Prove that $G$ is isomorphic to $\text{Inn}(G)$ if $G$ has trivial center $Z(G)$.
Detail in bijection between Inn(G) and G/Z(G)?
" java.lang.IllegalArgumentException: uri.getScheme() == null! " error using JavaFX to play audio Skyrim - Companions attacked me for no reason? Conditionally enabling systemd files through Debian packaging I've created a  package which installs a service.  On our embedded devices, I want this package to automatically enable the service.  On our developer workstations, I want the developers to systemctl start foo manually (it's a heavy service, and so it just consumes resources if run all of the time on a desktop environment).  How can I go about prompting the user for their decision during the apt-get step? Is that the best solution?  Note, I've created the package using dh_make and debhelper and enabled it with:  %:     dh $@ --with=systemd  override_dh_systemd_enable:     dh_systemd_enable --name=foo foo.service Physical meaning of this integral in $k$-space I am trying to solve an integral in $k$-space where I want to calculate the ratio of the average energy of an arbitrary electronic band ($E(k)=k^n)$ to the square of average group velocity of electrons($v_g   = k^{n-1})$ approximately in the form of this expression given by $$L=\frac{\frac{\sum_{\mathbf{k}}k^{n}}{\sum_{\mathbf{k}}1}}{\left(\frac{\sum_{\mathbf{k}}k^{n-1}}{\sum_{\mathbf{k}}1}\right)^2}\;.$$  Now, I want to do this for $d$-dimensions, so I convert this sum to integral.  $$L=\frac{\dfrac{\int_{0}^{k_f}k^{n} d^d k}{\int_{0}^{k_f}1d^d k}}{\left(\dfrac{\int_{0}^{k_f}k^{n-1}d^d k}{\int_{0}^{k_f}1d^d k}\right)^2}$$ where $d^dk  = \dfrac{d \pi^{d/2}}{\Gamma(\frac{d}{2}+1)}k^{d-1}dk$ is the volume element in $d$-dimensional space.  I want to get a simple expression for $L$ and how it depends with $k_f,n$ and $d$. any physical insight into this integral could also be helpful. I am a British national living in Spain and my passport is either lost or stolen. I noticed this two days ago when I was intending to take a trip to Salzburg. As it happens, I managed to travel using my UK Driver's Licence. I think a severe mistake was made, as was pointed out to me in Austria, but as they were Schengen Countries, apparently all that is needed is a proof of identity, not a 'travel document'.  My question, therefore, is this. I have business trips over the next three weeks taking me from Spain to Germany, Czech Republic, Austria, and Italy, then back to Germany, and then to the UK. If I obtain an Emergency Passport from the Consulate here in Barcelona, would this be valid as an identity document within Schengen, before I eventually 'cash it in', so to speak, as a travel document when I make my trip from Germany to the UK?  I am hoping so, as I don't fancy my chances of getting back to the UK in time to secure an appointment for a fast-track passport. I am going to call the consulate tomorrow, but would appreciate any advice or prior experience. Scaling HUD with variable resolution Why are continuous functions the "right" morphisms between topological spaces? What are the advantages and disadvantages of using ARC? Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous? Let $(X,d)$ and $(Y,\rho)$ be metric spaces and $f:X\to Y$ be a function and suppose for any Cauchy sequence $(a_n)$ in $X$, $(f(a_n))$ is a Cauchy sequence in $Y$.  Is $f$ continuous?  Let $f$ be continuous, is it uniformly continuous? Please check the below  awk '/SOURCE/ {print $3}' /MAC/Delete_Name.txt |      while IFS= read -r file; do find /OS/ -iname "$file.pdf" ; done    This results in output like this:  /OS/001DAY/11file/cooke.pdf   We want it to only print the file's path, like this:    /OS/001DAY/11file/ How long can you store used cooking oil How long can you store used cooking oil then re-use it? I deep fried a turkey one year ago and have had it refrigerated since. Let me know I have upvotes even after hitting the rep cap When you cap, you don't see any upvotes you get on your profile, therefore, you don't have any update on how your questions / answers are doing unless you look at them manually.   Capping the 200 daily rep is not a reason to stop posting here so could I get notified somehow that my posts are being voted on ? Maybe put a little +X in a different color letting me know that I got these votes but I won't get the reputation for it.   I can go and see in my reputation feed inside my profile and see it :    So I don't see why it wouldn't show up in the feed above.  Maybe putting the feed button green without any +X just like when you aquire a badge. Is it correct to say "I kindly request you to..."? I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two:   $13^{100} \bmod 7$ $7^{100} \bmod 13$   I've also heard of this formula:  $$a \equiv b\pmod n \Rightarrow a^k \equiv b^k \pmod n $$  But I don't see how exactly to use that here, because from $13^1 \bmod 7$ I get 6, and $13^2 \bmod 7$ is 1. I'm unclear as to which one to raise to the kth power here (I'm assuming k = 100?)  Any hints or pointers in the right direction would be great. How do you pass a function as a parameter in C? I want to create a function that performs a function passed by parameter on a set of data. How do you pass a function as a parameter in C? Is it possible to follow a user automatically? If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$ Prove that if $G$ is abelian then the set $H$ of all elements of $G$ that are their own inverses is a subgroup of $G$.   Naturally in an abelian group, $ab = ba$ for $a, b \in G$, however I'm not sure how to show the set elements that are their own inverses is a subgroup of $G$ using arbitrary elements. Sensitivity to initial conditions and topological transitivity Forgive the possibly naive question, but I'm returning to a basic undergrad-level study of chaotic dynamical systems and can't quite seem to reconcile the notion that in order for a dynamical system to be considered chaotic, it must have positive global Lyapunov exponents. Such exponents, of course, drive the divergence of trajectories. However, topological transitivity implies that trajectories can get arbitrarily close as well over some finite time. It seems that positive Lyapunov exponents would disallow this mixing. Is there a point at which these positive exponents no longer describe the system, and the mixing behavior begins? Calculation of number density from material density Material density is given by $ \rho =m/V$, where $m$ is mass and $V$ is volume. Again number density given by $n=N/V$, where $N$ is the total number of particle. How can I calculate number density $n$ from material density $ \rho $. Continuous function on closed unit ball Take a continuous mapping $f: \bar{B^{n}} \rightarrow \bar{B^{n}}$, where $\bar{B^{n}}$ is a closed unit ball in $\mathbb{R}^{n}$. Assume that $f(x) \neq x$ for every $x \in \bar{B^{n}}$. Define another function $r$ by following the directed line segment from $f(x)$ through $x$ to its intersection with $\partial B^{n}$, and let the intersection point be $r(x)$. Is it immediately evident that $r$ is a continuous function? Is so how does it follow? Thanks.