how to assign value to pointer string in C
Why do I get a segmentation fault when writing to a "char *s" initialized with a string literal, but not "char s[]"?
How to derive the standard symplectic form on a 2-sphere in cylindrical polar coordinates? I have already know that at a point $p\in S^2$ with $u,v$ the tangent vectors at $p$. Then the standard symplectic form is $\omega_p(u,v) :=\langle p,\,u\times v\rangle$ where $u\times v$ is the outer product. My question is: How can one deduce from this that the symplectic form is $dz\wedge d\theta$ in the cylindrical polar coordinates $(z,\theta)$ on $S^2$? Here, $z$ is the height and $\theta$ is the angle. Thanks. I have to prove by induction that $$\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$$, using the identity $\begin{pmatrix}n \\ r-1 \end{pmatrix}+\begin{pmatrix}n \\ r \end{pmatrix}=\begin{pmatrix}n+1 \\ r \end{pmatrix}$. I'm fine with everything except the inductive step, where I only managed to get as far as $$\sum_{r=0}^{k+1}\begin{pmatrix}n \\ r \end{pmatrix}= \sum_{r=0}^{k}\begin{pmatrix}n \\ r \end{pmatrix}+\begin{pmatrix}n \\ k+1 \end{pmatrix}$$ I tried to then use the identity and substitute $\begin{pmatrix}n \\ r \end{pmatrix}=\begin{pmatrix}n+1 \\ r \end{pmatrix}-\begin{pmatrix}n \\ r-1 \end{pmatrix}$ but all this did was just take me around in a circle. I also couldn't substitute $2^k$ for $\sum_{r=0}^{k}\begin{pmatrix}n \\ r \end{pmatrix}$ since this didn't properly simplify to give $2^{k+1}$. However, I think that I have to obtain the expression $\sum_{r=0}^{k}\begin{pmatrix}n \\ r \end{pmatrix}$ since it simplifies to $2^{k+1}$. But I've not been able to obtain this in anyway so I'm wondering if anyone can guide in what I need to or what direction I need to take to complete the inductive step. Possible to click on an object in the viewport and the object list hierarchy automatically goes to that object also? How do I compare version numbers in Python? ubuntu terminal is not working properly in vi editor How Triangle Law and Parallelogram law of addition of Vectors are different?Ain't they.  Please don't tell me the things written in book......give me the appropriate reason.And how do i distinguish between the two while adding vectors,what am i trying to say is i get really confused where to use parallelogram law and where triangle law  P.s:my basics are really weak though!May be the question might not be right Memory layout of a .NET array What is the memory layout of a .NET array?  Take for instance this array:  Int32[] x = new Int32[10];   I understand that the bulk of the array is like this:  0000111122223333444455556666777788889999   Where each character is one byte, and the digits corresponds to indices into the array.  Additionally, I know that there is a type reference, and a syncblock-index for all objects, so the above can be adjusted to this:  ttttssss0000111122223333444455556666777788889999         ^         +- object reference points here   Additionally, the length of the array needs to be stored, so perhaps this is more correct:  ttttssssllll0000111122223333444455556666777788889999         ^         +- object reference points here   Is this complete? Are there more data in an array?  The reason I'm asking is that we're trying to estimate how much memory a couple of different in-memory representations of a rather large data corpus will take and the size of the arrays varies quite a bit, so the overhead might have a large impact in one solution, but perhaps not so much in the other.  So basically, for an array, how much overhead is there, that is basically my question.  And before the arrays are bad squad wakes up, this part of the solution is a static build-once-reference-often type of thing so using growable lists is not necessary here. Usage of dash (-) in place of a filename For a command, if using - as an argument in place of a file name will mean STDIN or STDOUT.   But in this example, it creates a file with the name -:  echo hello &gt; -   How can I make - in this example mean STDOUT? Conversely, how can I make - mean a file named - in examples such as:  cat - Using right-hand Riemann sum to evaluate the limit of $ \frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$ I'm asked to prove that $$\lim_{n \to \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+4}+\frac{n}{n^2+9}+\cdots+\frac{n}{n^2+n^2}\right)=\frac{\pi}{4}$$ This looks like it can be solved with Riemann sums, so I proceed:  \begin{align*} \lim_{n \to \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+4}+\frac{n}{n^2+9}+\cdots+\frac{n}{n^2+n^2}\right)&amp;=\lim_{n \to \infty} \sum_{k=1}^{n}\frac{n}{n^2+k^2}\\ &amp;=\lim_{n \to \infty} \sum_{k=1}^{n}(\frac{1}{n})(\frac{n^2}{n^2+k^2})\\ &amp;=\lim_{n \to \infty} \sum_{k=1}^{n}(\frac{1}{n})(\frac{1}{1+(k/n)^2})\\ &amp;=\lim_{n \to \infty} \sum_{k=1}^{n}f(\frac{k}{n})(\frac{k-(k-1)}{n})\\ &amp;=\int_{0}^{1}\frac{1}{1+x^2}dx=\frac{\pi}{4} \end{align*}  where $f(x)=\frac{1}{1+x^2}$. Is this correct, are there any steps where I am not clear? Environment for two columns with lstlistings In order to reduce copy-pasting, I want to create an environment that will produce a two-column table with headers and two listings in different languages, like below:  \begin{tabular}{l l} Python &amp; Haskell \\ \hline \\ \lstset{language=Python} \begin{lstlisting} A \end{lstlisting} &amp; \lstset{language=Haskell} \begin{lstlisting} B \end{lstlisting} \end{tabular}   I want to use it like below, hiding everything but code:  \begin{comparison} A \vs B \end{comparison}   So far I tried making two new environments (instead of a \vs command inside) with \lstnewenvironment, where first environment had \tabularx command and second \endtabularx. I also tried creating normal \newenvironment for this tabular, &amp; for \vs command and manually inserting \begin{lstlistings} and \end{lstlistings} with code, but it stopped compiling when I put lstlistings inside.  How can I create such an environment?  EDIT: The most compact version I've came up with until now is  \newenvironment{comparison} {\begin{parcolumns}[nofirstindent,distance=0pt,colwidths={1=0.35\textwidth}]{2}} {\end{parcolumns}}  \lstnewenvironment{python} {Python \lstset{language=Python,frame=t}} {}  \lstnewenvironment{haskell} {Haskell \lstset{language=Haskell,frame=t}} {}   which is used like that:  \begin{comparison} \colchunk{ \begin{python} A \end{python} } \colchunk{ \begin{haskell} B \end{haskell} } \end{comparison}   I'm still unable to hide \colchunk{} within python or haskell environments. How to calculate the $H_2$ and $H_\infty$ norms of TransferFunctionModels or StateSpaceModels? Should the top navigation be frozen (optional)? In Excel, the window can be frozen in place in such a way that you can always see the name of the column even though you go way down below the 'fold' of the screen.  On SE, when you scroll, the whole page goes up (or down). This means the top navigation bar is scrolled off screen. I'm not sure if it would be a good idea or not to fix the top navigation to the top of the screen and let the rest of the content scroll.  What do you think about this, in terms of pros and cons?  [Update]  With the new Top navigation bar, kudos to the design team, I think this question becomes relevant again. I'm aware of the busload of downvotes, but still.  The top navigation bar doesn't occupy much space and has two notification areas:   Inbox Achievements   Having these two notifications visible at all times would be nice, IMO.  [Update]  I've just noticed that I haven't used the word "optional" in this discussion... My bad. In Excel, the Freeze function is controlled by the user. You can optionally Freeze part of the interface, and you can eliminate the Freeze at will. How do I delete files that are locked when no other app can delete them? So I found out that I had a Trojan on my external hard drive. My anti-virus app killed it, but it has created a bunch of random files on my computer which cannot be deleted. These are image files. They cannot be renamed - using any method - nor can they be moved, cut, copied, permanently deleted or even opened (in any program).  How can we rid these files from our system?  I have tried:   Right-click > Delete Shift+Delete (Permanently Delete) Swearing   and then:   FileASSASSIN from MalwareBytes Eraser program sdelete program several commands in cmd   but none of them have been successful. How can I completely obliterate these files? I would like to ask for some simple examples showing the uses of &lt;div&gt; and &lt;span&gt;.   I've seen them both used to mark a section of a page with an id or class, but I'm interested in knowing if there are times when one is preferred over the other. Is there a way to get a background in CSS to stretch or scale to fill its container? How to enable/disable a specific graphic card? I have been using the Copy Attributes add-on to copy some properties from active object to selected objects. This add-on is not enabled by default and must be explicitly enabled. But its a very useful workflow enhancing tool.    There is a limitation though. Not all properties can be copied and even those that can be copied are copied in groups (Its hard-coded in to the add-on).  My question is if there is a built-in feature or any another other way to copy any property from the active object to the selected objects? Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$ Show that if $f\in L^2 (\mathbb{R})$ then    $$\lim_{x \rightarrow \infty} g(x)=0,$$   where    $$g(x)=\int_x^{x+1}f(t)\,dt$$   Since $f \in  L^2 (\mathbb{R})$ then $f \in L^2[x,x+1]$ for every $x$. Then  $$|g(x)| \leq \left(\int_x^{x+1} f(t)^2 dt\right)^{\frac{1}{2}} \int_x^{x+1} 1 dt$$ $$|g(x)|\leq \left(\int_x^{x+1} f(t)^2 dt\right)^{\frac{1}{2}}$$ What is the relationship between ISO, aperture, and shutter speed? I know digital cameras have ISO options, and that ISO is the camera's sensitivity to light, but if you set  higher ISO then you can get a noisy image. I also know there are two other camera options, shutter speed and aperture.   What is the relationship of between them? Is there any equation, or something like that?  For example, if I set the ISO to 640, then how should I set the shutter speed and aperture? I have heard many (rather most) people, especially in the USA, saying:      I don't know nothing about it.   Is that correct? I always get a weird feeling hearing this and feel the correct one would be saying:     I don't know anything about it.