Segments of letters
Why can't "fi" be separated when being copied from a compiled pdf?
I'm reading a proof about Lagrangian => Hamiltonian and one part of it just doesn't make sense to me.  The Lagrangian is written $L(q, \dot q, t)$, and is convex in $\dot q$, and then the Hamiltonian is defined via the Legendre transform  $$H(p,q,t) = \max_{\dot q} [p \cdot \dot q - L(q, \dot q, t)]$$  Under the right conditions there exists a function $\dot Q (p,q,t)$ such that  $$H(p,q,t) = p \cdot \dot Q(p,q,t) - L(q, \dot Q(p,q,t), t)$$  i.e. when some $\dot Q(p,q,t)$ satisfies $p = \frac{\partial L}{\partial \dot q}\rvert_{(q, \dot Q(p,q,t), t)} = \frac{\partial L}{\partial \dot q}(q, \dot Q(p,q,t), t)$  (Finding this function is usually called "inverting p")  By taking partials in the $p$ variable and using the relationship, we can obtain the relationship  $$\dot Q = \frac{\partial H}{\partial p}$$  Because of the notation I chose, I get the strong urge to say $\dot q = \frac{\partial H}{\partial p}$  , and in fact this is what the textbook does. But have we proved this?    In other words, how can we deduce that  $$q'(t) = \frac{\partial H}{\partial p}(p(t), q'(t), t)$$ for any differentiable vector valued function $q$? (or maybe there are more conditions we need on $q$? Here  $$p(t) = \frac{\partial L}{\partial \dot q}(q(t), q'(t), t)$$ according to Lagrange's equations. Can you flash any android device with "fastbood flash" command (of the adb)? How do I change my timezone to UTC/GMT? Currently when I execute the date command from bash I get the following displayed  Thu May 17 12:21:00 IST 2012  Below is my timezone config based on executing dpkg-reconfigure tzdata     Current default time zone: 'Europe/Dublin'   Local time is now: Thu May 17 12:32:52 IST 2012.   Universal Time is now: Thu May 17 11:32:52 UTC 2012.     Any idea how I change from IST to UTC/GMT? Why is the comma splice an error? It's always drilled into us that we shouldn't use comma splices. They're bad, to be avoided and poor form.  But why? What makes the comma a faulty choice in something like this:     I never liked school, it was boring and repetitive most of the time.   It could be replaced with a semicolon, dash, period or colon and be "correct." Yet to a fair amount of people, the comma seems fine. If it weren't, it wouldn't be found so often in online forums, text messages, emails and so on.  What makes the comma between two sentences an error? I'd like to use a different + symbol in addition to + in math mode, preferably one which is just bolder than the standard one.  I'm currently using \pmb{+} from the amsbsy package, but it's a bit too lean for my taste, and it looks a bit pointy to the ends.   I am aware of \ding{58} from the pifont package, as well as \Plus from bbding, both of which seem to be non-math mode symbols, and look really bad next to math symbols.  Am I missing some other option to produce a bold +, apart from drawing the symbol myself? How do I get the current date and time in PHP? Which PHP function can return the current date/time? Down arrow button for choosing the desired site When searching for the desired SE site, the down arrow key (down) should work in order to choose the site one is looking for and hit enter to visit it, instead of using the mouse point to choose it. Would be pretty convenient. Footnotes in tables? I would like to have footnotes in tables, but the \footnote command does not work inside a table environment.  Googling one finds that this is , at least in the UK.  That link contains a list of solutions to the problem, but since the author of the FAQ does not believe that this is good style, no comparison is made between the different methods.  I am sure that there are good typographical reasons why in most situations it is undesirable to have footnotes in tables (although I have never come across them), however I have recently felt the need to do just this in a paper I am currently writing.  Therefore I'd like to ask two questions:   What are the arguments against footnotes in tables? If one really must go against the advice in 1., which method (whether considered in the  or not) would you recommend?   Thanks in advance.  Added  In response to ShreevatsaR's comment: I do not much care for where the text of the footnote appears.  I do however insist on the footnote marks being attached to the relevant entries in the table, so that I can avoid having to reference "the second entry in the eighth line of the table", etc... I have a Lenovo T570 with Xubuntu 18.04 LTS. My current issue is that my cpu speed stepping is kind of going nuts and does what ever it thinks its best.  Sample: when I run my IDE and cpu load increases during build time, the governor changes automatically. I caught the moment during compiling my project with the following call:  martin@martin-ThinkPad-T570:~$ while cat /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor; do sleep 1; done powersave powersave performance performance   cpufreq-info tells me this:  martin@martin-ThinkPad-T570:~$ cpufreq-info  cpufrequtils 008: cpufreq-info (C) Dominik Brodowski 2004-2009 Report errors and bugs to cpufreq@vger.kernel.org, please. analyzing CPU 0:   driver: intel_pstate   CPUs which run at the same hardware frequency: 0   CPUs which need to have their frequency coordinated by software: 0   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.25 GHz. analyzing CPU 1:   driver: intel_pstate   CPUs which run at the same hardware frequency: 1   CPUs which need to have their frequency coordinated by software: 1   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz. analyzing CPU 2:   driver: intel_pstate   CPUs which run at the same hardware frequency: 2   CPUs which need to have their frequency coordinated by software: 2   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.26 GHz. analyzing CPU 3:   driver: intel_pstate   CPUs which run at the same hardware frequency: 3   CPUs which need to have their frequency coordinated by software: 3   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz.   Please take a look at     current policy: frequency should be within 3.50 GHz and 3.50 GHz.       The governor "performance" may decide which speed to use   Afterwards to go back to powersave I use my little script:  martin@martin-ThinkPad-T570:~$ cat cpu_freq_save.sh  #!/bin/bash sudo cpufreq-set -g powersave -c 0 --min 400MHz sudo cpufreq-set -g powersave -c 1 --min 400MHz sudo cpufreq-set -g powersave -c 2 --min 400MHz sudo cpufreq-set -g powersave -c 3 --min 400MHz   Which resets the min frequency and the governor but as soon as I compile again with my IDE every time the governor and the min frequency changes again.  Any idea how I can disable that automatic change?  PS: If you need more details, just tell me where to find them and I will provide them I'm looking for a way to insert continuous colour legend for a raster layer.  I managed to create discrete symbols with values along the bar, but I would like to have a continuous bar with some values on the bar, similar to the old plugin "One-Band Raster", that it doesn't work with the QGIS version higher than 1.7  I tried to set in properties->style, where I selected the  Render Type "Singleband pseudocolor" and see the "generate new color ramp" box.  I tried both "Continuous" or "Equal interval". However, in the Composer the legend always is displayed with discrete symbols.  Is there any way that can make QGIS Composer to display a nice continuous band for a raster layer? Finding the limit of $(1-\cos(x))/x$ as $x\to 0$ with squeeze theorem How do I find:  $$ \lim_{x\to0}\frac{1-\cos(x)}{x} $$  Using the squeeze theorem.  Particularly, how would I arrive at its bounding functions?   If possible, please try not to use derivatives. The complex general linear group is a subgroup of the group of real matrices of twice the dimension and with positive determinant.  Let us decompose complex matrices $M$ as $M=A+iB$, where $A,B$ are real matrices. Now consider the correspondence $$f(A+iB)=\begin{pmatrix} A &amp; -B \\ B &amp; A\end{pmatrix}.$$  If $\det f(M)=|\det M|^2$ for square matrices, then we would have $GL(n,\mathbb C)\subseteq GL_+(2n,\mathbb R)$ with the identification $M\to f(M)$, which is an injective homomorphism. In other words, the complex general linear group would be a subgroup of the group of real matrices of twice the dimension and with positive determinant.  How is $\det f(M)=|\det M|^2$? How would I import/export Blender's preferences? I constantly stay up to date with each new release of Blender, but this means my preferences are wiped clean each time. How do I export/import these preferences to avoid loosing my carefully crafted set up each time? t-test or z-test: assume normality or s≈σ? Let's say I have a large sample ($n&gt;30$) with mean $\bar{X}$ and standard deviation $S$. I can calculate only: $T=\frac{\bar{X}-\mu}{S/\sqrt{n}}$.  If I want to use t-test for a hypothesis, then I have to assume normality of the population. If I want to use z-test for a hypothesis, then I have to assume that $\boldsymbol{s\approx\sigma}$.  What is the less important assumption? What test should I do? Should I do t-test, z-test or doesn't matter? On the Goblet of Fire Barty Crouch exactly got Mad-Eye's voice when he transformed into him, but on the Deathly Hallows, they were all able to have their own voices instead of Harry's. Why is the effect of the polyjuice potion inconsistent? Let's say that there is a question asked in a bad manner, in a way that the question is missing. For example the user shows the code and doesn't explain very well which is the problem.    Usually someone starts digging in the OP mind posting comments and asking him for details. It may happen that the question gets edited and the OP edits it to a valid question.    Do you usually give the OP time to edit the question or you immediately vote to close it? I'm trying to find the roots of $x^4+1$. I've already found in this site solutions for polynomials like this $x^n+a$, where $a$ is a negative term. I don't remember how to solve an equation when $a$ is a positive term as the equation above.  Thanks What can I do if a repository/PPA does not have a Release file? Given a file L with one non-negative integer per line and text file F, what would be a fast way to keep only those lines in F, whose line number appears in file L?  Example:  $ cat L.txt 1 3  $ cat F.txt Hello World Hallo Welt Hola mundo  $ command-in-question -x L.txt F.txt Hello World Hola mundo   I'm looking for a command that can handle a file L with 500 million or more entries; file L is sorted numerically.  Note: I'm halfway through an implementation for a command-in-question but I just wondered, whether one might be able to use some Unix tools here as well.    Update: Thank for all the answers, I learned a lot today! I would like to accept more one answer, but that's not possible. Square of a second derivative is the fourth derivative I have a simple question for you guys, if I have this:  $$\left(\frac{d^2}{{dx}^2}\right)^2$$  Is it equal to this:  $$\frac{d^4}{{dx}^4}$$  Such that if I have an arbitrary function $f(x)$ I can get:  $$\left(\frac{d^2 f(x)}{{dx}^2}\right)^2 = \frac{d^4 f(x)}{{dx}^4}$$  Sorry if it's a pretty simple question, but I was trying to simplify something like this:  $$\left(a \cdot \frac{d^2}{{dx}^2} - f(x)\right)^2 g(x)$$ that's where it came up.