I'm an ESTA holder regularly travelling to the US to see my girlfriend. I am a UK resident, in full time employment for a UK company.  This summer, I want to go over to US for 2-3 months (up to 90 days as ESTA permits), but I'd like to carry on working for my UK company over the internet. I would get paid to my UK current account - same way as it currently is. My employer is fine with that. I would go back to the UK within 90 days - as per ESTA's terms.  Is this legal or can I get in trouble? I'm finding very contradicting answers all over the internet.  In case you wonder, I'm the software developer.  Thanks.

I would like to travel in the USA for a period of 3 - 6 months. But I want to spend some time working for my employer (remote work) and getting paid by the employer. Is this possible under a tourist visa (B1/B2)?  I hope this is OK since I will not be getting paid by a US employer. I am in the IT trade so all that I will be needing is my own laptop and a connection to the internet. The money I earn would actually help me pay for the expenses I get during the holiday.


Here is my code.  led.cost=led.cost-((Ledger)mdisellList.get(ms)).cost;   Intial values of led.cost is 4119.7 and mdisellList.cost is 172.485. Both are double datatypes.  I've seen those values in that variables while debugging (no decimals after .7 or .485). No rounding of has done before this line. While subtracting 172.485 from 4119.7 it gives the result as 3947.2149999997 instead of 3947.215.  I want exact 3947.215 instead of 3947.2149999997.

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I have following code snippet:  console.log('**1**',parentNode.child.length); //1             for(var ch in parentNode.child)             {                 console.log('PTree root child',parentNode.child[ch]); //2             }   In //1 parentNode.child.length comes out to be 0 but still it goes inside the for loop and gives following output in line //2:  PTree root child (val) {         if (this.indexOf(val) === -1) {             this.push(val);         }          return this;     }   I am not sure why it is happening.

I've been told not to use for...in with arrays in JavaScript. Why not?


I came across the following sentence in a workbook:     There was a possibility of ... (he) going to England.   The book says the answer is his, not him.  Would him be grammatically incorrect? If so, why?

What, according to the functionalist, is the difference between things which merely have functional roles and things whose functional roles amount to their having a mind? Different people may interpret identical events or stimuli differently due to their having a mind that differs from your own.  Which part of English grammar stipulates using their in these sentences? For me it should be either "to them having a mind" or "to their having of a mind."


I’m using article class, and I want to change colour within the equation tag, multiple times. I found that using mathmode I can change colour, but I want to use equation tag instead. After having the multicolour equation I will link the file to a beamer for a presentation.   Is this possible (successfully linking changed colours from article to beamer as well)? If so, how?  So in my imagination it must be like in the visual. The visual is from   $ \color{yellow} A = \textcolor{blue}{B} \mathbin{\textcolor{red}{-}} \textcolor{green}{C} $    However, I need for example below. This doesn’t work for me.  \begin{equation} \color{red}A=\color{blue}B-\color{green}C \end{equation}

One can use the command such as \textcolor[rgb]{1.00,0.00,0.00}{boundary} to color the word "boundary" in a document.   Here is my question:  How to color the math symbols in $$? For example, can one turn $C^{2}$ into red in LaTeX?


Windows 8.1 came pre-installed in my laptop, I installed Debian 8 on dualboot, the day before yesterday I had to reset BIOS settings, after resetting BIOS is also reseted MBR for windows only, system kept booting windows. I tried several fixes but didn't work. I re-installed Debian 8 and installed a few updates and did sudo reboot. Now again it boots directly into Windows instead of showing grub2 menu for dualboot. Most of the time I like to use debian for it's speed performance and other awesome stuff but I sometimes also need windows for a few tasks. Any solution? >.> It's driving me crazy...

So I started out with a 250GB HDD, the stock drive from an EeePC 1015pem that I am trying to turn into a MintBook. The drive is physically operable, but all data has been nuked, including the old OS. Given this, I attached the HDD to my desktop and installed Linux Mint 16 Xfce from a live USB created through Unetbootin-585. Set aside 10GB for swap and 240GB for ext4 and /.  The drive now refuses to boot for either the desktop or netbook. Both motherboards are sounding the correct sequence of beeps, so they seem healthy, and I can successfully access the BIOS on both systems. However, the only thing that comes up after starting the computer is a nonresponsive command-line. There is no error message, no grub or grub-rescue, nothing.  Is there anything I can try besides reformatting and starting over? How would I go about installing a boot loader that can boot my OS?


In Star Trek Beyond, the Enterprise crashes on a planet inhabited by a murderous faction. Also on this planet the woman Jaylah hides out from this faction. There are several moments in which the antagonists acknowledge knowing about her and even being irritated by her presence.  Jaylah hides out in      what remains of the USS Franklin, a ship lost nearly 200 years earlier with all hands presumed dead. Her hideout is protected by traps and is obscured by some sort of hologram, rendering it invisible.   However, later we learn that      the Franklin's Captain, Mr. Edison, has survived and is now known as Krall, the big bad evil guy. Obviously, he must know where he parked his ship, right?   So, how is it that Jaylah can hide here? Why is rendering her hideout invisible any kind of protection?  I've seen  but I feel this is sufficiently different. I'm not interested in why the antagonist ignored the hideout itself, but why he didn't go looking for Jaylah here.

In Star Trek: Beyond, Jaylah has hidden the USS Franklin from Krall and his buddies using some sort of holo/light refraction cloaking technology.  How could this possibly work, as       Krall and his buddies actually crash-landed that very ship themselves sometime earlier? Surely they remember where their ship crashed, and a ship doesn't just corrode away that quickly (evidently).    There is even a log recording of 'captain Krall' which seems to be recorded ON the ship AFTER it crashed, so it should be weird to them if the ship suddenly had disappeared.   So how could Jaylah hide the ship?


what should I write The complicated political situation will affect/effect our timeline? Please help me.

I've noticed that some people use effect and affect interchangeably. What are the differences between these two and when are the proper situations to use each of them?


I am currently on season 3 of Star Trek: TOS, and wanted to know if/how watching in this order will affect the story (NO SPOILERS PLEASE!!!):  Star Trek: TOS Star Trek: TAS Star Trek movies 1-7 Star Trek: TNG Star Trek movies 8-10 Star Trek: DS9 Star Trek: VOY Star Trek: ENT  If there is a problem please say how I should watch instead. Thanks!

I don't know anything about Star Trek except for the fact that it's about spaceships.  In  the person only wanted to watch the TV series. I want to watch every movie and TV series there is about Star Trek but I don't know where to start. I found this page on  which is about a time line. Do I need to watch it in this order? Are the movies and TV series related?


I need to find sum of $$\sum_{k=1}^n \frac{k}{(k+1)!}$$ using sums of differences I tried to add something to find it , tried to find some differences that would help. But I hadn't result. I know that it would be very easy. But I'm new studying sums.

I'm finding a closed form to  $\sum^{n}_{k=1} \frac{k}{(k+1)!}  (n \leq 1) $ (in a environment of induction and recurrence)   I've been trying to solve it without success, can anybody help me (?)  The last thing I've tried to do is write the expression as a Non-Homogeneous Linear Recurrence:   $ f(1) = \frac{1}{2} $   but, actually I have no idea of how to attach it.   $ f(n+1) = f(n) + \frac{1}{(n+2)n!} $


I think I have a valid proof for the irrationality of $\sqrt{n}$, when $n$ is not the square of a positive integer. My teacher taught us a different method to prove $\sqrt{2}$ is irrational, which is perfectly valid, but my method just seems a little neater to me and it works in general for any value of n that isn't a perfect square .  Firstly, lets assume $\sqrt{n}$, when $n$ is not the square of a positive integer, is rational. Hence:  $\sqrt{n}$ = $\displaystyle\frac{a}{b}$, where  $a, b\in\mathbb{N}$ $b\neq0$  Therefore, by squaring both sides we find:  ${n}$ = $\displaystyle\frac{a^2}{b^2}$  Hence, we see $a^2$ = $nb^2$ $(1)$  Let $a$ have a prime factorisation of $a= \prod\limits_{i=1}^n {p_i}^{e_i}$, where ${p_i}$ is a prime, and ${e_i}$ is the multiplicity of the prime power ${p_i}$. Hence, $a^2$ will have a prime factorisation of $a^2= \prod\limits_{i=1}^n {p_i}^{2e_i}$.  Also, we can state $b$ in the form of $b= \prod\limits_{i=1}^n {q_i}^{f_i}$, hence $b^2$ can be expressed as $b^2= \prod\limits_{i=1}^n {q_i}^{2f_i}$, where ${q_i}$ is a prime, and $f_i$ is its corresponding multiplicity.  Now consider equation $(1)$. We know that $n$ is not a perfect square of a positive integer, so the multiplicities in its prime factorisation must not all be even, as a number is a perfect square if, and only if, (iff), the multiplicities of its prime factors are all even. Hence, it is impossible for equation $(1)$ to hold, as the multiplicities on the LHS must all be even, and on the RHS, it is impossible for this to be the case, as the multiplicities in $b^2$ are all even, but in $n$ they are not. Hence, the product of these two can never have even multiplicities for all prime factors, hence equality can never hold.  Hence, this results in a contradiction, so our initial assumption that $\sqrt{n}$, when n is not the square of a positive integer, being rational was false, hence $\sqrt{n}$ must be irrational, for $n$ not being a perfect square.

Possible Duplicate:          I have this homework problem that I can't seem to be able to figure out:Prove: If $n\in\mathbb{N}$ is not the square of some other $m\in\mathbb{N}$, then $\sqrt{n}$ must be irrational. I know that a number being irrational means that it cannot be written in the form $\displaystyle\frac{a}{b}: a, b\in\mathbb{N}$ $b\neq0$ (in this case, ordinarily it'd be $a\in\mathbb{Z}$, $b\in\mathbb{Z}\setminus\{0\}$) but how would I go about proving this? Would a proof by contradiction work here?  Thanks!!


I always see this in lots of code:  String s; if (s == null || s.isEmpty()) { //do something }   but isn't just enough  String s; if (s.isEmpty()) { //do something }   I am curious especially when I check JavaFX TextField emptiness.

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


I've follow the instructions what I've found here, and I saw it in a lot of posts.  The /etc/security/limits.conf  *         hard    nofile      500000 *         soft    nofile      500000 root      hard    nofile      500000 root      soft    nofile      500000   The end of tye sysctl.conf  fs.file-max = 2097152   Restart the machine and after all here is the ulimit  root@my-machine:/etc# ulimit -a core file size          (blocks, -c) 0 data seg size           (kbytes, -d) unlimited scheduling priority             (-e) 0 file size               (blocks, -f) unlimited pending signals                 (-i) 31333 max locked memory       (kbytes, -l) 16384 max memory size         (kbytes, -m) unlimited open files                      (-n) 1024 pipe size            (512 bytes, -p) 8 POSIX message queues     (bytes, -q) 819200 real-time priority              (-r) 0 stack size              (kbytes, -s) 8192 cpu time               (seconds, -t) unlimited max user processes              (-u) 31333 virtual memory          (kbytes, -v) unlimited file locks                      (-x) unlimited   Can somebody tell me why open files is 1024 and my changes why do not effects?

I've run ulimit -n 65536, added the following lines to /etc/security/limits.conf:  *    soft nofile 65536 *    hard nofile 65536 alix soft nofile 65536 alix hard nofile 65536 root soft nofile 65536 root hard nofile 65536   And added session required pam_limits.so to both:   /etc/pam.d/common-session /etc/pam.d/common-session-noninteractive   And fs.file-max = 65536 to /etc/sysctl.d/60-file-max.conf.  Still, after restarting and running ulimit -n on my session, I only get 4096 (was 1024 before).  What am I missing?


sorry if my english is not perfect, I'm writing in latex but I've a problem ... this is my code:  \documentclass[a4paper,10 pt]{report} \usepackage[italian]{babel} \usepackage[bibstyle=numeric,citestyle=numeric]{biblatex} \bibliography{Biblio}  \newcommand{\e}{\`e }  \title{title} \author{Francesco Serra}  \begin{document}  \maketitle \tableofcontents  \input{Introduzione.tex}  \nocite{*} \printbibliography  \end{document}   File "Introduzione.tex" is quite easy  \chapter{Introduzione}  something ...  \section{Mammografia e tomografia} something else  \begin{figure}[h] \includegraphics[width=0.7]{./Immagini/Mammo} \end{figure}   All works without problem without the figure, while adding code about figure compiler gives me these errors:  Paragraph ended before \Gin@iii was complete  \begin{figure} on input line 12 ended by \end{document}. \end{document} You can't use `\end' in internal vertical mode \end{document}  \begin{figure} on input line 12 ended by \end{document}. \end{document}  Missing } inserted \end{document}  Emergency stop No "backend" specified, using Biber backend. 'babel' detected but 'csquotes' missing.   Someone can help me? Thank you

Different websites suggest using one of those two packages.  \usepackage{graphicx} \usepackage{graphics}   What are differences between them? Which is better?


I have already download Firefox for Lubuntu a (Firefox.tar.bz2 file) and I have extracted the file after downloading. I have lot of files in that folder. from there, which file do I need to select for installation? can you please help me with the installation steps  I have no idea about Linux please help in detail

I want to install the latest Firefox on my Ubuntu (64bit) box.  What is the best way to do this? Is there a specific update site or should I download the binaries manually? If doing manually, in which directory should I put the files? In my home directory, or is there a better place?


I am getting exception in the log. The stack trace ens with "... 11 more". But want to see actual 11 more lines, not just "... 11 more". Is there a way to start java the way that it gives full picture of the call stack on exception?

Lots of times in Java logs I'll get something like:  Caused by: java.sql.BatchUpdateException: failed batch     at org.hsqldb.jdbc.jdbcStatement.executeBatch(jdbcStatement.java:1102)     at org.hsqldb.jdbc.jdbcPreparedStatement.executeBatch(jdbcPreparedStatement.java:514)     at org.hibernate.jdbc.BatchingBatcher.doExecuteBatch(BatchingBatcher.java:48)     at org.hibernate.jdbc.AbstractBatcher.executeBatch(AbstractBatcher.java:242)     ... 113 more   Does anyone know how to get the full stacktrace showing (i.e. show the other 113 lines)?    The  for Throwable have a pretty detailed explanation of what's going on.


I want to print a box into the Java console using Unicode characters, but for some reason it gives me this runtime error:  --------------------Configuration: PacManGame - JDK version 1.7.0_25 <Default> - <Default>-------------------- Exception in thread "main" java.lang.NullPointerException     at Scoreboard.genTopLine(Scoreboard.java:35)     at Scoreboard.<init>(Scoreboard.java:17)     at PacManGame.main(PacManGame.java:36)  Process interrupted by user.   code:   Does anyone know what's wrong?


I am not trying to do cheeky things, but my need is just to have two scripts for adding or removing IP routes using the following command in batch scripts:  Add route:   @echo off route add -p 20.20.188.0 mask 255.255.255.0 192.168.122.254 exit   delete route:  @echo off route delete 20.20.188.0 exit   My question is that now I cannot get it run just by double-click on the batch file. I always have to right click and choose: Run as Administrator option even my user is in the Administrator group.  Is there any way to introduce a command like sudo in Linux or anything else that can make me happy by just double-clicking on the file.   UPDATE:  I tried the runas solution  but as the answer state:      Note, however, that this is not exactly like sudo - you can't use it   to elevate yourself, just run something as a different user. If you're   already have administrative rights, a runas to your account will give   you the same access as the regular command (unless, of course, you   runas a different administrator account, which will grant those   administrator's rights to the new shell).   It is not a solution for my problem.

On Linux, we can use  sudo bash   to run a shell as the superuser.  On Windows 7, we can use     Start menu -> (in search box, type) cmd -> Right click on search result and choose Run as Administrator   to run a command prompt as an administrator. Is there also a command prompt line that is like Linux's sudo or su so as to start a shell as an administrator?


I created a script to dd sdb to sdc on my older computer with Ubuntu 13. It ran when I clicked on it – asked if I wanted to run in terminal or edit it. On a newer computer, with Ubuntu 14, I created the same script on my desktop and made it executable, but when I click on it, the file simply opens in an editor with no opportunity to execute it. So I copied the 'Simple Bash Example' script from "" and made it executable. Same result; click on it and the file simply opens in an editor with no opportunity to execute it.  (I have not tried reverting to Ubuntu 13.)  What am I doing wrong?

When I double-click on a script in Nautilus to run it, the script just opens in my text editor with no option to run it. Using Nautilus, how do I run executable text files and/or scripts?


This question is very similar to  In fact, this is the way I installed Avro earlier.   Recently I have installed Ubuntu 17.04 in a new laptop, and followed the same process given in the link. However, after installing (and following the steps) the font is not showing up as Bengali. In n fact, it started typing in Arabic!  Any idea what went wrong? I have followed all the processes multiple times.

I upgraded one of my machines to Ubuntu 17.04. May be it is related, may be it is not, but for this machine,  switched to Malay (Jawi) after upgrade.   My other two machines, running Ubuntu 16.04 are working fine.  Please see these self explanatory screenshots.      I tried removing and re-adding the keyboard, uninstalling and  the keyboard without any avail.   Whenever, I switch to Avro keyboard, I get texts in Arabic.


The answer is no for familiar operations of addition and multiplication. But could there exist any other operation that could turn the set of all negative real numbers into an abelian group. If yes, what is it? If no, how could I prove it?

The real numbers with addition, $\left( \mathbb{R}, + \right)$, and the positive-real numbers with multiplication, $\left( \mathbb{R}_{>0}, \cdot \right)$, both are Abelian groups. For reasons of symmetry, I think that it should be also possible to construct the group of negative-real numbers.  How does the operation $$ \ast : \mathbb{R}_{<0} \to \mathbb{R}_{<0} $$ have to look like to make $$ \left( \mathbb{R}_{<0}, \ast \right) $$ an Abelian group?


I have been following a researcher since last three years and have read all most all of his research papers (whichever is freely available). At the same time, I have been continuously upgrading my skills as per his research profile. I have got only one chance to prove my worth. What should I write in the e-mail, should I express my self or proceed as per normal formal applicant?

I know many master's students who get an opportunity to talk to their potential PhD advisors well before applying. In most cases this opportunity is available by the professors with whom they worked for their master's. Moreover, there are many others who establish a contact with professors by mailing them and enquiring about PhD vacancies.   My questions are:   How important is knowing an advisor prior to applying for PhD?  Does an email interaction play a vital role when the department makes its admit decisions? If email contact is important, can a student send out mails to 2-3 professors (working in the same area) in case one of them does not bother to reply? To sum up, is applying of any use (especially in top universities) when you have no contacts and only your credentials to bank on?


I am colorblind. I am looking for an app to help me identify colors by their basic names (blue, green, ...) when I am working on powerpoint or excel on mac (OSX 10.12).  On windows, I was using  quite successfully. This app translates the RGB code of the pixel under your mouse into intelligible color names such as blue, green, ... it's a real time-saver when you have to create powerpoints or excel.  I could not find anything similar so far on mac. I tried apps such as Visolve or Sim Daltonism but they did not have this simple functionality.  Please note I am not looking for a color picker such as DigitalColor Meter, that would just read out color RGB codes from pixels. I need a tool that "names" colors, stay on top of screen, with a compact window, just like whatcolor.

I used to find color codes which I want to use for texts or background colors on htmls with color edit tool of MS paint which pre-installed on Windows. But now I use Mac instead of Windows. How can I find color codes with Mac? Is an software like MS paint pre-installed on Mac?


First, I built a Nether Core Reactor (using the core, gold blocks, and cobblestone) and that worked. Instantly, it turned into obsidian. It used to occasionally light up and it would shoot out items. I dug up the obsidian with a diamond pic axe (all of it). I then went into a grassland and created the 4x5 nether portal using the obsidian, but whenever I went to light the inner on fire using flint and steel it light the obsidian on actual fire instead of making the portal. I don't know what I'm doing wrong.

Where do I light my nether portal on Minecraft Pocket Edition 0.10.5?


How did Newton come to postulate the law of inertia when every inertial body that he was considering was (by his own other hypotheses) being acted on by the force of universal gravitation.   In other words, he simultaneously posits the law of Inertia and then theorizes that the contrapositive of his statement is not testable ("If no forces act upon a body at rest, then it will stay at rest", but there is never a situation in which no forces are acting upon a body).   Did he get to this by considering the case of how the inertial velocity of something like a ball being swung on a string in a circle takes off in the direction of the tangent to the circle when the centripetal force is removed, or what were the observations that led to postulate this law? That's the only immediately testable example that I have been able to think of so far, as the same experiment with planets orbiting the sun is not/was not feasible to test in his day.    I'm guessing this law may have some historical context related to the philosophical question of "what makes things move" in Aristotle, and Newton used his law to resolve paradoxes that I am not familiar with.   Or is it something entirely different than what I'm thinking, in that what he actually meant was "it takes less force to keep a body in motion than it does to start a body in motion"?

Newton's second law says $F=ma$. Now if we put $F=0$ we get $a=0$ which is Newton's first law. So why do we need Newton's first law ?   Before asking I did some searching and I got this: Newtons first law is necessary to define inertial reference frame on which the second law can be applied.  But why can't we just use Newton's second law to define an inertial frame? So if $F=0$ but $a$ is not equal to 0 (or vice versa), the frame is non-inertial.  One can say (can one?) we cannot apply the second law to define a reference frame because it is only applicable to inertial frames. Thus unless we know in advance that a frame is inertial, we can't apply the second law.  But then why this is not the problem for the first law?  We don't need to know it in advance about the frame of reference to apply the first law. Because we take the first law as definition of an inertial reference frame.  Similarly if we take the second law as the definition of an inertial frame, it should not be necessary to know whether the frame is inertial or not to apply the second law (to check that the frame is inertial).


I cannot find real derivations and analysis of the . This can probably be a neat up-climb to a Cartan structural summit, or very close.  I am not asking this because I want it quantum. The naturalness and the easy way to have no singularities because the space time field itself yields to finite stress just due to asymmetry in the tensors is what's interesting. The Cartan theory makes the difference clear, so it is appealing.  Worm whole to the new space time instead of singularities. Much better.  Anyone has suggestions?   I do really mean arriving at the structural equations and the properties of the spin connection.

I want to delve into Cartan's formulation of General Relativity but it don't really know where to look. Does anyone have any book suggestions?


I have recently stumbled upon  on Stack Overflow where one person suggests using Short.parseShort(String s) and another Short.valueOf(String s).  I have tried both myself, and I found no difference in functionality and the  didn't really help me either:     Short.parseShort:   Parses the string argument as a signed decimal short. The characters in the string must all be decimal digits, except that the first character may be an ASCII minus sign '-' ('\u002D') to indicate a negative value or an ASCII plus sign '+' ('\u002B') to indicate a positive value. The resulting short value is returned, exactly as if the argument and the radix 10 were given as arguments to the parseShort(java.lang.String, int) method.      Short.valueOf:   Returns a Short object holding the value given by the specified String. The argument is interpreted as representing a signed decimal short, exactly as if the argument were given to the parseShort(java.lang.String) method. The result is a Short object that represents the short value specified by the string.   Both accept the additional Parameter radix, and both throw a NumberFormatException.  They seem to be identical, but if that is the case, why do both exist?

How is parseInt() different from valueOf() ?   They appear to do exactly the same thing to me (also goes for parseFloat(), parseDouble(), parseLong() etc, how are they different from Long.valueOf(string) ?  Also, which one of these is preferable and used more often by convention?


I got a sentence where I was asked to correct/improve it by choosing one of the given options. I was sure of using "Few" instead of "Some" with people but it turned out that I was wrong. I thought using  "Few people" was correct. The question sentence is below:  Some people has all the luck even when they did not try very hard.  a) Some people have all b) Few people have all Please help me get rid of this confusion between "some / few people". Same goes with "few children/ some children". I think "few" has to do something with negative meaning sentences and "some" with positive sense making sentences?

I have a question about choice of using this phrases. What different between "Some words" and "a few words"?  What I need to use?


Given a polynomial $f \in \mathbb{C}[x_1,\ldots,x_n]$, then how can I prove that  $f(a_1,\ldots,a_n) = 0$ implies $f$ is a summation of factors of $x_i - a_i$ for $i \in \{1,\ldots, n\}?$  This is not at all obvious to me. Any help would be much appreciated!

I want to prove that the kernel of the evaluation map $s_a : \mathbb{C}[x_1,\dots,x_n] \rightarrow \mathbb{C}, x_i \mapsto a_i$ where $a = (a_1,\dots, a_n) \in \mathbb{C}^n$ is the ideal generated by $\{x_1 - a_1, \dots, x_n - a_n\}$.    The proof in the book first shows it easily for the case $a = 0$, and says that by substitutions of variables $x_i' = x_i - a_i$, you can show it for the rest of the cases.  I know that $f \in \ker s_a$ iff $f(a) = 0$.  And $\phi : \mathbb{C}[x_1,\dots, x_n] \rightarrow \mathbb{C}[x_1 - a_1, \dots, x_n-a_n], x_i \mapsto x_i - a_i$ is a surjective ring homomorphism.  Please give a hint and not the full answer.  Thanks.


When people speak of the electric charge of a black hole, do we actually mean it affects things outside of the event-horizon or is it just a property it has?

By the "No Hair Theorem", three quantities "define" a black hole; Mass, Angular Momentum, and Charge. The first is easy enough to determine, look at the radius of the event horizon and you can use the Schwarzschild formula to compute the mass. Angular Momentum can be found using the cool little ergosphere Penrose "discovered". However, I don't know how to determine the charge of the black hole.   How can an electromagnetic field escape the event horizon of a Reissner-Nordström black hole? Is there any experiment we could theoretically do to a black hole to determine its charge?


I was trying to format a USB stick, but accidentally typed the wrong disk in terminal:  diskutil eraseDisk /dev/disk_etc   I instantly stopped the process but it was too late - name had changed and it was already showing 2/2TB free on my SSD. I have yet to do anything to my SSD: no file transfers, no removals, unmounted.  Is there any way software-wise to not just recover files piece by piece, but the entire layout of the SSD folders and all? The software I have used so far just finds "Images", "Movies" etc., without the actual layout.  I am hoping this is possible purely due to the brevity of the formatting that occurred and the lack of data replacement.

What steps can I take to try to recover lost or inaccessible data from any storage device?  Answers:   This applies to any computer storage device, e.g. internal/external hard drives, USB sticks, flash memory. The most important thing is to STOP using it, any type of I/O can ruin your chances of a recovery.     We have separate questions covering common problems with USB flash drives in greater detail:


I would like to make a tabular with only 1 column. I want the tabular to have a fixed width and to contain several sentences. As some sentences may be long, several rows may be needed to hold 1 sentence. Here is what a tabular containing 3 sentences looks like (Sorry that I could not draw well the vertical and horizontal lines):  --------------------------- | Sentence 1 is very very | | very very long.         | --------------------------- | Sentence 2 is short.    | --------------------------- | Sentence 3 is very very | | very very very very ve- | | -ry very long.          | ---------------------------   So I do not want to manually separate a sentence into several rows, I would like latex to do it, once the width of the tabular is specified. So the height of the tabular is up to the length of all the sentences...   Does anyone know if it is possible?

Please, Help me inserting a table like this. I could not prepare this table easily because the long text i have to insert into the columns. I have been trying from some examples of stackechange but have not been successful. Perhaps the amount of text that includes the table. I am facing difficulties with merging the rows and columns. I am in an urgent need. Please Help !  Should I use all those packages?  What and how each package is used?  \usepackage{multirow} \usepackage{hhline} \usepackage{array} \usepackage{booktabs} \usepackage{tabu} \usepackage{makecell}    This is the example i wanna get Thanks    \documentclass[11pt]{book} \usepackage[utf8]{inputenc} \usepackage[spanish,mexico]{babel} \usepackage[T1]{fontenc} %\usepackage{amsmath} %\usepackage{amsfonts} %\usepackage{amssymb} \usepackage{graphicx} \usepackage{apacite} \usepackage{multirow} \usepackage{hhline} \usepackage{array} \usepackage{booktabs} \usepackage{tabu} \usepackage{makecell} \begin{document} \begin{table}[h] \caption{``“Utilidad y Derivación de las Emociones Primarias (Riso, W., 2008)''} \begin{center} \small \begin{tabu}{|[2pt]} >{\centering}p{3cm} | [2pt] >{\centering}p{3cm} \tabucline[2pt]{-} &{Emociones primarias} & {Derivación de las emociones primarias}\\ \tabucline[2pt]{-} \multirow{6}{*}{\parbox{3 cm}{\textbf{Dolor}} & \multirow{6}{*}{\parbox{3 cm}{textbf{Sufrimiento}}\\ & Avisa cuando un órgano físico está funcionando mal o está siendo agredido, para que sea reparado o defendido. & Indica que hay una estructura mental afectada o un apego irracional que debe ser trabajado.\\ &\textbf{Miedo} & \textbf{Miedo psicológico}\\ & Protege ante un peligro real.& Indica que se ha dejado de actuar. La parálisis es sostenida por ideas irracionales.  \tabucline[2pt]{-} \end{tabu} \end{center} \end{table} \end{document}


Suppose we are told that the linear size of everything in the universe has been doubled overnight. If we are told to measure the sizes, what will we do. I don't think we are going to measure  everything by scale. What should we do to check the truth of statement then? In my view i think that speed of light is not changed,so if we use it to measurement, it's gonna helpful. The problem arises when i thought what will happen if time start running at half the speed? I m stuck here now

By my understanding, if everything doubled in size, such as the Sun and the Earth, and because the space in between them (which is nothing) can't expand, would the gravities greatly change and the Earth be pulled into the Sun?


Where should I put systemd file for e.g. Nginx nginx.service or something like that on Ubuntu 16.04 ?

I  that there are two folders for unit files (not in user mode). /usr/lib/systemd/system/: units provided by installed packages /etc/systemd/system/: units installed by the system administrator  Conflicting with this understanding is the answer to this question: . Can someone fill in the missing information so that I understand what is going on? (UPDATE: The answer has been updated, and my understanding no longer conflicts with it.) Also, it seems that the scripts are organized in subfolders within the /etc/systemd/system/ folder: getty.target.wants multi-user.target.wants  In another location I read that there are other locations. It seems these are for user-specific services. /usr/lib/systemd/user/ where services provided by installed packages go. /etc/systemd/user/ where system-wide user services are placed by the system administrator. ~/.config/systemd/user/ where the user puts its own services.   Update 2015-08-31: For the sake of others, here is a link to a related question I recently asked:


I'm looking for a way to determine which packages I have installed on my system after having installed the OS.  Say for example I install Xubuntu 16.04, which already comes with a certain number of packages. Then I setup all my work stuff and install a whole bunch of other packages.  Is there a way to list only the packages that I personally installed after my distribution was installed ?

How can I list installed packages by installation date?  I need to do this on debian/ubuntu. Answers for other distributions would be nice as well.  I installed a lot of stuff to compile a certain piece of code, and I want to get a list of the packages that I had to install.


Yes, I know this has been asked a lot. But, it confuses me, since the results on google for this search show different methods (listed below)  $(document).ready(function() {     if ($('#DivID').length){         alert('Found with Length');     }      if ($('#DivID').length > 0 ) {         alert('Found with Length bigger then Zero');     }      if ($('#DivID') != null ) {         alert('Found with Not Null');     } });   Which one of the 3 is the correct way to check if the div exists?  EDIT: It's a pitty to see that people do not want to learn what is the better approach from the three different methods. This question is not actually on "How to check if a div exists" but it's about which method is better, and, if someone could explain, why it it better?

How can I check the existence of an element in jQuery?  The current code that I have is this:  if ($(selector).length > 0) {     // Do something }   Is there a more elegant way to approach this? Perhaps a plugin or a function?


When I was in the Army, I was taught that you addressed an individual officer as "Sir" or "Ma'am". You address groups of officers as "Gentlemen" or "Ladies", not "Sirs" or "Ma'ams".  Example: Approaching a group of male officers, I would salute and say "Good morning, gentlemen" not "Good morning, sirs."  Now, whenever someone says "Sirs", I cringe.  It sounds as bad as if someone said "Ma'ams".    But is it actually incorrect, or is it strictly an Army thing?  Note: I'm not talking about the rare situation where you might be introducing someone to a group of knights and saying "May I present Sirs Galahad and Lancelot"

A security guard wishes to address multiple people respectfully at once. Does he say:     Sorry, sir, but this ID is invalid.   or     Sorry, sirs, but your IDs are invalid.   or something like     Sorry, gentlemen, but your IDs are invalid.


TP-Link TD-W8968 advertises print server support for Win and Mac OS. Does it support printing with Ubuntu OS?

I am a bit financially strapped and received a Gateway GT5056 tower. The tower has an AMD dual core 64-bit processor in it. Will Ubuntu 12.04 run on this machine? I will not have any other application other than LibreOffice installed.


How do you pronounce “asks” in “She asks too many questions”? Is it possible to omit the “s” while we are speaking?

I know the correct pronunciation (I think) of the words "ask" and "asked", but I quite often hear them pronounced as "ahks" and "ahksed" (almost like an "r" sound). I've heard it both in conversation and on television shows (both Australian and American).   Are these pronunciations due to dialect, or are they alternative pronunciations or incorrect pronunciations? If they are the correct pronunciation, should I use them or the "normal" pronunciation?


I'm sending a XMLHttpRequest from a js file to a php file. The php file gets results from a MySql Database stored on a Ubuntu Remote Server. In the Database, I have stored a movie title 7 Años. The php code keeps echo ing 7 A�os. How to fix this issue? Where is this issue happening exactly?  I have included the lines header("Content-Type: UTF-8"); and mysqli_set_charset($connection, "UTF8"); in the beginning of the php file.  The Column Collation:

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


Given two lists of dictionaries:  >>> lst1 = [{id: 1, x: "one"},{id: 2, x: "two"}] >>> lst2 = [{id: 2, x: "two"}, {id: 3, x: "three"}] >>> merge_lists_of_dicts(lst1, lst2) #merge two lists of dictionary items by the "id" key [{id: 1, x: "one"}, {id: 2, x: "two"}, {id: 3, x: "three"}]   Any way to implement merge_lists_of_dicts what merges two lists of dictionary based on the dictionary items' keys?

I have two Python dictionaries, and I want to write a single expression that returns these two dictionaries, merged (i.e. taking the union).  The update() method would be what I need, if it returned its result instead of modifying a dictionary in-place. >>> x = {'a': 1, 'b': 2} >>> y = {'b': 10, 'c': 11} >>> z = x.update(y) >>> print(z) None >>> x {'a': 1, 'b': 10, 'c': 11}  How can I get that final merged dictionary in z, not x? (To be extra-clear, the last-one-wins conflict-handling of dict.update() is what I'm looking for as well.)


I currently have ubuntu 12.04 installed on my computer, but i wan't to change back to Windows 7, but when i tried to install Windows 7 via a DVD/CD, it couldn't install on any of my hard drives. This is mainly because my hard drive's file system is "ext4" and not "ntfs." Also i have tried to format the drive, but it shows up with an error stating that my hard drive is "busy."

I want to know how to make a drive ( non-system ) from EXT4 to NTFS. Can anyone help me out?


I've created a custom class with key-value options using pgfopts. So far this is working fine. Now I would like to create a key which can take a random string including equal sign and comma.  The below example will illustrate my needs.  \begin{filecontents}{\jobname.cls}     \ProvidesClass{\jobname}[2018-11-20 v1.0 SE Test package]     \RequirePackage{pgfopts}     \pgfkeys{         testproj/.cd,         mystuff/.store in = \myValue,         mystuff = {} % <-- Set default to empty     }     \ProcessPgfOptions{/testproj}     \LoadClass[\myValue]{article}     \endinput \end{filecontents} % ------------------ \documentclass[mystuff = {hello=SE,test=1}]{\jobname} %\pgfkeys{/testproj/mystuff = {hello=SE}} % <-- working as aspected \begin{document}     myValue: \myValue \end{document}   The key mystuff should take any string and should be passed as class option. The problem is that mystuff will only take "hello" as argument instead of the whole content inside the parenthesis "hello=SE,test=1".  How can I manage to pass a random string as class option including a equal sign and a comma using pgfopts?

The following produces error! The error is solved if no space exists between text= and {5in,8in}. This is really weird! Why is this happening with LaTeX?  \documentclass[a4paper,10pt,onecolumn,oneside, portrait]{article}  \usepackage[text= {5in,8in},centering]{geometry}  \begin{document}      \section{What Endogenous uncertainty is:}  yes  \subsection{Type as it is : Stochastic and determ! } on  \subsubsection{Well there is more than it} Yes    \end{document}


My problems: Windows 7 is not working and GRUB is "gone". This is what's happend:  Note: my OS is in Norwegian so I tried to translate it as good as I can.   I'm on the internet when there come up a notification that there's only ~2Gb of free space on my hard drive. Windows asks me if there's something I can delete. I choose some folders and delete them. I reboot to windows and a startup repair thingy comes up but can't find and/or repair the problem(s). In the diagnistics and repair details log is says (among other things) "Boot Manager can't find OS loader". There's 2 failed tests at the bottom: File repair, failed, error code 0xa; Repair of data storage for startup configuration (?), failed, error code: 0x2. I found somewhere to try some commands: bootrec /fixmbr, bootrec /fixboot, bootrec /scanos and bootrec /rebuildbcd, rebooted but nothing had changed. I could still get to Ubuntu from GRUB. Then I tried to activate a partition (at the time I didn't know what that would do). I used diskpart --> list disk --> select disk X --> list partition --> select partition X (here I didn't know which partition to activate, so I made my best guess (the biggest primary), which was wrong. When I rebooted it is said something along: can't find a OS. There was no GRUB. I found a lightweight linux (puppy linux), got it on a usb, live booted, activated partition no. 1 on the hard drive, rebooted, and now it goes straight to windows (without the GRUB), to the startup repair program.   This is where I am now. Back to the beginning, only worse.  I don't know what info you'll need, so just ask. Also I'm quite new when it comes to partitioning and the like.  What partition should be active? I've got 2 primary, 1 extended and 2 logical (ubuntu?)

i got problem about my PC, my pc use dual OS, but after I install windows the grub cannot detect my BAcktrack,my Backtrack location in /dev/sdaa4, I try to repair but error :  sudo su mkdir /media/bt mount /dev/sda4 /media/bt   error you must specify the filesystem type next i try another command  mount -t ext4 /dev/sda4 /media/bt   error again  wrong fs type, bad option, bad superblock on /dev/sda4, missing codepage or helper program or other error   So what can i do for repair my grub?


So my Google accounts primary email address has changed.  This means now when I log into SO, I don't have access to my old posts as a new account seem to have been created :-(  Is there anyway to merge my old SO account into my new account?

I accidentally posted a question without being logged in. Is there a way to associate that question with my account?   For more information, visit "" in the .   a.k.a. How can you link a registered account to a cookie-based account? a.k.a. How do I merge an unregistered account with a registered account a.k.a. Merging users a.k.a. How do I associate anonymous questions I’ve asked with my registered account? a.k.a. Is there a way to claim an unregistered user? (in case anyone searches with those terms)


For example I have this string: hello:there:world  How do I split these three words to string array, I mean the final result will be this:  arr[0] = "hello"; arr[1] = "there"; arr[2] = "world";   Thanks in advance.

I'm trying to iterate over the words of a string.  The string can be assumed to be composed of words separated by whitespace.  Note that I'm not interested in C string functions or that kind of character manipulation/access. Also, please give precedence to elegance over efficiency in your answer.  The best solution I have right now is:  #include <iostream> #include <sstream> #include <string>  using namespace std;  int main() {     string s = "Somewhere down the road";     istringstream iss(s);      do     {         string subs;         iss >> subs;         cout << "Substring: " << subs << endl;     } while (iss); }   Is there a more elegant way to do this?


I've been seeing this "style" of minimalist icon more and more, with that "shadow" on the bottom right. Is there a specific name for this? Thanks.

I want to buy some stock photos like the ones below. What is this design called?  I don't even know how to start searching...


Buying a Canon eos 2000d.  Building 2 soft light box with some white fabric and cheapo led strips with some dimming circuit.  Building a white paper desk for background  i have some photoshop and photograpy skills  Could i shot decent product photos with those equipment.  My target quality is this   thanks for your input

My friend asked me to create a photo like this:    I noticed that its shadowless and my first question is whether it was setup to be shadowless, or was it made shadowless in post? How many lights are involved here? I think there's one for the background, and one above the product pointing something like 30 degrees down, and then some reflectors to the side. Just guessing.   I did some Googling and came across . How could that be shadowless? Looks like the product is a few feet above the ground, which is a white seamless background, and the camera and all the lighting are all pointing down. How could there be no shadow on the ground?  Thanks!


Consider the following awk statement which sums the values of column 1 in a file  cat $1 e | awk '      {total=total+$1}   # this comment does not contain any single quote marks                    END {printf("%.2f\n",total)}                '   It works as expected.  Now let's keep the same statement, but change the comment to have a single quote mark inside  cat $1 e | awk '      {total=total+$1}   # don't do this                     END {printf("%.2f\n",total)}                '   When I run this in either Mac Os or Centos, I get the following error  ./bad_sum: line 2: syntax error near unexpected token ` ./bad_sum: line 2: `                  END {printf("%.2f\n",total)}'   It looks like awk is trying to match the quote mark in don't with the quote mark after awk and thus gets confused. But since comments are supposed to be ignored, how can this be explained?

I'm reading shell tutorial today from   In which it mentions:     If a single quote appears within a string to be output, you should not put the whole string within single quotes instead you whould preceed that using a backslash () as follows:   echo 'It\'s Shell Programming'   I tried this on my centos server, it doesn't work, a > prompts out to hint me type more.  I was wondering, since two single quotes transform every special characters into normal characters,  which include escape symbol \, but exclude itself, the ', how should I represent a single single quote 'in a single-quoted phrase?


On document ready, I have the page calling ajax and displaying a table of results.  The rows can be updated by clicking a button, the button then calls a function which posts the update to the server.   I have this working without enclosing the click function in the document ready function but once I combine them it doesn't work.  html

   Javascript  $(document).ready(function(){      $('.approveCredit').on('click', function(e) {         e.preventDefault();          var creditid = $(this).attr('creditid');         var allocatedcreds = $(this).attr('allocatedcreds');          $.ajax({             url: "assets/ajax/addcustomer.php",             type: "POST",             data: {creditid: creditid,allocatedcreds: allocatedcreds},             success: function(result){                 alert('Credit Applied!');                            },             error: function(exception){                 alert('Exception:' +exception);             }         });      });      $.post('assets/ajax/calldata/newreqs.php', function(data) {         $('#newreqs').html(data)     });  });   Data Called

 #	 Name	 Requested Credits	 Notes from User	 PO	 Date Requested	 Status	 Actions

 <?php    $count = 1;     while ($row = mysql_fetch_array($test))       {?>
        <?php echo $count++;?>	        <?php echo $row['user_id'];?>	        <?php echo $row['credits'];?>	        <?php echo $row['notes'];?>	        <?php echo $row['po'];?>	        <?php echo $row['date_received'];?>	        <?php echo $status;?>
                <a class="btn btn-xs btn-default approveCredit" type="button" allocatedcreds="<?php echo $row['credits'];?>" creditid="<?php echo $row['id'];?>" data-toggle="tooltip" data-original-title="Approve Credit Request">

  <?php } ?>

   As mentioned, this works when I don't encase the click function in the document ready function, however, when encasing nothing works.  The reason why I encased the click function is because I wanted to create a onpage refresh after the data had been updated on the server.

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


I have noticed people use this sentence to reply to written mails but I often ask myself; why use "hear" when you "read" ?  Is it just a generally accepted phrase or people do use it wrongly ?

I'm from Russia and I've got a problem with writing a letter. Can I use the phrase "glad to hear such news" if I'm not speaking with a person? Isn't it better and more correct to use "glad to know"?


I'm trying to sort a file using the Sort command but its not working:  The file contains lines like:  photo1 photo11 photo12 photo13 photo17 photo18 photo19 photo2 photo22 photo23 photo25 photo26 photo27   I'm using the command, sort -k6 Photos so that it start sorting after the string "photo", can someone tell where I'm going wrong??


Please see  for bios error messages.  I bought a Lenovo Ideapad 100S 11IBY that has 32bit-uefi boot. It came with Windows 10 but b it is a Intel Atom laptop and I wanted to install lxde Linux on it to use its resources well.   After a lot of online research I managed to create a UEFI 32-bit bootable lubuntu USB using linuxium (lubuntu with kernel patch for baytrail processor), and it worked!  I was happy with the installation but yesterday I decided I wanted to install mate desktop environment through terminal. After a reboot the laptop never booted to Ubuntu.   These Error messages appear again and again.:  Ubuntu failed to boot   and  boot device missing   I have tried all sorts of 32bit uefi bootable usbs, windows 10 recovery USB, and windows 10 installation USB but nothing boots.  On the boot menu I just see two repeated optiond, both options say "Ubuntu" and both fail to boot.  Can someone help me either installing back windows 10 or somehow get PST the boot errors? See the linked video at the top for error messages on my screen.

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


How can one create a single first line indent?  The idea is to produce the same exact effect as the Microsoft Word "First line indent":    That produces an output, such as:   Side-note: the purpose is not to indent the paragraph, but rather make the extended line (big sentence - not new line) start before the normal (not indented) first line. That is to say, how can one outdent all lines except the first one (including a section, subsection, etc)?  Thanks in advance!

I am trying to write a text where the first line of each paragraph has an indent(tab). But for some reason, in a chapter or a section or subsection, except the first paragraph, the rest of the paragraphs have an indent(tab). Is there any way to add an indent to the first paragraph in a chapter or section or subsection?


If $f: R \to R$ is a non constant, thrice differentiable function such that $f(1+ \frac{1}{n}) = 1$ for all integers, then find $f''(1)$  Since function is continuous so, $f(1) = 1$  I have this formula for $f''$   $f''(c) =\lim_{h \to 0} \frac{f(c+h) + f(c-h) - 2f(c)}{h^{2}}$ So $ f''(1) =\lim_{n \to \infty}\frac{f(1 + 1/n) + f(1- 1/n) - 2f(1)}{1/n^{2}}$ Then I used L' hospital, but ended up getting $f''(1+1/n)$ which is just $f''(1)$   Any suggestion or hint would be helpful.

Let $f:\mathbb R \rightarrow \mathbb R$ be a non-constant, thrice  differentiable function such that $f(1+1/n)=1$ for all $n \in \mathbb Z$.  then what is the value of $f^{\prime \prime}(1)$?   Answer is 0


I have many input sources - English, French, Chinese Simplified and Japanese Hiragana, and pressing cmd+space or ctrl+space to scroll through the menu just doesn't do the trick. Is there a way to set up a keyboard shortcut to switch to one specific input source? e.g. cmd+ctrl+1 for english and cmd+ctrl+2 for french etc.? If using automator (or terminal) can solve the problem, I would gladly use it. Thanks.

I like making a habit to use the different languages I study, to keep that knowledge fresh. So I like typing in those languages when I get the chance. But swapping keyboards under OSX is just a little too cumbersome.  For example, I was just typing the name of one of my co-workers in its original 汉子 form instead of as an English transliteration. It's nice. It reminds me to pronounce her name properly, with tone, etc., which otherwise doesn't come naturally. The transliteration of her name is especially misleading. Everyone at the company is pronouncing it wrong.   But to swap into writing 汉子 I have to mouse up to the top menu bar, select a new keyboard, type, mouse back up to the top bar, and then select back into English. I know there's a keyboard shortcut, but with 5 different keyboards active in my menu, cycling through 5 to get to the one I want feels just as cumbersome.  Is there a way to attach a hotkey to a specific keyboard, or some other way to make swapping character sets lighter?


since for a fixed $\omega$, $B_s(\omega)$ is continuous in $s$ then $B^2_s(\omega)$ is Riemann integrable w.r.t. $s$ :   $X(\omega) = \int_{0}^{1} B_s^2(\omega) ds \implies X =  \lim_{n \to \infty} \frac{1}{n}\sum_{k = 1}^{n} B^2_{\frac{k}{n}}  =  \lim_{n \to \infty} \frac{1}{n}\sum_{k = 1}^{n} Y_k$  I would like to use the strong law of large numbers but I don't have independence of the $Y_i$'s.  I know for one that for $t \geq s$, the increments $B_t - B_s$ are independent of $B_s$, maybe we can somehow use this property here ?

I don't have a background of stochastic calculus.   It is known  that definite integral of standard  from $0$ to $t$ results in another Gaussian process with slice distribution that is normal distributed with mean equal to $0$ and variance $\frac{T^3}{3}$ i-e  $$ \int_0^{t} W_s ds \sim \mathcal{N}(0,\frac{t^3}{3})    $$  Question:  What if we square the standard Wiener process and then integrate i-e $$ \int_0^{t} W_s^2 ds \sim ?    $$  Would that be scaled Chi-square distributed ?


Today I had this weird empty window pop up and I don't know what it is, where it comes from, what it does nor how to get rid of it. It's just an empty window with only the title bar showing, but an empty title, in the old Windows style.  It looks like this:   Any ideas how I can find out more about this window? Right-clicking on it does nothing. I can move it, it's always on top of all other windows.  I'm using Windows 7 64 Bit.

There is a tiny window that I am unable to identify or close. It is big enough for me to move but I can't seem to stretch it to make it bigger, I can't close it. It does not appear to be any of the items listed as Applications in the Task Manager.  Is there any sort of program that allows me to identify a process by clicking on the window of the application?  I really want to know what this is. If I log out it goes away but something I am doing is causing it to re-appear.  Any ideas how best to troubleshoot it?


There is a problem with Freemind 0.9, which is the version I get if I use sudo apt-get install freemind.   When trying to share a .mm file between Windows Freemind and Ubuntu Freemind, I get the error      Error while parsing file:freemind.main.XMLParseException: XML Parse   Exception during parsing of a map element at line 1: Expected: =   Googling, I find advice at  to instead use Freemind 1.0.   I don't do a lot of manual installs in Linux.   I first download, then unzip, and put the directory in /opt/. I then add to ~/.profile the line export PATH=$PATH:/opt/freemind-bin-max-1.0.0_RC_4/.   But this seems to only work for calling freemind.sh from the terminal. I'd like to call from the launcher.   Is there a better way to do all this? Is there a relatively easy way that is also better?   I've checked the  site, they only provide 0.9 for Debian.   Note: I am Kubuntu user.

Will Unity allow making custom launcher icons from .desktop files or via menu editing system? (Right now the launcher doesn't give the option to "keep in launcher" on all programs.  For some programs I use, I have to make custom launchers or .desktop files.  For instance, daily blender builds are generally just folders with an executable.  In basic Gnome or KDE, I can make a new menu entry with the menu editing system. Then, I can also add it to Docky either from the menu or by dragging a .desktop file to it. Unity launcher doesn't support drag and drop, so thats not a bug or anything, but when I open a .desktop file, it has unpredictable results. Most time it will not have "keep in launcher". Sometime it will have a pinnable item without the .desktop's icon, and if I pin the item to the launcher, it will not call upon the program again after closing it. I've also gotten it to just work with a .desktop file for celtx.


I am seeing many videos saying that 1 Joule is the work done to lift ~100g through a distance of 1m (like this one ). The idea is that 100g has a gravitational force downward of 1 Newton. So lifting it means applying 1 Newton over 1m, and therefore is 1 Joule.  But if I apply 1 Newton upward, and gravitational force is 1 Newton downward, the object shouldn't move.  So I believe you need to apply a force greater that 1 Newton in order to lift it.  Or am I missing something?  Would it be more accurate to say that 1 Joule is the work done by gravity to make fall 100g by 1 meter?

From Wikipedia: The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product: $$W = Fd.$$  If I lift some object from a ground, the force to be put in above equation is the gravitational force $mg$.   But while I am moving the object upwards, against the gravity, I must pull the object with greater force than $mg$, right? So the net force is $F_{myforce}-mg$ which results in object being lifted. But this is not the case. Why? Does it matter how strongly I pull the object?  What work will I do if I move this object in absence of gravity (in space)? Will work done be zero or not?


Prove that every bilinear form $f:\mathbb R^n \times \mathbb R^n\rightarrow \mathbb R$ has a basis $\{v_1,\ldots,v_n\} \subset \mathbb R^n$ such that $f(v_i,v_j)=-f(v_j,v_i)$ for every $i\neq j$.  I have no idea how to start thinking about this one. Should I actually "build" the required basis or what? Any ideas ?  thanks

I didn't want to bloat the title, i'll also add that the basis is in ${\mathbb{R}^n}$. This question seems kind of easy, but its from a test so I assume there is a catch here somewhere.   I tried to prove it by contradiction. Assume by contradiction that there exists no basis that satisfies the condition. But as known, every bilinear form can by identified by a matrix so that $A_{ij} = f(v_i,v_j)$. If there is no basis so $f(v_i,v_j) = -f(v_j,v_i)$ it means there is no skew-symmetric matrix which can identify a bilinear form over $\mathbb{R}$ which is obviously not true( I guess an example can be given here, I think ).  This proof just seems to simple to be true, but I can't seem to figure what could be wrong with it. I'll greatly appreciate any tips, thanks!


I've searched to find an answer to my specific question but could not find one that matched. I understand that return 0 and return EXIT_SUCCESS essentially do the same thing of saying that the program ended successfully, but what if you do return 1 or return 2 or any other int value for that matter? Do different int values mean different things to the compiler or is returning any int simply mean that the program terminated successfully, in which case it doesn't matter what int value you put in? To my (limited) knowledge, it seems that int main() just needs to return any int in order to terminate. Am I wrong?  Thanks and I apologize if this was asked before, I just wasn't able to find it.

What is the correct (most efficient) way to define the main() function in C and C++ — int main() or void main() — and why? And how about the arguments? If int main() then return 1 or return 0?  There are numerous duplicates of this question, including:       — For C++, with a very good answer indeed.     Related:


I am looking for the smallest number larger than $0$ which when multiplied by $2$, forms a permutation of itself.  I quickly remembered that the number $142,857$ does that, as well as with all numbers up to $6$ (including). This is the first cyclic number, formed by the fraction of $\frac{1}7$  But a computer program quickly showed that the smallest number that does what I asked for is $125,874$, because $125,874*2 = 251,748$. Interestingly, this number is a permutation of $142,857$ too.   But my question is, how can I find this smallest number without a computer program or pre-knowledge, but only with logic and algebra?   Thanks!

Can you find the smallest positive number such that if you shuffle the digits of the number in a particular order, the shuffled number becomes twice the original number.  Source:   I understand the answer is $125874 => 251748$  $251748$ is twice the $125874$ and have same digits $1,2,4,5,7$ & $8$  but how to solve this non programmatic ?


I was trying to solve some change of basis exercises, so I've done them and I want you to tell me if I've done it correctly.     1) Given the coordinates system $(O'; X'' Y'')$ asociated to the    basis $B=[{b_1=\frac{1}{\sqrt{2}}; \frac{1}{\sqrt{2}};  > b_2=\frac{-1}{\sqrt{2}}; \frac{1}{\sqrt{2}}}]$ with origin in    $O'=(2;5)$, find the intersection between $Q: y''^2=-4 \sqrt{2} x''$    and the straight line in $(O,XY)$ $V=(0;5)+t(-1;1) t\epsilon R$    Well, first I tried to write $Q$ in terms of $X$ and $Y$, and not in terms of $X''$ and $Y''$. I used the formula:  $(\begin{matrix}  X''\\  Y'' \\  \end{matrix})$ =$(C)_B$ × $(\begin{matrix}  X-2\\  Y-5 \\  \end{matrix})$   Then I replaced those values in the equation of $Q$ and I got $Q: \frac{(-x+y-3)^2}{2}=-4 \sqrt{2} \frac{(x+y-7)}{\sqrt{2}}$   After that, I found the intersection between $Q$ and $V$ using equations and I got that the intersection points in $(O;XY)$ are $P_1(3;2)$ and $P_2(-1;6)$      2)Given the coordinates system $(O,X'Y')$ asociated to the basis    $B=[{b_1=\frac{1}{\sqrt{2}}; \frac{1}{\sqrt{2}};  > b_2=\frac{-1}{\sqrt{2}}; \frac{1}{\sqrt{2}}}]$ with origin in    $O=(0;0)$ and the ellipse $9X'^2+5Y'^2-3X'+2Y'-10=0$ find the    coordinates of the centre of the ellipse in $(O,XY)$    So, here I found the centre of the ellipse in $(O,X'Y')$ and it was $(\frac{1}{6}; - \frac{1}{5})$, then, doing something similar to what I've done before I found out that the centre in $(O,XY)$ was $( \frac{11}{30 \sqrt{2}};$ $\frac{-1}{30 \sqrt{2}}$)

I tried to solve the following exercises, so I want to ask you if my answers are correct.     1) Given the coordinates system $(O'; X'' Y'')$ asociated to the    basis $B=[{b_1=\frac{1}{\sqrt{2}}; \frac{1}{\sqrt{2}};  > b_2=\frac{-1}{\sqrt{2}}; \frac{1}{\sqrt{2}}}]$ with origin in    $O'=(2;5)$ and the system $(O;XY)$ asociated to the standar basis, find the intersection between $Q: y''^2=-4 \sqrt{2} x''$    and the straight line in $(O,XY)$ $V=(0;5)+t(-1;1) t\epsilon R$    Well, first I tried to write $Q$ in terms of $X$ and $Y$, and not in terms of $X''$ and $Y''$. I used the formula:  $(\begin{matrix}  X''\\  Y'' \\  \end{matrix})$ =$(C)_B$ × $(\begin{matrix}  X-2\\  Y-5 \\  \end{matrix})$   Then I replaced those values in the equation of $Q$ and I got $Q: \frac{(-x+y-3)^2}{2}=-4 \sqrt{2} \frac{(x+y-7)}{\sqrt{2}}$   After that, I found the intersection between $Q$ and $V$ using equations and I got that the intersection points in $(O;XY)$ are $P_1(3;2)$ and $P_2(-1;6)$      2)Given the coordinates system $(O,X'Y')$ asociated to the basis    $B=[{b_1=\frac{1}{\sqrt{2}}; \frac{1}{\sqrt{2}};  > b_2=\frac{-1}{\sqrt{2}}; \frac{1}{\sqrt{2}}}]$ with origin in    $O=(0;0)$ and the ellipse $9X'^2+5Y'^2-3X'+2Y'-10=0$ find the    coordinates of the centre of the ellipse in $(O,XY)$    So, here I found the centre of the ellipse in $(O,X'Y')$ and it was $(\frac{1}{6}; - \frac{1}{5})$, then, doing something similar to what I've done before I found out that the centre in $(O,XY)$ was $( \frac{11}{30 \sqrt{2}};$ $\frac{-1}{30 \sqrt{2}}$)


I have a folder on Windows that contains files whose name contain unicode extended characters (simplified chinese). I'd like to grab a list of these files. Of course, cmd won't display them correctly, but I was hoping Powershell could.  Unfortunately, the result of the dir command isn't any better. When I search existing questions, everything is about the file encoding, not displaying the file name.  I'm not looking to make any system-wide change like changing the system locale or the default code-page, but I would expect PowerShell to be able to handle unicode output on screen.

Currently I'm running Windows 7 x64 and usually I want all console tools to work with UTF-8 rather than with default code page 850.  Running chcp 65001 in the command prompt prior to use of any tools helps but is there any way to set is as default code page?  Update:  Changing HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Nls\CodePage\OEMCP value to 65001 appear to make the system unable to boot in my case.  Proposed change of HKEY_LOCAL_MACHINE\Software\Microsoft\Command Processor\Autorun to @chcp 65001>nul served just well for my purpose. (thanks to )


Show that $\operatorname{Hom}_{\mathbb{Z}}\left ( \mathbb{Z}/n\mathbb{Z},\mathbb{Z}/m\mathbb{Z} \right )\cong \mathbb{Z}/\left ( n,m \right )\mathbb{Z}$  I think that the hom-set (of $\mathbb{Z}$ module homomorphisms ) is isomorphic to $\left \{ a\in \mathbb{Z}/m\mathbb{Z},na=m\mathbb{Z} \right \}=\left \{ k+m\mathbb{Z} \right \}$ where $m\mid (nk)$ but I can't show that it's isomorphic to $\mathbb{Z}/\left ( n,m \right )\mathbb{Z}$

Describe explicitly $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_n, \mathbb{Z}_m) := \{\varphi:\mathbb{Z}_n \rightarrow \mathbb{Z}_m \mid \mathbb{Z}\text{-linear homomorphism}\}$  There is an answer to this question that says $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_n, \mathbb{Z}_m) \cong \mathbb{Z}_{(n,m)}$ where $(n,m)=\gcd(n,m)$. But I am having some trouble seeing this.  For the sake of an argument, suppose the above answer is true, that $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_n, \mathbb{Z}_m) \cong \mathbb{Z}_{(n,m)}$. Suppose $n=4$ and $m=8$. Then $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_4, \mathbb{Z}_8) \cong \mathbb{Z}_4$.   Now consider each of the following maps in $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_4, \mathbb{Z}_8)$:  $\varphi_1(1)=1$   $\varphi_2(1)=2$   $\varphi_3(1)=3$   $\varphi_4(1)=4$   $\varphi_5(1)=5$  $\varphi_6(1)=6$  $\varphi_7(1)=7$  Are each of these maps not unique? If there are two that are identical, could you please explain which two and why? Thank you!  My alternate answer is that $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_n, \mathbb{Z}_m) \cong \mathbb{Z}_m$, since I think each $\varphi \in \operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_n, \mathbb{Z}_m)$ is uniquely determined by where it maps $\varphi(1) \in \mathbb{Z}_m$.


Everyone.  I am new to LaTex, so I apologize if this has been answered before.  I am using TexWorks to write my novel.  It appears that the novel class is not working.  it crashes.  Has anyone else experienced this?  Thanks, ML

I am writing a novel and fairly new to using LaTeX.  Please bare with me if this is a silly question.  I am working off of the novel demo LaTeX file using the TexWorks software.  I have inserted my words into the file.  When I run the LaTeX code, I get the error message saying "! LaTeX Error: File `novel.cls' not found."  Do I need to download this file from somewhere?  If so, where can I get it?


I saw some responses here saying that the singularity into the black hole is one dimension object so my question is : is it possible that the singularity is simply a merger of the 4 dimensions of the spacetime? Is it possible physically and mathematically that many dimensions can merge into one ?

Should a black hole be considered two-dimensional or three-dimensional?  It means that a black hole doesn't occupy space, but interacts with it. Or it actually occupies space, and still interacts with it?


I got stuck on this problem. So I really appreciate if anyone can give me some hint to move on. Thanks a lot.     Prove that an entire analytic function $f:\mathbb{C} \rightarrow \mathbb{C}$ is a constant function if $f(z) = f(z+1)=f(z+i)$ for all $z \in \mathbb{C}$   As far as I know, there're some famous theorems on how to prove an entire analytic function is constant, like Liouville theorem, maximal modulus theorem, identity theorem... But I still can't figure out how to apply those to this problem. I think about the dense property of $\mathbb{Q}$ in $\mathbb{R}$, so I tried to prove that $f(z) = f(z+q)$ for all $z \in \mathbb{C}$ and all $q \in \mathbb{Q}$, then use the continuity to prove that it's true for $q \in \mathbb{R}$. But I can't prove that statement.

Let $f: \Bbb C \to \Bbb C$ be an entire (analytic on the whole plane) function such that exists $\omega_1,\omega_2 \in \mathbb{S}^1$, linearly independent over $\Bbb R$ such that: $$f(z+\omega_1)=f(z)=f(z+\omega_2), \quad \forall\,z\in \Bbb C.$$Prove that $f$ is constant.   The intuition seems clear to me, we have the three vertices of a triangle given by $0$, $\omega_1$ and $\omega_2$. All points in the plane are one of the vertices of that triangle under a suitable parallel translation. The constant value will be $f(0)$, fine. Throwing values for $z$ there, I have found that $$f(n\omega_1) = f(\omega_1) = f(0)=f(\omega_2) = f(n\omega_2), \quad \forall\, n \in \Bbb Z.$$  I don't know how to improve the above for, say, rationals (at least). Some another ideas would be:   Checking that $f' \equiv 0$. I don't have a clue of how to do that. Write $w = a\omega_1+b\omega_2$, with $a,b \in \Bbb R$, do stuff and conclude that $f(w) = f(0)$. This approach doesn't seem good, because I only have a weak result with integers above. Finding that $f$ coincides with $f(0)$ on a set with an accumulation point. This seems also bad: the set on with $f$ coincides with $f(0)$ by which I found above is discrete.    Nothing works and this is getting annoying... And I don't see how analyticity comes in there. I'll be very thankful if someone can give me an idea.  (On a side note.. I know that this title is not informative at all. Feel free to edit if you come up with something better.)


I am a beginner in Blender 3D, but I can already appreciate the power of this app.   I downloaded this book -->   However, I am encountering a lot of problems because my version 2.72b and most of what I am reading refers to UI which dates back to older versions.  Can someone help me identify a beginners book (in pdf format) that is updated for the version 2.70+.

Since asking for tutorials, videos, resources, links to other content or downloads is considered off topic here, this is a specifically created Community Wiki which gathers resources for Blender and it has been approved by the .  Just write in the appropriate answer/section. If you have concerns, questions, post a  question, so we don't clutter the comments, but you can link your meta question from the comments.  Questions regarding such resources are not allowed anymore, except for very specific and on topic requests (ask on  if you're unsure about your question). Follow the instructions made in the question about how to post, what can be posted, etc.  Learning             Assets    (also see: )   Reference Images/Blueprints (also see: )    Tools    (also see: )      Other   Special Interest ()     Also see the .


Let $A$ and $B$ be two positive semi-definite $n\times n$ matrices. We say $A\geq B$ if $A-B$ is positive semi-definite.    Let $A^{\frac{1}{2}}$ be the square root of the positive semi-definite matrix $A$.  How to prove if $A\geq B$ then $A^{\frac{1}{2}}\geq B^{\frac{1}{2}}$?  I could prove  this for $B=I$, (i.e., $A\geq I \implies A^{\frac{1}{2}}\geq I$. But I am not able to prove it for the general case.  Note:  1) All positive semi-definite matrices are symmetric for me.   2)Square root of a matrix:- Let $A$ be a symmetric matrix, then there exists  an orthogonal matrix $P$ such that $P^TAP=diag(\lambda_1,\lambda_2,\cdot, \lambda_n)$, where $\lambda_1,\lambda_2,\cdot, \lambda_n$ are eigenvalues of $A$.   Define $A^{\frac{1}{2}}:=Pdiag(\lambda_1^{\frac{1}{2}},\lambda_2^{\frac{1}{2}},\cdot, \lambda_n^{\frac{1}{2}})P^T$ for a positive semi-definite matrix $A$. (Notice, $\lambda_i^{\frac{1}{2}}$ are well-defined as $\lambda_i$'s are non-negative (since A is positive semi-definite).

I remember reading somewhere about the following properties of non-negative definite matrix. But I don't know how to prove it now.  Let $A$ and $B$ be two non-negative definite matrices. If $A^2\succ B^2$, then it necessarily follows that $A\succ B$, but $A\succ B$ doesn't necessarily leads to $A^2\succ B^2$.  How can you prove it? Thanks!


Suppose I'm given a polynomial $P(z)=z^n + a_{n-1}z^{n-1}+\ldots+a_0$ in closed unit disk and know that $|P(z)|$ doesn't exceed $1$ in the domain: then $P(z) = z^n$ is it's only possible form My work. If $P(z)=z^n+a_{n-1}z^{n-1}+\ldots+a_0$ then $$P(1)=1+a_{n-1}+\ldots+a_0$$ and since $|P(1)| \le 1$ we have $|1+a_{n-1}+\ldots+a-0|$$\le 1$. I'm just stuck here not able to proceed any further Any idea as how to proceed.

Given a polynomial $ P(z) = z^n + a_{n-1}z^{n-1} + \cdots + a_0 $, such that   $\max_{|z|=1} |P(z)| = 1 $      Prove: $ P(z) = z^n $      Hint: Use cauchy derivative estimation    $$ |f^{(n)} (z_0)| \leq \frac{n!}{r^n} \max_{|z-z_0|\leq r} |f(z)| $$ and look at the function $ \frac{P(z)}{z^n} $     It seems to be maximum principle related, but I can't see how to use it and I can't understand how to use the hint.


I sometimes need abstract dynamic lines in some works. The image attached is a good example of what i'm trying to re-create. Any suggestion or good starting point / tutorial on how to create these sort of lines on illustrator (or photoshop) ?

I am trying to create an effect like this one in Illustrator, but I haven't been able to achieve a great result. I would really appreciate a little help, even if it is just the name of the effect. Also, if it is easier in another tool like photoshop, please let me know.   I have mostly tried a combination of the blend and warp tools. I haven't had any other ideas, or any luck googling.


How would you suggest using a forward slash (/) between multi-word phrases? Should a slash be even used between multi-word phrases?  For example -      Following are the open/in progress issues.   or     Following are the open/ in progress issues.   or     Following are the open/in-progress issues.   P.S. - The example sentence is just for explaining the problem, I'm not necessarily looking for an alternate way to put the same point forward.

I don't want to get into the proper use of the phrase 'and/or', but rather to investigate the use of the forward slash between other words. Examples:   I have an interview with him/her this afternoon. He has a large binder/notebook.   And even separating just letters:   I connected the i/o ports. (input/ouput) Mark the field as n/a. (not applicable) I did it w/o her help. (without)   It seems as thought the forward slash can be used to indicate an option, display ambiguity, shorten 2 words and shorten 1 word (and others).  Is it OK to use a slash to separate these words/letters (yes, that was intended), or is it better to explicitly say 'his or her'? One more thing, is it correct to 'chain' these phrases together? I'm horrible with examples but here's one:   I don't open letters/mail that aren't/isn't addressed to me.


When we rotate a right angled triangle about its perpendicular we get a solid cone. For a right-angled triangle the centre of mass is at its centroid i.e., at  $(\frac h3, \frac b3)$. If we consider a solid cone to be made up of many right-angled triangles, the centre of mass should be at a height of $\frac h3$ from the base whereas it is at $\frac h4$ from the base for a solid cone. I have obtained the proper answer through integration but I am unable to figure out where I am going wrong in this logic. Kindly point out where I am going wrong.

How can a distinction be made between the centre of mass of a right circular cone    As a uniform solid ($\frac{h}{4}$ from base, where is $h$ is height) and  That composed of infinitesimally small thickness of right triangles of the same height and base (same as radius of cone). In which case it apparently appears to be $\frac{h}{3}$ from base.


“I met a friend walking down the street.”  Does it mean I was walking, or that my friend was walking, or both are possible?

I want to visit clubs with attractive women.   This phrase can be interpreted in two ways:    I want to visit clubs myself, but the clubs I visit should have  attractive women.  I want to take attractive women to clubs; the clubs themselves may  or may not already have attractive women.    Is there a name for this ambiguity? It seems fairly common. I want to  say "dangling participle", but I'm pretty sure that's wrong.  Is this the equivalent of Grouch Marx's "I shot an elephant in my pajamas... how he got into my pajamas, I'll never know"?


I am connected to a machine via SSH and I often need to listen to WAV files on that machine. I usually open another terminal window and do ssh host 'cat /path/to/sound.wav' | aplay, but that's tedious since I have to enter my password every time (I cannot use public-key authentication) and the file paths are long.  What I would like to do is start magic-command on my local computer, and then whenever I need to listen to a remote file, run play-locally sound.wav from the remote shell and hear the sound from my speakers. Is this possible?

So I have finch, a command line chat client (think pidgin) running on a remote machine that I ssh into. finch has notification sounds and can run a command when certain events occur, letting you pass the sound file in as %s. e.g. mplayer %s  from the remote machine, when the notification occurs, what kind of command could I run to play whatever %s is on my local machine?


On an exam I took recently, I was challenged with the following problem but couldn't come up with an answer. I couldn't find the answer by searching the forum either so I hope it hasn't been asked before. Any help on how to answer, and if possible how to think when challenged with this kind of problem, is much appreciated:     Problem Create a Lebesgue measurable set $E\subseteq [0,1]$ such that $0<m(E \cap I)<m(I)$ for all intervals $I=(a,b)$, where  $0\leq a<b\leq 1$ and m is the Lebesgue measure.

I was wondering how one can construct a Borel set that doesn't have full measure on any interval of the real line but does have positive measure everywhere.   To be precise, if $\mu$ denotes Lebesgue measure, how would one construct a Borel set $A \subset \mathbb{R}$ such that $$0 < \mu(A \cap I) < \mu(I)$$ for every interval $I$ in $\mathbb{R}$?   Moreover, would such a set necessarily have to contain infinite measure?


I have assigned vertexes on the head where hair grows from. I am now in the stage of animation. My problem that when I move the head of my cartoon, hair does not move with the head. What shall I do, any advice.

I created a model with make human and added hair via the emitter tool.  I added clothes and rigged the person with pitchipoy.  Everything seems to be moving right except for the hair.  While animating the object the hair stays in place, shouldn't it follow the emitter and the bones?  Or do I have to add bones for the hair somehow as well?


canonical commutator relation(CCR) can be derived by switching classical poisson bracket to quantum commutator and this process is called as canonical quantization.  $[x_i,p_j]_{PB}=\delta_{ij} →\frac{1}{ih}[x_i,p_j]=\delta_{ij}$  and also, the classical hamilton's equation of motion can be written by this quantum meachanical language,  $ \frac{dp}{dt}=[p,H]_{PB},\frac{dq}{dt}=[q,H]_{PB} →i\hbar\frac{dp}{dt}=[p,H],i\hbar\frac{dq}{dt}=[q,H]$  This is the heisenberg equation of motion as far as I know.  I want to know, how to derive schrodinger equation from this heisenberg equation of motion.  Maybe it looks like a stupid question. But please help me.

How do you derive the  (wave mechanics, time dependent state) from  (matrix based, time dependent operators)


I'm trying to create a list box on a 3d view panel but I can't seem to find the correct control in the list of properties that have an associated UI or in any other related documentation. What I'd like to do is instantiate on of these:  within a blender python script. Does the API expose these controls and if not, is there some way of creating a custom control with its own drawing and mouse handling routine within python or would I have to add that in C++ and expose it to python (which is probably a bit more involved than I have time for at the moment)

How can I make a Interface which is similar to the Material-Interface within Blender via Python?    It should look like these. Could you guide me to the right direction? I don't think it's in bpy.ops, right?  Thank you very much!


I have a project I am working on that involves a view screen I made. At one point, just to tinker with it, I was trying to get a video rendered on that view screen. All that ended up happening was Blender rendered only that video and not the whole project. I set it up with the movie clip editor section. I decided it wasn't going to work for what I wanted to do anyway so I deleted that video and just put an image on the view screen. I am trying to get Blender to render the project again but it still is only rendering images from the deleted video. I deleted the video from the movie clip editor but it is still being rendered. Its got to be a simple setting I am overlooking, or at least I hope so. How do I get Blender to go back to rendering the whole project I am working on? If more info is needed, please just ask and I will provide whatever is needed.

Blender is rendering an older version of my project, not the most recent one. I have made it using the Blender Render but it does not want to render in cycles either. A black and grey screen is rendered as if everything is transparent. Checked general camera, lighting and compute devises in case I messed something up but I can't find anything. All my textures and objects look normal, does anybody know what is wrong or what to check?  Ok added link:


I really like that in the new Ubuntu 20.04LTS the repositories are always updated to the latest. When a new version of a software comes, I dont have to do it manually. But, this at times is problematic, because, sometimes, until I'm finished with a project, I'd not like to upgrade version of a software. How can I stop automatic upgrade for a specific app or atleast downgrade it to a previous version after the upgrade?

Because of  I'd like to prevent apt-get upgrade and Update Manager from updating the "libgtk2.0-0" package.   How can this be achieved?


I tried to attach a 1TB WD Passport external and got the message:     Warning: The driver descriptor says the physical block size is 2048   bytes, but Linux says it is 512 bytes.   I decided to run the following command:   sudo dd if=/dev/zero of=/dev/sdc bs=2048; sync   It's been running for 2 days straight and haven't completed  Did I use the wrong command to fix the block size? If so, how can I safely exit and start over?   I would like to use the external drive to transfer and store files from different systems  edit: Since I wasn't sure if interrupting would be bad, I let it finish but got error     dd: error writing '/dev/sdc': No space left on device   Note: several people marked this as exact duplicate and linked to  but that's not what I'm looking for. Not looking to create live usb.

I was using:  dd  if=/path/to/my/ubuntuiso/ubuntu.iso  of=/dev/sdb1  bs=4M  &&  sync   In order to create bootable Ubuntu USB drives on older Ubuntu versions. It was working perfectly. Sometimes I used the Startup Disk Creator program, which  worked well.  But when I use the same methods on Ubuntu 16.04 LTS, I get some warnings while formatting it afterwards.   The installation media works as expected, but when I try to format that USB stick after my work is done, I get the following warning :    The partitioning of that Pendrive looks strange :    And it also shows my 16GB pendrive as 64GB.  After struggling a lot with Gparted, I will somehow format it. But Why is it happening like this ?? Is there any better methods of creating bootable Ubuntu in 16.04 ?  EDIT : there is a related question . But my question is not about how to format it properly. My question is "How to create a bootable USB without that errors." & "Wht are the causes of that error"


Is it considered a bad practice to combine a loose equality check (foo != null) with a strict equality check (bar === true)?  In my opinion, they should both be compared with the strict equality, or both be compared with the loose equality check.  Is there ever a scenario where I would need to have a loose equality check combined with a strict equality check?  Thanks Stackoverflow!   Looking forward to your insight!  const foobar = foo != null && bar === true;   Edit, this question differs from  because, this is particularly on combining a loosely equal comparison with a strict equal comparison. This stack overflow question referenced above is only in conjunction with using one or the other.   I am particularly interested if its ever a valid use case to use both a loose equal, with a strict equal inside a comparison.

I'm using  to go through JavaScript, and it's returning many suggestions to replace == (two equals signs) with === (three equals signs) when doing things like comparing idSele_UNVEHtype.value.length == 0 inside of an if statement.  Is there a performance benefit to replacing == with ===?   Any performance improvement would be welcomed as many comparison operators exist.  If no type conversion takes place, would there be a performance gain over ==?


We had a SQL expert suggest rebuilding our table indexes weekly.  We're currently doing this Saturday night and it causes lots of timeouts during the rebuild process.  I'd like to avoid the timeouts if possible, so is it a good idea to do the weekly index rebuild?  We're running MS SQL server 2014.  UPDATE We get this error during the rebuild "System.Data.SqlClient.SqlException: Timeout expired. The timeout period elapsed prior to completion of the operation or the server is not responding. "  Thanks!

When should I rebuild the indexes in my relational database (SQL Server)?    Is there a case for rebuilding indexes on a regular basis?


there are two ways to define a constructor with basic data:  var Person1 = function() {     this.name = "Wayne"; }; var Person2 = function() {}; Person2.prototype.name = "Wayne";   whats the difference between that?

What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something };


After researching pure CSS ways to "sticky" my footer, I am at a loss. Here is the structure of the layout on my site:

     What I have tried with some success is adding   min-height: 100vh;   to the "content" section, but it's still not good enough.  Any suggestions to make the

 stick to the bottom?

I have a simple 2-column layout with a footer that clears both the right and left div in my markup.  My problem is that I can't get the footer to stay at the bottom of the page in all browsers.  It works if the content pushes the footer down, but that's not always the case.


I am new to to Light Path Node in Blender and was wondering if there is way of using a HDRI Background in the world settings while excluding specific Objects in the Scene from the direct illumination from the used Background? So that those excluded objects are getting a toonish kind of look. I just can´t get my head around this topic. Thank you for your help.

My question is, how would I make the visible HDRI/Enviroment Map be image 1 and then have reflections as Image 2? If someone can post a node setup, or a .py file that would be great <3 I was thinking maybe using the Is Camera Ray node but I'm not confident it would work, and have no idea where to start.


First off I apologize if this is the wrong place to ask this question, if it is please direct me to the correct place. Ok with that out of the way I have a question about where to host my website. I am a fairly experienced web developer who hosts my stuff on a github.io page. This has worked for me but I want to try and get into hosting my own server  that I control. Can you Webmasters please give me an idea of what website I could use that would allow me to have a custom domain and have a server that would run basic things like php, mysql and server side scripts. I have read  but it did not tell me what services would provide the best web hosting for my needs.   Other Details:  My site will probaly only get 10-20 visits a day so I'm not looking for heavy traffic web hosting  PHP supported needed  mysql support would be nice but, I can live without it  I would like to only be spending around $15 a month  I would need a custom domain I don't want any of that www.myname.bu1.4.com/freehosting

This is a "catch-all" question designed to serve as an answer for all questions about choosing web hosting.  Pro Webmasters no longer accepts new questions about how to choose hosting.  All future questions pertaining to finding web hosting should be closed as a duplicate of this question. For more information about this policy please see .    How to find web hosting that meets my requirements?  What we're looking for in answers to this question are the basics about web hosting:   What is web hosting? What is the difference between shared, VPS, and dedicated hosting? How does a content delivery network relate to web hosting? Anything else you feel is helpful in finding a web host.   What we do not want is:   Endorsements or recommendations for specific web hosts We do not want your experience or other subjective information (just the facts please)


I have a friend that says "I and John went to the store"  instead of "John and I went to the store".   Is this still correct?

I've always been taught to put myself last when referring to myself in the same sentence as others but the usage of "me and..." seems to be everywhere these days. The misuse of the word "me" instead of "I" aside, is there some new rule I haven't heard of? Shouldn't we put ourselves last regardless of the "me"/"I" usage?  Examples of "correct" usage:      My friends and I went for some ice   cream. Did you see my friends and me   at the ice cream stand?   Examples of "incorrect" usage:     Me and my friends went for some ice   cream. Did you see me and my friends   at the ice cream stand?   Note: I was also taught that the only person who could put themselves first was the queen.


We want to clear the multiple sites cache from one site, currently we have multi-site configuration. Is there any module?

I am using Drupal multi-sites (single codebase, multiple sites/*). Along with this, I have started using Drush aliases to manage them:  $ cat sites/all/drush/aliases.drushrc.php <?php $aliases['localdev'] = array(   'site-list' => array(     'site1',      'site2',     'site3',   ), ); ?>   This allows me to easily perform actions on all sites:  $ drush @localdev cc all   >> I've also just discovered that I can just use , and forgo the drushrc file.  Doing this, will execute "cc all" on each of my sites in series (one at a time).  I'd like to take this to the next level and try to run these commands on all sites simulantiously. I've been doing some reading, and am under the impression that Drush   support this. The  takes $backend_options, which can contain (from function documentation):   *      'invoke-multiple'  *        If $site_alias_record represents a single site, then 'invoke-multiple'  *        will cause the _same_ command with the _same_ arguments and options  *        to be invoked concurrently (e.g. for running concurrent batch processes).  *      'concurrency'  *        Limits the number of concurrent processes that will run at the same time.  *        Defaults to '4'.   What I can't figure out, however, is how do I actually use this from the Drush command line. Is there an option I need to pass to Drush, or do I need to set something in a settings file?   Any info will be much appreciated - my curiosity is piqued!   UPDATE  Based on the answers below, I was able to create a simple test that demonstrates Drush's behaviour, and draw some conclusions:  Drush's default behaviour when executing operations on multiple sites is to use concurrent processes:  $ drush @localdev ev "drupal_set_message(time()); sleep(5);"  Continue?  (y/n): y site1             >> 1360512943      [status] site2             >> 1360512943      [status] site3             >> 1360512943      [status]   This is true even when not using aliases, and is also true when using Drush's built-in @sites alias. These two commands yield identical behaviour as above:  $ drush site1,site2,site3 ev "drupal_set_message(time()); sleep(5);" $ drush @sites ev "drupal_set_message(time()); sleep(5);"   To change the number of concurrent processes (default is 4), the '--concurrency=N' option can be passed in the drush command. For example, if I want serial execution, I can set the number of concurrent processes to 1:  $ drush @localdev ev "drupal_set_message(time()); sleep(5);" --concurrency=1  Continue?  (y/n): y site1             >> 1360513387      [status] site2             >> 1360513393      [status] site3             >> 1360513399      [status]