When viewing an image in zoomed mode, the up-down arrow keys do not allow me to pan in it. I have not found any other shortcuts to pan without using the mouse.
When I'm going through a whole bunch of shots to determine which to delete and which to flag, it's fastest for me to just keep both hands on the keyboard.  However, if I want to zoom in to 100% on a picture and then pan to a specific area, it seems I can only get halfway there -- 'Z' to zoom, but then I'm stuck having to pick up the mouse to pan around.  I was excited to find page-up/page-down/home/end can be used, but they seem to exist to provide an exhaustive, linear scrolling of the image, panning top-to-bottom then left-to-right, without unconstrained 2d movement.  Is there some way to toggle the arrow keys so they can pan instead of navigate to the next/prev photo?  Something else?  Or am I out of luck?
Transposing rows and columns I have a file with the lines like below.  title1:A1 title2:A2 title3:A3 title4:A4 title5:A5  title1:B1 title2:B2 title3:B3 title4:B4 title5:B5  title1:C1 title2:C2 title3:C3 title4:C4 title5:C5  title1:D1 title2:D2 title3:D3 title4:D4 title5:D5  How can I achieve this?   title1    title2     title3    title4 A1         A2         A3         A4 B1         B2         B3         B4 C1         C2         C3         C4 D1         D2         D3         D4 Are there recommendations or pitfalls for playing an archer cleric? In my 4E game, a player is going to try an elven cleric with a longbow (and a mace, just in case). She chose mostly ranged powers. Are there any caveats to playing such a character, or any builds that I could recommend for her? If it is given that component of acceleration perpendicular to the velocity of a body has a constant, non-zero magnitude, how can we mathematically prove that the trajectory of the body will be circular?   I have basic knowledge of calculus, vectors and co-ordinate geometry. I can prove that the trajectory of a body in projectile motion is parabolic. I tried to follow a similar method to get an equation of circle but couldn't succeed. I tried forming parametric equations of x and y in terms of time t (the way we proceed when proving the parabolic path of a projectile) but could not reach the conclusion.  Edit: I have edited the question in order to improve it. However I still can not share my work on this question as I had asked the question almost 6 months ago and now I can not find where I tried solving it. Sincerely sorry for that. Rotate a long bar in space and get close to (or even beyond) the speed of light $c$ How do I find the right size of filters for a lens? I tried to rev a file and then pipe it to cat &gt; same_file but it was turning into a blank file.    While I tried rev file.txt | cat &gt; file2.txt &amp;&amp; mv file.txt file2.txt; it worked.    Even rev file.txt | cat &gt;&gt; file.txt; worked.  But when I tried rev file.txt | cat &gt; file.txt it failed. Limit of divided integrals Prove that: $$\lim\limits_{m\to \infty} \frac{\int\limits_0^{\pi/2}(\sin(x))^{2m} dx}{\int\limits_0^{\pi/2}(\sin(x))^{2m+1} dx} = 1$$  I had tried to get it from inequalities like $$(\sin(x))^{2m+1} \le (\sin(x))^{2m} \le (\sin(x))^{2m-1}$$ But I always hit a wall in that regard (I integrate the sin functions and from there keep on going but there it ends). $\newcommand{\Var}{\operatorname{Var}}$In this  is claimed that if the equation of errors in OLS is given by: $$u=y - X\beta$$ Then in the presence of heteroscedasticity the variance of $u$, will not be constant, $\sigma^2 \times I$, where $I$ is an identity matrix, but: $$\Var(u\mid X)=\sigma^2\Omega$$ In order to account for the heteroskedasticity, we can estimate the transform system, such that $P$ is a transformation matrix. $$Py=PX\beta-Pu$$ Where "the variance of a constant matrix $P$ times a random vector $u$" is: $$\Var(Pu\mid X)=P\Var(u\mid X)P'=P(\sigma^2\Omega)P'$$ Can somebody explain me the proof for that? (complex measures) $d\nu=d\lambda +f\,dm \Rightarrow d|\nu|=d|\lambda| +|f|\,dm$ and $f\in L^1(\nu)\Rightarrow f\in L^1(|\nu|)$ Two simple exercises on complex measures I don't know how to solve, from Folland's Real Analysis. I find it difficult to manipulate the definitions in computations. For context, if $\nu$ is a complex measure on $(X,\mathcal{M})$ then $|\nu|$ is defined as $d|\nu|=|g|\,d\mu$ where positive measure $\mu$ and $g\in L^1(\mu)$ are such that $\nu \ll \mu$ and $\nu = g\,d\mu$ (and in the textbook it's shown that this definition does not depend on the choice of $\mu$).     1) Let $\nu$ be a reguar complex Borel measure on $\mathbb{R}^n$, $m$ denote   Lebesgue measure, and   let $d\nu = d\lambda + f\,dm$ be its Lebesgue-Radon-Nikodym   representation. Then ("it is easily verified")   $d|\nu|=d|\lambda|+|f|\,dm$.      2) If $f\in L^1(\nu)$ then $f\in L^1(|\nu|)$. I was able to prove the   reverse implication, but not this one.   The definition of $|\nu|$ in the case of real signed measures (as $|\nu|=\nu^+ + \nu^-$) makes sense to me but I can't see intuitively into the definion of $|\nu|$ for complex measures as given in the textbook. Do you have any advice on this?  Thank you! Export beamer slides to powerpoint/openoffice-impress/keynote editable format I usually prepare my talks using powerpoint/openoffice-impress/keynote, where I explaing programs, pseudocodes, etc. Recently I was thinking about creating text-only, code-only and pseudocode-only slides with beamer and then exporting them somehow to powerpoint where I modify them to add figures or some minor details for polishing the presentation, which are usually hard to do with beamer. I googled a bit around and found that beamer can export to PDF or PS but not to powerpoint. I wonder anyway if you know some possibility of conversion from beamer to on-screen editable powerpoint/openoffice-impress/keynote. Spontaneous electroweak symmetry breaking (i.e. $SU(2)\times U(1)\to U(1)_{em}$ ) is at scale about 100 Gev. So, for , gauge bosons $Z$ &amp; $W$ have masses about 100 GeV. But before this spontaneous symmetry breaking ( i.e. Energy > 100 GeV) the symmetry $SU(2)\times U(1)$ is not broken, and therefore gauge bosons are massless.  The same thing happens when we go around energy about $10^{16}$ GeV, where we have the Grand Unification between electroweak and strong interactions, in some bigger group ($SU(5)$, $SO(10)$ or others). So theoretically we should find gauge bosons $X$ and $Y$ with masses about $10^{16}$ GeV after GUT symmetry breaks into the Standard Model gauge group $SU(3)\times SU(2)\times U(1)$, and we should find massless X and Y bosons at bigger energies (where GUT isn't broken).  So this is what happened in the early universe: when temperature decreased, spontaneous symmetry breaking happened and firstly $X$ &amp; $Y$ gauge bosons obtained mass and finally $Z$ &amp; $W$ bosons obtained mass.   Now, I ask: have I understood this correctly? In other words, if we make experiments at energy above the electroweak scale (100 GeV) we are where $SU(2)\times U(1)$ isn't broken and then we should (experimentally) find $SU(2)$ and $U(1)$ massless gauge bosons, i.e. $W^1$, $W^2$, $W^3$ and $B$ with zero mass? But this is strange, because if I remember well in LHC we have just make experiments at energy about 1 TeV, but we haven't discovered any massless gauge bosons. How to change the date format? $\mathbb Q$ is not the direct product of two non-trivial groups. I know this has been asked before, in a bunch of places, so I expect it to be closed as a duplicate at some point, but I'd like to know if my own proof works. If the proof is incorrect, please limit answers to pointing out the errors. If the proof is correct, then thoughts on improving it would be appreciated.  Prove that $\Bbb Q$ is not the direct product of two non-trivial groups.  —Aluffi exercise II.3.5. My proof Suppose that $\Bbb Q = G \times H$, neither $G$ nor $H$ trivial. First note that $0_G$ is the only element of $G$ with finite order: If $m\ne 0$ and $m\cdot g=0_G$, then $m\cdot(g,0_H)=0_{G\times H}$, contradicting the fact that $\Bbb Q$ has no non-zero elements of finite order. Suppose that for some $m\ne 0$ and some $n\ne 0$, $\pi_G(m/n)=0_G$. Then $0_G=n\cdot\pi_G\left(\frac m n\right)=\pi_G\left(n\cdot\frac m n\right)=\pi_G(m)=m\cdot\pi_G(1)$. Since $\pi_G(1)$ has finite order, we conclude that $\pi_G(1)=0$. Since $\Bbb Z=\langle 1\rangle$, $\pi_G$ maps every integer to $0_G$. Now let $a$ and $b$ be non-zero integers. Then $b\cdot\pi_G\left(\frac a b\right)=\pi_G\left(b\cdot \frac a b\right)=\pi_G(a)=0_G$. As above, this shows that $\pi_G\left(\frac a b\right)=0_G$. Thus if $\pi_G$ is not an injective function, then it must map everything to $0_G$, so $G$ will be a trivial group. The same result holds for $\pi_H$. Since by assumption, $G$ and $H$ are non-trivial, $\pi_G$ and $\pi_H$ are both injective functions, which is of course impossible. Restoring MySQL database from physical files Is it possible to restore a MySQL database from the physical database files. I have a directory that has the following file types:  client.frm client.MYD client.MYI    but for about 20 more tables.  I usually use mysqldump or a similar tool to get everything in 1 SQL file so what is the way to deal with these types of files? Is it generally true that if $|P(A)|=|P(B)|$ then $|A|=|B|$?  Why? Thanks. How to highlight important parts (with a gray background) In the below link        the author highlights anything which is important using a greyish color background. For example, if you see Equation 1.5.3 (which on page 22 of the book) it is highlighted in grey. I would like to know the TeX commands for producing similar output. Invalid selectOptions found. Use SelectOption type in Apex Mounting a device — role of /dev, /media and /mnt, and the mount command I have several closely related questions about what happens when I insert a CD. The files on the CD /media/Ubuntu\ 11.04\ i386/, but from what I've seen /dev/cdrom is also involved.   What is the difference between /dev, /media and /mnt? Following is what I have found from internet but I still have little idea:        /dev — this folder contains device   files    /media — this is a mount point for   removable devices   /mnt — this is a temporary mount point     What is the purpose of mount? In other words, if a device has been represented by the OS as a device file under /dev, why can it not be accessed via the device file directly without mounting?   Is mount only used for storage device, not for non-storage device, such as graphical card, network card, camera, ...? Where is a device file under /dev mounted to, under /media or under /mnt? I remember I have seen both, but am curious when to mount to which? I found my CD was automatically mounted to /media/Ubuntu 11.04 i386. I guess the device file of the CD is /dev/cdrom, but I cannot confirm it by looking into /dev/cdrom and /media/Ubuntu 11.04 i386:  $ ls -l /media/Ubuntu\ 11.04\ i386/ total 3522 -r--r--r-- 1 Tim Tim     143 2011-04-27 13:04 autorun.inf ... $ ls -l /dev/cdrw lrwxrwxrwx 1 root root 3 2011-05-28 15:12 /dev/cdrw -&gt; sr0 $ ls -l /dev/cdrom lrwxrwxrwx 1 root root 3 2011-05-28 15:12 /dev/cdrom -&gt; sr0   How can I find out which device file is for my CD? I added two torus objects, and when I click one of them, it also selects the other. They both share the same node thing. I want to delete one of them, but it keeps on deleting the other with it. I can't even undo placing the second torus without removing the other. What does the notation like 8.6e-28 mean? What is the 'e' for?