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How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access? How to write a unit-test / test class for trigger? How do I write a unit-test / test class for a trigger?  What are my options?   Inline with the trigger?  New Class? is a wonderful freeware Windows swiss-army-knife for image viewing &amp; editing.  For me, the key features are fast viewing, simple editing (crop, contrast, brigthness, rotation, resampling), file operations (delete, copy to folder) and extended image information access (exif data) combined in the same interface. Versatile batch jobs are a very nice bonus.  But unfortunately IrfanView is for Windows only, and isn't . What would be the nearest equivalent for linux? Something wrong with monthly user rep - some users show quarterly figures? Why are these constructs using pre and post-increment undefined behavior? DEFINE vs Variable in PHP Why does this excerpt say that unbiased estimation of standard deviation usually isn't relevant? I was reading on the computation of the unbiased estimation of standard deviation and the source I read stated      (...) except in some important situations, the task has little relevance to   applications of statistics since its need is avoided by standard   procedures, such as the use of significance tests and confidence   intervals, or by using Bayesian analysis.   I was wondering if anyone could elucidate the reasoning behind this statement, for example doesn't the confidence interval use the standard deviation as part of the calculation? Therefore, wouldn't the confidence intervals be affected by a biased standard deviation?  EDIT:  Thanks for the answers so far, but I'm not quite sure I follow some of the reasoning for them so I'll add a very simple example. The point is that if the source is correct, then then something is wrong from my conclusion to the example and I would like someone to point how how the p-value doesn't depend on the standard deviation.  Suppose a researcher wished to test whether the mean score of fifth graders on a test in his or her city differed from the national mean of 76 with a significance level of 0.05. The researcher randomly sampled the scores of 20 students. The sample mean was 80.85 with a sample standard deviation of 8.87. This means: t = (80.85-76)/(8.87/sqrt(20)) = 2.44. A t-table is then used to calculate that the two-tailed probability value of a t of 2.44 with 19 df is 0.025. This is below our significance level of 0.05 so we reject the null hypothesis.  So in this example, wouldn't the p-value (and maybe your conclusion) change depending on how you estimated your sample standard deviation? $n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$ How does one prove that if $n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $ \displaystyle n \mid \frac{a^{n}-b^{n}}{a-b}$ where $a,b, n \in \mathbb{N}$.  What i thought of is to consider $$(a-b)^{n} \equiv a^{n} + (-1)^{n}b^{n} \ (\text{mod} \ n)$$ and if we suppose that $n$ is odd then we have, $$(a-b)^{n} \equiv a^{n} -b^{n} \ (\text{mod} \ n)$$ and since $n \mid (a^{n} - b^{n})$ we have $$(a-b)^{n} \equiv 0 \ (\text{mod} \ n) $$  I think i am far away from the conclusion of the problem, but this is what i could work on regarding the problem. 32 bit or 64 bit OS on a 512 mb VPS? I am planning to rent a VPS service with following basic specification:   512mb of RAM 1 CPU 20gb HDD (4gb of it is swap) Ubuntu 10.10 server   I am able to choose between a 32 bit or 64 bit install of Ubuntu server as the operating system.   My question is would it be better to chose a 32 bit operating system since I will have only 512mb of RAM, rather than using a 64 bit operating system and dealing with the additional overheads?  edit:  I have installed Ubuntu server 10.10 32 bit and 64 bit on VirtualBox. After a minimalistic installation with only ssh server, the 32 bit installation consumes 63mb of RAM when first boot up and 64 bit consumes 85mb of RAM.  After installing and running  daemon, 32 bit consumes 99mb of RAM when first boot up and 64 bit consumes 128mb. If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$ I was working my way through some number theoretic proofs and being a newbie am stuck on this problem :     If $(x, 4) = 2$ and $(y, 4) =2$, then $(x + y, 4) = 4$,     where $(a,b)$ denotes the greatest common divisor of $a$ and $b$.   My Solution  (Incorrect)   $x-4 = 2t$ $y-4 = 2p$ $x + y - 8 = 2(t+p) \Rightarrow x + y - 4 = 2f + 4 = 2(f+2)\Rightarrow 2$ divides $(x+y , 4)$   My Question:  My solution is definitely inadequate. Can someone help me out? Prove that $371\cdots 1$ is not prime Prove that $371\cdots 1$ is not prime.   I tried mathematical induction in order to prove this, but I am stuck.  My partial answer:  To be proved is that $37\underbrace{111\cdots 1}_{n\text{ ones}}$ is never prime for $n\geq 1$. Let $P(n)$ be the statement that $37\underbrace{111\cdots 1}_{n\text{ enen}}$ is not prime.  For $n=1$, we can write $371=7\cdot 53$, and therefore $P(1)$ is true. Let $P(k)$ be true for $k&gt;1$. Then we now have to prove that $P(k+1)$ is true.  I found that $37\underbrace{111\cdots 1}_{k\text{ ones}}$ can be written as $37\cdot 10^k+10^{k-1}+10^{k-2}+\cdots +10^0$ and that $37\underbrace{1111\cdots 1}_{k+1\text{ ones}}$ can be written as $37\cdot 10^{k+1}+10^{k}+10^{k-1}+\cdots+10^0$.  I think I'm pretty close to the answer know, but I don't know how to proceed. Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$ Let IG denote Inverse-Gamma distribution   .   If $X\sim IG(\alpha,1)$ and $Y\sim IG(\beta,1)$. Show that   $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$   I tried with jacobian transformation taking $Z=\frac{X}{X+Y}$ and $W=Y$ then $$X=\frac{WZ}{1-Z};Y=W$$  $$\frac{\partial(z,w)}{\partial(x,y)}=\frac{1}{(1-z)^2}$$  $$f_{z,w}(z,w)=f_x(\frac{wz}{1-z})f_y(w)(1-z)^2$$ $$f_{z,w}(z,w)=\frac{1}{\Gamma{(a)}}(\frac{wz}{1-z})^{-\alpha-1}e^{-\frac{(1-z)}{wz}}\frac{1}{\Gamma{(\beta)}}w^{-\beta-1}e^{-\frac{1}{w}}(1-z)^2$$  but I'm stuck, in some place I read that $\frac{X}{X+Y}$ is a type 3 Beta distribution, but I can't show that. Solve the recurrence $T(n) = 2T(n-1) + n$ Solve the recurrence  $T(n) = 2T(n-1) + n$ where $T(1) = 1$ and $n\ge 2$.  The final answer is $2^{n+1}-n-2$  Can anyone arrive at the solution? Right click not working on Ubuntu 18.04 I have installed Ubuntu 18.04 LTS on my HP Pavilion series laptop. After installing this version of Ubuntu, right click is not working of my touchpad. How can I solve this?  BTW:  does not have any solution which which is working for me. PS:- Problem remains after selection area in gnome-tweak-tool Is it alright to use lowercase "i" or should you always use "I" (uppercase)? When I use TikZ tree with nodes with rounded corners, the connecting lines do not touch the nodes (near corners) but end where would rectangle end. Is there an easy way around it?  \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture} [sibling distance=100]    \node[rectangle, draw, rounded corners = 3]{ }   child { node { } }   child { node { } }   ; \end{tikzpicture} \end{document} While trying to ask a question, I got the error message     This question body does not meet our quality standards. Please make sure that it completely describes your problem - including what you have already tried - and is written using proper grammar.    Why am I getting this message? What can I do to get the system to accept my question? Can you be more specific? What are good resources on how to ask high-quality questions?      For more information, see  in the . A diffeomorphism whose tangent map preserves dot products is an isometry. I'm having trouble solving the following problem.  If $F:\mathbb{R^3} \to \mathbb{R^3}$ is a diffeomorphism such that $F\ast$(the tangent map of $F$) preserves dot products, show that $F$ is an isometry. (Hint: Show that $F$ preserves lengths of curve segments and deduce that $F^{-1}$ does also.)  I'm trying to proceed as in the hint, but I'm stuck on the first step, showing the $F$ preserves lengths of curve segments. Moreover, how does showing that both $F$ and its inverse preserves length of curve segments show that it is an isometry. And how do I characterize the curve segments. I would appreciate any solutions, hints or suggestions. I'm using python in QGIS. I have a layer of polygons (its a result of some earlier dissolving and has no overlapping polygons but some holes and islands in holes etc). I want to build a new layer which contains one polygon representing a bbox of the first layer with each polygon cut from it.  Essentially I want to "invert" the layer I have so that where the was polygon, now there is not, and where there was not polygon now there is. All inside a bounding box of the original layer.  I can build a bbox easily and I tried to "subtract" the polygon layer from my new bbox polygon layer but the process slows to a stop and then crashes my PC. Here's the algorythm  processing.runalg("qgis.difference","path/to/polygon.shp","path/to/bbox.shp","path/to/result.shp")   I dont care about attributes (obviously). I just need to cut one set of polygons from one larger polygon.  It seems so simple, I wish I could find a simple command or script to acheive this. As stated at the top I'm looking for a solution in python in QGIS. How can I get this symbol without using bbold? A solution I saw somewhere suggested to use   \usepackage{bbold} $\mathbb{1}$   which works well and I get what I want. However, now other symbols used to represent real numbers, natural numbers, etc look ugly.    I'd like them to look (without using bbold)    I'd like to only use that package to achieve that strange double one. Is there any way I can do that?