I am going to download &amp; install java on Ubuntu 12.04 LTS (32-bit system)  On java download page, there are 2 download options.     Java for Linux Platforms   Java for RPM based Linux Platforms     Which would be better suited for Ubuntu?
I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7?
What is $\log(1)$ to the base of $1$? My teacher says it is $1$. I beg to differ, I think it can be all real numbers! i.e., $1^x = 1$, where $x\in \mathbb{R}$.  So I was wondering where I have gone wrong. traceroute TCP equivalent for Windows Prove this inequality $\sum \cos{A}\ge\frac{1}{4}(3+\sum\cos{(A-B)})$ I'm using BibLaTeX to handle my bibliography and I want a reference to be placed in a footnote on every page where I cite the same work and have the same number. Also I want to be able to cite the same work on one page several times. The latter could be done by using  from the Joseph Wright's blog. However, it puts a reference in a footnote only once. Why do we use Hermitian operators in QM? Position, momentum, energy and other observables yield real-valued measurements. The Hilbert-space formalism accounts for this physical fact by associating observables with Hermitian ('self-adjoint') operators. The eigenvalues of the operator are the allowed values of the observable. Since Hermitian operators have a real spectrum, all is well.  However, there are non-Hermitian operators with real eigenvalues, too. Consider the real triangular matrix:  $$ \left( \begin{array}{ccc} 1 &amp; 0 &amp; 0 \\ 8 &amp; 4 &amp; 0 \\ 5 &amp; 9 &amp; 3 \end{array} \right)  $$  Obviously this matrix isn't Hermitian, but it does have real eigenvalues, as can be easily verified.  Why can't this matrix represent an observable in QM? What other properties do Hermitian matrices have, which (for example) triangular matrices lack, that makes them desirable for this purpose? For $x$ and $\lambda$ complex, if $|x| \gt \frac{1}{2} + \sqrt{\frac{5}{4} + |\lambda|}$ then $|x^2+\lambda| \gt |x| +1$ I have a point $(X,Y)$ on an elliptical curve $E(a,b)$ where $a=-3$ and $B$ is a large number that is in hexadecimal from -51BD. To compress this point oficially in a program, we know that every $X$ on the curve has two $Y$'s, one even and one odd. Therefore, we only need to store whether the corresponding $Y$ point we are storing is even or odd. So to store the point $(X,Y)$ now, we shift $X$ ridding of its most significant bit and add $1$ if the $Y$ point is odd. Therefore, one can think of the compressed point being $2 \cdot X+B$ ($B$ is the bit we added to tell if $Y$ was odd or even) since the multiplication by $2$ is implied because of the shift. I understand this completely. It's recovering the original point that has me confused.  Since a point on the curve is given by the equation $y^2=x^3+ax+b$, we can find square roots officially in $\mathrm{GF}(p)$. The following from my spec is what confuses me.  If $p$ is prime and congruent to $3$ mod $4$, one of its square roots is $z^{(p+1)/4} \bmod p$ and the other is $p-z^{(p+1)/4} \bmod p$. How would I solve this? What is $z$?  For example, I know how to extract the $x$ point so let's say I simplify the right side of the equation to be $7$ and $p$ is $11$. Would I be trying to solve for the square root that's equal to $7$ mod $11$? I am preparing a document in French, using the "babel" package with option "french" and using commands that include colons and semicolons. My problem is, the French spacing before colons and semicolons disappears when the commands are printed. I do not understand why, have not been able to find an answer. Below is a MWE.  \documentclass{article} \usepackage[french]{babel} \newcommand\deuxpoints{Texte: texte} \begin{document} \deuxpoints\ \endgraf Texte: texte \end{document} What should children call a step-grandparent? My mom remarried to a great guy who has been absolutely wonderful to my kids. Ever since my mom and he were dating my kids have called him Mr. Joe. Lately my mom has been bugging me to get the kids to call him Grampa.  I agree that he deserves more respect than Mr.  The problem is that he isn't their real grampa so I don't really want them calling him that. Does anybody have any suggestions on what we should have the kids call him? They are 9 and 12 years old.  EDIT: I appreciate the comments regarding different variations of grampa and hearing how others have no issues with calling their step-granddad grampa. But I was hoping maybe someone has some suggestions for names that show the importance of the step-granddad without calling him some variation of the grampa name but still has a feeling of warmth and family in the name (I hope that makes sense). Are there any countable Hausdorff connected spaces? Do countable Hausdorff connected topological spaces exist? Convolution operator has norm 1 with respect to $L^2$ norm Let $C_c(\mathbb{R})$ be the following:  $$C_c = \{ f \in C(\mathbb{R}) \mid \exists \text{ } T &gt; 0 \text{ s.t. } f(t) = 0  \text{ for } |t| \geq T\}$$  Let $T_n \in L(C_c(\mathbb{R}))$ be a linear operator such that:  $$T_n u = \delta_n *u, \forall u \in C_c(\mathbb{R}),$$  where  $$ \delta_n(t)= \begin{cases}        n^2(t+1/n) &amp; -1/n \leq t \leq 0 \\       -n^2(t-1/n) &amp; 0 &lt; t \leq 1/n \\       0 &amp; \text{elsewhere}     \end{cases} $$  I have to prove that with respect to the 2-norm, the operator $T_n$ has $\|T_n\| = 1$ and I have succeeded in proving that $\|T_nu\|_2 \leq \|u\|_2, \forall u \in C_c(\mathbb{R}).$  Now, I remained  to prove that $\exists \text{ } u \in C_c(\mathbb{R}) \text{ s.t. } \|T_nu\|_2 = \|u\|_2$, but I really don't get how $u$ should be shaped in order to satisfy it. I would like to be able to transpose a tabular(x) table like in the following example. It is not necessary to be completely automated, but I don't want to change the data order, which is a painful and stupid. By "not completely automated" I mean that e.g. the headers can be done seperately etc.  Let's see the MWE:  \documentclass{article}  \usepackage{booktabs} \def\Midrule{\midrule[\heavyrulewidth]}  \begin{document}  \centering  \begin{tabular}{*6c}\toprule \bfseries Name &amp; Alice &amp; Bob &amp; Chuck &amp; Dave &amp; Eve\\\Midrule \bfseries Sex &amp; Female &amp; Male &amp; Male &amp; Male &amp; Female\\\midrule \bfseries Age &amp; 18 &amp; 19 &amp; 20 &amp; 21 &amp; 22\\\bottomrule \end{tabular}  \bigskip  Which I want to look like  \bigskip  \begin{tabular}{*3c}\toprule \bfseries Name &amp; \bfseries Sex &amp; \bfseries Age\\\Midrule Alice &amp; Female &amp; 18\\\midrule Bob &amp; Male &amp; 19\\\midrule Chuck &amp; Male &amp; 20\\\midrule Dave &amp; Male &amp; 21\\\midrule Eve &amp; Female &amp; 22\\\bottomrule \end{tabular}   \end{document}     Note: I know that , but I would like to get it without expl3 (mostly because people would might use my code quite often have an old LaTeX installed and I cannot be convincing them to change this). Arguably the most famous scene in Star Wars is when Darth Vader reveals to Luke Skywalker that      He is Luke's father.   This surprise was kept secret to most of the crew and even the cast , with Dave Prowse, the actor playing Darth Vader, delivering a fake line, the actual line being overdubbed. (Of course, Darth Vader wasn't voiced by him in the first place; all lines were overdubbed by James Earl Jones).   Like Mark Hamill relates in :     But, for example, your big scene, one of the classic cinematic moments when Darth Vader divulges his true identity, is no longer a revelation.       It's such a great moment! The fake line that was put in there just to try and keep the secret was "You don't know the truth: Obi-Wan killed your father!" But as much as I enjoyed leaking false information, it was a wonderfully hard secret to keep because (Irvin) Kershner, the director, brought me aside and said "Now I know this, and George knows this, and now you're going to know this, but if you tell anybody, and that means Carrie or Harrison, or anybody, we're going to know who it is because we know who knows."   So how do we explain ?       And [David Prowse] offered a glimpse of a possible plot for the second sequel. Darth Vader and Luke Skywalker, the young hero in the first film played by Mark Hamill, are hooked up in a do-or-die light saber duel when Luke learns that Darth is, in fact, his long-lost father.   So exactly how secret was this secret anyway?    As DVK points out , the newspaper article is probably authentic. Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem] How can I show that $(n-1)!\equiv-1 \pmod{n}$ if and only if $n$ is prime? Thanks. Prove: If a sequence converges, then every subsequence converges to the same limit. I need some help understanding this proof:  Prove: If a sequence converges, then every subsequence converges to the same limit.  Proof:  Let $s_{n_k}$ denote a subsequence of $s_n$. Note that $n_k \geq k$ for all $k$. This easy to prove by induction: in fact, $n_1 \geq 1$ and $n_k \geq k$ implies $n_{k+1} &gt; n_k \geq k$ and hence $n_{k+1} \geq k+1$.  Let $\lim s_n = s$ and let $\epsilon &gt; 0$. There exists $N$ so that $n&gt;N$ implies $|s_n - s| &lt; \epsilon$. Now $k &gt; N \implies n_k &gt; N \implies |s_{n_k} - s| &lt; \epsilon$.   Therefore: $\lim_{k \to \infty} s_{n_k} = s$.   What is the intuition that each subsequence will converge to the same limit I do not understand the induction that claims $n_k \geq k$ Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$ Following my  the book then asks      Use this to determine when the field extension  $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$  is biquadratic (where $a,b\in\mathbb{Q}$)   "this" means what proved in the linked post.  My thoughts: First, I don't know what to say when $a^2-b$ is not a square. When $a^2-b$ is a square I think that the extension is of degree $2$ if $a=b$, this leaves the case $a\neq b$ which I am also having problems with and I don't know what to do (I have some cases like if $m,n$ are different primes then the degree of the extension is $4$, but I don't have something that is general)  Can someone please help my do this exercice  ? When I try to create a reaction from chemmacros/reactions I got the following error. I dunno what I am missing. Please help. Thank you.     line 11: Undefined control sequence. \end   line 11: Missing number, treated as zero. \end   line 11: Missing number, treated as zero. \end     Minimum Working Example    \documentclass[12pt,a4paper]{article} \usepackage{chemmacros} \chemsetup{modules={reactions}} \begin{document} \begin{reaction}     A + B -&gt; C \end{reaction} \end{document} How to develop RPG Damage Formulas? I have two submit buttons in a form. How do I determine which one was hit serverside? How is the minimum of a set of IID random variables distributed? If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?