How can I make the box distribute evenly? code as below:  \documentclass[border=5pt]{standalone} \usepackage{tikz} \usetikzlibrary{matrix,positioning} \begin{document} \begin{tikzpicture} \def\lw{1pt} %define linewidth here \tikzset{box/.style={draw,rotate=90,inner sep=0pt,line width=\lw,     minimum width=2.2cm,minimum height=2.2cm,text width=1.6cm}} \matrix (M1) [matrix of nodes,draw,inner sep=2pt,         row 1/.style={align=right},         row 5/.style={align=left},         row sep=-\lw,column sep=-\lw,         nodes={box},nodes in empty cells]{  & PORCH 1st &  & DOOR & \\  &  &  &  & \\  &  &  &  & \\  &  &  &  & \\  & BSMT & GARAGE & PORCH 2nd & \\}; \end{tikzpicture} \end{document}   Now the output seems ugly:

I wanted to draw an almost empty matrix of nodes with TikZ similar to the left most one below. All nodes would have same size (through minimum width and minimum height) and no separation between columns and rows. But when I include a text which needs two lines I obtain the central matrix and, if the text just needs one line the right most one. I don't know what's wrong. Do you? I'm using CVS version of TikZ.  \documentclass[tikz,border=2mm]{standalone} \usetikzlibrary{matrix}  \tikzset{ proces/.style={draw, minimum height=15mm, minimum width=2cm, outer sep=0pt, text width=1.5cm, align=center} }  \begin{document} \begin{tikzpicture}  \matrix (A) [matrix of nodes,nodes=proces,nodes in empty cells] {  & \\  & \\ };  \begin{scope}[xshift=4.5cm] \matrix (A) [matrix of nodes,nodes=proces,nodes in empty cells] {  & OOO OOO \\  & \\ }; \end{scope}  \begin{scope}[xshift=9cm] \matrix (B) [matrix of nodes,nodes=proces,nodes in empty cells] {  & A \\  & \\ }; \end{scope}  \end{tikzpicture} \end{document}


I am supposed to show that the axiom of replacement implies the axiom of seperation and I am not sure if my solution is correct.   I am trying to show that given any set A and Property P(x) there is a subset of A which contains exactly the Elements for which P(x) is correct.(set 1)  I choose the Property P(x,y)=P(x) and y=x. By the replacement axiom (y:P(x,y) is true for some x in A) (set 2) is a set.  I now have to show that set 1 = set 2. If x is an Element of set 1 than the Element y=x must be an Element of set 2 because for x in A we have y=x and P(x). If y is an Element of set 2 than by the definition of set 2 y=x and P(x) and x is in A so y is also an Element of set 1.  I am very new to proving stuff so I am grateful for any feedback.  Regards James

Axiom $3.6$ (Replacement). Let $A$ be a set. For any object $x \in  A$ and any   object $y$, suppose we have a statement $P(x, y)$ pertaining to $x$ and $y$,   such that for each $x\in A$ there is at most  one $y$ for which $P(x,y)$ is   true. Then there exists a set $\{y: P(x, y) \text{ is true for some } x \in A\}$    such that for апy object $z$,  $$ z\in \{y : P(x, y)\text{ is true for some } x \in A\}  \iff  P(x,z)\text{ is true for some } x \in A.$$      Axiom $3.5$ (Specification). Let $A$ be a set, and for each  x$\in$  $A$, let $P(x)$ be a property pertaining to $x$ (i.e., $P(x)$ is either  a   true statement or a false statement). Then there exists a set,  called   $\{x \in A : P(x) \text{ is true}\}$ (or simply $\{x \in A : P(x) \text{ for short}\}$),  whose elements are precisely the elements $x$ in $A$ for which $P(x)$  is true. In other words, for any object $y$,  $$у \in \{x \in A: P(x)\text{ is true}\} \iff (y \in A \text{ and } P(y)\text{ is true}).$$   I have to show that $3.6\implies 3.5.$  Proof: By $(3.6)$ we can assume the following set $$\{x:P(x,x)\text{ is true for some }x\in A\}.$$ Let $Q(x)=P(x,x)$ then we get the set $$\{x\in A:Q(x) \text{ is true for some }x\},$$ which is what $(3.5)$ wants. Is this proof correct?  PS. I have read other answers to this question on MSE, but none of them use this formulation of the axiom and I guess use more formal notation. I am learning from Tao's Analysis book and so I've not been introduced to such notation.


Let's say I have one website abc.com.my, and now I want to create a new domain xyz.my but with its own meta description and meta title which points to abc.com.my. So I need to create one index.html inside the xyz.my domain then redirect to abc.com.my.  So in SERP I hope to see xyz.my with its own meta description and meta title and abc.com.my with a different meta description and title but both point to abc.com.my. So will this affect my ranking or is it bad for SEO?

Lets say I have a domain already, for example www.automobile4u.com (not mine), with a website fully running and all.  The title of my "Website" says:    <title>Used cars - buy and sell your used cars here</title>   Also, lets say I have fully SEO the website so when people searching for the term buy used cars, I end up on the second or first page.  Now, I want to end up higher, so I go to the google adwords page where you can check how many searches are made on specific terms.  Lets say the term "used cars" has 20 million searches each month.  Here comes the question, could I just go and buy that domain with the search terms adress, in this case www.usedcars.com and make a redirect to my original page, and this way when people search for "used cars", my newly bought domain name comes up redirecting people to my original website (www.automobile4u.com)?  The reason I believe this benefits me is because it seems search engines first of all check website adresses matching the search, so the query "used cars" would automatically bring www.usedcars.com to the first result right?  What are the downsides for this?  I already know about google spiders not liking redirects, but there are many methods of redirecting...  Is this a good idea generally?


What is correct?  1.) The topic is smart homes.  2.) The topic are smart homes.  Regarding 1.) It sounds wrong for me, but in my opinion grammatically correct. Regarding 2.) It sound right, but grammatically incorrect.  Thanks!

My fish's native habitat is rice fields. My fish's native habitat are rice fields.   Which one is correct? I'm pretty sure it's the first, since 'is' modifies 'habitat,' but it still sounds weird...


I'm very new to LyX and LaTeX, but keep seeing it mentioned while Googling for composing a novel.  I'm understanding that it might offer the simplicity of being able to focus on writing the story, without worrying about the format, while at the same time handling the format so everything is arranged precisely, and with perfect type-setting, and ready to go.  And, that with the Outline/Table-of-Contents tab, on LyX, I'll be able to see the arrangement of chapters and scenes to move them around, cut-and-pasting them as necessary.    I'm thinking that if I learn LyX, I can just enter the text, then draft and re-draft it to perfection and see the whole content.  Unlike some of the special novel writing software that's out there already, at the end of my project, with LyX, I should have a novel that I can print, and it should actually be ALREADY formatted like a book, ready to go (without having to send off to a professional publishing house for conversion using their secrete software ;-)   And, unlike Word, Libre-Office, or Abiword, I won't have to spend the majority of my time worrying about arranging the format, fonts, layout, etc... In short, I should be able to focus on creating the story rather than creating the book, at the end everything will be in its proper spot.    And so, I'm wondering if I'm understanding the potential power of LyX and LaTeX correctly, that its main use is for any document that uses a strict pre-defined format, such as creating Text Books with very complex formats and/or formula, or a novel with simple, but strict, format requirements.    I keep reading about "templates", "classes" and "modules", to which I really don't understand the difference just yet.   But I'm looking for one designed for novels.  Should I try to learn LyX and LaTeX, and try to find a template to compose a novel, or am I trying to figure out how to operate a bulldozer to move a small bucket of dirt? :-)   If not, please recommend a novel template or module?

I'd like to use LaTeX to typeset a novel. Could you recommend me any template?  What I mean is a template (some .tex file) where I can include my chapterN.tex files (mainly plain text) and get a pretty good design with zero work :)


I was wondering if there is some mathematical approximation for calculating the ratios of factorials. I don't mean a shortcut to deriving the factorial results through a means like Stirling's Formula, but of bypassing the factorial calculations altogether when the final ratio would actually turn out to be a small number. The reason I'm asking is that I occasionally run into manifestations of this problem when teaching myself to convert statistical and data mining equations into T-SQL code, where the highest precision float data types can only go up to about a 135! or so before triggering arithmetic overflows. The final product of these ratios, however, is often much smaller even when very high values are plugged in, and would fit comfortably within the range of the data types I'm using.  For example, 200! is beyond the range of our data types. But if you plug it into the equation N! / (N -1)! it would return 0.0049751243781094527363184079602, which fits easily. What I need is some general-purpose method for reaching the same answer (or something close to it) without using factorials as either the divisor or dividend. Approximations would be acceptable.   I'm also running into a similar issue when nearly infinitesimal decimal points are tacked onto the end of divisors. For example, I found it difficult to code the Hosmer-Lemeshow Test because the final test statistic often involves computations like this: 1 / (1 + some number like 0.1-E50). When the two parts of the divisor are added together, the infinitesimal part is rounded off in almost all computer languages I've heard of. Like the factorial ratios, the final product would fit easily within most high-precision data types, but cannot be reached through the standard equation. Is there a means of approximating these type of equations as well (or even of factoring them by splitting the divisor somehow?).   Thanks for any help in advance. In order to avoid duplicating any existing questions I tried to do some searches across the Internet and in CrossValidated on this issue over the last month or so on both, but may be using the wrong search terms, because I'm coming up empty. I figured CrossValidated would be the right forum, since I'm encountering these issues from time to time with various statistical and data mining algorithms, most recently the Hosmer-Lemeshow Test.

I have a Dirichlet distribution from which I'm maximizing $\alpha$ by calculating the log likelihood with the following equation  $p\left(s|\alpha\right) = \sum\limits_{i=1}^O\log\left(\frac{n_i!}{\prod\limits_{j=1}^kn_{ij}!}\frac{\Gamma\left(\alpha_0\right)}{\Gamma\left(\sum\limits_{j=1}^k\left(n_{ij}+a_j\right)\right)} \prod\limits_{j=1}^k \frac{\Gamma\left(n_{ij}+\alpha_j\right)}{\Gamma\left(\alpha_j\right)}\right)$  I have a python script to calculate the log likelihood. It works for small values, but when $n_{ij}$ gets high $\Gamma\left(\sum\limits_{j=1}^k\left(n_{ij}+a_j\right)\right)$ and $\Gamma\left(n_{ij}+\alpha_j\right)$ python runs into overflow error (the max for math.gamma is between 171 and 172).   Is there a way to change the likelihood function so that $\Gamma\left(\sum\limits_{j=1}^k\left(n_{ij}+a_j\right)\right)$ and $\Gamma\left(n_{ij}+\alpha_j\right)$ don't run into overflow errors. Can I just divide the values in $\Gamma$ by for example 100, if I then compare the likelihood between $p(s|\alpha)$ with different $\alpha$ values do the best $\alpha$ values still have the highest likelihood?


In most popular explanations of General Relativity, both in print and film/television, gravity is demonstrated using an example of a 2 dimensional plane being flat, then when putting a heavy object in it it curves the plane into a funnel shape and you can visualize how other objects roll down the funnel into the gravity well simulating something like the orbits of the planets around the sun as an example.  However this demonstration relies on the notion of "down", or even the actual gravitational attraction on Earth, so that the objects in orbit roll or fall down the well.  This kind of explanation seems to rely on a force in order to explain that the force of gravity is just the curving of spacetime. At the very least I find this to not really explain how the theory of General Relativity actually works.

Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing?


I wish to get GIMP as well as Krita working on my new RaspPi4. How do I go about doing this?

How can I install applications like Google Chrome on Ubuntu?  Are there any commands to install an application?    Index of answers:


I have a 4 GB drive with Time Machine backups on it that I've not used in a couple of years.  It's nearly full.  I wanted to start using it again, but first I wanted to remove ~2/3 of the backups, to free up space, while keeping a good sampling. Thus I removed 50 of the 70 backups (cmd-delete in Finder), alternating removing two and keeping one while going through the entire list chronologically; as a consequence, what remains goes back just as far, just with less frequency.   But, after doing this, the drive is still nearly full.   I figured that's because I needed to empty the trash, but when I tried to do that it removed items slowly, and then stopped. So I stopped the emptying and checked trash, and saw nearly nothing had been removed.  I then ejected the drive, after which the trash was empty.  But when I re-mounted the drive, the items in trash all reappeared.   There is a procedure given in this thread, but the behavior the OP describes doesn't exactly correspond to what I'm seeing:    So: Should I try the terminal command in the above thread?  Or do the problems I'm having indicate my Time Machine partition may be corrupted?  If the latter is the case, it would make the most sense to just reformat the disk and start clean.  Granted, it would be nice to have some of the old backups, but I don't have a critical need for them (not critical enough to buy a new disk and put this one in storage).  UPDATE: Never mind. I tried adapting the instructions given in the post Allan linked, and couldn't get them to work.  So I just erased & reformatted the entire disk and started over.  In retrospect, my mistake was following an answer I found elsewhere on apple.stackexchange.com, which said one could delete individual backups in Finder by dragging them to the Trash.  I should have instead used tmutil in Terminal.

I was going to delete the Time Machine backups. I made a mistake and instead of deleting them using Time Machine, I just moved the Backups.backupdb folder to the trash. Now, if I try to empty the trash, Finder attempts to count the number of files that will be deleted, and this process is incredibly time-consuming, because the Finder tries to count each file in each backup. The same thing happens if I try to move the Backups.backupdb folder from the trash back on my hard drive where it was before.  What can I do in this situation? How can I delete the backups?


I try to use list-comprehensions see link here:  but it create generator instead of return list And when I try to convert it to list- it work only once, and then the list disappear  values=[3,"fasdf",99]   vv=(str(x) for x in values)   vv  <generator object <genexpr> at 0x047D2F08>  list(vv)  ['3', 'fasdf', '99']   list(vv)  []  values   [3, 'fasdf', 99]

When should you use generator expressions and when should you use list comprehensions in Python?  # Generator expression (x*2 for x in range(256))  # List comprehension [x*2 for x in range(256)]


This is from Discrete Mathematics and its Applications Here is the definition of countable that the book uses  and how to determine if two sets have the same cardinality  Here is the example that the book gave  Here is some work I added to the example  What I realized from the example was that the function n/2 would map an even positive integer to a positive integer and the function -(n - 1)/2 would map an odd positive integer to a negative/zero integer. I then showed that both functions were one to one and onto. From this, I reasoned that there is a one to one correspondence from the set of positive integers to all integers because there are functions that map from an positive integer to an integer and that one positive integer will map to one unique integer and that every integer has a positive integer that will map to it. Is this reasoning correct? I tried to apply this idea to the next example the book provided that I didn't really understand. Here is the book example I don't really understand  Is there any equation that can be used to map a positive integer to a positive rational number, just like the equation in the last example to map a positive integer to an integer so I can go through my little proof to understand this better?

I remember my professor in college challenging me with this question, which I failed to answer satisfactorily: I know there exists a bijection between the rational numbers and the natural numbers, but can anyone produce an explicit formula for such a bijection?


Can anyone help me please? Don't know where to start since the numerator looks complicated. Thanks!

I'm not sure how to go about this. Does it involve using MVT?  I got as far as saying $e = \frac{e^x - e^y}{x-y}$.


Given a Ruby class with a static method like  class Foo   def self.bar     puts "Hello"   end end   I always accessed the method via  Foo.bar   However, I just noticed that you can also do  Foo::bar   Why is that? Is there a semantic difference? My initial idea was that it's a matter of treating Foo as a class object (in which case the first version seems plausible) vs. treating it as a "namespace" like a module, in which case the second version makes sense.

Simple question, but one that I've been curious about...is there a functional difference between the following two commands?  String::class String.class   They both do what I expect -- that is to say they return Class -- but what is the difference between using the :: and the .?  I notice that on those classes that have constants defined, IRB's auto-completion will return the constants as available options when you press tab after :: but not after ., but I don't know what the reason for this is...


How to find the net electric force exerted on rod 2 by rod 1, both being on the x-axis, both having the same length and constant linear charge density, being some distance apart?  More specifically, if rod 1 is on the x-axis from $-L$ to $L$ and rod 2 is on the x-axis from $L+x$ to $3L+x$, and both have the same lambda linear charge density, what is the net force of rod 1 on rod 2?  I understand that the electric field created by the first rod is not uniform over the space occupied by the second rod.   I know $F=qE$, where $F$ and $E$ are vectors, and the electric field for continuous charge distribution formula.  However, I don't know how to proceed with solving this problem using this information. In particular, there are two position vectors that vary (identify positions with different electric fields, not one point), instead of 1 as usual. Please help by identifying the strategy and starting point to solve this problem. I drew a diagram and wrote down the equations but further than this I've failed to go. Thank you for your help.

A line is charged uniformly with the linear density $\lambda$ . What is the force between two sections with lenghts $l_{1}$ and $l_2$ if their end points are separated with distance $r_{0}$?  I have calculated that the electric field from the section on the right is:  $$ E(x)=-k \lambda \frac{l_{2}}{(l_{1}+x)(l_{1}+l_{2}+x)}  $$  I am not sure how to get the force. I tried:  $$ dF=E(x)dq=\lambda E(x)dx \Rightarrow F=\int_{0}^{l_{1}}-k \lambda^2 \frac{l_{2}}{(l_{1}+x)(l_{1}+l_{2}+x)} dx $$ But probably it isn't the right way.   Thank you for any help in advance.    ------------------------------------------------------------------------------  propposed solution:      $$ dF(x_1)= (\lambda dx_1) \int_{l_{1}+r_{0}}^{l_{1}+r_{0}+l_{2}} \frac{\lambda dx_2 }{4\pi \epsilon_0 (x_2-x_1)^2}=k\lambda^2\frac{l_{2}}{(x_{1}-l_{1}-r_{0})(x_{1}-l_{1}-l_{2}-r_{0})}dx_1 $$ The net force:  $$ F=\int_{0}^{l_{1}} F dx_1=\int_{0}^{l_{1}}k\lambda^2\frac{l_{2}}{(x_{1}-l_{1}-r_{0})(x_{1}-l_{1}-l_{2}-r_{0})}dx_1=k\lambda^2log(\frac{(l_{1}+r_0)(l_2+r_0)}{r_0(l_1+l_2+r_0)}) $$


I know that is is illegal for Israeli citizens to enter area A of the West Bank. However, foreign citizens that enter Israel are usually allowed to travel to such areas.   Are holders of an A1 visa (residence visa valid for 3 years) in a foreign passport covered under the ban on Israelis entering (such visa holders would have both an Israeli non-citizen-resident ID Card and a foreign passport)? Or does this ban exclusively apply to those who are citizens?

My understanding is hazy, but I've been told that to get from certain parts to others, like Jerusalem to Bethlehem, you may need to cross non-Israeli-controlled areas.  Does this mean you'd need your passport and a different visa, or can you just cross through these zones if you're not from the area (ie just a random tourist from far away)?


This is basically a follow-up to the comments on  which I couldn't find to be settled anywhere. I learned that you can write ordinary bracket simply using  f(x)   but that you can also use  f \left( x \right)   where the latter automatically adopts the brackets' size, but creates a space between the function and the bracket.  My question is: when is one supposed to use which version. Is the second version only used when the "content" of the bracket is not an argument of some function? What if it is a long and complex argument, where I want the brackets to be increasing in size? Would I then use  f \! \left( long expression \right)   or is there some other solution for this?    Edit: While I found some solutions regarding the space adjustment, I was still wondering when to use which approach, i.e. whether there are some "best practice rules" for this.

What is the difference between ( and \left( in LaTeX? Sometimes, when the content is small, it does not seem to matter which pair I use.  What is the best practice when it comes to which parentheses use?


Installed Ubuntu for first time and when I restarted I could not remember my password. How do I retrieve it or create new one?

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


It is known that  any infinite cyclic group can never be a vector space , from this we can derive that if $(F,+,.)$ is an infinite field then $(F,+)$ cannot be cyclic . I am asking , is there any infinite field $(F,+,.)$ such that $(F^*, . )$ is a cyclic group ? (, where $F^*:=F$\ $\{0_F\}$ )

Let $F$ be a field and $F^\times$ be its group of units. If $F^\times$ is cyclic, then show that $F$ is finite.  I'm a bit stuck. I know that I can represent $F^\times = \langle u \rangle$ for some $u \in F^\times$ and that we must have that $|F^\times| = o(u)$, where $o(u)$ denotes the order of $u$ in $F^\times$.  I tried assuming $o(u) = \infty$, but I'm not sure exactly where to go from there. I was wondering if I could get a hint.


My roommates and I were looking at dutch redband treasure chest candies . One pack contains 14 chests with candy as treasure inside. On the face of every chest is 1/12th of a treasure map displayed. in other words, when you have 12 distinct pieces of the map, you have completed the "puzzle". We were wondering, what is the probability that you receive a full map in one pack? We assume that:  the supplier does fill the packs randomly and the supplier has an infinite supply of every map piece  So as a more general problem: We have a 12 sided dice, which is thrown 14 times. What is the probability that we get each face of the dice at least once.

It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here?


I have a dual SIM mt6589 based Android 4.2.1 phone, and I have no idea where the apps are getting installed.  My phone has an Internal SD card(built in), An External SD card and something called Phone Storage(/data ??)  Anyway the apps are supposed to be saved to my External SD but they get saved to Phone Storage.     Screenshots (click images for larger variants)  Also the option move to External SD card is greyed out(It was available before!!). My vold.fstab file   dev_mount sdcard /storage/sdcard0 emmc@fat /devices/platform/goldfish_mmc.0 /devices/platform/mtk-msdc.0/mmc_host dev_mount sdcard2 /storage/sdcard1 auto /devices/platform/goldfish_mmc.1 /devices/platform/mtk-msdc.1/mmc_host

I have installed a few Android applications both with the adb install MyApplication.apk command and via a webserver (like an alternative to Android Market).  But where in the Android file system on my phone is the MyApplication.apk file placed? Are applications installed with adb install not placed in the same directory as applications downloaded from the Market?  I found some applications on /system/app but I can't recognize them as some downloaded from Android Market or the one I have installed with adb install.  Where on the system is applications that I have installed located?  My phone is not rooted, and I am running Nexus One with Android 2.2.1.


For some reason Gmail has started blocking e-mail from my domain (flanigan.net).   I have had DKIM (opendkim), DMARC (opendmarc), and SPF implemented for some time. I am not on any of the SPAM or issues list that I can find. I have no history of bad behavior or issues, and I have no problem with sending e-mail to any other domain (yahoo, outlook.com, etc, etc).   The message I get back is unhelpful. I have filled in all the forms and done all the Gmail help guides I can find.   I just do e-mail from home use and for some friends and charities I support. All said and done only 40 users. Again no history of issues or SPAM.   Bounced Message Headers below:      Subject: Returned mail: see transcript for details   Date: 2016-12-16 11:10   From: Mail Delivery Subsystem    To:       The original message was received at Fri, 16 Dec 2016 11:10:19 -0500 from     >ns1.flanigan.net [IPv6:::1]      ----- The following addresses had permanent fatal errors ----- >>        (reason: 550-5.7.1 [2600:3c02::f03c:91ff:fe89:bda4      12] Our    system has detected that)      ----- Transcript of session follows ----- ... while talking to gmail-smtp-in.l.google.com.:    DATA    550-5.7.1 [2600:3c02::f03c:91ff:fe89:bda4      12] Our system has    detected that   550-5.7.1 this message is likely unsolicited mail. To reduce the amount of spam  550-5.7.1 sent to Gmail, this message has been blocked. Please visit <<< 550-5.7.1    550 5.7.1  for more information. u1si2266860ywd.269 - gsmtp   554 5.0.0 Service unavailable      Reporting-MTA: dns; ns1.flanigan.net   Arrival-Date: Fri, 16 Dec 2016 11:10:19 -0500

This is a  about how to handle email sent from your server being misclassified as spam.  For additional information you may find these similar questions helpful:                    Sometimes I want to send newsletters to my customers. The problem is, that some of the emails get caught as spam messages. Mostly by Outlook at the client (even in my own Outlook 2007).  Now I want to know what should be done to create "good" emails. I know about reverse lookup etc., but (for example), what about a unsubscribe link with an unique ID?  Does that increase a spam rating?


This is the symbol...    It's like a uppercase and cursive l.

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


when connected to ethernet my wireless automatically disables.  i try to re-enable it but it quickly disables again.  went to bios and the power management setting for this is unchecked, so, it's not the issue.  i want wireless on at the same time to connect my wireless hard drive and wireless printer.  how to keep the wireless enabled when connected through ethernet? this is for WINDOWS 10 ONLY not 7

A ethernet (Lan server) connection makes the WiFi disable automatically in windows 8.1. By switching on the WiFi manually let only WiFi to run for few moments and the WiFi goes off again. How can I fix this?


Prove that $$ (\sin \theta+\csc \theta)^2+(\cos\theta+\text{sec}\theta)^2\geqslant 9 $$ My attempt: I started by expanding this and got $5+ \csc^2\theta + \sec^2\theta$, after I made this $5+ \frac{1}{\sin^2\theta}+\frac{1}{\csc^2\theta}$ but now I am not able to proceed and not getting how to prove this expression $\geq 9$. So kindly help me.

I used the following way but got wrong answer $$A.M. \ge  G.M.$$ $$ \frac{\sin \theta + \csc  \theta}{2} \ge \sqrt{\sin \theta \cdot \csc \theta}$$ Squaring both sides, \begin{equation*} (\sin\theta + \csc\theta )^2 \ge 4 \tag{1}  \end{equation*} Similarly \begin{equation*} (\cos\theta + \sec\theta )^2 \ge 4 \tag{2} \end{equation*} Adding equation (1)  and (2)  \begin{equation*} (\sin\theta + \csc\theta )^2+(\cos\theta + \sec\theta )^2 \ge 8 \end{equation*} What is wrong?


#include <stdio.h> #include <math.h>  void swap(char* x, char* y) {   char temp;   temp = *x;   *x = *y;   *y = temp; }  int compare(char a, char b) {   if((int)a > (int)b)   {     return 1;   }   return -1; }  int bubbleSort(char *a, int n, int (*compare) (char, char)) {   int i, j;   for(i = 0; i < n; i++)   {     for(j = 0; j < n - 1; j++)     {       if(compare(a[j], a[j + 1]) > 0)       {         swap(&a[j], &a[j + 1]);       }     }   } }   void main() {   char* name = "Stackoverflow";   int i;   bubbleSort(name, sizeof(name) / sizeof(char), compare);   for(i = 0; sizeof(name) / sizeof(char); i++)     printf("%c ", name[i]); }   I have no clue about why this code is giving segmentation fault, I know the case when the segmentation fault occurs,that is, when the application tries to access the memory location out of its dedicated memory.

The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC.


So I have noticed that there are exact solutions to the exact question I found on an assignment sheet for a unit/class that I am currently doing (the source is from another college's publication on their own assignment). My question is that: is my professor allowed to use this particular question (which is identical in every way, even the wording) in an assignment given to us? Does this not count as being academically dishonest on the professor's part? I know that if I use these solutions it is plagiarism, but isn't using this question in an assignment given to us without any citations or references to the original source, counted as plagiarism on the professor's part?

I have a professor at my university who uses content from an un-cited textbook that he has never referenced anywhere, including his green sheet (syllabus), as an additional resource. At least some slides he has used include parts of content that have been re-worded and others that are 100% the same. I noticed this by Googling for textbooks on the material we're studying in class and found that examples given in one that I found were exactly the same as what he has provided.  Would this technically be plagiarism? Should he be given the benefit of the doubt in this situation?


Which prime numbers in $\mathbb Z$ are precisely the prime elements of $\mathbb Z[i]$ and why?  In my book it has been left as an exercise to show that a prime number in $\mathbb Z$ is a prime element of $\mathbb Z[i]$ if and only if it is of the form $4k + 3$.  How can I proceed?Please help me.  Thank you in advance.

So far, I know if $p$ is a rational prime, then $(1)$ if $p\equiv 3\mod4$, then $p$ is prime in $\mathbb{Z}[i]$. $(2)$ If $p\equiv1\mod4$  then $p=π_1 π_2$ where $π_1 $ and $π_2$ are conjugate, Then $π_1 $ and $π_2$ are primes in $\mathbb{Z}[i]$. $(3)$ $2=(1+i)(1-i)$, then $(1+i)$and$(1-i)$ are primes in $\mathbb{Z}[i]$.  What's are all the prime elements in Gaussian integers $\mathbb{Z}[i]$? For example, $-3$ are prime in $\mathbb{Z}[i]$, but not in the above $3$ cases.


I understand how the sum of the bottom row of Pascal's triangle is equal to $2^n$, but how is this formula equal to zero?  Shouldn't it be 1?  $\binom{n}{0}-\binom{n}{1}+\binom{n}{2}+...+(-1)^{n}\binom{n}{n} = 0$

Let $n$ be a positive integer. Prove that   \begin{align} \sum_{k=0}^n \left(-1\right)^k \binom{n}{k} = 0 . \end{align}   I tried to solve it using induction, but that got me nowhere. I think the easiest way to prove it is to think of a finite set of $n$ elements, but I can't find the solution.


The main requirement is to find travel time with traffic data between two locations or zip-code.  Inputs parameters would be from Location, destination, arrival time(this is between 6AM 8AM), mode of transportation, traffic model.  Based on the above input parameters in my google script function it should return travel time but I'm getting an error that      Service invoked too many times for one day: route. (line 40).    and I'm using the custom function below and there are 40 rows in my sheet:      function GetDurationNormal(location1, location2, mode) {   //var arrive = new Date(new Date().getTime() + (10 * 60 * 60 * 1000));//arrive in ten hours from now  // var arrive=new Date(2019, 09, 07, 06);// 7th of September 2019 06:00 am   var arrive = new Date();   arrive.setHours(9,0,0,0);   var directions  = Maps.newDirectionFinder().setArrive(arrive)   .setOrigin(location1)   .setDestination(location2)   .setMode(Maps.DirectionFinder.Mode[mode])   .getDirections();   // Get a script lock, because we're about to modify a shared resource.   var lock = LockService.getScriptLock();   // Wait for up to 30 seconds for other processes to finish.   lock.waitLock(20000);   Utilities.sleep(1000);  return directions.routes[0].legs[0].duration.text;

Credit:   function getDirection(city1, city2, unit) {   var directions = Maps.newDirectionFinder()     .setOrigin(city1).setDestination(city2)     .setMode(Maps.DirectionFinder.Mode.DRIVING)     .getDirections();   var d = directions.routes[0].legs[0].distance.text;    var distance, value = d.split(" ")[0].replace(",", ""), text = d.split(" ")[1];   if(text == unit) {     distance = value;   } else if(text == "km" && unit == "mi") {     distance = value / 1.6;   } else {     distance = value * 1.6;   }   return Math.round(distance); }   I have used this code snippet in one of my sheets. I am working on a dataset with roughly 6000 entries and I am getting some errors because of the large volume.      Script invoked too many times per second for this Google user account. (line 0).      Service invoked too many times for one day: route. (line 4).   I considered purchasing a Google Apps business account to increase my quota, but that might not even help. Do you maybe have any advice for me in this regard?


I know so many Stack Exchange sites, but I'm a bit confused about where to ask about problems we face in our cell phones. Or any type of any other electronic device.  I am facing so many problems with my phone. So I have so many questions about mobile phones. Please let me know if there is any forum related to mobile phones.

I know about , but from all indications it is all about computer hardware.   Is there any Stack Exchange site where I can ask questions about problems on my phone?


I ran an old problem here (see an  dated back to 2017) - I recently switched from Blender Version 2.79b to 2.8 respectively 2.9... When modelling some glass now for a new gold decal/foil sticker design, my render (Cycles) came out the way as shown below! Superstrange with a ghost picture. The glass is supposed to only show the decal to a restricted area (like the complete frog you can see...). This is like what I want to build:  Oh, of course, I UV-unwrapped the section I wanted to put the decal on - I did it a lot successfully in Blender 2.79b, you know...:  But this is the Render outcome:  And this is the node setup I built and used:  And here's the "Frog Mask" I intended to use for the gold foil material - Black and Transparency:  The glass should be clear except for the centered complete frog design. Oh - The Frog of course is not yet of a gold material - I just wanted to get the setup right first... But like 6 hrs up until now made no change...

I'm designing this animal-type creature, and want to add a transparent .png image to its face with the face features (object has a subsurf). On the left is the image with the features, on the right is the part of the object where I want it to be.    I tried to import the image as a plane, but matching the shape of the plane with the face didn't work, and the lines of the face left shadows on the head, and could be seen as a different object from some angles (although it's the closest I've gotten yet). It looked like this:    So , I tried selecting the faces of the head that the features should go over, and create a new material for it. Unfortunately, since the .png is transparent, the result produced was this:    (where it's impossible to tell the transparency from a black background default color, and where I wouldn't know where to start to adjust size and position).  I also tried UV mapping, but then the whole object became black with the features repeated all over.   Is it something I have to go into Nodes for? I'm kind of stuck here. Creating a new material and applying it is simple, but applying a material that is an image is a bit more complex it seems... Ideally, I would reproduce the same technique for the adhesive bandage on its arm (seen on the right of image 1).


When I press the "favourite" button beneath a question in the Android app, there is no way to unfavourite it (from the app). I receive a success message, but when I click the button again, it just says I have already favourited the question. If this was never intended to be a feature, I will make a feature request.

I'm using the official Stack Exchange mobile app for iOS or Android, and  My app crashed! It doesn't look good on my new smartphone. It won't run after I updated my device. I noticed another bug. I have an idea for a new feature which is currently not in the app.  How do I report bugs with or request features for the iOS and Android apps? Also:  I've used the built-in functionality of the app to report a bug or submit a feature request. Did I do the right thing? The app prompted me to post on Meta after an error occurred. Should I post about it here? I'm wondering why the latest version is from 2017. I've heard rumors that the apps are no longer supported; is that true? I can't find the app on my device's app store anymore! Where did it go?     We get a lot of bug reports from users about the mobile apps, which are unsupported, and at the moment, there is no centralized Q&A pair for those to be closed as duplicates of (the relevant answers are spread across multiple unrelated questions). This question is an FAQ proposal, to serve as a directly-related duplicate target for those questions.


I'm a beginner in web-development. I want to send the data to the servlet, but I got an NullPointerException .   For example the value of nickname = admin and I can see it. When I press the button to post to the servlet I can't pass data it seams that all data are null. I can't understand why. I have load the data from another (jsp + servlet) to this that I'm posting.  Jsp           <form name="admin_view_user" action="${pageContext.request.contextPath}/admin/users/user/activate" method="POST">

          <c:choose>             <c:when test="${active =='1'}">
Ok

             </c:when>                 <c:otherwise>
Post

                     <input class="commitbutton" type="submit" alt="buttonActivete" name="buttonActivete" id="buttonActivete" value="Activet" />

             </c:otherwise>         </c:choose>

                  Nickname	                                      <c:out value="${nickname}"/>

&nbsp;
 </form>
   Servlet  @WebServlet(name = "AdminActivate", urlPatterns = {"/admin/users/user/activate"})  public class AdminActivate extends HttpServlet {  /**  * Processes requests for both HTTP GET and POST  * methods.  *  * @param request servlet request  * @param response servlet response  * @throws ServletException if a servlet-specific error occurs  * @throws IOException if an I/O error occurs  */ protected void processRequest(HttpServletRequest request, HttpServletResponse response)         throws ServletException, IOException {      ServletContext servletContext = getServletContext();     try (PrintWriter out = response.getWriter()) {         ViewUserAdminActivet controller = new ViewUserAdminActivet();         Map<String, String[]> parameterMap = request.getParameterMap();         String nickname = parameterMap.get("nickname")[0];         System.out.println(nickname + "________________________________");        // controller.execute(servletContext, parameterMap, request, response);     }     }   In this line I got the exception Map<String, String[]> parameterMap = request.getParameterMap();

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?


This is part of a homework assignment so I'm only looking for a hint on how to solve this.  The question is to find the sum of the series $\sum\limits_{n=1}^\infty \frac{(-1)^{n-1}}{(2n-1)3^{n-1}}$  I have no idea how to even begin. Thanks.

Trying to find the sum of the following infinite series:  $$ \displaystyle\sum_{n=1}^{\infty}\frac{{(-1)}^{n-1}}{(2n-1)3^{n-1}}$$  Any ideas on how to find this sum?


I have a tree with 100GB of data, and I'd like to scp it to a remote machine. A large portion of the data is in hidden .files that I'd like to keep locally, but I don't need it remotely.  Is it possible to copy over via scp or another method the entire tree without the hidden files?

I want to back-up all files from my laptop partitions to external HDD.  I ran, for example  cp -a /med*/ravb*/*00   /med*/ravb*/M*L*/7.3GB_CP && echo "7.3GB BACKED UP PROPERLY" || echo "7.3GB FAILED TO BACK UP"   The issue is that dot files are also getting included which I don't want. What should I do so as to ignore all dot files for backing up.


Suppose $f: E \subseteq  \mathbb{R}^n \to \mathbb{R}^m$ is a differentiable map with $E$ open and connected. If $f'(x)=0$ for all $x \in E$, prove that $f$ is constant.  My attempt:  For all $x \in E$, choose an element $\epsilon_x >0$ such that the ball $B(x,\epsilon_x) \subseteq E$. Then it is obvious that  $$E= \bigcup_{x \in E} B(x, \epsilon_x)$$  Now, consider the corollary of theorem 9.19 in Rudin:     Suppose $f$ maps an open, convex set $E\subseteq \mathbb{R}^n$ into   $\mathbb{R}^m$, $f$ is differentiable in $E$ and $f'(x) = 0$ for all   $x\in E$, then $f$ is constant.   Applying this proposition to the map $f$ restricted to a ball $B(x, \epsilon_x)$ implies that $f$ is constant on every ball in the union written above.  Intuitively, I can see that the connectedness will imply that we can get from one ball to another balls using chains of "between-balls', or otherwise we will get a separation of $E$ as disjoint union of open sets.  I struggle to make this formal though.  Any help is much appreciated!

I am trying to show that a function that is locally constant on a connected space is, in fact, constant. I have looked at this  but my approach is a little different than the suggested approach and I'm unsure about the final step and would appreciate a tip. Here is what I have so far:  Let $f$ be a locally constant function on the connected space $U$. Assume that $f$ is not constant. Then, there are distinct points $x$ and $y$ such that $f(x) \neq f(y)$. Now, since $f$ is locally constant there are neighborhoods $V_x$ of $x$ and $V_y$ of $y$ such that  $$ f(V_x) = k_x, \;\; f(V_y) = k_y $$ for some constants $k_x \neq k_y$ .It follows that $V_x \cap V_y =\emptyset$  Now, let $A = U-V_x \cup V_y$ and $B = V_x \cup V_y$ so that $U = A \cup B$. With this, we have expressed $U$ as a union of disjoint sets. Since $V_x$ and $V_y$ are open $B$ is open. Note that if $A$ is empty we are done because $V_x$ and $V_y$ would comprise a separation of $U$ wich would imply that the assumption about f being not constant was faulty. So, assume $A$ is nonempty.  At this point, I want to show that $A$ itself is open. If I can do this, I believe the proof will be complete. One way I've thought about doing this is to choose a neigborhood of some point $a \in A$ and if it is not already disjoint from $B$, shrink it until it is. This would then demonstrate that $A$ is open.   Am I on the right track here?


I implemented ANN and my dataset have the first 100 data from class 1, and next 100 from class 2,..., and last 100 from class 10 (so I have 10 binary output units). I do back_propagation on my data to learn weights, but when I feed the new weights with training data again to the ANN, it predicts everything from class 10 which is the last 100 data's class. I am new to ANN, what am I missing?

I'm training a neural network but the training loss doesn't decrease. How can I fix this?  I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my network's performance doesn't improve on the training set.    This question is intentionally general so that other questions about how to train a neural network can be closed as a duplicate of this one, with the attitude that "if you give a man a fish you feed him for a day, but if you teach a man to fish, you can feed him for the rest of his life." See this Meta thread for a discussion:   If your neural network does not generalize well, see:


I built a web app with PHP, including forms, and I register the data from the users to my MySQL database.  Before the registration, I use filters to sanitize some inputs. For example, the name field only accepts usual letters, or the age field only accepts integers.  When I display the data, I have to escape it to protect against XSS, but in this case, is the data containing the age dangerous? It can be an integer, according to the database, so why escape it?  For the name data, it's type CHAR according to the database, so it could be dangerous. I filtered it. Is it safe now? Or must I imagine the worst? (my database could have been corrupted ?)  If I have to escape in my 2 examples, why do I have to filter the inputs?

User equals untrustworthy. Never trust untrustworthy user's input. I get that. However, I am wondering when the best time to sanitize input is. For example, do you blindly store user input and then sanitize it whenever it is accessed/used, or do you sanitize the input immediately and then store this "cleaned" version? Maybe there are also some other approaches I haven't though of in addition to these. I am leaning more towards the first method, because any data that came from user input must still be approached cautiously, where the "cleaned" data might still unknowingly or accidentally be dangerous. Either way, what method do people think is best, and for what reasons?


I have a bunch of files and I want to rename them using regular expressions.  I want to do this in a Linux Command line. I have the files report1.txt report2.txt report3.txt  How can I rename these so that they state myreport1.txt myreport2.txt myreport3.txt  Please let me know, I've searched the internet and they have many complex examples.

Rename all the files within a folder with prefix “Unix_” i.e. suppose a folder has two files a.txt and b.pdf than they both should be renamed from a single command to Unix_a.txt and Unix_b.pdf


was wondering if there was a link to blender 2.79b as I can't seem to find a download link anywhere.

I currently have version 2.74. How do I update to version 2.76? I do not see any links in the UI to update my version of Blender


I can't think of the word and it's been bothering me for some time now. I have attempted to reverse search it, to no avail. If someone could oblige me with the word whose definition means to oversimplify an often complex issue, I would most appreciate it!

Like when you want to say that you'll tell a short version of something which would alter the accuracy of the original version.  I was thinking of "In a nutshell" and "To make a long story short", but I felt like those phrases did not place emphasis on the "there might be an insignificant loss of accuracy" aspect.


I am looking for a short story about a dystopian society that I read in a High School English Lit book. I am pretty sure it was my Jr. year, circa 1991, the book was a few years old, probably published in mid to late 80s. I went to High School in Oklahoma, the story was in English.  I do not know the name of the author either, but I don't believe it was anyone well known (or at least not well-known to an 11th grader in the early 90s).  The story is set in a world where everyone must be equal. The powers that be implement this by handicapping people that have "better" qualities. For instance, I believe there was a ballet dancer on the TV, and the narrator comments that she must be really pretty to have to wear such an ugly mask.  The narrator was a man watching TV at home. His wife seemed to be kind of dull, and he was periodically hit with a shock collar or something to keep him from thinking too deep a thought (he was above average intelligence and this was his handicap).

I read this book in Middle School and I can't for the life of me remember the title, but I can remember what it was about for the most part:  Takes place in the future, the government imposes laws that outlaw people from being different in appearance and skill level. For example, if you are fast or strong or tall, they will put weights on you to weigh you down so that you'll be more slower/shorter and more like the average. Another example, if you are pretty the government issues you "ugly glasses" etc.  Basically, it's all about making sure everyone is equal and punishing the extraordinary.  One of the main characters (a man) decides to literally loose himself of his shackles and weights, breaking them to display his power (if I'm remembering correctly).   Any ideas folks?


You can fly from Vienna (VIE) to Addis Ababa (ADD) for 526€.  However, flying from Vienna (VIE) to Cape Town (CPT) connecting through Addis Ababa (ADD) is only 419€.  So when flying to ADD, it is cheaper to book a flight to Cape Town and not take the connection than to book a flight directly to ADD.  As you can see in the pictures, the 419€ VIE-CPT flights even include the exact  526€ VIE-ADD flight.    How is this possible?

Based on the question , I got curious. Is there a guide or resource that describes how the price of a ticket is determined?  When you search you often see curious effects like cheaper tickets for a flight from A to B with a layover compared to a direct flight. This seems counter-intuitive from an outsider's perspective since you fly twice. Also one way tickets more expensive than 2 ways.  It can be a short set of rules. Something that helps someone to get started with finding good prices. I know these can be very complex and they probably change over time and over airline interests but there is probably a simplified set of rules that can be enunciated.


I've just filed a somewhat broad question on superuser and received feedback saying I was posting off-topic in this forum. Hence my meta question, where would this very question fit in best?  The question:     stackexchange? serverfault? ProWebmasters? WordPress? ...?

In the last month or two I've noticed my questions are becoming increasingly dev ops related and less related to server fault or stackoverflow. Examples include 0MQ compiling issues or problems in TCP.  The field of Dev Ops is ever increasing, and I know teams who have rewritten protocols and entire NGINX modules but their problems aren't necessarily software or hardware related. They can be hybrid problems or caused by a programming error that didn't respect a firewall keep-alive.  I think many users may be confused as to why they see some of these questions and simply say they're off-topic. But now that our economy is cloud-based and SaaS companies do not control the hardware, Dev Ops have high value in the field of software development.  Where do we put these off-topic questions?  Update: example  This question was about 0MQ and probably only someone working in Dev Ops would have a clue. It was multi-faceted and involved Java bindings, Visual Studio, and C compiling    This question was about redis which both requires networking, server and software expertise. It took some time to track the bug to the Scala client itself:


I have long integers (11 characters) stored as text in a shapefile that I need to convert to integers, but when I attempt to convert them in the QGIS field calculator, I get the following error:  Eval Error: Cannot convert '26001980100' to int   The value in the error code above is the value from the first row in the field. I though this might be due to a field width constraint in shapefiles for integer columns, so I then imported the shapefile into a spatialite database and tried again without success. In both cases I was trying to create a new field populated by the converted values. How can I convert this field to integer?   The problem appears to goes deeper: after creating a new field and populating it with the integer values via the spatialite command line tool, QGIS does not then "see" the new field in the updated table. Am I out of luck with long integers in QGIS?  QGIS 2.12.3  Edit: I'm not sure whether this is a duplicate because the error appears specific to cases of converting strings having a length greater than 10 to integer. I tried the answer supplied  to convert to integer without luck. However, I was able to use that answer to convert the field to REAL, which is adequate for my purposes. The field in question is a foreign key, and the tables containing the primary key all store the values as INT, so I wanted to be consistent, but I can still join INT to REAL.

I want it to know how to convert string field values to integer values in QGIS Dufour... there are numbers and strings in the same field, when I use toreal(string) it stops and it won´t create the field.


Im trying to use hex value for bullet in CSS as mentioned here   Note that I don't want to use
 element just to show bullet

                       Link1

  .mybullet {     content:"\2022 ";     color:#f00; }   however its not working. Here is the JsFiddle

How do you use the CSS content property to add HTML entities?  Using something like this just prints &nbsp; to the screen instead of the non-breaking space:  .breadcrumbs a:before {     content: '&nbsp;'; }


True or false: If $B$ is any echelon form of matrix $A$, and if $B$   has three nonzero rows, then the first three rows of $A$ form a basis   for Row $A$.      Solution: False. Row operations may change the linear dependence   relations among the rows of a matrix.   I thought that to find the basis for a row space, we would need to put it in row echelon form, which would involve row operations. If it's in row echelon form, wouldn't the three nonzero rows be at the top and the zero rows at the bottom, and thus be able to conclude that the statement is true

I'm having troubling finding an example/proof that the following statement is true.     Row operations on a matrix A can change the linear   dependence relations among the rows of A.   Any tips on understanding this would be greatly appreciated.


I've got a fresh install of Windows, but I just noticed that my ethernet card will not work. Checking the device manager, it appears as "Ethernet Controller" and is missing a driver. Is there any way to detect what device it is and what driver I need?

I had to reformat my machine because I had a virus. My machine did not come with a driver disk. How can I install drivers after having reinstalled Windows?


$$\sum_{i=1}^N   \frac{1}{\sin^2(\frac{i \pi}{2 N})} = \frac{1}{3}(2N^2+1)$$  How can I prove this ?  Thank you.

Question : Is the following true for any $m\in\mathbb N$?   $$\begin{align}\sum_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}=\frac{m^2-1}{3}\qquad(\star)\end{align}$$   Motivation : I reached $(\star)$ by using computer. It seems true, but I can't prove it. Can anyone help?  By the way, I've been able to prove $\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{{\pi}^2}{6}$ by using $(\star)$.  Proof : Let  $$f(x)=\frac{1}{\sin^2x}-\frac{1}{x^2}=\frac{(x-\sin x)(x+\sin x)}{x^2\sin^2 x}.$$ We know that $f(x)\gt0$ if $0\lt x\le {\pi}/{2}$, and that $\lim_{x\to 0}f(x)=1/3$. Hence, letting $f(0)=1/3$, we know that $f(x)$ is continuous and positive at $x=0$. Hence, since $f(x)\ (0\le x\le {\pi}/2)$ is bounded, there exists a constant $C$ such that $0\lt f(x)\lt C$. Hence, substituting $x={(k\pi)}/{(2n+1)}$ for this, we get $$0\lt \frac{1}{\frac{2n+1}{{\pi}^2}\sin^2\frac{k\pi}{2n+1}}-\frac{1}{k^2}\lt\frac{{\pi}^2C}{(2n+1)^2}.$$ Then, the sum of these from $1$ to $n$ satisfies  $$0\lt\frac{{\pi}^2\cdot 2n(n+1)}{(2n+1)^2\cdot 3}-\sum_{k=1}^{n}\frac{1}{k^2}\lt\frac{{\pi}^2Cn}{(2n+1)^2}.$$ Here, we used $(\star)$. Then, considering $n\to\infty$ leads what we desired.


I want to create new numbered tcolorbox environments, so that every group has its own  numbering. I can do this by following code. \usepackage[most]{tcolorbox} \documentclass{article} % group of alerts \newtcolorbox[auto counter, number within=chapter]{alertbox}[1][]{     colback=red!10!white,     title=\textbf{Alert~\thetcbcounter :} {[#1]~}, } % group of notes \newtcolorbox[auto counter, number within=chapter]{notebox}[1][]{     colback=blue!10!white,     title=\textbf{Note~\thetcbcounter :} {[#1]~}, } \begin{document}    \begin{alertbox}[Food] % Alert 1.1: Food         Food is ready    \end{alertbox}    \begin{alertbox}[Drinks] % Alert 1.2: Drinks         Drinks are ready    \end{alertbox}    \begin{notebox}[Food] % Note 1.1: Food         Caution! Food is hot.    \end{notebox}    \begin{notebox}[Drinks] % Note 1.2: Drinks         There is Cola in Drinks!    \end{notebox}  \end{document}  But, this leads to code repetition. I'm trying to avoid this by creating a command that constructs tcolorbox environment. \newcommand{\declarenumberedbox}[3] {    \newtcolorbox[auto counter, number within=chapter]{#1}[1][]{        colback=#2,        title=\textbf{#3~\thetcbcounter :} {[                            ]~},                                           %% custom title must be here   %%                                           %% what should be filled here? %%    } } %% approximately how I want my code to look like  %% (or some equivalent ways to achieve this). \declarenumberedbox{alertbox}{Alert}{red!10!white} \declarenumberedbox{notebox}{Note}{blue!10!white}

I've seen sometimes that people use a double pound sign (##) when defining/using arguments.  What is the difference between the normal argument, #1, and the double sign one, ##1? Are there any restrictions for its use? Can you list the good practices, if any, for this type of arguments.


I am beginning to learn WPF. My first exercise is to find an open source application about 3D Objects, ImagesEditor, and then edit/improve it.   Now I want you introduce some application for me to download.

I have programmed with WPF for more than a year. When I started there weren't so many examples and guidelines to follow, now the situation is much more better.  I would like to ask you some help in listing the best WPF (open) source code examples or projects that you suggest to study in order to learn more about project structure, best practices, etc.  Thank you, Marco


I have a query that searches text using a regex:  $filter = ['word' => new MongoDB\BSON\Regex("some text","i")]; $query = new MongoDB\Driver\Query($filter);   I now want to be able to search for text that does not contain the text: e.g. [^(some text)]  The first issue I'm having is that I can't get the NOT to work, it appears that ^ can only be used to force the start of the string. Here is what I tried to find text without the letter 'a' in:  $pat = '[^a]'; $filter = ['word' => new MongoDB\BSON\Regex($pat,"i")]; $query = new MongoDB\Driver\Query($filter);   That just returns all documents with a value set for 'word'  I also tried:  $pat = '^a';   But as expected, that returns all documents that start with an 'a'.  How can I get this to work?

I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "<Regex for 'doesn't contain hede'>" input   Desired output:  hoho hihi haha


In the PHP $_SERVER variable, four variables reference the file requested.:  ["SCRIPT_FILENAME"]=>   string(21) "/webroot/file.php" ["REQUEST_URI"]=>       string(9) "/file.php?param=valyou" ["SCRIPT_NAME"]=>       string(9) "/file.php" ["PHP_SELF"]=>          string(9) "/file.php"   Would/Could any of these array members not refer to the actual file requested via URL? For example, URL rewriting, which I don't have experience with or plan on using for this project.  I notice "REQUEST_URI" also includes GET variables, which I don't need.

I am building a PHP application in CodeIgniter. CodeIgniter sends all requests to the main controller: index.php. However, I don't like to see index.php in the URI. For example, http://www.example.com/faq/whatever will route to http://www.example.com/index.php/faq/whatever. I need a reliable way for a script to know what it's address is, so it will know what to do with the navigation. I've used mod_rewrite, as per CodeIgniter documentation.  The rule is as follows:  RewriteEngine on RewriteCond $1 !^(images|inc|favicon\.ico|index\.php|robots\.txt) RewriteRule ^(.*)$ /index.php/$1 [L]    Normally, I would just check php_self, but in this case it's always index.php. I can get it from REQUEST_URI, PATH_INFO, etc., but I'm trying to decide which will be most reliable. Does anyone know (or know where to find) the real difference between PHP_SELF, PATH_INFO, SCRIPT_NAME, and REQUEST_URI? Thanks for your help!  Note: I've had to add spaces, as SO sees the underscore, and makes it italic for some reason.   Updated: Fixed the spaces.


I have been playing around with tikz-cd for quite a while and I love it, except when it comes to 3d-cubic diagrams. I have not found a viable solution so far and all the solutions out there seem to have an issue. The one that came closest to solving my problem was this one :   \documentclass{article} \usepackage{tikz-cd} \begin{document}  $$ \begin{tikzcd} S'Sc \ar{rr}{} \ar{rd}{} \ar{dd}{}  &                                               & T'Sc \ar{rd}{} \ar{dd}{}  &                   \\                                     & S'Sc' \ar[crossing over]{rr}{}                &                           & T'Sc \ar{dd}{}    \\ S'Tc \ar{rr}{} \ar{rd}{}            &                                               & T'Tc \ar{rd}{}            &                   \\                                     & S'Tc' \ar{rr}{} \ar[<-,crossing over]{uu}{}   &                           & T'Tc           \end{tikzcd} $$ \end{document}   but in the output, the arrow shown by \ar[<-,crossing over] has a smaller arrow tip than my other arrows; this issue seems to be caused by <- (the point is to reverse its direction).  What is the issue with the commands -> and <- which makes the arrow tip they generate smaller than the other ones?

I have been using tikz-cd to create commutative diagrams. I just upgraded to version 0.9b from 0.3c and now there is a problem with the arrow tips. I like to use the 'tikz' solid tips. The following diagram is fine:  \documentclass[11pt]{article}  \usepackage{tikz-cd} \usetikzlibrary{arrows}  \title{} \date{}   \tikzset{    commutative diagrams/.cd,    diagrams={>=latex}}  \begin{document} \begin{tikzcd}[row sep=scriptsize, column sep=scriptsize]  & f^* E_V \arrow[dl] \arrow[rr] \arrow[dd] & & E_V \arrow[dl] \arrow[dd] \\   f^* E \arrow[rr, crossing over] \arrow[dd] & & E \\   & U \arrow[dl] \arrow[rr] & & V \arrow[dl] \\   M \arrow[rr] & & N \arrow[uu, crossing over, leftarrow]\\ \end{tikzcd} \end{document}   and gives the following output:    However, if I change to solid tips (which take up less room and look better on the rather larger diagram I am really building) by adding an arrow style specification to the tikzset:  \documentclass[11pt]{article}  \usepackage{tikz-cd} \usetikzlibrary{arrows}  \title{} \date{}   \tikzset{    commutative diagrams/.cd,    arrow style=tikz,    diagrams={>=latex}}  \begin{document} \begin{tikzcd}[row sep=scriptsize, column sep=scriptsize]  & f^* E_V \arrow[dl] \arrow[rr] \arrow[dd] & & E_V \arrow[dl] \arrow[dd] \\   f^* E \arrow[rr, crossing over] \arrow[dd] & & E \\   & U \arrow[dl] \arrow[rr] & & V \arrow[dl] \\   M \arrow[rr] & & N \arrow[uu, crossing over, leftarrow]\\ \end{tikzcd} \end{document}   I now get the following output in which the tips are missing from all lines that use the 'crossing over' feature PLUS the two diagonals from U and V and the horizontal from M to N:    This behaviour was not exhibited in v.0.3c. Any ideas how to fix it?  Thank you.


I made a mistake and no I want to get rid of this Get:8 [https://dl.winehq.org/wine-builds/ubuntu](https://dl.winehq.org/wine-builds/ubuntu) bionic InRelease \[6,259 B\]  Err:8 [https://dl.winehq.org/wine-builds/ubuntu](https://dl.winehq.org/wine-builds/ubuntu) bionic InRelease    The following signatures couldn't be verified because the public key is not available: NO\_PUBKEY 76F1A20FF987672F  Reading package lists... Done  W: GPG error: [https://dl.winehq.org/wine-builds/ubuntu](https://dl.winehq.org/wine-builds/ubuntu) bionic InRelease: The following signatures couldn't be verified because the public key is not available: NO\_PUBKEY 76F1A20FF987672F  E: The repository '[https://dl.winehq.org/wine-builds/ubuntu](https://dl.winehq.org/wine-builds/ubuntu) bionic InRelease' is not signed.  N: Updating from such a repository can't be done securely, and is therefore disabled by default.  N: See apt-secure(8) manpage for repository creation and user configuration details.

I added some extra repositories with the Software Sources program. But when I reload the package database, I get an error like the following:     W: GPG error:  trusty InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 8BAF9A6F   I know I can fix it using apt-key in a terminal, according to the official Ubuntu documentation. But I would have liked to do it graphically. Is there a way to do this without using a terminal?


The first is a declared function and the others are functions stored in variables, this is what I know. Are there other differences between these ways to declare function? Function name(){} const f_name = function (){} const f_name =()=>{}

I've recently started maintaining someone else's JavaScript code. I'm fixing bugs, adding features and also trying to tidy up the code and make it more consistent.  The previous developer used two ways of declaring functions and I can't work out if there is a reason behind it or not.  The two ways are:  var functionOne = function() {     // Some code };     function functionTwo() {     // Some code }   What are the reasons for using these two different methods and what are the pros and cons of each? Is there anything that can be done with one method that can't be done with the other?


I am opening Word from within a Console Application. How can I ensure the Console remains the active window, even after I have shown the Word Application?  using System; using Microsoft.Office.Interop.Word;  namespace WordDocumentObject {     class Program {         static void Main(string[] args) {             _Application app = new Application();             app.Visible = true;              //Activate the console window here              Console.WriteLine("Press any key to continue...");             Console.ReadKey(true);         }     } }

How can I bring a console application window to front in C# (especially when running the Visual Studio debugger)?


Am using this code for deleting the specific file in all directories and sub directorates in a drive but its not working. please help me in this regard. If i want to delete the specific file in all drives how to do.      static String refile= "input.txt";       public static void deletemyfile(File directory) {     if (directory.exists()) {            File[] files = directory.listFiles();            if (null != files) {                  for (int i = 0; i < files.length; i++) {                         System.out.println(files[i].getName());                         if (files[i].isDirectory()) {                                deletemyfile(files[i]);                          } else  {                               String temp ;                             temp = files[i].getName();                                                           if (temp==refile){                              System.out.println("name matched and about to delete");                              (files[i]).delete();                           } else{                              System.out.println("name not matched");                         }                            }                  }            }     } else {System.out.println("wrong path");     }   }

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


I have some experience with 3D parametric CAD (e.g. Solidworks, Autodek Inventor). So far, I have watched the official Blender tutorials 3 times and read a complete book about Blender. I am wondering if I will need to undergo a paradigm shift to successfully model in Blender. Suppose I am drawing a wooden stool. In parametric CAD, I would design a leg (1 object) with a hole that fits a screw, make the seat (another object) with 4 holes for the 4 leg screws, and make a screw (yet another object). Then in the final assembly, I will assemble 4 legs and the seat by putting in 4 screws. Drawing finished. What is the process in Blender? Do Blender users make only one object called "Stool" and model the shape of the stool without regard for the components of the object (e.g. legs, screws, seat)? What if the screws are important (e.g. I need to be able to accurately take the stool apart)?

Is there any benefit of creating model in one piece or I can create separate pieces and just overlap them to create a visually joint part.  For example, the below image were made from two parts 1. Blade 2. Spinner  Is there any benefit to model them (e.g. extrude from the spinner) or it is actually ok to have them separated since visually I can achieve the same effect (See picture 2)


Is there a way to resize the rightarrow so that it can adjust to the width of the text over it?  \documentclass[12pt, a4paper, english]{article} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \usepackage{amsmath} \usepackage{babel}  \begin{document} \begin{equation}   \overset{\text{l'Hopital's rule}}{\Longrightarrow} \end{equation} \end{document}   The code above only generates result like this, which is non-adjusted.

I know it's possible to have \xrightarrow (text), but if I try to do \xRightarrow (text) I get an error each time. Does anybody know if it's a syntax error or if there is a other way to produce the \Rightarrow with text above?


I have two tables, one containing all the quantities of products by country and another table that contains the prices by country.  When I add a condition for example country = "ch", I have the price correct for this country, I want to return different prices for all countries. How can I do that?  Here's my query:  SELECT      items.prod,     items.qty_fr,     items.date,     products.price FROM items LEFT JOIN products     ON products.product = items.prod WHERE     products.country = "CH" GROUP BY     items.prod   This is the result of my query:  It returns the first value      Here's my first table:     My second table :


I have downloaded the appropriate Linux distro (in this case ) and I have partitioned the USB with Disk Utility and attempted copying both the Fedora iso, and a Fedora iso converted to the Mac .img format.  When I booted (holding option key) the USB with Fedora didn't show up in either case in boot manager.  What needs to be done for Mac to consider the USB "bootable" and for it to be visible in "boot manager" when holding option key?

I'd like to take a Linux ISO (e.g., CentOS, Ubuntu), and create a bootable USB drive. (It will be used for booting on a stock PC, not on the Mac). How do I go about creating such a drive using a Mac?


I randomly tried to execute the following command in bash1  cat /some/file | ssh user@machine 'cat >/destination/file   There are no keys installed on the remote machine, so the only way to authenticate is with the password mechanism. I thought this wouldn't work, since the pipe will disconnect SSH's stdin from the terminal. I was surprised when I was prompted for a password, and the file was successfully sent.  Any thoughts on how SSH is able to read the keyboard to prompt for a password, despite not being connected to it?    1I am aware there are better alternatives to copying a file between two machines.

I don’t actually need to run the command below, and I am aware of ssh keys if I did want to log in without typing a password. I would just like to know how ssh seems to circumvent my file redirection.  Running the following command, ssh prompts me for a password:  ssh nobody@192.168.1.151 > /dev/null 2> /dev/null < /dev/null   How does this work? stdin, stdout, and stderr are all redirected, but ssh still manages to print a prompt on my screen and read what I type. I tried adding the ssh arguments -t -t and -T (not both at once), to enable or disable pseudo-tty allocation, but it made no difference.  I also tried closing all input and output this way, although I don’t know if I typed it correctly. Still, ssh prompts for a password:  (exec 0<&- 1<&- 2<&- 0>&- 1>&- 2>&-; ssh nobody@192.168.1.151)


I have two functions: but calling like this: pack<int>(some_vector, something_else)  some_vector would be like this: std::vector<int> some_vector;  throws a compilation error:  LNK2019 Unresolved external symbol in main.obj  Both the functions are defined, and calling pack with an int instead of a vector compiles just fine. I want to add more pack functions to accept maps, tuple's etc (as first argument). Is this the correct way of going about this? (I am not that experienced with c++)  template <typename T> void pack(std::vector<T>& src, byte::container& dest, bool initial) {     size_t n = src.size();     size_t s = 0;     uint8_t prefix;     uint16_t post_prefix = n;     bool use_post_prefix = false;     if (n <= 15) {         prefix = fixarray_t(n);     }     else if (n <= max16) {         prefix = arr16;         use_post_prefix = true;     }     else if (n <= max32) {         prefix = arr32;         use_post_prefix = true;     }     if (initial) {         dest.clear_resize(int(n * 0.4));     }     dest.push_back(&prefix);     if (use_post_prefix) {         dest.push_back(&post_prefix);     }     for (uint32_t i = 0; i < n; i++) {         pack(src[i], dest, false);     } }  void pack(uint64_t src, byte::container& dest, bool initial) {     uint8_t prefix;     if (src <= max4) {         prefix = ufixint_t(src);         dest.push_back(&prefix);     }     else if (src <= max8) {         prefix = uint8;         dest.push_back(&prefix);         dest.push_back(uint8_t(src));     }     else if (src <= max16) {         prefix = uint16;         dest.push_back(&prefix);         dest.push_back(uint16_t(src));     }     else if (src <= max32) {         prefix = uint32;         dest.push_back(&prefix);         dest.push_back(uint32_t(src));     }     else if (src <= max64) {         prefix = uint64;         dest.push_back(&prefix);         dest.push_back(uint64_t(src));     }     else {         throw std::range_error(std::to_string(src) + " out of range!");     } }

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


Let $(X_1,X_2)$ be a pair of uniformly distributed random variables with $S=[-1,1]\times[0,1]$. Are $X_1$ and $X_2$ independent? Are $X_1$ and $X_2$ correlated.  My approach for independence:  For independence I think what was has to be shown is that $$f(x_1,x_2)dx_1dx_2=f(x_1)dx_1f(x_2)dx_2$$ where for $X_1$ the density is $$f(x_1)dx_1=\frac{1}{1-(-1)}dx_1=\frac{1}{2}dx_1$$ and for $X_2$ the density is $$f(x_2)dx_2\frac{1}{1-0}dx_2=dx_2.$$  I'm very confused on what $f(x_1,x_2)$ is.  My approach for correlation:  No approach yet. But I found out that two random variables are uncorrelated iff $cov[X_1, X_2]=0$. How can I show that for the above problem?

For a random variable $X \in \mathcal{R}^n$ from a uniform distribution, are the components independent? i.e,  $Pr(X_1,X_2,...,X_n) = Pr(X_1)Pr(X_2)....Pr(X_n)$   If so, does it depend on the uniform distribution? e.g if the uniform distribution is a p-dimensional hypercube.


root@mcdartey-hp-g56-notebook-pc:/home/mcdartgey# dpkg -i google-chrome-stable_current_amd64.deb Selecting previously unselected package google-chrome-stable. (Reading database ... 221126 files and directories currently installed.) Preparing to unpack google-chrome-stable_current_amd64.deb ... Unpacking google-chrome-stable (51.0.2704.63-1) ... dpkg: dependency problems prevent configuration of google-chrome-stable:  google-chrome-stable depends on libappindicator1; however:   Package libappindicator1 is not installed.  dpkg: error processing package google-chrome-stable (--install):  dependency problems - leaving unconfigured Processing triggers for man-db (2.7.5-1) ... Processing triggers for gnome-menus (3.13.3-6ubuntu3) ... Processing triggers for desktop-file-utils (0.22-1ubuntu5) ... Processing triggers for bamfdaemon (0.5.3~bzr0+16.04.20160415-0ubuntu1) ... Rebuilding /usr/share/applications/bamf-2.index... Processing triggers for mime-support (3.59ubuntu1) ... Errors were encountered while processing:  google-chrome-stable

How do you install Google Chrome on Ubuntu?


The machine will start automatically in ten minutes.      The machine will start automatically within ten minutes.   What's the difference between the two sentences?

1.These symptoms  resolve  completely within  1  to  2  weeks.      2.These symptoms  resolve  completely  in  1  or  2  weeks.   I wanted to know whether the duration phrase "within 1 to 2 weeks" and " in 1 or 2 weeks" are the same.


My current rank is Nova Master (Nova 4) and I've won 6 games straight. Also was I either 1st or 2nd in my team.   After that, I tied one time, and won 4 games in a row. I still haven't ranked to Master Guardian.   What's keeping me from ranking up? I've been playing with a friend who won 4 (from start of Nova 4 to end) and ranked. Also was he below me most of the times.

Ever since I started playing with CS:GO, I've been in the bronze rank in Classic Competitive. No matter how many rounds I win, how many times I am the MVP, I won't get a new rank.    How does the ranking system work? How do you progress?


I tried googling this but most answers that came up were regarding "cash" as bank deposits that a check is normally issued against.  Not "cash-cash" or physical cash, as a bunch of bank notes.  Say one were to buy a $200K home or a $40K car in the U.S. but wished to pay in physical cash.  Is it even legal past a certain amount?  What kind of scrutiny can (s)he expect from regulatory agencies, IRS etc. if such a transaction surfaces up?

I saw  recently where a man withdrew $600,000 USD in cash from his bank.  I'm sure many folks here would advise against this move for obvious (and perhaps not-so-obvious) reasons.   My question: suppose you did this and then, some months later, changed your mind and wanted to re-deposit with a bank.  I assume the gent cannot simply walk into a bank with $600,000 USD and deposit it, right?  Wouldn't money-laundering alarms be raised?  Wouldn't the IRS like to know where the money came from?


Let $(X,d)$ be seperable metric space, then $(Y,d_1)$ where $Y \subset X$ and $d_1$ is induced metric on a subspace $Y$. Then $(Y,d_1)$ is a seperable metric space, too.  I think it is quite easy to prove using the second axiom of choice. My question is that this problem states it is not neccessarily true that when we talk about topology space instead of metric space.  Can anyone explain why and give an counterexample?   Thanks

I'm trying to find an example of a non-separable subspace of a separable space.  What kind of examples are there?


I am trying to get some understanding about how pass by value & return are happening in C functions. I cam across a piece of code as follows:  #include <stdio.h>  int fun(int ii, int jj) {  int kk, ll;  kk = ii + jj;  ll = ii * jj;  return (kk,ll); }  int main() {  int i=4, j=5, k, l;  k = fun(i, j);  l = fun(i, j);  printf("%d %d\n", k, l);  return 0; }   Now apparently I am not getting any errors when I am trying to return 2 values through fun().  Also, the value that is returned by fun() is ll i.e 20 (=4*5) and not kk. Further, If I rewrite the return statement as :  return (ll,kk);   the value returned is that of kk ie. 9 (=4+5).   Query: Why this is so?


Show that $\text{gcd}(m+n,m) = \text{gcd}(m,n)$  Here is what I have so far, using the definition of $\text{GCD}$ for some integer d we have  $d = x(m+n) + y(m)=(x)(n) + (x+y) m$ Now let $x' = x+y$ and $y'=y$,  $d'= x'(m) + y'(n)=(x+y)m+y(n)$ where $\text{GCD}(m,n)=d'=d$  Is this reasoning sufficient?

I know that Greatest common divisor of two positive integers $a$ and $b$ is the largest positive integer that divides both $a$ and $b$, but how can I use that to prove that $\gcd(a, b) = \gcd(a, b-a)$.


Is there any rule for the pronunciation of 'Con' words like :  Constant, Constraint, Constitute, Constituent etc. My confusion is with these sounds 'kɒn' and 'kən'.  For Constiuent it is /kənˈstɪtjʊənt/ but in Constitute it's /ˈkɒnstɪtjuːt/.

I know there is no strict rule on pronunciation of words in English but here my question is about the words which begin with 'con' and 'com', more than asking general rule. When I look at the words begin with 'con' and 'com', I see mostly two patterns : One of them is schwa /ə/ sound and the other one is /o/ or /ɒ/ sound.But the second  pronunciation can be pronounced slightly differently depending on dialect. An example word for the first pronunciation is the word computer whose pronunciation is represented    in Cambridge Online Dictionaries. An example for the second type of pronunciation for "co" could be the word contrast whose pronunciation is represented     in Cambridge Online Dictionaries. So my question is there any rule/pattern which can help us guess how to pronounce these words correctly? I am not asking about the words like cool, come or coke. My question is about words like contract, combination, continue, combat.


I am trying to create a tree Structure Where I create a Parent and Children on button Click. HTML created on Button Click let createChild = document.getElementById("addChild"); createChild.addEventListener("click", function() {   let li = backend.querySelectorAll("li");   let lastLi = li[li.length - 1];   let parentLi = lastLi;   parentLi.innerHTML = "";   parentLi.innerHTML += `<span class ="caret-down" >Parent</span>            <ul class='nested'>            <li>Child</li>            </ul>`; });  But When I want To create a toggle function for Caret.I want to call All Caret class and launch a ClickEvent on it. But Click Event Not Working ClickEvent Code let carets = document.getElementsByClassName('caret-down'); for (var i = 0; i < carets.length; i++) {   carets[i].addEventListener('click', function() {     debugger;     this.classList.toggle('caret')     parent = this.parentElement;     parent.querySelector('.nested').classList.toggle('active')   }) }

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 recently installed Ubuntu 16.04 on my Dell Inspiron 15 7559.  Specs:    Intel® Core™ i7-6700HQ CPU @ 2.60GHz × 8  1TB drive  16GB memory NVidia Geforce GTX 960M   Everything works apart from my nvidia card. I have tried installing many versions which all led to low graphics mode error. I recently tried the v384 driver and my system booted up normally and I thought I'd succeeded, but I was wrong. My Additional Drivers page shows that I have nvidia 384 selected but nvidia x server is empty and system info still shows that I'm running Intel Skylake.   How can I fix this?

I just ordered the Nvidia GTX card. I have a dilemma, though. Should I keep using the driver which is available in "additional drivers" in Ubuntu, or should I install the driver from the Nvidia site?  So which driver is the best for me?


I realized that, aside from a warning, nothing is stopping you from running  sudo apt purge apt   If someone did run that, how do you reinstall apt, because you no longer have apt to install with?

I have accidentally removed apt-get, how do I reinstall it?  $ sudo apt-get update sudo: apt-get: command not found  $ sudo dpkg-reconfigure apt /usr/sbin/dpkg-reconfigure: apt is broken or not fully installed    I would like to mention I do not want to reinstall Linux!


Is it possible for Ubuntu to work with MTK6572 Dual Core ARM Cortex A7 family CPU@1.2GHz  processor in a tablet? As far as my research has gotten me I've found that this cpu is x86 but I'm not entirely sure if that's the only thing I need to be looking for. I'm a newby to the whole tablet scene so if you have any advice as to what other tablet hardware aspects I should be planning ahead for other than the requirements posted by Ubuntu it would be greatly appreciated.  If you do find a good answer can you post the link where you found this info? It would expand my research capabilities and eliminate my need to ask these questions in the future as I came up pretty dry on the google haha.

With the announcement of the Ubuntu Phone OS I'd like to know what phone (and tablet) models are supported at this time.  Note from foss & Oli: We are making this the master question for all future "Will this work on <insert random tablet/phone/device here>?!" questions


Myself is Divya.. i am new to Linux/Unix.. i have a question on user and group management..  I read that for deleting a group a group must be empty..  I want to delete a primary group without deleting the users(as they belongs to other groups which is their secondary group)  for example I want to delete a group called ABC which contains the users U1,U2,U3,U4 whereas U1 and U4 belongs to another secondary group called DEF and GHI respectively.  ABC is the primary group for U1 and U4. let me know he command/s..  Thanks

I added a user account to the admin group and discovered I added wrong user. So I now have to remove the account from the admin group.   How can I remove an account from a group without deleting the user?


Not sure if this is a new issue or not but I have noticed recently that when I am signing up on a new Stack Exchange Site it appears that it logs me in. However when I go to take an action on that site such as cast a vote on a question/answer or leave a comment it informs me that I must login to the site in order to perform that action.  After I sign up on the site it does appear as if I am logged in as it shows my avatar and reputation along with inbox and reputation notifications in the top bar. However when I refresh the page it resets to a not logged in state and I have to log in to do anything and afterwards the site functions as expected.  Is the way this is behaving a bug or am I not understanding how the signup process should work? This happened to me last night on a site and today on another site.

I've created account on Server Fault with the "Join this community" button. It seems to be created as I see my picture and a starting 101 reputation on top. But when I tried to upvote I got a message I need to login and where I clicked on a different question it showed me I'm not logged in.    I think it didn't even create my account since later I clicked the signup button again, it asked me with which Google account I want to create it (I've two associated with my Chrome browser).


The terms "pretty nice" and "nice" can perhaps not be compared in regards to nicety.  I find "pretty nice" to be a more informal way of relaying that something is rather awesome.  In one way the adverb (?) in this example also tune the somewhat ecstatic adjective down a bit. At the same time I notice the use of, for example, "pretty nice" when it looks like the person intend to say "very nice" – which in turn is not to tune down. Can one perhaps say that "pretty nice" in general means "very nice"? (Thus nicer the nice. :P)

I am aware that there are plenty of threads on intensifiers(very, rather, pretty, quite, fairly, etc.), both on this site and on the web, because of their ambiguity in terms of meaning. What I have learned is that their meaning can change depending on which country you are from, which context they are used, or your intonation. So instead of comparing all intensifiers, I decided to make my question more specific. I chose to focus on the word pretty because of its "common" usage.  So as we can see, the word pretty has two meanings and unfortunately they are "pretty" opposite. My question is can you tell me, just by taking into account  the example sentences below, in which sentences "pretty" means "fairly,", and in which it means "very?"  Does "Tom looks pretty tired" always mean "Tom looks a little/fairly tired" ?


Ques : Let $N$ be the number of functions $f: \{1, 2, 3,\dots, 2018\} \to \{1, 2, 3,\dots, 2018\}$ satisfying $f(j) < f (i) + j - i$ for all integers $i,j$ such that $1 \leq i < j \leq 2018$.  Find $N$.  My development so far : difference of elements' value in domain is strictly greater than that in Co domain. Hence every consecutive number should be mapped to a lesser or equal number the previous number is mapped to. Hence the function should be non-strictly decreasing.

I stumbled upon a question given like:  Let $m$ and $n$ be two integers such that $m \geq n \geq 1$.   Count the number of functions $$f: \{1, 2, · · · , n\} \to \{1, 2, · · · , m\}$$ of the following two types:  (a) strictly increasing; i.e., whenever $x < y, f(x) < f(y)$, and  (b) non-decreasing; i.e., whenever $x < y, f(x) \leq f(y)$.  I tried in the following way.  For (a). We can say $f(n)>f(n-1)$ AND $f(n)>f(n-2) \ldots f(n)>f(1)$ (total $n-1$ elements)  Similarly for $f(n-1)>f(n-2), f(n-1)>f(n-3) \ldots f(n-1)>f(1)$ (total $n-2$ elements)...  and $f(2)>1$  Like this $$(n-1) + (n-2) + \ldots + (1) = \frac{n(n-1)}{2}$$  Is this correct?  For (b). Since there's equality, it will be $$n + (n-1) + ... (1) = \frac{n(n+1)}{2}$$  Is my approach correct? Any help is appreciated. Thanks in advance.


I have a system with 3GB RAM installed. I am planning to move to Windows 8 and am considering whether to install the 32bit or 64bit version.  Regarding CPU, drivers and software there are no issues for me.  I am however concerned about the following (possible?) trade-off:   With 3 GB clearly I do not require 64bit at the moment. But on the one hand, installing 64bit windows would give me an easy upgrade path for future RAM increases. On the other hand, 64bit binaries are known to be 30% larger. (Larger pointers need more space.) On hdd this is not an issue for me, but what about RAM? Assuming I am running identical scenarios on 32bit and 64bit systems, will I find the on a 64bit system I require <30% more ram under identical circumstances? Then moving a 3GB machine to 64bit would appear not ideal.   Can anybody comment on this tradeoff?

I've recently purchased Windows 7 Ultimate.  I have an AMD Athlon64 X2 5000+ with 2GB DDR2 RAM.  I know RAM has gotten much cheaper, I know, I know, but I am not going to be able to upgrade my RAM for about a year.  My question is obviously this; will I get any benefit from installing 64-bit Windows over 32-bit if I'm only using 2GB of RAM?    As I understand, the minimum requirement is 2GB & max is 192GB so if the minimum for 64-bit is 2GB & the minimum for 32-bit is 1GB will I lose performance if I chose to install 64-bit at it's minimum requirement over 32-bit whose minimum is half the amount?  I would like to install the 64-bit edition if only because it's the future.  192GB of RAM! that's incredible! Plus I've heard it simply performs better.  But that is with a larger amount of RAM.  I've tried to make this question as easy to decipher as possible.  Any advice would be greatly appreciated.


What I want to do is put a command block down and do a command every 1 minute! How do I do this without redstone repeaters? I am doing this for a server!

I found 11 questions like this on gamingSE already, but none of them have proper and up-to-date answers. So I'm creating this Q&A:  How do you either activate a command x seconds/minutes/hours/… in the future or every x seconds/minutes/… in a loop?  Repeating command blocks and ticking functions execute 20 times per second, redstone is  in many situations and most of the extremely fancy solutions, like falling blocks in cobwebs, have broken over time or are needlessly complicated.


I'm currently stuck on this problem:     Let $m$ and $n$ be positive integers, and $F_k$ be the free group generated by $k$ elements. Prove that there is a homomorphism from $F_n$ onto $F_m$ if and only if $m$ is less than or equal to $n$.    My thought was to try abelianizing the free groups and using a homomorphism from the abelianized free groups to $\mathbb{Z}^n$ and $\mathbb{Z}^m$ respectively, but that has so far proved unfruitful.   Can someone help me find a better way to approach this problem?

Let $F_a$ be the group which is freely generated by $a$ elements. How to show that there is a homomorphism from $F_a$ onto $F_b$ if and only if $b\le a$?  I was thinking one possibility is if $F_a$ generated freely by $\{x_1, \dots , x_a\}$ and $F_b$ generated freely by $\{y_1, \dots , y_b\}$ then consider map which says $\phi(x_i)=y_i$ for $1\le i \le b$ and $y_1$ otherwise. I do not know if this works or even how to proceed. How to show this fact?


I bought a laptop a while ago and I'm sort of through with Windows. I wanted to try Ubuntu but I don't know which version I should take. I got a Samsung NP300E5A-S02NL  It has a  Intel I3 2330M @2.2GHz Processor 8GB of ram Nvidia GeForce 520MX a chipset Intel HD Graphics videocard   I know for windows there is a need of x64 to get full use out of your 8GB of ram, is this the same for Ubuntu?

What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit?


I want to get the last day of the current month as cleanly as possible.  I am thinking something like datetime.datetime.last_date_current_month() in a similiar fashion of datetime.datetime.today()   datetime.date.today().replace(month=datetime.date.today().month +1, day=1) - relativedelta(days=1)  works but is horrible :)

Is there a way using Python's standard library to easily determine (i.e. one function call) the last day of a given month?  If the standard library doesn't support that, does the dateutil package support this?


I made a blender animation, and when I rendered it, it just became alot of pictures and no video. How can I make it a video instead of having a bunch of pictures?

Yesterday I was working on a simple animation, an animated logo.   Here is an image of the progress:    I already have the animation working and everything is okay with the project, but I can't figure out how I can render the animation and turn it into an AVI format video.  How do I render an animation in Blender?