What is $\mbox{Hom}(\mathbb{Z}/2,\mathbb{Z}/n)$?
Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module
How can I implement a download rate limited in Java? display only 3 foreach result per row Integral Representation of the Zeta Function: $\zeta(s)=\frac1{\Gamma(s)}\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$ How does one get from this $$\zeta(s)=\sum_{k=1}^{\infty}\frac1{k^s}$$ to the integral representation $$\zeta(s)=\frac1{\Gamma(s)}\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$$ of the Riemann Zeta function?  I can see that it can be rewritten as  $$\Gamma(s)\zeta(s)=\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$$ and the Gamma function as an integral yields  $$\zeta(s)\int_{0}^\infty \frac{x^{s-1}}{e^x}dx=\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$$  But this approach does not work as the right integral does not converge.  So how does one go from the summation to the integral representation? When I was using ubuntu 14.04, it's easy to set title. Just press F2 or move mouse to top menu. But there is no menu on ubuntu 16.04 and press F2 can't change the title. What should I do? After converting to nodes in order to render using Cycles I've no idea where to enable the z-transparency. I guess the image textures alpha channel needs to be pluged somewhere but I've no idea which node would be suitable.   The question is how could I correctly setup the nodes to have the same effect as when using z-transparency in BI?      The materials original settings for BI are:    Which renders like:    I had no luck with DarenWs suggestion: !! c operator, is a two NOT? How to interpret this yum dependency error? I'm trying to install XRDP and I'm hitting the following:  [root@box ~]# yum -y install xrdp Loaded plugins: fastestmirror, langpacks Loading mirror speeds from cached hostfile  * base: centos.serverspace.co.uk  * epel: mirrors.coreix.net  * extras: mirror.sov.uk.goscomb.net  * updates: mirror.sov.uk.goscomb.net Resolving Dependencies --&gt; Running transaction check ---&gt; Package xrdp.x86_64 1:0.9.10-1.el7 will be installed --&gt; Processing Dependency: xrdp-selinux = 1:0.9.10-1.el7 for package: 1:xrdp-0.9.10-1.el7.x86_64 --&gt; Processing Dependency: xorgxrdp for package: 1:xrdp-0.9.10-1.el7.x86_64 --&gt; Running transaction check ---&gt; Package xorgxrdp.x86_64 0:0.2.10-4.el7 will be installed --&gt; Processing Dependency: xorg-x11-server-Xorg(x86-64) = 1.20.4 for package: xorgxrdp-0.2.10-4.el7.x86_64 ---&gt; Package xrdp-selinux.x86_64 1:0.9.10-1.el7 will be installed --&gt; Finished Dependency Resolution Error: Package: xorgxrdp-0.2.10-4.el7.x86_64 (epel)            Requires: xorg-x11-server-Xorg(x86-64) = 1.20.4            Installed: xorg-x11-server-Xorg-1.20.1-5.6.el7_6.x86_64 (@updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.6.el7_6            Available: xorg-x11-server-Xorg-1.20.1-3.el7.x86_64 (base)                xorg-x11-server-Xorg(x86-64) = 1.20.1-3.el7            Available: xorg-x11-server-Xorg-1.20.1-5.el7.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.el7            Available: xorg-x11-server-Xorg-1.20.1-5.1.el7.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.1.el7            Available: xorg-x11-server-Xorg-1.20.1-5.2.el7_6.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.2.el7_6            Available: xorg-x11-server-Xorg-1.20.1-5.3.el7_6.x86_64 (updates)                xorg-x11-server-Xorg(x86-64) = 1.20.1-5.3.el7_6  You could try using --skip-broken to work around the problem  You could try running: rpm -Va --nofiles --nodigest   Now, I get that it's missing a dependency, however, it appears to be saying it requires xorg-x11-server-Xorg version 1.20.4.   It then continues to say version 1.20.1-5.6.el7_6 is installed.  From where I'm sitting, 4 is in the range 1-5 so I'm unclear what the issue is. They all seem to be for the right architecture.  Is 1-5 a version string in and of itself as opposed to a range, or -if not- what am I missing?  Solution: Thanks to , here's a workaround:     Having the same issue, I installed manually archived xorgxrdp   yum -y install https://archive.fedoraproject.org/pub/archive/epel/7/x86_64/Packages/x/xorgxrdp-0.2.9-1.el7.x86_64.rpm   then   yum -y install xrdp and it works Show $$\frac{(2n)!}{n!\cdot 2^n}$$ is an integer for $n$ greater than or equal to $0$.   Could anyone please help me with this proving? Thanks! How to delete all music on my iPhone How can I reliably and accurately identify the passive voice in writing or speech? How do I install wine? 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? I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've been writing a  (the specifics of which are out of scope), which has me thinking about the problem because I decided to handle angle units as dimensioned quantities, which seemed natural to enable the unit conversion with degrees. The overall purpose of the library is to disallow operations that don't make sense because they violate the rules of dimensional analysis, e.g. adding a length quantity to an area quantity, and thus provide some built-in sanity checking to the computation. Treating radians as units made sense because of some of the properties that dimensioned quantities seemed to me to have:  The sum and difference of two quantities with the same dimension have the same physical meaning as both quantities separately. Quantities with the same dimension are meaningfully comparable to each other, and not meaningfully comparable (directly) to quantities with different dimensions. Dimensions may have different units that are scalar multiple (sometimes with a datum shift).  If the angle is treated as a dimension, my 3 made up properties are satisfied, and everything &quot;makes sense&quot; to me. I can't help thinking that the fact that radians are a ratio of lengths (SI defines them as m/m) is actually critically important, even though the length is cancelled out. For example, though radians and steradians are both dimensionless, it would be a logical error to take their sum. I also can't see how a ratio of something like (kg/kg) could be described as an &quot;angle&quot;. This seems to imply to me that not all dimensionless units are compatible, which seems analogous to how units with different dimensions are not compatible. And if not all dimensionless units are compatible, then the dimensionless &quot;dimension&quot; would violate made-up property #1 and cause me a lot of confusion. However, treating radians as having dimension also has a lot of issues, because now your trig functions have to be written in terms of $\cos(\text{angleUnit}) = \text{dimensionless unit}$ even though they are analytic functions (although I'm not convinced that's bad). Small-angle assumptions in this scheme would be defined as performing implicit unit conversions, which is logical given our trig function definitions but incompatible with how many functions are defined, especially since many authors neglect to mention they are making those assumptions. So I guess my question is: are all dimensionless quantities, but specifically angle quantities, really compatible with all other dimensionless quantities? And if not, don't they actually have dimension or at least the properties of dimension? PHP: Return all dates between two dates in an array Comparing StringBuffer content with equals How to install "vanilla" TeXLive on Debian or Ubuntu? Debian and Ubuntu have very good texlive packaging. But I'd like to use tlmgr to have a more fine-grained control about upgrades and which packages I want to be installed.   So how do I install "vanilla" TeXLive on Debian/Ubuntu?   Also how do I make dpkg aware that I have TeXLive installed? I'm trying to solve the well known Coupon Collector's Problem by explicitly finding the probability distribution (so far all the methods I read involve using some sort of trick). However, I'm not having much luck getting anywhere as combinatorics is not something I'm particularly good at.   The Coupon Collector's Problem is stated as:  There are $m$ different kinds of coupons to be collected from boxes. Assuming each type of coupon is equally likely to be found per box, what's the expected amount of boxes one has to buy to collect all types of coupons?  What I'm attempting:  Let $N$ be the random variable associated with the number of boxes one has to buy to find all coupons. Then $P(N=n)=\frac{|A_n|}{|\Omega _n|}$, where $A_n$ is the set of all outcomes such that all types of coupons are observed in $n$ buys, and $\Omega _n$ is the set of all the possible outcomes in $n$ buys. I think $|\Omega _n| = m^n$, but I'm not even sure about that anymore, as all my attempts so far led to garbage probabilities that either diverged or didn't sum up to 1. So we learned telescoping series in class and I came across this question in my textbook and I tried to evaluate it, but I don't understand how to do it.   $$ \sum\limits_{k=1}^n\left(k \cdot k!\right) $$  According to the answers:  $$ \sum\limits_{k=1}^n\left(k \cdot k!\right) = (n+1)! - 1 $$  We learned how to simplify certain telescoping series using partial fractions but I don't have any idea on how to start this question. Why do video cables (DVI, VGA) still screw in? I guess I could imagine that there was a time when accidentally disconnecting the monitor would have been catastrophic, though I don't see that being the case today.  Is it just a legacy holdover that they are still secured with screws?  Also, why is it that the video connection is really the only one that is still secured this way?  It seems like the power cable would be a better candidate to be secured with screws.  That really could be catastrophic.  In the end, the reason this question occurred to me is that I've never had a video cable come out when not screwed in, so why the significant security? How to configure Jaybird with hibernate I read it in English in the United States, somewhere in the 1990s. I got it off of the big bookshelf in our family room, which means it could be a good bit older; some of the books were my Dad's. At the beginning, a young boy (maybe an early teen?) leaves his house, where he lives with his parent or parents, and takes a test to become a spaceship pilot for the military. Part of the test judges reaction speed, and he fails the test. He later learns (I think when he's approached by an agent of the government) that he "failed" because he has some sort of enhanced fortune that meant that he was actually giving the results before they could be displayed on the screen. At the time, I remember thinking that the book felt a bit like a Star Wars rip-off.  Years later, I read that one of the Star Wars books (probably now Legends) had Luke similarly failing the Imperial Academy test because he gave his answers too quickly, and it amused me that I was uncertain as to which had come first.  I don't remember anything concrete about the cover, although I have a general impression that it was white. Definitely futuristic. My impression was that the boy was wearing a white uniform for the testing and that the government agent who spoke to him had a grey beard, but I might be mixing bits of Star Wars in there.