the equation holds for all real values $t$, it must be that $ae+b\overline{e}=0$, and as a result $ad+b\overline{d}+c=0$. How can we get to a condition involving only $a,b,c$ from here?


So, I was playing a survival game on easy.at night, there were hostile mobs, but, when the sun had fully rose, all of the monsters were gone, even the spiders, creepers and endermen. this also happened in a creative game.      I would really like an answer, please leave one if you get the chance.  Thanks!


Ignoring me the whole day or for the whole day

Is “ignoring me the whole day” grammatically correct?


Application names in launcher are truncated, can it be tweaked?

After clicking on the bottom left 9 dots icon, aka Show Applications, there is a launcher. I can't find its actual name.  The text under the icons is truncated to the width of the icon, truncating almost every application name, and it's making the launcher very uncomfortable to use.  What can I do to see the application names entirely ?


I am trying to add in a .bib file created by BibDesk to my report. I have saved the .bib file in a different folder. However, it will not import in the typeset.  I tried to follow the Overleaf  but when that didn't work, I tried using natbib.  In the preamble, I have included:  \usepackage{cite} \usepackage{natbib} \addbibresource{/Users/Jenny/Desktop/EC/Components/References.bib}   In the body, I have added in:  \bibliography{/Users/Jenny/Desktop/EC/Components/References} \printbibliography     But when I typeset it, my TOC does not come up with the section and the bibliography does not print after the conclusion and before the Appendices.  I would like to also know how to style the bibliography in the Harvard way.  Many thanks in advance for your suggestions.  Jenny


StackOverflow Reputation Stopped Incrementing

A few days back I had 997 on StackOverflow, that same day it dropped to something 978 without any negative feedback.  It stayed at that level the rest of the day although I was getting +1's.  Then that evening it suddenly jumped to 1084.  And not it's stuck again at 1084.  What can be going on here?


How can I make a Click-once deployed app run at startup?

How can I make a Click-once deployed app run a startup?  The best option I found by searching was to set the Publisher on the app to Startup, so the Start menu shortcut would be placed in the Startup folder, but that seems like a huge hack and I would like there to be a Start menu icon people can find.  What options do I have?


Escaping single quotes and unicode symbols in php

I am using php to develop a news app where the admin will feed in the news item with its descriptions and finally get displayed to users. I am using mysql database.  Everything seems to be working fine but I am not able to escape single quotes as well as display certain currency symbols in my output text. I am using UTF-8 charset. I have used str_replace function but to no avail. I have also tried htmlentities($mystring, ENT_QUOTES | ENT_IGNORE, ‘UTF-8) and this actually ignored (removed) the single quotes and symbols instead of escaping and displaying them as they are. I am also using UTF-8_general_ci in the table column of mysql.  This is my code for retrieving the data :  try{     $pdo = new PDO("mysql:host=$hostname;dbname=$dbname",     $username,$password);     $pdo->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);     $pdo->setAttribute(PDO::ATTR_EMULATE_PREPARES,   false);     $stmt = $pdo->prepare("SELECT * FROM feed WHERE news_id = ?");     $stmt->bindParam(1,$myval);     $stmt->execute();     while($myrow = $stmt->fetch()){         $newarray[] = $myrow;     }     $mystring = $newarray[0]['body'];     $mystring = str_replace("'","/'",$mystring);     echo $mystring; } catch(PDOException $e){     echo 'Failed to retriev database item ' . $e->getMessage(); }   Below is an example output:     International Monetary Fund�s (IMF�s) Extended Credit Facility (ECF) programme, the raising of the $3-billion Eurobond at a lower coupon rate, and the positive Fitch rating of Ghana should be enough to demonstrate that, the economy is on track to impact the strength of the Ghana cedi. �In the last couple of weeks, the Bank of Ghana for instance, released a large chunk of dollars to players in the banking industry to meet our requirements. That was unprecedented and we feel that should the speculations stop, the Ghana cedi will stabilise the way we want it�,


Migrated questions don't show a "last activity" status in the questions list

This is almost certainly not important enough to unleash the programmers immediately, but I thought I would add it for posterity, and because someone was kind enough to  on a site meta.  When a question is migrated inside the network, it appears that the question shows up on the main page without detailing what the activity is    The question indicated above with a delightful freehand red ellipsoid should have probably said     migrated 26 minutes ago   in order to follow the pattern of other actions.


Why wasn't Snape punished for attempting to save Harry's life?

In the first book of Harry Potter, it is revealed that Snape was not trying to curse Harry's broom; he was trying to save him. But we also learn that Professor Quirrell was behind it the whole time, with Voldemort living behind his turban. Voldemort probably knew everything happening around Quirrell, so why didn't he punish Snape for betraying him and helping Harry?


Got any tips or tricks for Terminal in Mac OS X?

One tip or trick per answer.  My favorite is   open .   Opens the folder you're currently browsing in Finder. You can also pass URLs, images, documents or else to open.  If you specify a program name with -a you can pass the URL, image, document or folder to that program instead, e.g. open -a Preview image.png, overriding the default program set for the filetype.  Please don't post duplicates. Search in the question like this: inquestion:this ls -l  Mac OS X specific answers only.


Could not load file or assembly 'System.Web.Mvc, Version=4.0.0.1' or one of its dependencies. The system cannot find the file specified

I upgraded my solution from MVC 3 to MVC 4 due to required code (DayPilot MVC - Calendar Controls).  Everything works on my laptop, where I developed the project, now I need to push this to UAT, and on the server, I get this following error:    I tried to install the MVC version via nuget, and update everything, and still nothing.  Any ideas where to look or what to change, will be highly appreciated.


Normality assumption in linear regression

As an assumption of linear regression, the normality of the distribution of the error is sometimes wrongly "extended" or interpreted as the need for normality of the y or x.  Is it possible to construct a scenario/dataset that where the X and Y are non-normal but the error term is and therefore the obtained linear regression estimates are valid?


There seems to be a split between those who say the backer board should go over the tub flange and those who say it should go above. Those who say over say so for drainage. Those who say above seem to suggest because of the surrounding drywall plane.   The tile expert forums go with it over the flange; seemingly the general contractor forums suggest above. Most forums suggests a vapor barrier even with Hardi Backer.  How does a person make the right decision with so many conflicting viewpoints? I know in other posts, the two options are covered; however, little is discussed with regard to the problem of going over the tub flange causing the drywall plane to be uneven. Shimming for example over 1/4" would seem to be a problem blending the CPU board with the drywall. How is that done successfully?


Can we use  return statement in finally block. Can this cause any problem?


Can anyone explain the need for atomicity and volatile variables in simple English?

I am reading Esteban Herrera's Java 8 Programmer II Study Guide. I already understand the keyword "synchronized," but not "volatile." In the first chapter, the author makes the case for the "volatile" keyword. First, he points out an issue with the following code.  class Singleton {     private static Singleton instance;     private Singleton() { }     public static Singleton getInstance() {         if(instance == null) {             synchronized (Singleton.class) {                 if(instance == null) {                     instance = new Singleton();                 }             }         }         return instance;     } }   He calls the above code imperfect, arguing, "The JVM, or sometimes the compiler, can optimize the code by reordering or caching the value of variables (and not making the updates visible)." He recommends adding the volatile keyword to the Singleton instance field because this ensures that its read and write operations will be atomic rather than cached in the case of multiple threads.  I do not fully understand Herrera's argument. What does it mean to reorder the value of variables, and why would this be a problem? What does it mean for read/write operations in multiple threads to be atomic, and why is this necessary? Every explanation that I have found online is likewise full of jargon. Can anyone explain the volatile keyword in layman's terms without assuming a prior understanding of the above terms?


Strange NTFS Partition, Seemingly Created by Windows 10 Update?

So I used to have a partition mounted as F:, and it was my old Mac's hard drive (Disk3 in the screenshot below) using a a free HFS+ driver I found when running Windows 8. I've never been able to mount that partition since updating to Windows 10, so naturally haven't seen that drive letter in a while.  Recently however, I started getting windows popups about disk F: having low space... this was news since it's not supposed to be there, but it turns out that there's a 450MB partition on my main SSD that's being mounted as F:, and I swear I'd never noticed it prior to this behaviour. What's even more odd is that if I right-click on it in Disk Management the only option is "Help...", i.e. I can't change drive letter assignments etc.  Does anybody know if a recent update would have introduced this, and whether or not I can safely delete it?


\bordermatrix with brackets [ ] instead of parentheses ( )

I have the following code:  \documentclass{article} \begin{document} $ M = \bordermatrix{~ & x & y \cr               A & 1 & 0 \cr               B & 0 & 1 \cr} $ \end{document}   But this code makes a matrix with () and i would like it to be with [] How do i do this?


"Listen to me play the flute" vs "listen to me playing the flute"

I see this expression "He listens to me play the flute". Is it correct ? And what about ""He listens to me playing the flute". What is the current form of this expression. I didn't find the answer either in dictionaries or grammar books. Thank you.


Closed-form term for $\sum_{i=1}^{\infty} i q^i$

I am interested in the following sum $$\sum_{i=1}^{\infty} i q^i$$ for some $q<1$.   Is there a closed-form-term for this? If yes, how does one derive this?  I am also interested in   $\sum_{i=x}^{\infty} i q^i$  for some $x>1$.


I'm trying to learn about the use of generic types and I've noticed something weird when I was experimenting with some lines of code. The first piece of code is inside a class named "A": public void func(int k, List list) {     list.add(9);     list.add(true);     list.add("a string");     }  The second piece of code is in a different class, inside the main function: List<Integer> arr = new ArrayList<Integer>();         arr.add(14);         System.out.println(arr.toString());         a.func(8, arr);         System.out.println(arr.toString());  Running the code results in this lines being printed:  [14] [14, 9, true, a string]  This got me pretty confused since arr is an ArrayList of type Integer, how can it contain objects of type boolean and String? Is there a transformation of the list in the function func to a raw type (which mean it becomes of generic type Object)? And if so how is it possible since you cannot do this for example: List<Integer> arr = new ArrayList<Object>();? Would love some clarification on this, maybe it will help me grasp this subject of generic types better. Thanks!


Let $G$ be a finite group with cardinality not divisible by $3$. How can one show that for every $g \in G$ there is an $h \in G$ such that $g=h^3$?

Let $G$ be a finite group whose cardinality is not divisible by $3$. How can one  show that for every $g$ belonging to $G$ there exists an $h \in G$ such that $g=h^3$?


I am a little at a loss.  A couple years before my mother-in-law passed away she signed her house over to my wife and her sister via a quitclaim deed.    After she passed we sold the house for $80,000. The money was used to pay off the mortgage, some other funeral expenses, and sent $15,000 to other family members.  All the money was dispersed at the closing of the house.  My wife and her sister each ended up with about $20,000.  How do we go about claiming this income?  Since there was a quitclaim deed I guess we technically owned the house for a few years prior to its sale.  How does that affect our tax and what is the basis?  Is the basis the selling price(fair market value) or something else?  How much does each sister claim for gains?  Sorry it this is a jumble of questions I am just trying to get this straightened out before tax is due.


I would like to install Python 3.5 in my new 18.04 Ubuntu release. I don't want it to be my default version. I just need it to run a specific app. Can anyone help?


If a horse pulls the carriage, the carriage should pull the horse with equal force (Newton's third law), then how does the whole system move? I drew the free body diagram but not yet figured what makes the whole thing move. Please give me an explanation.


Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$

Prove that for all  $n \in \mathbb{N}$: $$2^{n-1}(a^n + b^n) \ge (a + b)^n$$ I used induction (for $k = 1,2,...n-1$), and ended up with the following equation:  $$(a + b)(a + b)^{n-1} \le (a + b)(a^{n-1} + b^{n-1})2^{n-2}$$  Now, I have a feeling I'm on the right track, but I'm not totally sure. Could someone give me a pointer one where I should go from here? Any help would be greatly appreciated. Thanks!


Can the genetic codex from Man of Steel still be used in the future?

Or did the end of the movie mean that all Kryptonians were completely extinct?   I was a bit confused by the end because it seemed to suggest that all kryptonians were completely extinct. But Jor-El couldn't have known and did not plan on having Zod follow his son to earth, especially with one of those birthing chambers in tow. So he must have assumed that there was another way..  Is it possible that Superman can still use the codex?


Is there a word similar to “verbatim” but means "too many meaningless words used"?

Is there a word similar to verbatim but means "Too many meaningless words used"?  I am looking for a word which describes the statement is meaningless with too many words.


Proof that $f(x) = x^2$ is continuous ($\delta-\epsilon$)?

I wanted to know if there's anything wrong with my proof below.  $f(x)=x^2$ and let $c$ be an arbitrary constant.  $\mathbf1.$  First, $0<|x-c|<\delta$  Now, $|x^2-c^2|=|x+c||x-c|\le(|x|+|c|)|x-c|<\epsilon\Rightarrow|x-c|<{\epsilon\over|x|+|c|}\le{\epsilon\over|x|}\Rightarrow|x-c|<{\epsilon\over|x|}$  So we have $\delta={\epsilon\over|x|}$ that satisfies the necessary condition: if $0<|x-c|<\delta$ then $|f(x)-f(c)|=|x^2-c^2|<\epsilon$  $c$ was arbitrary, so we can see that $f(x)$ is continuous, except not necessarily at $x=0$.  We need to make sure that $f(x)=x^2$ is continuous at $x=0$, since in the previous section, we can't have $|x|=0$.  $\mathbf2.$ For $x=0$,   $0<|x-0|<\delta\Rightarrow|x|<\delta$ , and  $|x^2-0|=|x^2|=(|x|)^2<\epsilon\Rightarrow|x|<\sqrt\epsilon$  So we have $\delta=\sqrt\epsilon$ , and thus we can see that $f(x)=x^2$ is continuous at $x=0$ as well.  From conclusions drawn at the end of $\mathbf1$ and $\mathbf2$, we have shown that $f(x)$ is continuous on $x\in\mathbb R$  I just started learning about $\epsilon-\delta$. If you spot any error(s), please let me know how to correct them. Thanks!


Need help figuring out substitution with recurrence equation.

I need help with an Algorithm text book problem. The problem is the following  T(n) = 2T(n/2) + n  We guess that the solution is T (n) = O(n lg n). Our method is to prove that T (n) ≤ cn lg n for an appropriate choice of the constant c > 0. We start by assuming that this bound holds for ⌊n/2⌋, that is, that T (⌊n/2⌋) ≤ c ⌊n/2⌋ lg(⌊n/2⌋). Substituting into the recurrence yields.  This is the answer that is given.     T(n) ≤ 2(c ⌊n/2⌋lg(⌊n/2⌋)) + n  Step 1    ≤ cn lg(n/2) + n                Step 2    = cn lg n - cn lg 2 + n         Step 3    = cn lg n - cn + n              Step 4    ≤ cn lg n,                      Step 5   However, there is a couple steps that confuses me.   In step 2 shouldn't lg(n/2) be lg n since we should multiply it by 2?  In step 3 I am completely confuse on why we subtract cn lg 2 + n  from cn lg n  Any tips or suggestions are appreciated. I am trying to learn this on my own, but I need someone to guide me on this.


Is it possible to abort a previously-running Ajax request?   var xhr = $.ajax({     type: "POST",     url: "some.php",     data: "name=John&location=Boston",     success: function(msg){        alert( "Data Saved: " + msg );     } });


2 questions. Please answer seperately.   I want to dual boot Windows 7 Ultimate with Windows 7 Professional. Is it possible? Can Windows 7 32-bit be dual boot with Windows 7 64-bit?


Is it correct that a sphere of water the size of Venus's orbit would instantly be a black hole?

Let's say I have a genie and wish for a sphere of water at earth density the size of Venus' orbit - would it be instantly indistinguishable from a supermassive black hole due to the schwarzchild radius exceeding the volume at normal density? Would it also outweigh Sagittarius A* at 150 million Suns? I've taken the , the density formula, and solved for r with the density of 1000 kg/m^3 Apologies, I don't know how to do formula.


Bash function that creates an alias gets called endlessly

I ran the following Bash function that adds a string with expanded variables, into the end of my bashrc:  alias() {     echo "alias $repo=\"$HOME\"/$repo/$repo.sh" >> "$HOME"/.bashrc     source "$HOME"/.bashrc 2>/dev/null } alias   To run it I copied it, pasted in the Bash terminal (there it appeared once) and executed by hitting Enter.  The output I got in ~/.bashrc was about a thousand lines of the above string:     alias $repo=\"$HOME\"/$repo/$repo.sh   The very last command (source /home/user/.bashrc) kept being executed endlessly (I assume due to endless calling to the function) so I immediately aborted with the ^C key combo.    After removing all thousand repeats of the string with a Nano mark-set and cut operation, I desire to ask why did this happen (and keep happening)?


Counting The Number of Equivalence Relations on a Set

I am trying to solve the following problem from a textbook: Let $S$ be a set with cardinality $2m$. Give a closed-form expression for the number of equivalence relations on $S$ where every equivalence class has two elements. My approach thus far: Every equivalence relation partitions $S$ into $m$ different subsets/classes. Thus, counting the number of equivalence relations is equivalent to counting the number of ways of choosing $m$ different objects in a $2m$-element set. And this is given by $\binom{2m}{m}$. Is my approach correct? If not, how can I solve this problem? I would appreciate any help on this!


How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?   im trying to use AM-GM  $\sqrt[n]{ \frac{1}{x_1} \frac{1}{x_2} \frac{1}{x_3} ..\frac{1}{x_n}}   \le \sum_{k=1}^n \frac{{\frac{1}{x_1} +\frac{1}{x_2}+ \frac{1}{x_3}+ ..\frac{1}{x_n}}}{n}$  $ln\sqrt[n]{ \frac{1}{x_1} \frac{1}{x_2} \frac{1}{x_3} ..\frac{1}{x_n}} \le ln \frac{1}{n} \sum_{k=1}^n {\frac{1}{x_1} +\frac{1}{x_2}+ \frac{1}{x_3}+ ..\frac{1}{x_n}}$  $ \frac{1}{x_1} \frac{1}{x_2} \frac{1}{x_3} ..\frac{1}{x_n}\le  \sum_{k=1}^n {\frac{1}{x_1} +\frac{1}{x_2}+ \frac{1}{x_3}+ ..\frac{1}{x_n}}$  im not sure is this right or not, however i dont know how to include the $n^2$ in the nominator? is there also alternative proof using jensen inequality?


Removed several programs using "sudo apt-get purge wine\*"

I have been using wine for a while now but it started showing some problems a few days ago so I used this command to remove it  sudo apt-get purge wine\*   Now my system has none of the in built programs such as the terminal or the software center. What can I do to get them back apart from re installing Ubuntu?


How can I create text with a neat quad topology for deformation?

I was trying to do a simple text warp effect in Photoshop and the built-in effects didn't give me the exact shape I wanted, so I decided to give it a shot in Blender. Blender's versatility allowed me to easily warp and scale the text, but the problem is that the text mesh I created had extremely poor topology which doesn't deform well. Ideally, I would like to have a very even quad topology.  I can create the desired topology manually using the steps shown in the image below:    This allows me to use proportional editing lattice or bend modifier and get a clean deformation. However, this is quite time-consuming, so I was wondering if there is a simple function that will allow me to get a result similar to that shown in step 3. but a bit more automated to save time and allow iteration if I need to change the text? Basically, I need something like the dynamesh remesh feature of zbrush that takes an input mesh and slices it into an even grid. Does this exist in Blender?


How to disprove the statement that n points divide a circle in $2^{n-1}$ regions?

The statement is:     n points on a circle divide it in $2^{n-1}$ regions.   I have used geometry to figure out that indeed, this statement is false, but I was wondering how to dis-prove this statement using simple and logical mathematics.  What I did for this, is if $n$ points, then there will be $^nC_2$ lines. Intersections in the lines can be $0$ or $n-1$ or $n$ only.  Am I going in the right direction and how should I go on with this to find something about the regions the lines divide the circle into.  Edit: I don't want to dis-prove this with a counter example, I am thinking of doing this in the way I have started, with logic and simple mathematics.


Show that the Limit does not exist as xyz approaches 0,0,0

Show that the Limit doesn't exist $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{xyz}{x+y+z}$ I try to replace all of $x$, $y$, and $z$ with what they are actually approaching. But I'm stuck there and I can't prove that the Limit doesn't exist


How can I add two graphs next to each other in a same page and place?


How far do I need to extend bellows to achieve particular minimum focal length

If I have a 200mm lens, and want to focus at, say, 450mm from the camera, two questions:   can I (do I need to) use bellows to achieve this? is there a formula for how to work out how much extension I need on the bellows to achieve the minimum focal length?


After I login ubuntu, as usual, I check upgradable packages by running: sudo apt update. Then the result is:      36 packages can be upgraded. Run 'apt list --upgradable' to see them.   I continue with the command:sudo apt upgrade but I got error:     E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable)   E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend), is another process using it?   I waited for a few moments and then I rerun the previous command and it told me:     2 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   Is it an apt error or there's an update process running on the background?


Bring two handbags worth $400 into India duty free

I am an Indian citizen residing in Canada for the last 4 months. If I carry two new handbags to India worth $300 approx, would I be required to pay import duty. I checked the website and it says that you can bring valuables worth Rs.35000 (approx. $600). I just want to make sure that new handbags won't be a problem.


how to create desktop short cuts as the different user logins?


How does the basic RS Flip-Flop (also known as latch) works?

Ok this is a basic question but i am not able to figure out how does this work  1: This is the representation of the RS Flip-Flop with the truth table given in my  book    I am not able to connect the truth table to the representation as inn my knowledge every time the answer should be same, which i know that i am wrong so please help me.  2: what does Disallowed and no change stands for.  Thanks  Akash


Will the desktop be consuming resources if Im not using it?  If so, how do I turn it on/off?


Selenium Tests run in the background when TeamCity CI is run as a Windows service

Our test suite is written in Python and makes use of the WebDriver Python bindings. We are looking into moving to TeamCity for continuous integration. The setup I have in mind is a build triggered for the UI tests when the source code build finishes.  The problem is that if TeamCity build agent is running as a Windows service, then the WebDriver tests are run in the background (and it takes forever to run even a single test). The workaround is to start the TeamCity build agent manually. Now the browser is visible, has focus and the tests run fine. The catch is, if the machine running the build agent is restarted, one would need to remember to start the build agent again.  Has anybody implemented a similar setup ?   How can I get around this problem of having to run the build agent manually?


How should I parse the sentence "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo."

Why is the following statement valid, and how can I break it down so that it is easier to understand?     Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.


Airpods microphone is noisy on Macbook (input format: 8 Hz, 1 ch 16 bit, SCO codec)

Airpods microphone has very poor quality on my Macbook (input format: 8 Hz, 1 ch 16 bit processed by SCO codec):      As a temporary solution, I use the built-in microphone but I'd like to find out how to fix it on Airpods side.  Device info:   MacBook Pro (Retina, Mid 2012)  macOS Mojave 10.14.4  AirPods 1


How to increase battery life on Ubuntu 20.04 and what power saving software should I install, if any?

I recently installed Ubuntu 20.04 LTS on my Lenovo Ideapad Flex 5 and realized that battery life in Ubuntu is not as good as Windows. The battery drains faster in Ubuntu. I have seen the questions in Ask Ubuntu about this, but I haven't found anything that regards Ubuntu 20.04 LTS. I've done some research and found out that the battery drain is because most vendors optimize their drivers for Windows and with Linux, you have to hope that the kernel drivers do the job (which they usually do). After that, I researched how to increase my battery life and almost all sources I found recommended installing tlp or powertop or something similar to these. But I have a few questions.  Does tlp, powertop, and similar software actually affect battery life?  If the answer to 1 is yes (in a positive way), what would you recommend I install (such as whether I should  install tlp or powertop by itself or in a combination)?  Are there any other ways to increase battery life in Ubuntu 20.04?   Note: I am a beginner to Linux and Linux distros and do not want to mess with anything advanced that may negatively affect the system. I may not be able to immediately know how to tweak any of the aforementioned software, so please suggest any tweaks if they are needed to get results. And if it helps to know, here are my system specs: OS: Ubuntu 20.04.1 LTS x86_64 Host: 81X2 IdeaPad Flex 5 14ARE05 Kernel: 5.7.17-050717-generic CPU: AMD Ryzen 7 4700U with Radeon Graphics (8) @ 2.000GHz GPU: AMD ATI 04:00.0 Renoir (These were given by neofetch) P.S: If you need anything else, just ask. Thanks in advance!


How many Jedi were there at the time of the purge?

Episode III obviously doesn't show ALL the Jedi being eliminated as a result of Order 66.  What I've never heard, though, is how many Jedi were in existence at the time of Order 66.  Is there any definitive count as to how many of them were alive at the time of the purge and how many were victims of Order 66?


Is it possible to put a new line character in an echo line in a batch file?  Basically I want to be able to do the equivalent of:  echo Hello\nWorld   You can do this easily enough in Linux, but I can't work out how to do it in Windows.


I'm currently unit testing .NET application with NUnit framework. Some of the methods we use involve getting X509Certificate2 object as input and checking if one or more properties match certain crateria. For example, method that check whether the thumbprint exists in a very specific list. Thus, I need a way to mock or fake the X509Certificate2 object so that I can control what the thumbprint field will return or what are the extentions list will contain. One way I can approach this is to create the special certificates and use them as resources in the tests project (hard coded or embedded resource). I'm searching for a different solution, if it's even possible. And suggestions will be greatly appreciated! Thanks in advance :)


Manual Mode : Dark picture even in broad daylight

I am a new DSLR user. Whenever I click a picture using Manual mode the picture is pitch black. You cannot see anything. Which setting should I change? How can I overcome this problem? It's only like this in the manual mode.  Help!


I am seeking to run a common Java program in both Windows and Linux.  The program needs to do some things differently on each platform.  So how can / should my Java program detect it is running under Linux vs. Windows?


The integral is:  $$\int_{0}^{1} \dfrac{\ln(x+1)}{x^2+1} dx$$  This is a Putnam question from my calculus book. It was in the section about trig substitution. However, I see no way of how mixing a trig function with a natural logarithm would make it any easier. I've tried the substitution $x=\tan \theta$ and got $$\dfrac 12\int \ln(1+\tan \theta)^2 d \theta$$  However, I wasn't able to simplify it to any integrable form.


Same amount of calories burned for half the reps and double the weight?

So I was looking at the work= force x distance equation and was just wondering if for example I normally do 100 dead lifts at 100 pounds.  Would I get the same calories burned if I did 50 dead lifts at 200 pounds.  According to the work formula I am doing the same amount of work.  If this is true how do you know our muscles use the same energy at double the weight and half the reps?  How can we prove that our muscles are burning the same energy with half the reps at double the weight.  Do we just accept it because it satisfies the work formula?


Conversion from char data type to float, int or decimal data type in C# is Incorrect

This is my first time writing codes in C# and I tried converting char data type ('2') to an int, float and decimal data type but I am getting a very awkward and unexpected result and I want to know why? Here is the code; using System; using System.IO; using System.Linq; using System.Collections.Generic;   namespace Practice {    public static class Program    {       public static void Main()       {          int number = (int) '2';          Console.WriteLine(number);          Console.Read();       }    } }  But instead of returning 2 like I expected, the console returns 50 and I am very very very confused right now! Some please, what's going on?


Why Goldbach's conjecture is difficult to prove?

Why Goldbach's conjecture is still non-solved and is difficult to prove? What makes the mathematicians fail when trying to prove it?


What is the next number in the following set ?  $$1,11,21,1211,111221, \ldots$$


I want to activate the . But I can't find the /etc/fstab on my mac. osx 10.11.5 El Capitan


Increment Brightness by value using xrandr

So I have an Alienware 13 R3 with the OLED display, and for the first time I was able to change the brightness using the xrandr command. The problem was the absence of backlight in OLED displays, so I couldn't change the brightness wither with the keyboard, or in any other way. So now that I know I can change it, I want to put a key binding to change the brightness by let's say 0.1. I used this command to change the brightness:  xrandr --output eDP-1-1 --brightness .5   Does anyone know what command to use not to set the brightness, but to increase or decrease it by some value, so I can bind a macro to it. Thanks in advance!  P.S. I am completely new to Linux, so please don't go hard on me :P


I am getting error   #1064 - You have an error in your SQL syntax; check the manual that  corresponds to your MySQL server version for the right syntax to use near '"insert into all_booking(name,address,event_type,hallNo,arrival_time,arrival_da' at line 1     Query I tried  insert into hall_booking(name,address,event_type,hallNo,arrival_time, arrival_date,dep_time,dep_date,identity,emailid, contact,total_members,desc,catering,service, decoration,other)   values ('$nm','$add','$typ','$roomno','$arrv', '$arrivaldate','$departure','$dDate','$idt','$emailid', '$cont','$desc','200','200','200', '200')"


List down values that match a specific sequence in other column in PostgreSQL

Suppose we have a table that shows the vacation destinations for some people with their vacation date (in January). Date       |   Name   |   Destination 01/01/2021 |   Andy   |   Thailand 01/01/2021 |   Ben    |   Singapore 02/01/2021 |   Andy   |   Japan 02/01/2021 |   Andy   |   Canada 03/01/2021 |   Ben    |   USA 04/01/2021 |  James   |   Thailand 05/01/2021 |  James   |   Thailand 06/01/2021 |  James   |   Japan 07/01/2021 |  Ben     |   Canada 08/01/2021 |  James   |   Canada  How do we list down those who have destinations in the exact following order: Thailand - Japan - Canada? (If someone has destination in the same country multiple times in sequential order then it counts as one appearance) The expected output is the name of the person: Name       Andy     James


Existence of minimal $\sigma$-algebra and transfinite induction

It is well-known that:     Given a set $X$ and a collection $\cal S$ of subsets of $X$, there exists a $\sigma$-algebra $\cal B$ containing $\cal S$, such that $\cal B$ is the smallest $\sigma$-algebra satisfying this condition.   Certain texts, Lieb and Loss, Analysis, for instance, state that the proof of this assertion requires transfinite induction. On the other hand, one can define $\mathcal B$ to be the intersection of all $\sigma$-algebras containing $\cal S$. Which statement is correct? Or, is there a hidden transfinite induction contained somewhere?  I must confess here that I have only vague ideaos of the rigorous set-theoretic foundations of mathematics.


Does Wall of Fire get to deal its damage twice (minimum), when normal creatures are trapped within the circle?

Let's say a character casts  in the ring shape, choosing the inside of the wall as the side that does damage. A creature is inside the ring.  When the spell is first cast, the creature must make a Dex save or take 5d8 damage. Then, on the creature's turn, it wants to move out of the ring, and it will need make another Dex save as it moves through the wall. Effectively, a single casting will require a creature inside the ring to make a minimum of 2 saves in a normal movement situation. Correct?  Note: I realize by the time characters are level 7+, there are many ways to avoid the second Dex save, including flying over the wall, burrowing under the wall, teleporting out, casting a barrier spell within the ring, being immune to fire, etc. I'm just asking about normal movement situations without other tricks, to ensure I've understood the spell. Thanks!


How to add a image with alpha channel over a material?

I have a cube that have the original Blender material (diffuse BSDF, color is white), and I want to add a icon on it  The problem is I added a .png image onto the box, but then the face become black, and that really confuses me  I am a noob to 3d modeling, so please advise, sorry for my bad English..


Why is step function not used in activation functions in machine learning?

The activation functions I have seen in practice are either sigmoid or tanh. Why isn't step function used? What is bad about using a step function in an activation function for neural networks? What are the effects of using step function? In what ways are sigmoid/tanh superior over step?


I've found that there WAS a sandbox gem (created by the guys that made  but it was compatible only with Ruby 1.8. Another problem is that I cannot find it anymore (it seems they stop serving the gem from the servers...).  So, is there any secure way of running ruby in a sandbox (so you can run it from your browser)? Or an easy way to run (for example lua/python) in a sandbox (no filesystem access, no creation of objects etc) and be called from Ruby (Rails 2.2)?  I want to make an application like try_ruby even without having a ruby underneath. But it has to be an easy language (I saw there was a prolog in ruby, even a lisp but I don't think they are easy to learn languages...).   So, do you have any suggestions or tips? Or should I just start creating my own DSL in Ruby (if there is a solution in creating a somewhat safe system)?  Thx


Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$

So, if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$ means $1=ax+by$, and want to show $a^2x+b^2y=1$. By squaring $1=ax+by$ both sides, I get, $1=(ax)^2+b(2axby+by^2)$. It doesn't help my proof. Please help me with this proof.


Showing a Ring of endomorphisms is isomorphic to a Ring

Im trying to show that $\mathrm{End}(\langle \mathbb{Z},+\rangle)$ is naturally isomorphic to $\langle \mathbb{Z},+,\cdot\rangle$, but I'm not quite sure which ring homomorphism to use.  Thank you


A "proof" for $0=1$ by integrating $\int \frac{dx}{x\ln x}$ by parts

Let's consider the indefinite integral $$\int \frac{dx}{x\ln x}.$$ We will compute it by integrating by parts: $$\int \frac{dx}{x\ln x}=\int (\ln x)'\frac{dx}{\ln x}=1+\int \frac{dx}{x\ln x}.$$ Hence, $0=1$. The question is : is there anything wrong in these computations?    Note: I came across this example while reading a book on counterexamples in real analysis. I thought that the people here would find this funny, especially because the error is not so obvious to everyone.


Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.

The statement I am trying to prove:  Let $\{ f_n \}$ be a sequence of equicontinuous, real valued, uniformly bounded   continuous functions on $\mathbb{R}$. Show that $\{ f_n \}$ has a convergent subsequence   which converges uniformly on any bounded subset of $\mathbb{R}$ and pointwise on all   of $\mathbb{R}$ to a continuous function. (Royden pg 210, problem 9).  I believe the first portion follows directly by Arzela Ascoli, once it is noted that if we are given some bounded subset $E$, we can look at $\overline{E}$ a compact set on which the family is equicontinuous and uniformly bounded.  For pointwise convergence on all of $\mathbb{R}$, the question seems to require some sort of diagonalization argument: Take some dense sequence of $\{x_i\}$ (the reals are separable) and write columns of $f_n$ applied to each individual point. There will be a convergent subsequence by Bolzano-Weirstrass and since the outputs are real and bounded by the uniform boundedness of the family. I am a bit fuzzy on this part: Repeating this literally pointwise and moving far enough diagonally, we can correct for different convergence "speeds" pluck out a single convergent subsequence for any given epsilon and have $\sup|f_n(x)-f(x)|<\epsilon$ for any given epsilon. Finally, continuity should follow from an $\epsilon/3$ argument and equicontinuity of the family.  However, in formalizing the above, I am getting caught up in the notation of that sort of argument and am hoping for a more elegant solution. Is there a better way? Am I just generally confused and that's why I'm having trouble writing things down formally?   Thanks!


I have the Nikon d3300 and would like a better wide angle lens. Specifically for portrait photography. I'd like a nice blurred background as well. What do you suggest as the best and most affordable lens? Thank you.


I'm mainly interested in the swimming capabilities of the T-800, T-1000, and  T-X, though it's fine to speak of the other terminators as well.


Difference between [ and [[ in if statements

The following code  if [ $a == "apple" ]; then     echo "True" else     echo "False" fi   outputs "True" ("False") if a="apple" (a="plum"). The comparison fails if one uses wildcards:  if [ $a == "appl"* ];   and is fixed if one replaces [ by [[:  if [[ $a == "appl"* ]];   What is the difference between [ and [[ in if statements?


I know that some plants die for old age like a  lettuce. But there are trees like Baobabs or larger Ficus in the tropics of whom we don't know their age. And trees like , which die for environmental factors and not by age.   However, E.g. when we multiply vegetatively an olive or cacao tree, we use a fragment or clone from a unique individual passing the same genetic information, again and again.   Then, can these plants live forever?


What are the different use cases between an HMAC and digital signature?

I understand that both an HMAC and digital signature are used to check the integrity and authenticity of a message. Further, I understand that a digital signature is non-repudiatible.   What I do not understand is when to use an HMAC vs a digital signature, in practice. I appreciate the help!


Trigonometric identity: $\frac {\tan\theta}{1-\cot\theta}+\frac {\cot\theta}{1-\tan\theta} =1+\sec\theta\cdot\csc\theta$

I have to prove the following result :  $$\frac {\tan\theta}{1-\cot\theta}+\frac {\cot\theta}{1-\tan\theta} =1+\sec\theta\cdot\csc\theta$$  I tried converting $\tan\theta$ & $\cot\theta$ into $\cos\theta$ and $\sin\theta$. That led to a huge expression which I wasn't able to simplify.  Please help!!!


Ubuntu 14.04 LTS: session does not start and comes back to login

I have completed all suggested updates for 12.04 LTS after a long time of inactivity with my administrative account as the old laptop (Sony Vaio) was used by my wife only. After the update the Unity was gone (and a message like "Compiz was closed unexpectedly"). Trying every solution I found was not helpful. Eventually I upgraded to 14.04 LTS (by do-release-upgrade). When upgraded and rebooted, after logging in I get a pop-up "System problem detected". After a few seconds it comes back to login screen, and that's true for all users including guest user. I tried every suggested solution I found including changing lightdm to gdm to no avail. Again removed the Gnome desktop, problem persists. Would somebody please help to find a solution? I appreciate it.


I have a custom post type kalender, a template which displays all of the posts in this custom post type and a single-kalender.php. Everything works fine when the user is logged in but when logged out the single pages return a 404 error.  I'm assuming I get the 404 because I'm trying to display future posts when not logged in. How would I go ahead and solve this issue?  EDIT 1  $labels = array(   'name' => __('Events'),   'singular_name' => __('Event'),   'add_new' => __('Nieuw event'),   'add_new_item' => __('Nieuw event'),   'edit_item' => __('Event bewerken'),   'new_item' => __('Nieuw event'),   'view_item' => __('Bekijk event'),   'search_items' => __('Doorzoek Events'),   'not_found' =>  __('Niets gevonden'),   'not_found_in_trash' => __('Niets gevonden in de prullenbak'),   'parent_item_colon' => '' );  $args = array(   'labels' => $labels,   'public' => true,   'query_var' => true,   'menu_icon' => get_stylesheet_directory_uri() . '/img/events.png',   'hierarchical' => false,   'menu_position' => null,   'rewrite' => array( 'with_front' => false ),   'supports' => array('title','editor','thumbnail')   );   register_post_type( 'kalender' , $args ); flush_rewrite_rules();   EDIT 2  I've added some code in the 404.php template which would detect if the page which is trying to load is in the custom post type kalender. This works:  <?php      global $wp_query;      if ('kalender' == $wp_query->query_vars["post_type"]) {         include 'single-kalender.php';     }     else{ ?>         </div><!-- .menu-container -->         <h1>Error 404</h1 <?php } ?>   Now I'm trying to query that specific single custom post type in the single-kalender.php template but I can't get it to work. The following query outputs no posts, even though the found_posts variable is 1 (works as expected) but the posts array remains empty unfortunately.  global $wp_query; $name = $wp_query->query_vars["name"];  add_filter( 'posts_where', 'my_posts_where_from_today' );  $query = new WP_Query(array('post_status' => array( 'publish', 'future' ), 'post_type' => 'kalender', 'order' => 'ASC', 'name' => $name ));   When I use the generated query on my database it selects the single custom post type as expected, the generated query is the following:  SELECT   wp_posts.* FROM wp_posts  WHERE 1=1  AND wp_posts.post_name = 'slug-of-the-post' AND wp_posts.post_type = 'kalender' AND (wp_posts.post_status = 'publish' OR wp_posts.post_status = 'future') AND post_date > '2013-04-11'  ORDER BY wp_posts.post_date ASC    If you want to check the whole print_r($query) see here:


Why the maximum sparsity is 99.5% in collaborative filtering?

From  says     98.3% of the interaction matrix is sparse. For collaborative filtering to work, the maximum sparsity you could get away with would probably be about 99.5% or so. We are well below this, so we should be able to get decent results.   Why is 99.5% ?


Ajax returns success but doesn't change the database

I'm developing a small script of js to edit a profile in the way facebook used to be (click a button, edit and save without reloading the page). The problem is that when I run it, the ajax function returns sucess but akes no changes on the database. The function os js is this:  $('.savebtn').click(function(){             var editdata    = $(".editbox").val();             var parameter   = $(this).closest("td").find("#parameter").text();              var datastring  = "data="+editdata+"&parameter="+parameter;              var $t = $(this);              console.log(datastring);              $.ajax({                 type: "POST",                 url: BASE_URL + "/API/update_profile.php",                 data: datastring,                 cache: false,                 success: function()                 {                     $t.closest('td').find('.curr_value').html(editdata);                     $t.closest('td').find('.curr_value').hide;                     console.log(editdata);                     $(this).prev(".edit").hide();                     $(this).prev(".curr_value").show();                     $(this).prev('.edit_link').show();                     $(this).hide();                 }             });         });   (Ignore the $t thing, somehow this works like this, but not if I use $(this))  Ajax executes the code for sucess but doesn't update anything on the database.   The PHP code for the database is:  <?php  include_once("../../config/connect_db.php"); include_once("../../database/cliente.php");  $parameter = $_POST['parameter']; $data = $_POST['data']; $id = $_SESSION['id'];  var_dump($_POST);  try {     updateProfile($parameter, $data, $id); } catch (PDOException $e) {     echo 'Caught exception: ',  $e->getMessage(), "\n"; }   ?>    function updateProfile($parameter, $data, $id) {     global $conn;     $stmt = $conn->prepare("UPDATE biofood.users                              SET ? = ?                             WHERE id = ?");     $stmt->execute(array($parameter, $data. $id)); }   EDIT: As pointed out, this could be a problem with trying to pass a column name as a parameter. Changed the code to the following, but with no sucess:  function updateProfile($parameter, $data, $id) {     global $conn;     $query = "UPDATE biofood.users                SET $parameter = $data               WHERE id = $id";     $stmt = $conn->prepare($query);     $stmt->execute(); }


I'm trying to create question paper using Latex. Sample copy of expected header for first page is mentioned below. Note: Image above "First Page Header". Can you please suggest, how can I add table in header with Image on left hand-side as mentioned below. Is there any recommended package?


I have a theoretical question. I was reading about ridge regression, lasso and the elastic net, and is very impressed. One thing is not quite clear to me.  I would like to know when should I use each model: Linear regression, ridge, lasso and elastic net. What are the advantages and disadvantages of them all ?  I know that an advantage of the lasso is that it does not only shrinkage but also feature selection, it can force the coefficients to zero. Is there anything else ? Why using ridge then, ever ? And what about elastic net, can it shrink coefficients to zero? why would anyone want to combine lasso with ridge, I mean, lasso also shrinks the coefficients.  I am slightly confused.


Why doesn't xenodm starts the X Window System by default in OpenBSD?

During OpenBSD 6.2 install:   Do you want the X Windows System to be started by xenodm(1) [no]?   And the default answer is "no". Why does it brings it up, if the default is no?   The question: But why isn't it "yes" by default? Are there any "better" handlers that start the "GUI"?


How does length affect current carrying capacity

Will a wire have increased current capacity if the length is sufficiently small?  The reason I'm asking is that when doing PCB layout the vias often has thermal relief, which are small traces going from the via to track/fill around. But I've heard that because it's so short it doesn't really matter.  Is this true and can it be further extended to very short wires, or must you follow the rating of the wire?  If possible, how would one 'prove' that the wire can actually handle the current?


What Webserver Do I Need For A Social App

I am making a social application that its base work is like twitter.  When user opens app,it fetches data(texts and images) from server and listitems will be filled and users can be followed and etc.  I think number of users for it is up to 500,000 and i want to use node.js for server side because it's faster that php.  How should i find best webserver(VPS,dedicated,...) for this application?


Show that a $\sigma$-algebra is either finite or uncountable.

Question: How do I show that a $\sigma$-algebra is either finite or uncountable?  I am given the hint that $\mathcal{P}(\mathbb{N})$ is uncountable.  What I think I should do:  Suppose that S is a set and let $\mathcal{A}$ be a $\sigma$-algebra on S. We know that $\mathcal{A}\subseteq \mathcal{P}(S)$, where $\mathcal{P}(S)$ denotes the power set of $S$. I think I need to distinguish a couple of cases:    The case where $\mathcal{P}(S)$ is uncountable and thus infinite. The case where $\mathcal{P}(S)$ is countable and infinite. The case where $\mathcal{P}(S)$ is countable and finite.   I feel like my next step would be to show what each case would imply for $\mathcal{A}$, but I don't really know how.


Surjective, but not injective endomorphism

What is a (simple) example of a group $G$ with an endomorphism $G\rightarrow G$ That is surjective, but not injective?


Are there limitations on what spells a creature can cast while holding a readied spell?  To give an example, say that a cleric uses their action to cast, and hold, a sacred flame, with some arbitrary trigger. Are they, by RAW, allowed to cast a bonus action spell such as healing word?  Does this also work if the held spell is, say, ice knife and the bonus action spell is shillelagh?  This is different to , as I am asking whether there are restrictions on what can be cast while a creature is holding the spell.


Hightlight specfic digits within siunix's \num

I would like to highlight specific digits in a number. Since the number is large I would like to use \num{} from . Of course I can do it manually as in the MWE below, but was hoping that there might be an easy way to use the commented out syntax to accomplish this:  Code: \documentclass{article} \usepackage{xcolor} \usepackage{siunitx}  \newcommand*{\Color}[2][red]{\textcolor{#1}{#2}}%  \begin{document}  \num{99 976}  88\,9\Color{76} %\num{88 9\Color{76}}  77\,\Color{976} %\num{77 \Color{976}}  \end{document}


I've installed 11.04 but some windows effects were off, so I tried to re-enable them. While in the process, however, I ended up losing that handy menu (normally on top) where we have the Ubuntu icon, and the volume and shutdown menus.   How can we restore that panel?  Thanks in advance.


Chapter Citations are not being referenced in Dissertation

I am writing my dissertation with different chapters and articles referenced in each Chapter. I have one .bib file which contains all the articles, books but I want them to be referenced chapter wise. However, this is not working. (The compilation shows no error) I am trying the following: My main file looks like: \usepackage{datetime} \usepackage{graphicx} \graphicspath{ {Figures/} } \usepackage{caption} \usepackage{subcaption} \usepackage[a4paper,width=150mm,top=25mm,bottom=25mm]{geometry} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhead{} \fancyhead[RO,LE]{Thesis Title} \fancyfoot{} \fancyfoot[LE,RO]{\thepage} \fancyfoot[LO,CE]{Chapter \thechapter} \fancyfoot[CO,RE]{Author Name} \renewcommand{\headrulewidth}{0.4pt} \renewcommand{\footrulewidth}{0.4pt} \usepackage{lineno,hyperref,bm,amsmath} \usepackage{caption} \modulolinenumbers[250] \usepackage{subcaption} \usepackage[labelformat=parens,labelsep=quad,skip=3pt]{caption} \DeclareUnicodeCharacter{3B1}{$\alpha$} \usepackage{lineno,hyperref,bm,amsmath} \usepackage{times} \usepackage{algorithm}% http://ctan.org/pkg/algorithms \usepackage{algpseudocode}% http://ctan.org/pkg/algorithmicx     \title{Thesis Title} \author{Sauradeep Bhowmick} \date{\today}  \usepackage[a4paper]{geometry}  \usepackage[backend=bibtex,style=numeric-comp,sorting=none,natbib=true]{biblatex} \addbibresource{mybibfile.bib}  \begin{document}      \input{TitlePage}      \input{Abstract}               \tableofcontents          \listoffigures          \listoftables          \chapter{Introduction}     \input{chapters/Introduction}           \appendix     \chapter{Appendix Title}     \input{chapters/Appendix}           %% A list of publications can be created using this approach     \begin{refsection}         \nocite{Moes,Anderson}   % .bib keys of your own publications                  \printbibliography[heading=bibintoc,title={List of Publications}]     \end{refsection}      \end{document}  The Introduction file looks like: \begin{refsection}     \section{Section Heading}     Here's another citation!  \nocite{Rabczuk2007}          \printbibliography[heading=subbibintoc] \end{refsection}  My .bib file looks like this: @Article{Rabczuk2007,     author="Rabczuk, Timon     and Bordas, Stephane     and Zi, Goangseup",     title="A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics",     journal="Computational Mechanics",     year="2007",     month="Aug",     day="01",     volume="40",     number="3",     pages="473--495", }  @Article{Moes,     author ="Nicolas Moës and John Dolbow and Ted Belytschko",     title = "A finite element method for crack growth without remeshing",     journal = "International Journal for Numerical Methods in Engineering",     volume = {46},     number = {1},     pages = {131-150},     keywords = {finite elements, fracture},     doi = {10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J},     url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819990910%2946%3A1%3C131%3A%3AAID-NME726%3E3.0.CO%3B2-J}, }  @book{Anderson,     author = {Ted L. Anderson},     title = {Fracture Mechanics:     Fundamentals and Applications},     date = {24 June 2005},     edition = {3rd Edition},     publisher = {CRC Press},     location = {Boca Raton},     pages = {640 pages},     doi = {https://doi.org/10.1201/9781420058215}, }  The issue currently is not chapterwise citation, I cannot even list the refences in the main page. Please help me debug the issue with this.


I have this plot, with a very large scale for both x and y axes: \documentclass[border=2mm,tikz]{standalone} \usepackage{tikz} \usepackage{pgfplots} \usetikzlibrary{arrows.meta}  \pgfplotsset{     /pgfplots/layers/altorder/.define layer set={         axis background,axis grid,main,axis ticks,axis lines,axis tick labels,         axis descriptions,axis foreground     }{/pgfplots/layers/standard}, }  \begin{document}   \begin{tikzpicture} \begin{axis}[width=\textwidth,              xmin=-1e12, xmax=2e12,              ymin=-5e23, ymax=2e24,              axis line style = thin,              axis lines=middle,              axis line style={-{Stealth[length=2.5mm]}},              thick,              y tick label style={/pgf/number format/sci},              x tick label style={/pgf/number format/sci,                     rotate=45,                     anchor=east},              grid=major, grid style={dashed,gray!30},              set layers=altorder]      \addplot[draw=blue,thick,restrict y to domain={-5e23:2e24}] {x};  \end{axis} \end{tikzpicture}  \end{document}  I tried using label style={/pgf/number format/sci} but the result is not exactly what I was expecting:  Instead of being respectively in the upper left and the lower right, I would like that 10^24 and 10^12 were along the axes (respectively y and x), besides each tick, instead of 10^0 and 10^{-1}, which do not make sense. How to accomplish this requirement?  As requested, the code has been updated: now it is a MWE. It tries to plot x, but it actually doesn't show anything. It anyway shows the issue about the tick labels. The suggestion in the  has already been applied to obtain oblique tick labels.


When to use standalone lightmeter when your camera already has it?

I'm using Nikon FM2, it already has it's own internal light-meter.   I'm wondering if it's good enough.   When to use standalone lightmeter (like Sekonic) when your camera already has it?


Are terminating decimals dense in the reals?

I have read that rationals are dense in the reals, but I've been curious if the terminating decimals are as well. Since, in applied math, all effectively "real" numbers are approximated with terminating decimals, I would expect the terminating decimals to have this property, and if not I'm curious why. Here I'm defining the terminating decimals like this: $$D = \{\frac{m}{10^n} \in \mathbb{Q} : m \in \mathbb{Z} \wedge n \in \mathbb{N}_0\}$$.


More often than not, I find myself using a comma as sort of a pause. In most cases, it feels right. But I fear that I overuse commas and put them in places where they are not necessary. Some examples:   Both of which, are valid.  I was going to go to work but, I felt sick.    I find myself using commas after words like "but" or "then". Most reference works I've consulted have defined these commas as a preference. Am I completely wrong here? Am I overusing commas and confusing my readers? Any additional documentation on commas of this type would be greatly appreciated.


Table spreaded over multiple pages . Tabularx

To spread the table over multiple pages I know the utility islongtable But it seems that it doesn't work for tabularx . what is the solution. there may be duplication of question but couldn't find satisfactory answer.


Escape a string in SQL Server so that it is safe to use in LIKE expression

How do I escape a string in SQL Server's stored procedure so that it is safe to use in LIKE expression.  Suppose I have an NVARCHAR variable like so:  declare @myString NVARCHAR(100);   And I want to use it in a LIKE expression:  ... WHERE ... LIKE '%' + @myString + '%';   How do I escape the string (more specifically, characters that are meaningful to LIKE pattern matching, e.g. % or ?) in T-SQL, so that it is safe to use in this manner?  For example, given:  @myString = 'aa%bb'   I want:  WHERE ... LIKE '%' + @somehowEscapedMyString + '%'   to match 'aa%bb', 'caa%bbc' but not 'aaxbb' or 'caaxbb'.


For instance, the availability of pornography on the internet is the main cause(,) particularly for men to become ignorant to the pursuit of romantic relationships in the real-world.   Would I put a comma before particularly here? My colleague says so, but I am doubtful about that.   Alternatively, would I enclose particularly in commas or use a semicolon?


What do you call when you clasp your hands to propel someone up a wall?

I'm sure it had a name. It's when you clasp your hands (palms up) so the other person can stand on them and go up a wall (or a tree). Any suggestions?


Referencing tables when they are inside `onlyenv` (beamer)

It seems that I cannot reference tables when they are placed inside onlyenv, but . This applies to both of \cref and the traditional \ref    The topic  is not an answer to this question because my question is asking about referencing a table, not inserting its number in a caption.  Here is the MWE. This should be run twice to get the real result.  \documentclass[aspectratio=169, xcolor={x11names}]{beamer}   \usecolortheme{seahorse} \useoutertheme{miniframes} \useinnertheme{inmargin} \usefonttheme[onlylarge]{structurebold} \setbeamertemplate{caption}[numbered]  % Command to change margins for a page wide \makeatletter \newcommand{\framePageWide}{     \def\Gm@lmargin{5mm}%     \def\Gm@rmargin{5mm}%     \textwidth=\dimexpr\paperwidth-\Gm@lmargin-\Gm@rmargin\relax     \hsize\textwidth     \columnwidth\textwidth     \setlength{\linewidth}{\textwidth}     \hoffset=\dimexpr-\beamer@leftsidebar+\Gm@lmargin-0mm\relax } \makeatother \newcommand{\framePageWideEnumI}{\setlength{\leftmargini}{10mm}}       \usepackage{adjustbox}     \usepackage{ragged2e}     \usepackage{tabularx} % BEGIN_FOLD          \newcolumntype{C}{ >{\arraybackslash \Centering}X }              \newcommand{\scalelinespace}[1]{                 \rule{0pt}{#1\normalbaselineskip}                                         }  % END_FOLD      \usepackage{booktabs}     \usepackage{makecell}      \usepackage{amsmath}     \usepackage{amssymb, amsfonts}      \usepackage{cleveref}     \crefformat{table}{Table #1}   \begin{document}  {\framePageWide  \begin{frame}{Tables}  \begin{onlyenv}<1>      \framePageWideEnumI      \begin{itemize}         \item Item 1         \item Item 2     \end{itemize}  \end{onlyenv}  \begin{onlyenv}<2>      \begin{table}          \begin{adjustbox}{minipage={0.5\textwidth}, valign=t}              \caption{Time, in seconds, needed to calculate a single ${Z}_{bus}$ Element}             \label{table:results2}              \begin{tabularx}{\linewidth}{c C C}                  \toprule                  System Size & Our Method & Brown's Method                 \\                 \addlinespace                  200-bus & $4.3\times10^{-6}$ & $0.092$                 \\                 \Xhline{0.25mm}                  2383-bus & $3.8\times10^{-6}$ & $166.2$                 \\                 \Xhline{0.25mm}                  3120-bus & $3.2\times10^{-6}$ & $398.8$                 \\                  \bottomrule              \end{tabularx}          \end{adjustbox}         \hfill         \begin{adjustbox}{minipage={0.43\textwidth}, valign=t}              From \cref{table:results2} we see that              \begin{itemize}                 \item Our method is fast                 \item By contrast, Brown's becomes very slow when the system is large             \end{itemize}          \end{adjustbox}      \end{table}  \end{onlyenv}   \end{frame}  }  \end{document}


Prove that the expression is a perfect square

Let $m$ be a natural number. Define $f(m) = m + \lfloor\sqrt{m}\rfloor$. Prove that at least one of the number among $m, f(m), f^2(m), \ldots$ is a perfect square. Here $f^k(m)$ denotes the composition of $f$ over itself $k$ times.  I tried the question, but the greatest integer along with square root is creating trouble.


Why my website is excluding from search results after migration to https?

I've setup ssl certificate on my domain on 19th of February and redirected all pages to https version with 301 redirect code. From that day all of my indexed http pages are disappearing from results and no https alternative are shown instead of them. It appears that google is indexing my website as a new website and the pages are not ranked in the search engine.   When I search for my site, about 24500 pages are indexed in google but as I said none of them are shown in the search results.  What is the problem, and how can I fix it? Indeed I set up 301 redirect for all pages, none of https version of pages are replacing http version.  I've checked this question "" but the problem in this question is different from my site. In my case all of my https pages lost their rankings almost immediately.


Question:   Prove that a norm is always non-negative.   Assume that the norm is negative.   Define: $f: \mathbb{R}^{n}\rightarrow \mathbb{R}^{-}_{0}$  $v \mapsto \left ( \vec{v} \right )f=\left \| \vec{v} \right \|$  $\left ( \vec{u}+\vec{v} \right )f=\left \| \vec{u}+\vec{v} \right \| \in \mathbb{R}^{-}_{0}$ and  $\left ( \vec{u} \right )f=\left \| \vec{u} \right \|,\left ( \vec{v} \right )f=\left \| \vec{v} \right \|=\left \| \vec{v} \right \| \in \mathbb{R}^{-}_{0}$  At this point I am unable to progress further.  Any help is appreciated.


Let $p$ be a prime number of the form $4n+1$, and let $n$ be a natural number. Show that congruence $x^2\cong-1 \mod p$ is solvable. I tried solving by simplifying $\cong$ sing i.e. $x^2 + 1 = p.m$ or $x^2 = (4n+1).m -1$. But I can't  proceed after this


Prob. 10, Sec. 3.10 in Kreyszig's functional analysis book: Every isometric linear operator on a finite-dimensional inner product space is unitary?

Let $X$ be an inner product space such that $\dim X < \infty$, and let $T \colon X \to X$ be an isometric linear operator.   Since $\dim X < \infty$, $X$ is complete and thus a Hilbert space; since $T$ is isometric, $T$ is also injective and hence also surjective and thus bijective, because $\dim X < \infty$. So $T^{-1}$ exists.   How to show that $T$ is unitary. That is, how to show that the Hilbert adjoint operator $T^*$ of $T$ equals $T^{-1}$?   Since $X$ is finite-dimensional, we can choose an orthonormal basis for $X$; let $n \colon= \dim X$, and let $\{e_1, \ldots, e_n \}$ be an orthonormal basis for $X$.   Then, for each $i, j = 1, \ldots, n$, we have  $$\langle Te_i , e_j \rangle = \langle e_i, T^* e_j \rangle,$$ and,  $$\langle T^* T e_i, e_j \rangle =  \langle T e_i , T e_j \rangle = \langle e_i , e_j \rangle = \begin{cases} 1 \ & \mbox{ if  } \ i = j \\ 0 \ & \mbox{ if } \ i \neq j. \end{cases} $$  What next?


Why does InnoDB store all databases in one file?

It was convenient that MyISAM used to store each table in a corresponding file. InnoDB has made advancements in many aspects, but I wonder why InnoDB stores all databases in one file (ibdata1 by default).  I understand that InnoDB will map the location of data in the file by individual index files for tables, but I do not understand why it mixes all data in one file. And more importantly, why mix the data of all databases on the server?  An interesting feature of MyISAM is that one can copy/paste a database folder to another machine and then use the database (without a dump).


Evaluating $\int_{\mathbb R^n}e^{-\langle Ax,x \rangle}dx$ where $A$ is symmetric and positive definite

I was asked the following question, and while I think I made little progress, I'd like a push in the right direction.  Let $A$ be $n$x$n$ positive definite symmetric matrix with real entries. then for all $x \in \mathbb R^n$, evaluate the integral:  $$\int_{\mathbb R^n}e^{-\langle Ax,x \rangle}dx$$  Hint: Start by assuming $A$ is diagonal and remember that any symmetric matrix is also diagonlizable.  What I did:  I think the hint is good. Assume $A$ is diagonal with the entries $\lambda_1 ,\lambda_2 ,...\lambda_n$, then $\langle Ax,x \rangle=\sum_{i=1}^{n} \lambda_ix_i^2$  So now the integral becomes $$\int_{\mathbb R^n}e^{\sum_{i=1}^{n}\lambda_ix_i^2}dx$$  But what now? can we split integral and integrate by $x_i$ each time?


Every finitely generated algebra over a field is a Jacobson ring

Knowing that the polynomial ring in $n$ variables over a field $k$ is a Jacobson ring, how can we prove from it that every finitely generated $k$-algebra is a Jacobson ring?   EDIT: We define a ring to be Jacobson if every prime ideal is an intersection of maximal ideals.


Misaligned Images when printing on same piece of paper

I have a question regarding printing images side by side on the same piece of paper at different times.   I will first print an image on the paper at an exact location using photoshop, i will then take the same piece of paper align it correctly in the printer and then print the second image right beside it but when the printing is done there is a very small "offset" between the two images. Sometimes the second image has been shifted to the right by 1 mm or up by 1mm ect. If I were to print images of just colour there would sometimes be visible white lines between them or the ink would overlap and create darker lines. This problem doesn't always arise, sometimes it DOES align perfectly to the eye.  I am wondering what this problem is called, is it fixable(with my current printer) and what type of printer is best for reducing this effect(I have seen HP DesignJets but I'm not sure that they don't have this problem)?  Many thanks!


Consider two linear operators $\hat{A}$ and $\hat{B}$. Show that $e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2}$

For operators $\hat{A}$ and $\hat{B}$:    $[\hat{A},\hat{B}]=\hat{A}\hat{B}-\hat{B}\hat{A} \not=0$ but   $[[\hat{A},\hat{B}],\hat{A}]=[[\hat{A},\hat{B}],\hat{B}]=0$       Show that:      $$e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2} \space \space \space \space \space \space \space \space \space \space \space \space (1)$$   Hints:   Consider: $\hat{U}(t)=e^{t\hat{A}}e^{t\hat{B}}$ and show that $\frac{d}{dt}\hat{U}(t)=\hat{U}(t)e^{-t\hat{B}}\hat{A}e^{t\hat{B}}+\hat{U}(t)\hat{B}$ Consider $\frac{d}{dt}e^{-t\hat{B}}\hat{A}e^{t\hat{B}}$ to show that $e^{-t\hat{B}}\hat{A}e^{t\hat{B}}=[A,B]t+\hat{A}$   I verified 1. by differentiating: $\frac{d}{dt}(e^{t\hat{A}}e^{t\hat{B}})=e^{t\hat{A}}\hat{A}e^{t \hat{B}}+e^{t\hat{A}}e^{t\hat{B}}\hat{B}=e^{t\hat{A}}e^{t\hat{B}}e^{-t \hat{B}} \hat{A}e^{t\hat{B}}+e^{t\hat{A}}e^{t \hat{B}}\\=(e^{t\hat{A}}e^{t \hat{B}})(e^{-t \hat{B}}\hat{A}e^{t \hat{B}}+\hat{B})=\hat{U}(t)e^{-t\hat{B}}\hat{A}e^{t \hat{B}}+\hat{U}(t)\hat{B} \space \checkmark$  How do I show 2. though? Shouldn't it read: $e^{-t\hat{B}}\hat{A}e^{t\hat{B}}=[\color{red}{\hat{A},\hat{B}}]t+\hat{A}$?  How can I use these two hints to show $(1)$? I don't really see the connection. Does this identity have a name?


Using relative paths for Windows shortcuts

I have a folder scheme like (highly simplified version):  New Files  >Tools  >Scripts Tested Files  >Tools  >Scripts   ... and I'd like to have a shortcut in each folder from the "New Files" child folders, to the "Tested Files" child folder. But this folder may be moved around from time to time, which would break said shortcuts.  Is there a way to make a relative shortcut to each folder? I remember doing this in HTML where you could set a path, something along the lines of .../Files to go back to a parent and then into a new folder, but I'm unsure if this is something support under Windows shortcuts?  PS: The case of similarly relative shortcuts, when the target is a file, is dealt with in . In the present case the target is a Folder.


What is wrong in this proof: That $\mathbb{R}$ has measure zero

Consider $\mathbb{Q}$ which is countable, we may enumerate $\mathbb{Q}=\{q_1, q_2, \dots\}$. For each rational number $q_k$, cover it by an open interval $I_k$ centered at $q_k$ with radius $\epsilon/2^k$.  The total length of the intervals is a geometric progression that sums up to $\epsilon$.  Each real number is arbitrarily close to a rational number since $\mathbb{Q}$ is dense in $\mathbb{R}$. Thus, each real number is in one of the open intervals.  Thus the entire real line is covered by the union of the $I_k$, thus $\mathbb{R}$ is a null set with measure zero.  Clearly there is something wrong in the above proof, however I am not sure where is it?  Thanks for any help.


What Cartoon had a guy turn into monsters from cards

It was a show where a guys played a card game and eventually entered a world where said card game allowed you to turn into your cards and battle other players. I can't remember much besides small details like an area where the main characters would relax and get food watching other matches


Why can't we interpret likelihood as probability?

Something similar is asked here   My question is (despite all verbal explanation why it is not to be interpreted as probability): in discrete case I feel it can still be interpreted as probability as it is the product of probabilities of all data points.  So what is wrong if I do that?


Capitalization of "Theorem 1" in mathematics papers

In many mathematics papers, I read sentences like:     With an appeal to Theorem 4.5 we get …   Is the capitalization of theorem in this case correct? If it is correct why do we capitalize the word?


I've recently installed Ubuntu 12.04 it was working fine unless I messed up with a command. I change all user permissions(as they call ago permission in Ubuntu) by running command sudo chmod -R 777 /. Now system won't detect any external devices like USB or any internal hard disk,but strangely it detect my mouse and keyboard. And system is also not able to recognize any wired connection. By using chmod I think I messed up with admin privileges  and sudo command won't work.Is there Any other solution other than re-installing the whole OS? Can I restore my system in previous mode by any command?


Why don't solstices coincide with temperature extremes?

In northern hemisphere, the highest temperatures are usually in July — in the middle of calendar summer. See e.g. the climate chart on . But the solstices are on 20-21 of June, almost a month before the middle of July. If the sun is at its highest on solstice day, why isn't the temperature the highest at that time?


There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$. A point $P$ satisfies following condition: The straight line passing through $P$ and dividing the area of square $Q$ in the ratio $1:3$ does not exist.  Can we know the locus of $P$ and the area of the locus?


What physical properties does direction exhibit when applied on a physical on an object.    This maybe leaning into mathematics/philosophy but my question is what is direction? It is defined by wikipedia as: Direction is the information vested in the relative position of a destination (or target) point with respect to a starting point, absent the distance information. I have to some degree known that all my life. But lately I thought what IS direction if you know what I mean. What does direction measure fundamentally? I don't have advanced knowledge of physics but you get base units, why is direction not one or rather what kind of unit is direction? (I don't mean it basically, I just can't think how to put it into advanced terms) I might be overthinking it.. lol and I might look stupid but do you know what I mean?? Maybe I should head to the philosophy section. I put a large emphasis on (WHAT IS DIRECTION) in a deep intellectual and mathematical/physical way (do you get my drift?). Are there any important equations that define direction in mathematics and physics?. Are there any notable facts about direction (is there anything notable relating to direction when it comes to black holes, (for example at the centre))? You get direction in space and you also get direction in time, in what ways do these types of direction vary and are they or have been given different units of measurement. Do particles exhibit physical properties that define their direction (please try to understand I mean in a complex way not in ways like (particle A that has direction exhibit properties such as it moves from 0,1 to 7,0)). I would appreciate it a lot if you could expand on what I have asked and show some flare (what effects that are exhibited in quantum mechanics that relate to direction and the changes of what direction is in each nth direction with theory such as string theory). Maybe this is a simple concept and I will get embarrassed and get a very short answer but it just one of those questions that popped up in my head and seemed intriguing. Are there any cases that a physical particle or object does not exhibit direction (maybe it's in the 0 dimension... I don't have advanced knowledge).   I posted this question and I feel very nervous that I look very stupid please can someone confirm? I've been doing alot of programming so I can see where them mixup of concepts might come in.