Java code needs a system.out.println statement to run
Loop doesn't see value changed by other thread without a print statement
Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$ I have trouble on this question: "Characterize the groups G for which the map $$\iota: G \to G$$ sending $$x \mapsto x^{-1}$$ for all $x \in G$, is an automorphism of $G$." From  post I have seen that $G$ must be abelian. Can anyone propose another characteristic of $G$ that I can derive from the given conditions besides abelian? Thank you so much!! Why have view counters been modified? What is the difference between const_iterator and non-const iterator in the C++ STL? What is the difference between a const_iterator and an iterator and where would you use one over the other? What is "angle of view" in photography? I read on the :     Focal-length determines the angle-of-view seen through a lens for a   given sensor-size. With a full-frame sensor a lens gives the same   angle-of-view as it would on a 35mm film camera. With a smaller   sensor, the angle-of-view becomes smaller. The crop-factor, also   called FLM, is the ratio representing the difference in equivalent   focal-lengths. So a 150mm on a full-frame DSLR such as the Nikon D700   gives the same angle-of-view as a 100mm on a D7000 since its FLM is   1.5X.      Short focal-lengths show a greater angle-of-view compared to longer   ones. [...]   In layman's terms, what is angle-of-view? Is it the same as focal length? If not, how is it different? How is it used? Why do I need to know about it? Why isn't my website in Google search results? I have come across this .  Has anyone tried anything similar or does it work for you? Can you tell if an email customer / user enters is correct &amp; exists? Can I use older MySQL workbench with newest MySQL server? MySQL newbie here.  I'm using Ubuntu 16.04 (64-bit). I've successfully installed MySQL Community Server 5.7 and MySQL Community Workbench 6.3.  Unable to find these answers in the MySQL forums. I've asked this on Stack Exchange and it was suggested that I ask here instead. I've searched on Ubuntu Forum and here also but did not find an answer. One would think they are common questions but maybe not. Additionally, I cannot find a way to ask a new question on the MySQL Forum. I've spent a ton of time reading/researching/installing/uninstalling and reinstalling MySQL and community workbench on Linux Ubuntu 16.04 (64-bit) and do not want to lose the momentum I've gained. I'm actually making forward progress after a week or so of trial and error working on this up to a few hours per day. It appears that I cannot load MySQL Community Workbench 8.0 without Linux server installed. That seems to be one of the requirements if I understood correctly.  Can anyone tell me if MySQL Community Workbench 6.3 will work with MySQL Community Server 8.0 on Ubuntu 16.04 (64-bit)? I would still like to upgrade and use MySQL community server 8.0 if I can.  Can I use MySQL Community Server 8.0 on Linux Ubuntu 16.04 32-bit?   I've spent many hours googling it and looking on MySQL Forums but couldn't find the answer. Thanks much. ...Rick Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$? I'm trying to show that $\langle1-i\rangle$ is a maximal ideal of $\mathbb{Z}[i]$.  I started by assuming there is some ideal $A$ that properly contains $\langle1-i\rangle$, and then I want to show that $1 \in A$, and then I will have that $A= \mathbb{Z}[i] $, so $\langle1-i\rangle$ is maximal.  Is this the right approach?  Thanks  Second Attempt: Because $\forall a+bi \in \mathbb{Z}[i]$, we have $a+bi = (a+b) -b(1-i)$, then we have $a+bi - (a+b) = -b(1-i) \in \langle1-i\rangle$, which implies $a+bi +\langle1-i\rangle = a+b +\langle1-i\rangle$.  So every coset is of the form $c +\langle1-i\rangle$, where $c\in \mathbb{R}$.  Furthermore, $-i(1-i)^2=2 \in \langle1-i\rangle$. Write $c = 2q + r$, where $q,r\in \mathbb{R}$ and $r=0,1$.  Then because $2 \in \langle1-i\rangle$, we have $2q\in \langle1-i\rangle$ and therefore $2q= 2q+r-r = c-r\in \langle1-i\rangle$, so $c+\langle1-i\rangle = r+\langle1-i\rangle$, and every coset is of the form $0 + \langle1-i\rangle$ or $1 +\langle1-i\rangle$. Thus, $1 +\langle1-i\rangle$ is the only nonzero element, and is invertible with itself as its inverse.  Thus, $\mathbb{Z}[i]/\langle1-i\rangle$ is a field with two elements, and by a theorem, $\langle1-i\rangle$ must be maximal.  Is this correct? Special event cards and timing Prime factorization knowing n and Euler's function My task is to factorize $n$ knowing it has two factors and $\varphi(n)$. How can I do it?  Thanks for any advice. Is there a reason why the pin diagram of an RJ-45 looks like this?    I understand that the orange pair is used for Tx and the green pair for Rx. Why is it that the orange pair are kept together while the green pair are separated?  What are the consequences of messing around with this order as long as it is the same at both the ends? Joint distribution of a Normal and Truncated Normal I have a random variable $X\sim \text{Normal}(\mu,\sigma)$ and have the transformation $Y=\max\{0,X\}$.  Is the distribution of $Y$ a truncated normal where it is truncated to live on the positive half of the real line?  Secondly, is there a closed form solution for the joint distribution of a Normal random variable and a truncated Normal random variable? Geodesics equations via variational principle I would like to recover the (timelike) geodesics equations via the variational principle of the following action:  $$ \mathcal{S}[x] = -m \int d\tau = -m \int \sqrt{-g_{\mu\nu}\,dx^{\mu}\,dx^{\nu}} $$  Using an arbitrary auxiliary parameter $\lambda$, then one is able to rewrite the action and obtains: $$ d\tau = \sqrt{-g_{\mu\nu}\, \tfrac{dx^{\mu}}{d\lambda}\tfrac{dx^{\mu}}{d\lambda}} d\lambda $$ $$ -m \int d\tau = -m \int (d\tau / d\lambda) d\lambda =  -m\int\sqrt{-g_{\mu\nu}\, \tfrac{dx^{\mu}}{d\lambda}\tfrac{dx^{\mu}}{d\lambda}} d\lambda $$  Now we can vary the paths $x^{\mu}(\tau) \rightarrow x^{\mu}(\tau) + \delta x^{\mu}(\tau)$.  I need the following equation to be true, so i get the geodesics equations, but I don't know how one can say the following: $$ \int d\tau \,\delta g_{\mu\nu}\frac{dx^{\mu}}{d\tau} \frac{dx^{\nu}}{d\tau} = \int d\tau\, g_{\mu\nu, \rho} \frac{dx^{\mu}}{d\tau} \frac{dx^{\nu}}{d\tau} \delta x^{\rho} $$ I know there is a simpler action, which leads to the same equation of motion, but there one has to do the same manipulation, which I sadly don't understand.  Thanks for helping me! Linear regression with fixed point I have a data set to which I want to add a trend line. For my system, there will always be a fixed point on (2, 0). I have the line representing this system, but currently I do not account for the fixed point. Is there functionality to achieve this?  \begin{figure} \begin{tikzpicture} \begin{axis} [     ylabel={Some Time [ms]},     ]     \addplot[only marks, color=red, error bars/.cd,                        y dir=both, y explicit]         table [x=num_of_nodes, y=MyData, y error=stdev_delay_var] {MyData.dat};     \label{plot_one}     \addplot +[mark=none, dashed]          table[y={create col/linear regression={y=MyData}}]         {MyData.dat}; \end{axis} \end{tikzpicture} \caption{Test Results} \label{fig:test_results} \end{figure} A result of Stieltjes Integral While studying the Riemann - Stieltjes integral, I read this exercise in my book:  "Let $f:[a, b]\to \mathbb{R}$ be a bounded function. Denoted $L(P, f)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon&gt;0$, there exists $\delta&gt;0$ such that for every partition $P$ with $|P|&lt;\delta$, we have: $\underline{\int_{a}^{b}}f(x)dx-L(P, f)&lt;\epsilon$."  My question is: Can we generalize this problem for Stieltjes integral, with $\underline{\int_{a}^{b}}f(x)d\alpha$ instead of $\underline{\int_{a}^{b}}f(x)dx$?  Particularly, can we have this theorem?  Let $f:[a, b]\to \mathbb{R}$ be a bounded function and $\alpha$ is a monotonic function on $[a, b]$ . Denoted $L(P, f, \alpha)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon&gt;0$, there exists $\delta&gt;0$ such that $\underline{\int_{a}^{b}}f(x)d\alpha-L(P, f, \alpha)&lt;\epsilon$ for every partition $P$ with $|P|&lt;\delta$?  I don't know how the mesh of the partition relate to the function $\alpha$. Limit FTP access only to the /var/www with vsftpd I am running vsftpd as ftp server on my linux (rasbian), I log in to the machine as a root user.  I would like to be still locked to using only /var/www, how can I configure vsftpd conf to accomplish it? Why doesn't Ubuntu 16.04 in Windows have ubuntu.exe? In &quot;Introduction to Mathematical logic&quot; by Elliot Mendelson , page $59$ . I couldn't understand the basic preliminary notations for the rigorous definition of Satisfiability. For example , at a line they said, &quot;Moreover, instead of talking about the $n$-tuples of objects that satisfy a wf that has $n$ free variables, it is much more convenient from a technical standpoint to deal uniformly with denumerable sequences. What we have in mind is that a denumerable sequence $s = (s_1, s_2 , s_3 , ... )$ is to be thought of as satisfying a wf $\beta$ that has ${x_j}_1 , {x_j}_2 ,  ... , {x_j}_n$ as free variables (where $j_1 &lt; j_2 &lt; ... &lt; j_n$ ) if the $n$-tuple $\langle {s_j}_1 , {s_j}_2 ,  ... , {s_j}_n \rangle$ satisfies $\mathscr B$ in the usual sense.&quot; I didn't quite understand why they used ${s_j}_1$ and ${x_j}_1$ instead of $s_1$ and $x_1$ . Maybe there is a critical detail I am missing out? Also , Another passage for the rigorous definition: &quot;Let $M$ be an interpretation of a language $\mathscr L$ and let $D$ be the domain of $M$. Let $\sum$ be the set of all denumerable sequences of elements of $D$. For a wf $\mathscr B$ of $\mathscr L$ , we shall define what it means for a sequences $s= (s_1, s_2, ... )$ in $\mathscr L$ to satisfy $\mathscr B$ in $M$. As a preliminary step, for a given s in $\sum$ we shall define a functions $s^*$ that assigns to each term $t$ of $\mathscr L$ an element $s^{*}(t)$ in $D$.&quot; They did say that for each $s = (s_1, s_2, ... )$ , there is a defined function $s^*$ , but even after further reading the text afterwards , I still did not understand how exactly $s^*$ is defined from $s$ . Can someone tell me where the gap in my understanding here is? Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square. Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square. My work: $2xy\mid x^2+y^2-x \implies x^2+y^2-x=2xy\cdot k$ So,$x^2+y^2+2xy-x=(x+y)^2-x=2xy \cdot (k+1)$ And,$x^2+y^2-2xy-x=(x-y)^2-x=2xy \cdot (k-1)$ I found that for $x,y$ both odd, no solution exists. For $x$ even, and $y$ odd,no solution exists. Solution exists only for $x$ odd, $y$ even and $x$ even and $y$ even solution exists. Cannot do anything more. Please help! I've installed drush in /usr/local/lib/drush/drush and composer in /usr/local/bin/composer.  When I try to run drush /usr/local/lib/drush/drush I get the following:     /usr/local/lib/drush/drush: line 129: /Applications/MAMP/bin/php/php5.2.17/bin: is a directory /usr/local/lib/drush/drush: line 129: exec: /Applications/MAMP/bin/php/php5.2.17/bin: cannot execute: Undefined error: 0 –    OR the following:     Unable to load autoload.php. Drush now requires Composer in order to install its depedencies and autoload classes. Please see README.md   What am I doing wrong? I'd like to install drush to use with MAMP if anyone has any suggestions. I've done through the readme and nothing seems to be working.