How to install apps on iOS 7.1
How to install apps which require a newer version of iOS on a 1st gen. iPad?
underbrace matrix inside brackets I would like to put an underbrace below the matrix like this:  $$\left(\underbrace{ \left[\begin{array}{ccc}     a&amp;b&amp;c\\     d&amp;e&amp;f\\     g&amp;h&amp;i \end{array}\right]}_{A} \left[\begin{array}{c}     x_1\\     x_2\\     x_3 \end{array}\right]\right)$$     But I don't want the outer brackets \left( and \right) to stretch vertically. I want them to remain as if there was no underbrace. How to achieve that behaviour? Design a custom Beamer theme from scratch Problems with partial derivatives. How to determine equality for two JavaScript objects? A strict equality operator will tell you if two object types are equal. However, is there a way to tell if two objects are equal, much like the hash code value in Java?  Stack Overflow question  is similar to this question, but requires a more academic answer. The scenario above demonstrates why it would be necessary to have one, and I'm wondering if there is any equivalent solution. Is there a (basic) way to understand why a limit cannot be brought inside of a sum, in certain situations? I have seen that the method of "dominated convergence" implies that sometimes a limit cannot be brought inside of a sum, but is there a more basic way to understand this, preferably without using integrals?   A conceptual or simple answer would be helpful. Thank you! nVidia driver reset after each kernel update I am using the official nVidia driver because my card (GeForce 750 Ti) isn't yet supported by the Ubuntu one. Every time the kernel updates, my system breaks.  I've formatted my system two-three times because of kernel updates and today I decided to try to fix it. I tried to fix it with this method and surprisingly it works.   Switch to console (After waiting for the nVidia driver to crash, as it does when you switch consoles :p) Run a complete uninstall  sudo ./&lt;DRIVER&gt;.run -uninstall  Reboot and switch to the on-board card Update  sudo apt-get update sudo apt-get dist-upgrade  Reboot again Reinstall driver  sudo ./&lt;DRIVER&gt;.run  Reboot and switch back to the NVIDIA GPU   Is there a better/easier/faster way to update without going through all this? Equivalence Relation problem Word that means "the opposite of what you would expect" I'm looking for a word that means the opposite of what one would expect. This word might be used to express the surprise that a teenager's grandmother uses text messaging much more than he does, or that a city seems brighter at night than it does during the day.   I'm not seeking the word ironic or irony which refer to the use of something to describe its opposite experience or emotion. multiline command chunks in bash history into multiple lines In Bash (as well as Bash in WSL), multiline written commands can call-back with up/down arrows correctly also built-in history command report them correctly (until I'm still logged-in in bash). But after exiting from bash and press up/down arrows, multiline commands appears each as separate entries and that's because cat ~/.bash_history has chucked the command on multiple separate entries and writing problem here; the history command result messed too. I have set these options in ~/.bashrc shopt -s cmdhist lithist HISTTIMEFORMAT='%F %T '  and now writing problem fixed but history command still report in multiple line and separate entries (reading problem now). Bash version is 4.3, same issue on v4.4 there is  since a long years but no solution yet. Update: it's also to mention that below multiline command as an example is correctly displaying even after exit Bash: for i in {1..10} do echo $i done  but this is failing: awk ' { print $1}' &lt;&lt;&lt;'first last'  Update 2: the issue mentioned above is fixed in Bash v5.0.0+ that changed to recognize entries between &quot;timestamp as delimiter&quot; as single entry of command (HISTTIMEFORMAT, cmdhist and lithist must be set). jQuery - multiple $(document).ready ...? Why do shadows from the sun join each other when near enough? I was laying on my bed, reading a book when the sun shone through the windows on my left. I happened to look at the wall on my right and noticed this very strange effect. The shadow of my elbow, when near the pages of the book, joined up with the shadow of the book even though I wasn't physically touching it.   I have posted :The video seems to be the wrong way up, but you still get the idea of what is happening.  What is causing this? Some sort of optical illusion where the light gets bent?  Coincidentally, I have been wondering about a similar effect recently where if you focus your eye on a nearby object, say, your finger, objects behind it in the distance seem to get curved/distorted around the edge of your finger. It seems awfully related...  EDIT: I could see the bulge with my bare eyes to the same extent as in the video! The room was well light and the wall was indeed quite bright. I recently read that:     What our current level of thermodynamics does tell us though is that if there is such a thing as a Big Crunch, the universe will look a lot different as it heads towards collapse than it did when expanding – the universe started in a state of low entropy and high order and will end in a state of high entropy and   low order.   But shouldn't the order be in a high state and hence entropy becomes a low state in the Big Crunch (assuming a closed universe)?  The reason I write this is because the gravitational forces in a closed universe are so strong they will cause gravitational collapse so the universe will shrink and go backwards, eventually through all the stages of the big bang and become a singularity once more.   It was my understanding that a singularity has a state of high order and low entropy. Have I got this the wrong way round?   If so; Can someone please explain why? Primary decomposition of a monomial ideal Can anyone give me an idea about the primary decomposition of the ideal $I=(x^3y,xy^4)$ of the ring $R=k[x,y]$?    I am trying to connect the primary decomposition with the set Ass(R/I) which i have find before.. Let's say that there exists some "true" relationship between $y$ and $x$ such that $y = ax + b + \epsilon$, where $a$ and $b$ are constants and $\epsilon$ is i.i.d normal noise. When I randomly generate data from that R code: x &lt;- 1:100; y &lt;- ax + b + rnorm(length(x)) and then fit a model like y ~ x, I obviously get reasonably good estimates for $a$ and $b$.  If I switch the role of the variables as in (x ~ y), however, and then rewrite the result for $y$ to be a function of $x$, the resulting slope is always steeper (either more negative or more positive) than that estimated by the y ~ x regression. I'm trying to understand exactly why that is and would appreciate it if anyone could give me an intuition as to what's going on there. How much of an $n$-dimensional manifold can we embed into $\mathbb{R}^n$? I observed some naive examples. Spheres, for example, when we cut out one point, can be embedded into $\mathbb{R}^n$. And if we cut out a measure zero set of a projective space, it can be embedded into the Euclidean space of the same dimension. So I wonder if all manifolds can be embedded into a same dimensional Euclidean space when we cut out a measure zero set? Can anyone prove it or disprove it by giving me some counterexamples? how can i display the latest items from another site collection I have a web application, with three site collections . and i want inside my team site to be able to display the latest pages that  have been added to my enterprise wiki site collection. so what are the available approaches which i can follow?  Thanks in advance for any help.  Regards Is there an equivalent of 'which' on the Windows command line? As I sometimes have path problems, where one of my own cmd scripts is hidden (shadowed) by another program (earlier on the path), I would like to be able to find the full path to a program on the Windows command line, given just its name.  Is there an equivalent to the UNIX command 'which'?  On UNIX, which command prints the full path of the given command to easily find and repair these shadowing problems. I came to think about some situations where it would be almost impossible to miss a melee spell attack (target is grappling you or vice versa, target is holding you or is close to you, your character already has it's hand on the target, etc.). How do you manage those situations?    Do you give an advantage to the caster? Does the spell automatically succeed? Or you just don't ask yourself the question and just play along with the base rules? Does Hilbert's $\varepsilon$-calculus have any real problem when using for incomplete systems? Spacial curvature and expanding space If we take the analogy that in an empty space the space is just a flat sheet then if there is a single planet or a star then the flat sheet will curve below the planet leaving a curvature shaped like a hemisphere below the object, my question is, Does this curvature change as space expands?