Not possible to search for umlaute in LaTeX
What are good ways to make pdflatex output copy-and-pasteable?
Kill the [bugs] tag? It seems most of the questions tagged  on Stack Overflow are just intended to indicate "there's something wrong with my program", which would cover probably at least 80% of all questions on Stack Overflow.  There are some questions where it seems to refer to a possible bug in a framework or utility. I'm not sure the tag is really all that useful in that case either.  What does meta think? Is this intended behavior (with plain XeTeX):  \input tikz \tikz\draw[dashed] node {$3T\over4$}; \bye   It renders as: !?  The fraction line is dashed, too! Is this intentional? Is there something I can do to change that? I know I can separate the fraction into its own node, but other than that? Accessing the web page's HTTP Headers in JavaScript How do I access a page's HTTP response headers via JavaScript?  Related to , which was modified to ask about accessing two specific HTTP headers.     Related: A significant amount of zombies were detected in your city Can anyone please help and tell me if this sentence is correct?  &quot;A significant amount of zombies were detected in your city.&quot;  In my opinion it should be &quot;A significant amount of zombies was detected in your city.&quot; because &quot;amount&quot; should be in agreement with &quot;was&quot; even though amount usually refers to something plural. Are both (was and were) acceptable in this case? Edit1: Yes, &quot;number&quot; would be the correct one in this case. So allow me to ask one more thing.  &quot;A significant amount of purchases were detected...&quot;  Does the use of &quot;number&quot; apply in this case also? As purchase is not exactly a thing/person. And if no, is it correct to say &quot;A significant amount of purchases were detected...&quot;? Edit2: So, please tell me what is the correct phrasing?  &quot;A significant amount of purchases were detected...&quot; &quot;A significant amount of purchases was detected...&quot;  Or, since purchases are countable, is the use of &quot;number&quot; instead of &quot;amount&quot; correct here, as in:  &quot;A significant number of purchases were detected...&quot; &quot;A significant number of purchases was detected...&quot;  Or would amount be correct since a purchase involves money and it refers to the amount of money? Would greatly appreciate an answer, and if possible a detailed explanation. Self adjoint operators and trace class property This is a variation of the  questioned some time ago.  For a complex Hilbert space $H$ let $T: H \rightarrow H$ be a bounded operator. We call that $T$ is a trace-class operator if the following sum  $$\sum_{i}{\langle |T|e_{i}, e_{i} \rangle} &lt; \infty$$  converges, where $|T| = (T T^{*})^{\frac{1}{2}}$ is the absolute value of the operator.  Assume that  $$\sum_{i}{\langle Te_{i}, e_{i} \rangle}$$  converges for any basis in the space $H$. How to prove that if the aformentioned property holds then the operator is a trace class operator?  The progress on the problem is the following: Given an arbitrary bounded operator $T: H \rightarrow H$, one can use the following decomposition $$T = \big( \frac{T + T^{*}}{2} \big) ^{*} + i \big( \frac{T^{*} - T}{2i} \big) ^{*}$$  The latter line gives the decomposition $$T = A + i B$$ where $A, B$ are normal operators.  For the normal operators we can apply the spectral theorem that proposes that $T$ is unitary equivalent to  $$(UT U^{-1})(f(x)) = g(x) f(x)$$  where  $$U: H \rightarrow L^{2}(X, \mu)$$ $$g \in L^{\infty}(X, \mu)$$  Though this decomposition classify the operator in a broad sence, i see no direct way to conclude the statement. Are the any hints that may extend the previous argument? If not, are there any ways to conclude the statement? Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$? Let $A, B$ be similar $n \times n$ matrices over (say) $\mathbb{R}.$  Is it the case that $A+cI$ is similar to $B+cI$?    Here is an argument (which seems too good to be true...)  Since $A, B$ are similar, they have the same Jordan form. So we can write $PAP^{-1}=QBQ^{-1}=J$ for $P, Q$ invertible matrices.   Hence we have $P(A+cI)P^{-1}=PAP^{-1}+cI= J+cI.$ Similarly, we find $Q(B+cI)Q^{-1}=J+cI.$  Hence $A+cI$ and $B+cI$ are both similar to $J+cI$ and hence similar to each other.   Is this correct? In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?  I just dipped into a book, The Drunkard's Walk - How Randomness Rules Our Lives, by Leonard Mlodinow, Vintage Books, 2008. On p.107 Mlodinow says the chances are 1 in 3.   It seems obvious to me that the chances are 1 in 2. Am I correct? Is this not exactly analogous to having a bowl with an infinite number of marbles, half black and half red? Without looking I draw out a black marble. The probability of the second marble I draw being black is 1/2. How to capture workload from production to replay on test? I want to perform performance testing on my test server.  How can I capture workload from production and replay on my test server?   Basically I'm looking for detailed steps so that I can replay the workload from production to my test environment. If $[G' : G'']\leq p^2$, then $G'$ is abelian. Radius of Convergence when using Series[] Integral of $\frac{1}{x^4+1}$ Just doing this for revision, seems much harder than it should be, should I use $x=\tan u$ ? Any help appreciated. How to use resistors? I have a power supply of 5 volts @ 1A. I want to reduce the current from 1A to 250mA. Which resistor should be use?   I tried this equation(Ohm's Law):  R = V / I  = 5/(0.75)  = 6.66 Ohms.  I tried the 6.66 Ohm resistor but it only reduce few mili Amps. Deriving Newton's Third Law from homogeneity of Space How to activate GRASS GIS 7 plugin in QGIS 2.8? How did humans and vulcans communicate in Star Trek: First Contact? Find the derived subgroup of $A_4$.   Since it is $A_4$, for a permutation $\sigma$ to be in $A_4$, $\sigma$ must have a cycle structure of $2$ cycles. Therefore, $\sigma=(ab)(cd)$.  The commutator of such elements, would be obviously another permutation of $2$-cycle (of length $2$).  Does it mean that $A'_4=A_4$? Unique pair of positive integers $(p,n)$ satisfying $p^3-p=n^7-n^3$ where $p$ is prime Q. Find all pairs $(p,n)$ of positive integers where $p$ is prime and $p^3-p=n^7-n^3$.   Rewriting the given equation as $p(p+1)(p-1)=n^3(n^2+1)(n+1)(n-1)$, we see that $p$ must divide one of the factors $n,n+1,n-1,n^2+1$ on the $\text{r.h.s}$.   Now, the $\text{l.h.s}$ is an increasing function of $p$ for $p\ge1$. This implies that for any given $n\ge1$, there is exactly one real $p$ for which $\text{l.h.s}=\text{r.h.s}$. For $p=n^2$, we get $\text{l.h.s}=n^6-n^2&lt;n^7-n^3=\text{r.h.s}.$ This means that either $p&gt;n^2$ or $p&lt;n^2$ must hold.  Assuming $p&gt;n^2$, it follows that the prime $p$ cannot divide any of $n,n+1,n-1$. So $p$ must divide $n^2+1$ and hence $p=n^2+1\quad (\because p&gt;n^2)$.  Substituting the value of $p$ in the given equation we get, $n^2+2=n^3-n\implies n^3-n^2-n=2$. As the factor $n$ on the $\text{l.h.s}$ must divide $2$, the above equation has a unique integer solution $n=2$.  Finally, we get $(5,2)$ as the solution to the given equation.      But how do I conclude this is the only solution possible? Also, why does'nt $p&lt;n^2$ (the case which I ignored) hold? As a bonus question, I would like to ask for any alternative/elegant solution (possibly using congruence relations) to the problem. Let $\left| {{a_{ii}}} \right| > \sum\limits_{i \ne j} {\left| {{a_{ij}}} \right|} $.Why does $A$ is nonsingular? . Lightsabers are not made of light, nor have they anything to do with lasers (even if there are people who mistakenly refer to them as "laser swords").   Blaster bolts are also not lasers. They travel significantly slower than light, they travel even slower than ordinary bullets fired by gunpowder. (called slug throwers on the Star Wars universe)  Was there any use of lasers ever presented in the Star Wars universe, either as we use them today, or as weapons?  By laser I mean something which behaves like laser does, even if it's not called by that name in a movie or book. If something is called a laser (in the script or by fans) but clearly doesn't work like a laser (for example, it travels slowly, and in visible blocks) it doesn't count. Convert from MySQL datetime to another format with PHP