How to put a period after a matrix
How to put a full stop at the bottom, not mid-line, after an aligned matrix?
Another "can't use Alt. Series Conv. test" (How do I determine if it converges or diverges?) I am trying to design a circuit and was wondering how to design it that the 12V 800mAH NimH battery I am using will not overcharge. I have researched trickle charging and as far as I understand, a zener diode that regulates the voltage down to about 13.3-13.7V should do. I chose a 14V Zener, taking into account the .6-.7V drop.   I have heard that trickle charging is not the best for the battery, but am not sure how much more work designing a smart charger would take.  I was also thinking of using another diode to prevent flow back to the panels from the battery.         &ndash; Schematic created using  The three voltage sources on the left represent the solar cells, with the NiMH battery on the right.  I was wondering if I needed any additional components if I were to use three 5.5V solar cells in parallel outputting 40mA (16.5V total at 40mA, regulated to 13.3V by the zener) in order to prevent overcharging.  A similar question to mine was asked at  However, this dealt more with a larger lead-acid battery and used a voltage regulator with a schottky diode.   This link discusses almost my exact same question, but I was confused to the answer given which said that up to 1.45V per cell could be charged, taking my max charge voltage up to 14.5V.   Considering I am only outputting 40mA to an  800mAH battery, it seems that I may not need any more battery protection, but would love any input. Can somebody give me an example of a graph on eight vertices that has a pair of pseudosimilar vertices? Or, is it not possible? If it is not possible, please do not give me a proof, as I would like to figure out how to prove it myself.     Definition: vertices $u$ and $v$ in a graph $X$ are similar if there is an automorphism of $X$ that maps $u$ to $v$. If $u$ and $v$ are similar, then the vertex-deleted subgraphs $X-u$ and $X-v$ are isomorphic. If $X-u$ and $X-v$ are isomorphic but $u$ and $v$ are not similar, we say that they are pseudosimilar. How do I center text horizontally and vertically in a TextView? See dashboard as non logged user in community Is it possible, as a non logged user, to see report and dashboard in community when it is open to non logged user? And  for analytic dashboards? The  asks about functions $f \colon \mathbb R \to \mathbb R$ such that $$f(x+y)=f(x)+f(y).$$ It is a very well-known functional equation, which appears in various areas of mathematics ranging from exercises in freshman classes to constructing useful counterexamples for some advanced questions. Solutions of this equation are often called . Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) Is there some overview of basic facts about Cauchy equation and related functional equations - preferably available online? Why don't we pluralize "foot" in measurements? How do we know the universe is expanding, and not that its contents are shrinking? Is there a physical reason why not to think that instead of space expanding, all physical constants and parameters are shrinking (including of course the instruments we use to measure the constants) and space is static, or is it a case of Occam's razor? Data from multiple lists using single REST API call I usually disconnect my cellphone from the charger some time after it's fully charged because I'm afraid the battery could lose capacity over time if I don't. However, I believe modern electronics should be able to handle this kind of scenario and automatically stop charging the battery once it's full. Does this apply to modern Android phones? Or do I need to continue disconnecting it all the time? Do the search engines take the number of 404 errors returned by a site into account when calculating the site rank? For example I have 8,000 404 errors and I am thinking that that's affecting my SEO in a negative way.  However, I read  about 404 errors which suggests that they are not always a negative quality indicator.   So I am confused...are high numbers of 404 errors harmful to a site or not? Why is the range of inverse trigonometric functions defined in this way? My question is really simple, why is the range of the $\sin^{-1}(x)$, $\cos^{-1}(x)$ and $\tan^{-1}(x)$ defined as $[-\pi/2,\pi/2]$, $[0,\pi]$ and $[-\pi/2,\pi/2]$ respectively? Is there some particular reason? We could choose another range for each inverse trigonometric function. For example, we can pick $[0,\pi]$ to be the range of $\sin^{-1}x$.  EDIT  I've understood why the range of the sine and cosine has to be $[-\pi/2,\pi/2]$ and $[0,\pi]$ respectively. I'm still wondering why can't we define the range of the tangent as $[0,\pi]$ ODBC connection to Access database in 64-bit Windows My Android device won't connect. I've never got MTP to work, I've only ever got it to connect by USB mass storage, which was how it was working most recently. But now, since 13.04, it seems that option has been taken away entirely.  I need to be able to connect by USB to transfer files.  When I plug in the device I get an error that says Unable to open MTP device '[usb:002,003]':    After some web searching, I found that I might need a program called go-mtpfs, so I tried that, and it failed:  $ go-mtpfs /media/MyAndroid 2013/07/16 16:41:43 compiled against libmtp 1.1.5 Device 0 (VID=04e8 and PID=685e) is a Samsung Galaxy Y. 2013/07/16 16:41:43 found device Samsung: Galaxy Y (04e8:685e) @ bus 2, dev 3 :  LIBMTP PANIC: Unable to find interface &amp; endpoints of device 2013/07/16 16:41:43 rdev.open failed: open: open returned nil   How do I get my USB device to just connect, automatically, like it used to? Let V denote the Klein 4-group. Show that $\text{Aut} (V)$ is isomorphic to $S_3$ After a week in my Abstract Algebra class, the professor proposed this as a problem. I'm not entirely sure where to begin. $ V = \{ e, \tau, \tau_1, \tau_2 \}$, so I'm not sure exactly what is meant by $\text{Aut} (V)$. Is it simply saying that the only way to have an automorphism on $V$ is to rearrange the order of the elements of $V$ and therefore $\text{Aut} (V) \cong S_3$? I just asked my first question on stackoverflow and I'm really impressed that my question seems to be answered sufficiently already! See:    The issue I have is that the last two answers combined would provide the most complete answer. What's the proper way to go about combining them, marking the question answered, and giving credit where credit is due?  Thanks big time guys for saving us all from experts exchange hell!  Edit: Wow, 5 responses in 5 minutes. I think what makes the most sense is that I create my own answer out of the two. I don't think the second part of my question was answered though.  What is the proper way to give credit to the 2 answers that I'm combining? Is an upvote for each sufficient? How to reinstall default packages In an attempt to uninstall wine I ran the command sudo apt-get purge wine* which as you may have guessed removed many of the default packages. I am wondering if there is a way to use the installation disk to reinstall the default packages without overwriting the file system. Not sure if it makes a difference or not, but I am duel booting Windows 8 and Ubuntu 14.04 which was updated from Ubuntu 12.04.  Thanks in advance. Can someone please explain how I can install  in the following ways?   By using the package manager? By downloading and installing a pre-built package? Is Site Traffic Data Gone for Good After Fixing Previous Bug? There was a previous bug affecting site traffic statistics showing -zero- for months (). This has been fixed in that it is now graphing the data.  It appears that previous data may be lost? The graphs below are from . I don't have access to any other sites' graphs to see if they are showing similar results. In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first thing to do is to learn to learn derivative, integral and algebra" (I don't know how much precise I'm being because I've read it in Portuguese). I would to know if there is some book that deals with math as Feynman did it in this lesson (respecting formalities, but teaching how to use the practical rules)? Also, someone have any recommendations for algebra book (college level)?