Can we use @EJB annotation in Apache tomcat
How to deploy EJB based application on Tomcat
Do there exist an infinite number of 'rational' points in the equilateral triangle $ABC$? Let's call a point $P$ which satisfies the following condition 'a rational point'.  Condition: Each distance $PA, PB, PC$ from a point $P$ to three vertices $A, B, C$ of an equilateral triangle $ABC$ which has edge-length $1$ is rational number.  I'm interested in this point because I found the following three:  1. There exist an infinite number of rational points on an edge of the equilateral triangle $ABC$.  2. There exist an infinite number of rational points on the circumference of the circumscribed circle of the equilateral triangle $ABC$.  3. There exists a rational point in the equilateral triangle $ABC$.  Supposing that $A(0,\frac{\sqrt3}{2}), B(-\frac12,0), C(\frac12,0)$, one example for the above 3 is the following: $$P\left(\frac{61}{2058},\frac{220}{1029}\sqrt3\right), \left(PA, PB, PC\right)=\left(\frac{73}{147}, \frac{95}{147}, \frac{88}{147}\right).$$  I found this example by using computer. I found the other examples, but I don't know there exist an infinite number of rational points in the equilateral triangle $ABC$. Then, here are my questions.  Question 1: Do there exist an infinite number of rational points in the equilateral triangle $ABC$ ?  Question 2: Can we find all rational points in the equilateral triangle $ABC$ ? I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap I have written a small script to count number of occurrences of logs in a particular file. The following is my code:   #!/bin/sh count=1 while read line do     found=$( grep M $line )     OCCURENCE=$( grep M /log.txt)     if [ "$OCCURENCE" ]; then         echo $count")" $line &gt;&gt; filesave.txt     fi     count=$((count+1)) done &lt; log1.txt   but I am getting this error:  ./count.sh ./count.sh: syntax error at line 10: `found=$' unexpected The output from the following script \documentclass{article} \usepackage{tikz} \usepackage{graphicx} \begin{document} \begin{tikzpicture}   \node(title)[text width = 0.25\textwidth, text height = 3 cm, draw]{title};   \end{tikzpicture} \end{document}  is  How can I vertically align the text in the node? Specifying the text depth as in \node(title)[text width = 0.25\textwidth, text height = 1cm, text depth = 1 cm, draw]{     title line 1\\     title line 2\\     title line 3};  Does not result in the text being vertically centred. Why do we use microwaves in microwave oven? We know that any object above absolute zero emits electromagnetic radiation. So hotter the object shorter the wavelengths. In the electromagnetic radiation spectrum radio waves has the longest then microwave, then infrared, then visible light, then ultraviolet, then x-ray, then gamma rays. Why do we use microwaves in microwave oven when infrared and visible light are much hotter and how do microwaves cook food when they are cooler than visible light and others. "This site is all about getting answers. It's not a discussion forum. There's no chit-chat." The  has this text:     This site is all about getting answers. It's not a discussion forum. There's no chit-chat.   It's probably an oversight and copied from the regular site tours. Can it be reworded/removed?  Right above that text, there's this:      So each community has a meta to discuss site-specific issues, and Meta Stack Exchange is for conversations about problems and ideas that affect the whole network.   Don't they contradict eachother? Sigmoid vs Relu function in Convnets In general, when can I omit that from a sentence?   Can I omit that (emphasized) in sentence (2) below?        We say that such algorithms handle concept drift and can learn from time-changing data streams.   When the statistical properties of the target variable change, we say that concept drift has occurred.   She told me that some of her classmates failed.      To me, sentences (1) and (3) sound better without that. If I omit that from (2), it just doesn't sound right when I read it out loud. (I should point out I'm not a native speaker.)  How do you decide when to omit it? Is it just a matter of taste? (I know that is sometimes mandatory.)  Can you think of sentences that "sound better" with that? Can you think of sentences that "sound better" without that? Can you think of a few sentences where it is wrong to omit that? Prove that for all $n&gt;2$ there exists at least one prime $p$ such that $\sqrt{n}&lt;p&lt;n$ using elementary methods.  My try: If not, $\sum_{p&lt;\sqrt{n}} (\lfloor n/p \rfloor-\lfloor \sqrt{n}/p \rfloor) \geq n-\sqrt{n}$  then...? Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$ Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$.   My try:  Let $\mathbb Z^n\cong \mathbb Z^m $. To show that $m=n$.  Case 1: Let $m&gt;n$. Now that $\mathbb Z^m$ has $m$ generators whereas $\mathbb Z^n$ has $n$  generators and an isomorphism takes a generator to generator ; that is the contradiction.  Please correct me if I am wrong.  The case  $m&lt;n$ also follows similarly. Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$. $$\lim_{x \to 0} \frac{f(x)}{|x|}=1$$ Then prove that $f$ is not differentiable at $0$. I was given this assignment and I'm not sure about my proof.. it feels like I'm assuming too much and not explaining with enough detail. Is there anything I need to add to make it sufficient? Assume toward contradiction that $f$ is differentiable at $0$. Then by definition we know that $f$ is continuous at $0$. Therefore $\lim _{x\to 0}f\left(x\right)=f\left(0\right)$ We know that $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}=1$ Therefore we can conclude $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \left|x\right|=1\cdot 0=0$ But we can also rewrite this as $\lim _{x\to 0}\left(f\left(x\right)\right)\cdot \frac{\left|x\right|}{\left|x\right|}=f\left(0\right)\cdot 1=0$ Therefore $f(0) = 0$. Since $f$ is differentiable at $0$ we have $\lim _{x\to 0}\frac{\left(f\left(x\right)-f\left(0\right)\right)}{x-0}=\lim _{x\to 0}\frac{\left(f\left(x\right)-0\right)}{x}=\lim \:_{x\to \:0}\frac{\left(f\left(x\right)\right)}{x}\cdot \frac{\left|x\right|}{\left|x\right|}=\lim \:\:_{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\frac{\left|x\right|}{x}$ Since the one sided limits of $\frac{f\left(x\right)}{\left|x\right|}$ exist, and are both equal to 1, we have $\lim \:_{x\to 0^+}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^+}\frac{\left(f\left(x\right)\right)}{x}\cdot \:\:\:\frac{x}{x}=1\cdot 1=1$ $\lim \:_{x\to 0^-}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^-}\frac{\left(f\left(x\right)\right)}{-x}\cdot \:\:\:\frac{-x}{x}=1\cdot -1=-1$ Since the limit doesn't exist, we have a contradiction to the fact $f$ is differentiable at $0$. Therefore $f$ is not differentiable at 0. How to change from csh to bash as default shell I have csh as my default shell, as shown by echo $SHELL. I want to switch to bash as my default shell. I tried the following approaches to no avail:   With chsh I get:  chsh: can only change local entries; use ypchsh instead.  With ypchsh I get:  ypchsh: yppasswdd not running on NIS master host ("dcsun2").    I only have .chsrc in my home directory and I cannot find any .profile files in /etc. How can I change my default shell to bash? $F_\sigma$-subsets in a normal space can be separated Let $X$ be a normal Hausdorff space and let $C,D$ be two $F_{\sigma}$ subsets of $X$ such that $\overline{C} \cap D = \emptyset$ and $C \cap \overline{D} = \emptyset$.  Prove there exists disjoint open subsets $U,V$ such that $C \subset U$ and $D \subset V$.  No idea how to show this. Can you please help? I am currently thinking about open-sourcing a project of mine and am in the process of preparing the source code and project structure to be released to the public. Now I got one question: how should I handle the signature key for my assemblies? Should I create a new key for the open-source version and publish it along with the other files to the SVN repository? Should I leave the key out and everyone who wants to compile the code should generate his own key?  How do you handle this? I feel a little bit uncomfortable with releasing a signature key to the public. Centering \vdots in a system of many equations I have a system of equations with an arbitrary number of equations (k). I'd like to use \vdots to compactly describe the system, like so:  \begin{align*}   R(-1) &amp;= \sum_{i=1}^m A(i)R(i-1) \\   R(-2) &amp;= \sum_{i=1}^m A(i)R(i-2) \\         &amp;\vdots                    \\   R(-k) &amp;= \sum_{i=1}^m A(i)R(i-k) \end{align*}     I'd like the dots, however, to be centered with = or the entire equation. Is there an elegant way of centering a column or row with AMSMath? I'm currently using an unholy combination of whitespace operators (\; \, etc.) to get the job done. How to add new element to Varargs? Please help identify this 2-part TV movie: Alien woman crash-lands on earth, falls in love, 199x In a 'bulleted' list should items that happen to be complete sentences end with a period? How to draw a torus Is there an easy way to draw a contour image of torus below with tikz? Or for that matter with any other graphics package. What do the brackets around processes mean? $ ps -Awwo pid,comm,args   PID COMMAND         COMMAND     1 init            /sbin/init     2 kthreadd        [kthreadd]     3 ksoftirqd/0     [ksoftirqd/0]     5 kworker/u:0     [kworker/u:0]     6 migration/0     [migration/0]     7 cpuset          [cpuset]     8 khelper         [khelper]     9 netns           [netns]    10 sync_supers     [sync_supers]    11 bdi-default     [bdi-default]    12 kintegrityd     [kintegrityd]    13 kblockd         [kblockd]    14 kacpid          [kacpid]    15 kacpi_notify    [kacpi_notify]    16 kacpi_hotplug   [kacpi_hotplug]    17 ata_sff         [ata_sff]    18 khubd           [khubd]   What do the brackets mean? Does args always return the full path to the process command (e.g. /bin/cat)?