One of the common features of the Moon is the fact that only one face of the Moon is ever visible from Earth, regardless of how much of its orbit the moon has made about the Earth.  This would imply that the rotation of the moon about its axis relative to Earth's rotation is zero/very small. This seems like a very unlikely phenomenon that would arise randomly.  So, how did this lack of rotation arise? Is it the result of the means that the Moon was formed, or could it perhaps be caused by tidal effects due to the Earth's gravity?
I know that the rotation period of the moon equals its revolution period. It's just so astonishing that these 2 values have such a small difference. I mean, what is the probability of these 2 values to be practically the same? I don't believe this to be a coincidence. It's just too much for a coincidence. What could have caused this?
Where did dedicated.abac.net. come from in my rDNS and PTR records? So I followed this guide to the letter:   I did so for 3 domains.  When I "test" the records and enter: host 64.150.176.81 on my linux machine, it shows me 81.172.150.64.in-addr.arpa domain name pointer 64-150-172-81.dedicated.abac.net.  when it should be showing me 81.176.150.64.in-addr.arpa domain name pointer 64-150-172-81.example.com.  Has anybody encountered a similar problem?  I am hosting with codero, not abac.net btw. Find weak form of linear transport equation I am stuck on the following problem that says:       a) Find a weak formulation for the partial differential equation $${\partial u\over\partial t\ }+ c{\partial u \over \partial x\ }=0$$    b) Show that $u=f(x-ct)$ is a generalized solution of $${\partial u\over\partial t\ }+ c{\partial u \over \partial x\ }=0$$ for any distribution $f$    My Attempt:   I know that in order to find a weak form of a pde, we need to multiply it by a test function, then integrate it. Also, to find a generalized solution, we need to find a weak solution and just multiply it by the Heaviside function.  Let's take any test function $\phi $, then we have (integrating by parts second part of the integral) $$\int_{\Omega } ( {\partial u\over\partial t\ }+ c{\partial u \over \partial x\ })*\phi(x) dx= \int_{\Omega } {\partial u\over \partial t}\phi(x) dx - c\int_{\Omega } u(x,t)\phi'(x)dx$$ where $\phi $ vanishes at boundaries. So, is it the final form or can we proceed further? And how am I supposed to find a generalized solution?  Can someone help me out? Thanks in advance for your time. Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$ I know that the improper integral  $$ \int_0^\infty\frac{1}{(1+x^2)^s}\,dx $$ is convergent for $s&gt;0.5$ and divergent otherwise. Furthermore, it has a closed form for $s \in \mathbb{N}$ (this can be obtained using the Residue Theorem). My question is to know whether it has a closed form for any non-integer $s &gt;0.5$. Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$. In a USB cable, is it OK to swap the D+ and D- wires? I heard that D+ and D- are differential signals, does it matter if I swap them when connecting a USB device to the computer? I'm not quite sure how this happened, but somehow a completely empty hierarchy of directories has ended up in my repository:  com/ com/companyname/ com/companyname/blah/ com/sun/ com/sun/java/ com/sun/java/jax_rpc_ri/   I think what happened was that these directories did have files in them, but then a developer realized he/she shouldn't have checked them in in the first place since these are by-products of the build process, so he/she removed the files but somehow the empty directories are left in the repository as ancient relics.  How can I remove this from CVS? The only results I seem to be able to find on google say that there shouldn't be a need to remove empty directories as CVS won't keep them around in the first place, and that the -P (prune) options to cvs update should remove them from the working directory  - which is zero help if you actually have empty directories in your repository.  A cvs remove and cvs commit doesn't seem to take care of this situation:  $ cvs remove -Rf com cvs remove: Removing com cvs remove: Removing com/companyname cvs remove: Removing com/companyname/blah cvs remove: Removing com/sun cvs remove: Removing com/sun/java cvs remove: Removing com/sun/java/jax_rpc_ri $ cvs commit com cvs commit: Examining com cvs commit: Examining com/companyname cvs commit: Examining com/companyname/blah cvs commit: Examining com/sun cvs commit: Examining com/sun/java cvs commit: Examining com/sun/java/jax_rpc_ri $ ls -l com total 24 drwxrwxr-x  2 matt matt 4096 Oct 15 14:38 CVS drwxrwxr-x  9 matt matt 4096 Oct 15 14:38 companyname drwxrwxr-x  4 matt matt 4096 Oct 15 14:38 sun   It's still there!  Does SVN have this weird behavior too? How to find out when an Oracle table was updated the last time I'm running 12.04 - I installed kubuntu to try it out and realized that with all the bloatware applications that I didn't want it anymore - I was able to uninstall the kubuntu-desktop but there are still packages left over... How can I make sure I get rid of EVERYTHING Kubuntu installed - even the kde leftovers?  Here's some of what's left when I ran sudo apt-get autoremove kde then "tab" it displayed this:     kdeaccessibility              kdepim-runtime kdeadmin   kde-runtime kde-baseapps                  kde-runtime-data   kde-baseapps-bin              kdesdk-dolphin-plugins kde-baseapps-data   kde-style-oxygen kde-config-cron               kdesudo kde-config-gtk    kdeutils kde-config-touchpad           kde-wallpapers   kdegames-card-data            kde-wallpapers-default   kdegames-card-data-extra      kde-window-manager kde-icons-mono   kde-window-manager-common kdelibs5-data                 kde-workspace   kdelibs5-plugins              kde-workspace-bin kdelibs-bin   kde-workspace-data kdemultimedia-kio-plugins   kde-workspace-data-extras kdenetwork   kde-workspace-kgreet-plugins kdenetwork-filesharing   kde-zeroconf kdepasswd                     kdf kdepim-kresources   kdm kdepimlibs-kio-plugins        kdoctools   Those are all installed by kubuntu... correct?  I just want to go back to my Ubuntu 12.04LTS with Gnome2-classic and without all the kubuntu extras.  I started it off by just removing unnecessary apps that came with kubuntu-full - then realized I didnt want the whole thing at all and uninstalled kubuntu-full but it still says I have these as well:     alex@griever:~$ sudo apt-get --purge remove kubuntu-   kubuntu-debug-installer           kubuntu-netbook-default-settings   kubuntu-default-settings          kubuntu-notification-helper   kubuntu-firefox-installer         kubuntu-web-shortcuts Elementary central binomial coefficient estimates How to prove that $\quad\displaystyle\frac{4^{n}}{\sqrt{4n}}&lt;\binom{2n}{n}&lt;\frac{4^{n}}{\sqrt{3n+1}}\quad$ for all $n$ &gt; 1 ?     Does anyone know any better elementary estimates?   Attempt.  We have $$\frac1{2^n}\binom{2n}{n}=\prod_{k=0}^{n-1}\frac{2n-k}{2(n-k)}=\prod_{k=0}^{n-1}\left(1+\frac{k}{2(n-k)}\right).$$ Then we have $$\left(1+\frac{k}{2(n-k)}\right)&gt;\sqrt{1+\frac{k}{n-k}}=\frac{\sqrt{n}}{\sqrt{n-k}}.$$ So maybe, for the lower bound, we have $$\frac{n^{\frac{n}{2}}}{\sqrt{n!}}=\prod_{k=0}^{n-1}\frac{\sqrt{n}}{\sqrt{n-k}}&gt;\frac{2^n}{\sqrt{4n}}.$$ By Stirling, $n!\approx \sqrt{2\pi n}\left(\frac{n}{e}\right)^n$, so the lhs becomes $$\frac{e^{\frac{n}{2}}}{(2\pi n)^{\frac14}},$$ but this isn't $&gt;\frac{2^n}{\sqrt{4n}}$. Homotopy equivalence of universal cover As part of am exam question (Q21F ), I'm trying to prove that if $X$ and $Y$ are path-connected, locally path-connected spaces with universal covers $\widetilde{X}$ and $\widetilde{Y}$, respectively, then if $X \simeq Y$ then $\widetilde{X} \simeq \widetilde{Y}$.  My attempt might be correct, but it seems too complicated and amongst the jumble I may have made some incorrect assumptions. So what I'm looking for is (a) verification or correction; and (b) ideas as to how I could simplify my argument.    My argument:  Let $p:\widetilde{X} \to X$ and $q:\widetilde{Y} \to Y$ be the covering maps, and let $X \overset{f}{\underset{g}{\leftrightarrows}} Y$ be a homotopy equivalence.  Fix a point $\widetilde{x} \in \widetilde{X}$, let $x=p(x) \in X$ and $y=f(x) \in Y$, and fix $\widetilde{y} \in q^{-1}(\{y\}) \subseteq \widetilde{Y}$. Also let $x' = g(y) \in X$ and fix $\widetilde{x'} \in p^{-1}(\{x'\}) \subseteq \widetilde{X}$.  Define a map $\widetilde{f} : \widetilde{X} \to \widetilde{Y}$ as follows. For $\widetilde{z} \in \widetilde{X}$ let $\widetilde{u}:[0,1] \to \widetilde{X}$ be a path from $\widetilde{x}$ to $\widetilde{z}$. Let $z=p(z)$ so that $u=p\widetilde{u}$ is a path in $X$ from $x$ to $z$. Let $v=fu$, so that $v$ is a path in $Y$ from $y$ to $f(z)$. Lift $v$ to a path $\widetilde{v}$ in $\widetilde{Y}$ with $\widetilde{v}(0) = \widetilde{y}$. Define $\widetilde{f}(\widetilde{z}) = \widetilde{v}(1)$.  Notice that $q\widetilde{v}=v$ so that $q\widetilde{f} = fp$.  Define $\widetilde{g}:Y \to X$ analogously: For $\widetilde{z} \in \widetilde{Y}$ let $\widetilde{a}:[0,1] \to \widetilde{Y}$ be a path from $\widetilde{y}$ to $\widetilde{z}$. Let $z=q(z)$ so that $a=q\widetilde{a}$ is a path in $Y$ from $y$ to $z$. Let $b=fa$, so that $b$ is a path in $X$ from $x'$ to $g(z)$. Lift $b$ to a path $\widetilde{b}$ in $\widetilde{X}$ with $\widetilde{b}(0) = \widetilde{x'}$. Define $\widetilde{g}(\widetilde{z}) = \widetilde{b}(1)$.  Likewise, notice that $p\widetilde{g}=gq$.  Claim: $\widetilde{X} \overset{\widetilde{f}}{\underset{\widetilde{g}}{\leftrightarrows}} \widetilde{Y}$ is a homotopy equivalence.  We have $p\widetilde{g}\widetilde{f} = gq\widetilde{f}=gfp \simeq p$ and $q\widetilde{f}\widetilde{g} = fp\widetilde{g} = fgq \simeq q$.  This shows that $\widetilde{g}\widetilde{f}$ and $\widetilde{f}\widetilde{g}$ are covering translations (deck transformations) and are therefore homotopic to the respective identity maps. So we have a homotopy equivalence.    Any comments would be appreciated. Can you trip as part of a Tome of Battle Maneuver? If a ToB Maneuver such as Daunting Strike calls for a melee Attack as part of the maneuver, can this melee attack be resolved as a trip attack/include a trip attempt? Is there a single word that describes both Witches and Wizards? In the Harry Potter world, there's the term "muggle" for people with no magical abilities, "muggle-born" for those with magical abilities who's parents are muggles and "squib" for those with no magical abilities who's parents are magical.  But is there any collective term for all magical people (as opposed to wizards for males and witches for females)?  I don't recall seeing any word that refers to all men and women and children with magical abilities, and it's the only group left without noun or collective noun to describe them. My GNU/Linux system (Arch) now has libncurses.so.6 rather than libncurses.so.5. But I have upstream's vanilla TeX Live (fully updated) and xindy wants libncurses.so.5:    xindy --version   produces the following error  xindy release: 2.5.1 xindy script version: 1.18 /usr/local/texlive/bin/xindy.run: error while loading shared libraries: libncurses.so.5: cannot open shared object file: No such file or directory   And ldd can confirm the problem:  ldd /usr/local/texlive/bin/xindy.run    gives      linux-vdso.so.1 (0x00007ffc07997000)     libm.so.6 =&gt; /usr/lib/libm.so.6 (0x00007fab4d1b1000)     libcrypt.so.1 =&gt; /usr/lib/libcrypt.so.1 (0x00007fab4cf79000)     libncurses.so.5 =&gt; not found     libdl.so.2 =&gt; /usr/lib/libdl.so.2 (0x00007fab4cd75000)     libc.so.6 =&gt; /usr/lib/libc.so.6 (0x00007fab4c9d1000)     /lib64/ld-linux-x86-64.so.2 (0x00007fab4d4af000)   How can I use xindy without changing my operating system, while using vanilla TeX Live?  2 strategies have occurred to me:   compile xindy from sources against libncurses.so.6; compile and install libncurses.so.5 alongside libncurses.so.6.   Option (2) can be dodgy or can be fine, depending on the details. My suspicion is it may be dodgy for this library, simply because no packages are available for the old version of the library, which might mean there are problems having both installed. Moreover, since everything else is compiled against the new version, I'm not sure whether this would be enough for xindy anyway.  Option (1) I have no idea about. I don't know if this is even vaguely doable or, in fact, where the sources are or what might be required to compile them. (I don't suppose there's any chance a pre-compiled binary is available somewhere? But that is probably hoping for too much ;).)  What is the most practicable approach? How can I classify data with the nearest-neighbor algorithm using Python? Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$ Let $f$ be a nonconstant element of ring $\mathbb Z[x]$. Prove that $\langle f \rangle$ is not maximal in $\mathbb Z[x]$.   Let us assume $\langle f \rangle$ is maximal. Then $\mathbb Z[x] / \langle f \rangle$ would be a field. Let $a \in \mathbb{Z}$. Then $a + \langle f \rangle$ is a nonzero element of this field, hence a unit. Let $g + \langle f \rangle$ be its inverse. Then $a g - 1 \in \langle f \rangle$, hence $ag(x)-1 = f(x)h(x)$ for some $h \in Z[x]$, hence $ag(0) + f(0)h(0) = 1$, thus $(a,f(0))=1$ for all $a \in \Bbb Z$, contradiction, hence the proof.  Is my argument correct? Is there any other method? Is there an algorithm for N body simulations in General Relativity I am new to general relativity but have a background in computer science.  Why is it so hard to do n-body simulations in GR?  For example, there could be a program which takes the properties (mass, position, velocity, etc.) of each particle as input and numerically integrates the evolution of the system using discrete but very small time steps.  If we throw enough memory and computing power at it, we can get arbitrarily close to the 'real' solution.  I assume the entire histories of the worldlines would need to be known, in order to calculate things like gravitational waves.  I have downloaded programs which show the evolution of the Schrodinger equation, so I am surprised they are so hard to find for GR.  Some responses I've heard elsewhere are 'the equations are nonlinear,' but from what I hear numerical algorithms are great for these types of problems.  What types of numerical algorithms are out there for GR? I have 2 1tb hard drives on my computer with Windows 8 on the first hard drive and nothing on the other.  I want to install Ubuntu 14 on the second hard drive. I've looked up some guides and they all say to install Ubuntu on the sdb partition when booting off a usb stick. I have also seen some say to unplug the Windows HDD and then install Ubuntu onto the second HDD, and Ubuntu will automatically detect Windows and ask what you want to boot into upon boot.   I am really concerned about this - Will it ask me to choose what OS I want to boot into? Is there something like rEFInd(Mac) for Windows? Can anyone please give me a guide on how to do it without ruining my computer?  Thanks Why does the Community User reject / approve edits? Automatic field should take the required entry Where in Europe can I purchase a car without residency? I am not a resident anywhere and plan to travel for the foreseeable future, mostly in Europe. My country has good visa-free access to most of Europe, so it is conceivable I could remain without any residency for quite some time.  I enjoy driving, and maintaining cars, and I would like to purchase a car somewhere in Europe.  Where, if anywhere, in Europe (or outside of Europe, but with the ability to drive the car in Europe) can I legally purchase and insure a car as a non-resident? I am open to creative solutions like setting up a company to own the car, if the capital and ongoing paperwork requirements for the company are not too onerous.    I am aware that I could save money, get places quicker, etc, by taking trains or flying. I have a passion for cars and driving. Suggesting that I not buy a car is out of scope of this question.