Modern GCC interpreting `<` preceding template parameters as operator `<`
Where and why do I have to put the "template" and "typename" keywords?
Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$ I'm having trouble computing the integral: $$\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx.$$ I hope that it can be expressed in terms of elementary functions. I've tried simple substitutions such as $u=\sin(x)$ and $u=\cos(x)$, but it was not very effective.  Any suggestions are welcome. Thanks. I would like to configure my Ubuntu 12.04 server to synchronize its clock with a specific NTP server. Where to set this up? Will I lose previous purchases when I change country in iTunes Applications Don't Show Up in Spotlight Spotlight has stopped showing any results for my Applications. I've tried reindexing and removing the index so it rebuilds it. No change. I've tried adding Applications to the Privacy tab and removing it, no change.  I tried repairing disk permissions and redoing the above, no change. I've tried removing everything from the index except Applications and then I just get nothing for any search at all (except dictionary entries).  I tried adding a symlink in my homedir to Applications and reindexing, but no change.  Any ideas on what to do?  I'm running Snow Leopard.  This is driving me crazy!  Update: I've noticed that when I start a reindex with sudo mdutil -E / and then immediately do a Spotlight search for an app that the app shows up temporarily until Spotlight gets disabled due to active indexing.  After the indexing is done, the app entries go away. I need help to find the Galois Group of $x^5 +1$. I know that it has a 5-cycle and a 4 cycle and is not a subgroup of $A_5$. Thanks! How to compare two different files line by line in unix? File1:  123 234 345 456   File2:  123 234 343 758   Expected output: File3:  TRUE TRUE FALSE FALSE   so the code should compare two files and print 'TRUE' if it matches otherwise it should print 'FALSE' in the new file. Could anyone please provide the solution for this? A real $2 \times 2 $ matrix $M$ such that $$M^2 =  \begin{pmatrix} -1&amp;0 \\ 0&amp;-1-\epsilon  \\   \end{pmatrix}$$ (a) exists for all $\epsilon &gt; 0$. (b) does not exist for any $\epsilon &gt; 0$. (c) exists for some $\epsilon &gt; 0$. (d) None of the above is true.  Attempt: I couldn't think of any theory base to prove / disprove the existence of such a matrix. Could someone please give me a hint on how to go about this problem? Thank you very much for your help in this regard. In Volo's Guide to Monsters, there is a race in the bestiary called Grungs. Were these created for 5e specifically?  I'm pretty sure they were created for 5e, as they have no deities listed which is always a bit suspicious, but I'm just making sure. Why did Harime Nui's eye not heal? The question is:     When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?   The most obvious solution is a linear function of the form $f(x)=ax+b$. Is this the only solution?  Edit  I should add that $f:\mathbb R\to\mathbb R$ to the question. I have two files in these formats:   file1 :  air smell hand dude road cat   file 2:   air,4,21,01,13,3,2 smell,21,4,2,5,6 dude,1,31,42,1 road,1,4,2,1,4 cat,1,5,6,3,1 hand,1,4,2,1,6 mouse,1,3,5,6,2   what I want to do is print the entire row of file 2, if the first string in column 1 of file 2 is found in file 1, and I want to keep the order of file 1.   expected output:   air,4,21,01,13,3,2 smell,21,4,2,5,6 hand,1,4,2,1,6 dude,1,31,42,1 road,1,4,2,1,4 cat,1,5,6,3,1 Examples and Counterexamples of Relations which Satisfy Certain Properties Definition: Given a set $X$, a relation $R$ on $X$ is any subset of $X\times X$.  A relation $R$ on $X$ is said to be  reflexive if $(x,x) \in R$ for all $x \in X$, irreflexive if $(x,x) \not\in R$ for all $x \in X$, transitive if $(x,y) \in R$ and $(y,z) \in R$ implies that $(x,z)\in R$, intransitive (or antitransitive) if $(x,y) \in R$ and $(y,z) \in R$ implies that $(x,z)\not\in R$, symmetric if $(x,y) \in R$ implies that $(y,x) \in R$, antisymmetric if $(x,y) \in R$ and $(y,x) \in R$ implies that $x=y$.   Given any combination of the properties listed above, is there a nontrivial (i.e. nonempty) relation which satisfies that combination of properties? Best Pattern For Adding Commentary in align Environment? I've been using the align environment to line up equations in proofs/explanations/etc and I like to place parenthetical commentary for each step, similar to the code below:  \documentclass{article} \usepackage{amsmath} \begin{document}  \begin{align*}   f(ax + by) &amp; = f(ax) + f(by) &amp; (By Property 1) \\              &amp; = af(x) + bf(y) &amp; (By Property 2) \\ \end{align*}  \end{document}   The problem I have with this is that the commentary completely distorts the overall alignment of the equation area; far too much space is allocated to the column containing the commentary.  I would like, insofar as it is possible, for the equations themselves to be aligned in the center of the page and for the commentary to simply appear on the right without affecting the overall justification of the equations. What's the best way to achieve this? I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents: What is the "canary thread" and why is it starving? The following occasionally appears in /var/log/syslog:  rtkit-daemon[1145]: The canary thread is apparently starving. Taking action. rtkit-daemon[1145]: Demoting known real-time threads. rtkit-daemon[1145]: Successfully demoted thread 1431 of process 1368 (n/a). rtkit-daemon[1145]: Successfully demoted thread 1430 of process 1368 (n/a). rtkit-daemon[1145]: Successfully demoted thread 1368 of process 1368 (n/a). rtkit-daemon[1145]: Demoted 3 threads.   What's going on here? Difference between shutdown and shutdownNow of Executor Service How are POST and GET variables handled in Python? In PHP you can just use $_POST for POST and $_GET for GET (Query string) variables. What's the equivalent in Python? Why is the (free) neutron lifetime so long? A neutron outside the nucleus lives for about 15 minutes and decays mainly through weak decays (beta decay). Many other weakly decaying particles decay with lifetimes between $10^{-10}$ and $10^{-12}$ seconds, which is consistent with $\alpha_W \simeq 10^{-6}$.  Why does the neutron lives so much longer than the others? A hard problem on exponential integration Suppose $a : [0 , 1] \to \Bbb R$ is an infinitely smooth function. For $\lambda\ge1$, define $$F(\lambda) := \lambda \int_0^1 e^{\lambda t} a(t) \, dt.$$ If $\sup_{\lambda\ge1}|F(\lambda)|\lt\infty$, then $a$ is the identically zero function. Below are the some results I have derived:   Derivatives of any order of $a$ vanishes at $t = 1.$ For any $\delta\lt1$, $a(t)$ has a zero in the open interval $(\delta , 1).$  The same is true for all the derivatives of $a(t)$. This tells us that the $n^\text{th}$ derivative of $a$ has infinitely many distinct zeros for all natural $n$. If $a$ is analytic, then I can show that $a(t)\equiv 0.$ If $a(t)\ge0$ on $[0 , 1]$, then it is obvious that $a\equiv 0.$   I would appreciate any hint.  Actually $(1)$ and $(3)$ follows from $(2)$. For $(2)$, suppose that $a(1)\gt0$ (the case that $a(1)\lt0$ can be argued in the same way as the following), then there exists $\delta\lt1$ such that $a(t)$ is strictly positive on $I = [1-\delta , 1]$. Then write $F(\lambda) = \lambda\int_0^{1-\delta}e^{\lambda t}a(t)dt + \lambda\int_{1-\delta}^1e^{\lambda t}a(t)dt$. Now there exists $c\gt0$ such that $a(t)&gt;c$ on $I$ since $I$ is compact, so that the second term is bounded below by $c (e^{\lambda}-e^{\lambda(1-\delta)})$. But the first term is only $O(e^{\lambda(1-\delta)})$, so this contradicts the fact that $F(\lambda)$ is bounded. Morever, using the same idea and integration by parts, one can see that $n^{th}$ derivative of $a$ must vanish at $1$. Optional Methods in Java Interface