This question came just out of curiosity to know our friend the Stack Trace a little better.  As a C# (.NET) developer every one must have seen a yellow stack trace like the one below.    Most of the things in it are easily understood like the message Attempt to divide by zero and the method where it occur Page_Load even the path of the .cs file also. But after 3 years of experience the thing I still don't know is what those numbers with + sign at the end of methods denote in here, like +51, +92, +54 and +772.  Does anybody know what these are?
When reading a stack trace like:  [FormatException: Input string was not in a correct format.]    System.Number.StringToNumber(String str, NumberStyles options, NumberBuffer&amp; number, NumberFormatInfo info, Boolean parseDecimal) +2755599    System.Number.ParseInt32(String s, NumberStyles style, NumberFormatInfo info) +112    System.Convert.ToInt32(String value) +68   What do the +68, +112, etc. numbers mean. I'm guessing that they're offsets to something. If so, what?
How to construct a relative path in Java from two absolute paths (or URLs)? Open Mapping Theorem: counterexample The Open Mapping Theorem says that a linear continuous surjection between Banach spaces is an open mapping. I am writing some lecture notes on the Open Mapping Theorem. I guess it would be nice to have some counterexamples. After all, how can you appreciate it's meaning without a nice counterexample showing how the conclusion could fail and why the conclusion is not obvious at all.  Let $\ell^1 \subset \mathbb{R}^\infty$ be the set of sequences $(a_1, a_2, \dotsc)$, such that $\sum |a_j| &lt; \infty$. If we consider the $\ell^1$ norm $\|\cdot\|_1$ and the supremum norm $\|\cdot\|_s$, then, $(\ell^1, \|\cdot\|_1)$ is complete, while $(\ell^1, \|\cdot\|_s)$ is not complete.  In this case, the identity $$   \begin{array}{rrcl}     \mathrm{id}:&amp; (\ell^1, \|\cdot\|_1)&amp; \to &amp;(\ell^1, \|\cdot\|_s)     \\                 &amp; x &amp; \mapsto &amp; x   \end{array} $$ is a continuous bijection but it is not open.  I want a counterexample in the opposite direction. That is, I want a linear continuous bijection $T: E \to F$ between normed spaces $E$ and $F$ such that $F$ is Banach but $T$ is not open. This is equivalent to finding a vector space $E$ with non-equivalent norms $\|\cdot\|_c$ and $\|\cdot\|_n$, such that $E$ is complete when considered the norm $\|\cdot\|_c$, and such that $$   \|\cdot\|_c   \leq   \|\cdot\|_n. $$ The Open Mapping Theorem implies that $\|\cdot\|_n$ is not complete.  So, is anyone aware of such a counterexample? Can someone use DC generator along with electric motor to make electricity along with mechanical energy? I know this might sound stupid and maybe stupid totally, but I need some clarification....  I came through electric motor principle.  and then I came across the following link on DC generators    Now my question is, can't we combine them both to provide DC current with little DC used in motor side? By "combine," I mean using a DC generator coil only at the other side of the coil of the motor in the motor itself. The condition is that the 2 coils are connected via some apparatus that causes the 2nd coil to move along with the 1st coil.   In this way we can use both the mechanical energy produced by the 1st coil and the electrical energy produced by the 2nd coil, right?   This is a great concept if it works, right? Please throw some light on this. I thought this would be really simple, but it's presenting some difficulties. If I have std::string name = &quot;John&quot;; int age = 21;  How do I combine them to get a single string &quot;John21&quot;? Opening a non-utf8 encoded text file I sometimes need to open text files that are encoded in EUC-KR.    man gedit gives:      --encoding           Set the character encoding to be  used  for  opening  the  files           listed on the command line.    This can be used to open specific files with the desired encoding:  gedit --encoding euc-kr readme.txt   However, each file to be opened requires a similar command to be typed.  I can run iconv on the file(s), but then I have to deal with different file versions.    Do I have better options for dealing with non-utf8 text files? How to list files installed by a snap package? After a snap has been installed with sudo snap install [package] how can I list the files which have been installed by the snap? I would like to show that the function $\frac{1}{x}$ is not uniformly continuous on $(0,1)$ using two approaches.   First Approach:   We have the fact that if a function $f$ is uniformly continuous on an open interval $(a,b)$, then the function $f$ is bounded on $(a,b)$. By using its contrapositive, since $\frac{1}{x}$ is not bounded on $(0,1)$, it is not uniformly continuous.  Second Approach:  Proof by definition. Note that the definition of non-uniform continuity is:  There exists an $\epsilon_0&gt;0$ such that for all $\delta&gt;0$, there exists $x,y \in (0,1)$ such that $|x-y|&lt;\delta$ but $|\frac{1}{x} - \frac{1}{y}| \geq \epsilon_0$.  Assume that $\delta &lt; 1$. Let $x = y + \frac{\delta}{2} \in (0,1), y &lt; \frac{\delta}{2} \in (0,1), \epsilon_0 = 1$. Then we have   $$|\frac{1}{x} - \frac{1}{y}| = |\frac{1}{y + \frac{\delta}{2}} - \frac{1}{y}| = \frac{\frac{\delta}{2}}{|y(y + \frac{\delta}{2})|} &gt; \frac{\frac{\delta}{2}}{(\frac{\delta}{2})(\delta)} = \frac{1}{\delta} &gt; 1 = \epsilon_0 $$  If $\delta \geq 1$, then let $\delta^{\prime} = \frac{1}{\delta}$ so that $\delta^{\prime} \leq 1$. The rest proceeds the same as above.   Question: Are my two approaches correct? Do you ever need to specify 'javascript:' in an onclick? AFAIK, you never need to specify the protocol in an onclick:  onclick="javascript:myFunction()" Bad  onclick="myFunction()" Good  Today I noticed in  on Google Anallytics that they are using it:  &lt;a href="http://www.example.com" onClick="javascript: pageTracker._trackPageview('/outgoing/example.com');"&gt;   Is this example just plain wrong, or is there ever a reason to specify javascript: in anything other than a href? Can you contract the main verb '[I] have' in a sentence? I was using the amspset document class for generating exam practice problems. I had wanted to add some referencing to the problems so I started a new counter like this (adapted from some Tex Exchange post)  \newcounter{P} \newcommand{\plb}[1]{\refstepcounter{P}\label{#1} \textbf{P-\ref{#1}.}}  \begin{problem} \plb{p1} A parallel-wire transmission line is constructed of \#6 AWG copper wire (diameter $d=0.162$ in., conductivity $\sigma_c=5.8\times 10^7$ S/m) with a 12-inch separation in air. Assuming no leakage between the two wires, find $R'$, $L'$, $G'$, and $C'$. Assume a working frequency of 1 MHz. \end{problem}  \begin{solution} Using Table.~\ref{tab:tlparam} and Fig.~\ref{fig:tlempl},  \[ Rs = \sqrt{\pi f \mu_c/\sigma_c} = 2.61\times10^{-4}~ \Omega\] \[ R' = \frac{2R_s}{\pi d} = 4.04\times10^{-2} ~\Omega\text{/m} \] \[ L' = \frac{\mu_0}{\pi} \ln{\frac{2D}{d}}=2.0~\mu \text{H/m} \] \[ C' = \frac{\pi \epsilon}{\displaystyle\ln{\frac{2D}{d}}}=5.56 ~\text{pF/m} \] $G'=0$ because the problem states that there is no leakage between the two wires. \end{solution}  \begin{figure}[ht] \begin{centering}     \includegraphics{fig24}     \caption{(Fig.2-4 from FAE) A few examples of transmission lines.} \end{centering} \label{fig:tlempl} \end{figure}  \begin{table}[ht] \caption{(Table 2-1 from FAE)Transmission-line parameters $R'$, $L'$, $G'$, and $C'$ for three types of lines.}     \begin{tabular}{c}         \hspace{3cm}\includegraphics{tb21}     \end{tabular} \label{tab:tlparam} \end{table} ... and more   Now all the figure references stop working, I get "Fig. " instead of "Fig. 1". The table references are alright though. Any idea what the problem could be? How we can compare two coefficients of one linear regression? boolean[] vs. BitSet: Which is more efficient? What is more efficient in terms of memory and CPU usage — an array of booleans or a BitSet? Specific BitSet methods are not used, only get/set/clear (==, =, Arrays.fill respectively for an array). I created a model and added some Actions in the DopeSheet editor (more or less 5).  I exported the model to my game engine, saved the .blend file (Ctrl-S) and closed it.  Then I opened it again, and all the actions were gone, it just had the one I was using last.  The same happens with some preferences (for example, I disabled mip-maps on User Preferences -> System, and I have to re-enable it every time I open the .blend file again.  Does somebody knows how to restore the Actions and save everything? Thanks. Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$ When does $\,n\mid q^3 \Rightarrow n\mid q\,$? I think this is true because of prime factorisations, i.e.  If $3$ a factor of the prime factorisation of $q^3$, then $3$ is a factor of the prime factorisation of $q$.  Therefore If $3$ divides $q^3$, then $3$ divides $q$.  Or for a general case, if $n$ divides $q^3$; then $n$ divides $q$. Is this correct? I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated? Maybe this is an easy question, maybe not.  I have a select box where I hardcode with width. Say 120px.    &lt;select style="width: 120px"&gt;   &lt;option&gt;REALLY LONG TEXT, REALLY LONG TEXT, REALLY LONG TEXT&lt;/option&gt;   &lt;option&gt;ABC&lt;/option&gt; &lt;/select&gt;     I want to be able to show the second option so that the user can see the full length of the text.  Like everything else.  This works fine in Firefox, but doesn't work with Internet Explorer6. For some time, Microsoft has supported an option to remove the limit of 260 symbols for NTFS file name length.  The web is full of articles, describing what should be done.   Hit the Windows key, type gpedit.msc and press Enter. Navigate to Local Computer Policy > Computer Configuration > Administrative Templates > System > Filesystem > NTFS. Double click the Enable NTFS long paths option and enable it.   However, I don't have such option. Please see the screenshot below:    Am I missing some Windows update, or is it something else? What is the US Visa Waiver Program and what is an ESTA? Long rectangular quads? Or neat squarish quads with tris? For curved meshes I've often noticed that in my desperation to avoid tris, I tend to extrude the mesh in a way which creates these long rectangular quads:    In this case at least, the mesh is all quads, however the edge flow causes loopcutting to be awkward in some places:    I tried creating the same mesh with more even topology, however I found tris unavoidable. Maybe it was because I was starting with the long-quad mesh, but I also found myself using the knife tool for everything..    This makes loopcuts less necessary and easier to place in most cases, though the occasional tri does get in the way.  An annoying thing about the tris are the poles, though they aren't too noticeable in this particular case.    Both techniques seems to have their advantages and their disadvantages:    Which is considered "better", if any? Are there any better workflows for creating even topology with as few tris as possible? Or is there some trick I'm missing altogether?