How long before Ubuntu version no longer works?
How to install software or upgrade from an old unsupported release?
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal I want to find the rank of this $n\times n$ matrix \begin{pmatrix} 1 &amp; a &amp; a &amp; \cdots &amp; \cdots &amp; a \\ a &amp; 1 &amp; a &amp; \cdots &amp; \cdots &amp; a \\ a &amp; a &amp; 1 &amp; a &amp; \cdots &amp; a \\ \vdots &amp; \vdots &amp; a&amp; \ddots &amp; &amp; \vdots\\ \vdots &amp; \vdots &amp; \vdots &amp; &amp; \ddots &amp; \vdots \\ a &amp; a &amp; a &amp; \cdots  &amp;\cdots &amp; 1 \end{pmatrix}  that is, the matrix whose diagonals are $1's$ and $a$ otherwise, where $a$ is any real number.  My first observation is when $a=0$ the rank is $n$ and when $a=1$ the rank is $1.$ Then I can assume $a\neq 0, 1$ and proceed row reduction to find its pivot rows. I obtain  \begin{pmatrix} 1 &amp; a &amp; a &amp; \cdots  &amp; a \\ 0 &amp; 1+a &amp; a &amp; \cdots &amp; a \\ 0 &amp; a &amp; 1+a &amp; \cdots &amp; a \\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\ 0 &amp; a &amp; a &amp; \cdots  &amp; 1+a \end{pmatrix} by subtracting the first row multiplied $a$ for each row below the first, and then divides the factor $(1-a)$,  and stuck there. Any hints/helps? Enumerations on PHP I know that PHP doesn't yet have native Enumerations. But I have become accustomed to them from the Java world. I would love to use enums as a way to give predefined values which IDEs' auto-completion features could understand. Constants do the trick, but there's the namespace collision problem and (or actually because) they're global. Arrays don't have the namespace problem, but they're too vague, they can be overwritten at runtime and IDEs rarely know how to autofill their keys without additional static analysis annotations or attributes. Are there any solutions/workarounds you commonly use? Does anyone recall whether the PHP guys have had any thoughts or decisions around enumerations? Images for Area51 proposal community promotion on imgur.com? For each proposal on Area51, a promotional image is automatically generated and it shows the current state, e.g. number of followers/supporters or comitted. Example:    They’re obviously useful for  on existing sites. Alas, the current requirements for those say that the image needs to be hosted on imgur.com. I can easily provide the URL https://area51.stackexchange.com/ads/proposal/{proposal-number}.png in the image upload dialog, to get a cryptic imgur address back, but I’m afraid that it won’t update dynamically.  Please note that I was able to use the area51 URL on some sites until right now, when the poster generator seems to be broken or off-line, but on other sites the software stopped me from posting any image not hosted on imgur. Can we please have the dynamic posters working everywhere (and in “HiDPI”) or be assured that the external service will update them regularly? Prove using natural deduction $((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$ How do I prove the following using Natural Deduction?  $$((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$$   My current approach:  So instead of proving $(P \rightarrow R) \lor (Q\rightarrow R)$, I figure I just need to prove $(P \rightarrow R)$ and use disjunction introduction.  The problem is my hypothesis requires $P$ and $Q$. How do I "create" this Q? I tried using the Law of the Excluded middle, but it does not seem to work.  Any help or insights is deeply appreciated. Preventing itemize environment to insert initial vertical space I'm using itemize and tables like the following  \begin{tabularx}{\textwidth}{&gt;{\ttfamily}llX}  \toprule  \textbf{\rmfamily Operator} &amp; \textbf{Typen} &amp; \textbf{Regel} \\  \midrule  = &amp; Alle Typen &amp;   \begin{itemize}    \item This is how we roll    \item Maybe we can talk?   \end{itemize} \\  \bottomrule \end{tabularx}   But it keeps inserting a vertical space before the itemized list. How can I prevent it from doing so? Programming language books explain that value types are created on the stack, and reference types are created on the heap, without explaining what these two things are. I haven't read a clear explanation of this.  I understand what a stack is. But,    Where and what are they (physically in a real computer's memory)? To what extent are they controlled by the OS or language run-time? What is their scope? What determines the size of each of them? What makes one faster? How to synchronize systemd stop order from one service? Suppose I have a.service which I cannot modify, and b.service which I can modify, I want to see this stop order:  Stopping b.service ... Stopped b.service Stopping a.service ... Stopped a.service   instead of this:  Stopping b.service ... Stopping a.service ... Stopped b.service Stopped a.service   Assume that b.service may take at least 20 seconds to finish. How do I increase my code coverage, or why can't I cover these lines? How to find all subgroups of a direct product? I am wondering how do we find all subgroups of a direct product? Is there a method to find it?  For example, how can we find all the subgroups of $\mathbb{Z}_2\times\mathbb{Z}_2$?  There is the answer: $\{(0, 0), (1, 0)\}, \{(0, 0), (0, 1)\}, \{(0, 0), (1, 1)\}$, and the improper and trivial subgroup. But I do not know the method how to find it.   All I can think about is the following: since the order of $\mathbb{Z}_2\times\mathbb{Z}_2$ is $4$, the order of a subgroup of it can be $1,2$ or $4$.   If order is $1$, then it is trivial, and if order is $4$, it is proper. Then, the order of a subgroup is $2$. We know all the elements of   $\mathbb{Z}_2\times\mathbb{Z}_2$, so we try all the pairs.   Is that the method?   But what if we are given a bigger order product, such as $\mathbb{Z}_2\times\mathbb{Z}_8\times\mathbb{Z}_3\times\mathbb{Z}_9$? It looks very long to try all possibilities.   Can anyone help?  Thanks Abstraction VS Information Hiding VS Encapsulation Can you tell me what is the difference between abstraction and information hiding in software development?  I am confused. Abstraction hides detail implementation and information hiding abstracts whole details of something.  Update: I found a good answer for these three concepts.  for several citations taken from . I am buying a new desktop PC in early 2013, anyway this question should apply to someone intending to buy a new laptop/ultrabook as well.  This machine is not meant for gaming, and if I ocasionally do it, I can survive with minimum graphics. However I may need some heavy multimedia edition or multitasking at times, so basically  my greatest priority is a good processor, after that perhaps average graphic card (if onboards are not enough, I am still not informed enough about that), at least 4GB of RAM with possibility of expansion.  I know there are some PC models specially designed to ship with Ubuntu, which is the OS I use the most these days. However, most people around me use Windows and some software with unsupported versions for Linux and not having a Windows license becomes a bit problematic.  Given that, I would like to find information about which PC models or even manufacters currently on the market have the best compatibility with Ubuntu, I am still undecided between building my own desktop or buying a pre-made model, so I would like to find information both for certified models and certified hardware or even Ubuntu partners that may work closely with Canonical.  Where to find this information in order to make sure that I will have a good experience with Ubuntu on my new PC in the years to come? Sort order issue I'm having an issue sorting data in ascending order.   Right now the sort order is: 1.0.0  10.0.0 10.0.1 11.0.0 2.0.0 2.0.1 3.0.0 3.0.1 3.1.0  What I want is: 1.0.0 2.0.0 2.0.1 3.0.0 3.0.1 3.1.0 10.0.0 10.0.1 11.0.0  How can I achieve this? The datatype can't be number or currency because of the 2 decimals, so I used text-field. How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$ How would I go about proving that  $$|a|+|b| \leq |a+b|+|a-b|$$  Using the triangle inequality?  I tried squaring both sides, yielding:  $$|a|^2 +|b|^2 +2|a||b| \leq 2|a|^2+2|b|^2+2||a|^2-|b|^2|$$  Is it correct to move the terms to the other side? I tried $$2|a||b| \leq |a|^2+|b|^2+2||a|^2-|b|^2|$$ Then it is obvious that  $$0\leq |a|^2+|b|^2-2|a||b| +2||a|^2-|b|^2|$$ $$0\leq (|a|-|b|)^2 +2||a|^2-|b|^2|$$ $$0\leq ||a|-|b||^2 +2||a|^2-|b|^2|$$  But I have neither used the triangle inequality, nor it looks mathematically rigorous for my real analysis class. Any tips and tricks for solving these problems? I am nearing the end of my PhD and I would quite like to buy a "thank you" gift for my supervisor (although, she's the socially awkward type who I'm sure will be greatly embarrassed to receive one).  I'm just wondering whether a gift is the done thing? And if so, what sort of gift seems appropriate? I suppose a bottle of wine would be a safe choice? I want to initialize a struct element, split in declaration and initialization. This is what I have:  typedef struct MY_TYPE {   bool flag;   short int value;   double stuff; } MY_TYPE;  void function(void) {   MY_TYPE a;   ...   a = { true, 15, 0.123 } }   Is this the way to declare and initialize a local variable of MY_TYPE in accordance with C programming language standards (C89, C90, C99, C11, etc.)? Or is there anything better or at least working?  Update I ended up having a static initialization element where I set every subelement according to my needs. Error: Can't open display: 0 I installed WSL2 and I want to access WSL2 GUI apps from Windows 10. For this, I installed Xming and start it in "No client" mode. Xming startes, ok. After I open the WSL2 terminal and there execute these commands  export DISPLAY=:0   And after  xeyes   And get error   Error: Can't open display: :0   X11Forwarding checked, yes. Claim: Let $X$ be a metric space. If $A,B\in X$ are disjoint, if A is compact, and if B is closed, then $\exists \delta&gt;0: |\alpha-\beta|\geq\delta\;\;\;\forall\alpha\in A,\beta\in B$.  Proof. Assume the contrary. Let $\alpha_n\in A,\beta_n\in B$ be chosen such that $|\alpha_n-\beta_n|\rightarrow0$ as $n\rightarrow \infty$.  Since A is compact, there exists a convergent subsequence of $\alpha_n\;(n\in\mathbb{N})$, $\alpha_{n_m}\;(m\in\mathbb{N})$, which converges to $\alpha\in A$.  We have   $$|\alpha-\beta_{n_m}|\leq|\alpha-\alpha_{n_m}|+|\alpha_{n_m}-\beta_{n_m}|\rightarrow0 \;\;\;as\;\;m\rightarrow\infty.$$ Hence $\alpha$ is a limit point of B and since B is closed $\alpha\in B$, contradiction.  Is my proof correct? I feel as though I am missing something simple which would trivialize the proof. I can't seem to find a story related to mine so here it is.  I am 25 and a German citizen. In 1998 when I was 7 years old my family moved to the states and we stayed until early 2002 and left voluntarily. Basically we overstayed. I am aware that my parents had the ten year ban and since I was a minor at the time of our overstay I did not receive such ban.  Ever since 2002 I have not attempted to go back to the USA for any reason. However now that I am older I would like to go back for vacation and stay for a short period of time (one month) during my christmas break.  I've lived in Germany since leaving, have a great job, enough money in the bank account. My whole life is here and I have no intention on moving anywhere else.  After reading a bunch of stories online I have decided to apply for a B2 visa to be on the safe side but I was curious about the ESTA approval. For the last question. 8) Have you ever stayed in the United States longer than the admission period granted to you by the U.S. government?   I should put yes but is it a no if I stayed when I was a minor? And what are my chances on getting the B2 Visa? What is "all" in isset($wp_filter['all']) I'm a newbie in WordPress. I'm trying to understand how it generates the XHTML pages. I guess it's the function of do_action( 'hook-name' ) , but I'm stuck with the understanding of the instruction isset( $wp_filter['all] ) when reading the function do_action because I don't understand what is the meaning of the word all.  Is it a PHP feature or a WordPress one?