Vulnerabilities in Apache tomcat9
How can I tell if a CVE has been fixed in Ubuntu's repositories?
Allowing only one download per Apple ID During my studying to integration I find this integration.  So I tried to prove but I got stuk.  So I need help in this integration.  $$\displaystyle\int_{-\infty}^{\infty} \frac{x \sin (x)}{1+x^2}  dx = \frac {\pi}{e} $$ Find $\lim\limits_{x \to \infty} \frac{x}{(\log{x})^n}$ Find $\displaystyle \lim_{x \to \infty} \dfrac{x}{(\log{x})^n}$.   My book says that $\displaystyle \lim_{x \to \infty} \dfrac{(\log{x})^n}{x} = \lim_{y \to \infty} \dfrac{y^n}{e^y} = 0$, but I don't see how that is true. Folding a cube (animation) I'm trying to fold a cube with an animation. I've tried inverse kinetics with no luck. Here are some images that explain what I'm trying to do. I'm trying to make this so that    when the upper bone is pushed down, the box is folded to the ground. when the upper bone is pulled up, it unfolds the box. How should I print types like off_t and size_t? Let $f$ be an entire function with $|f(z)|\le 100\log|z|,\forall |z|\ge 2,f(i)=2i, \text{ Then} f(1)=?$  I have no idea how to solve this one!  $g(z)={f(z)\over \log|z|}$ Then Can I say $g$ is constant by Liouville Theorem? A rearrangement of an absolutely convergent complex series is also absolutely convergent I just completed the following proof.  Is it valid?   Let $\sum_{k=1}^{\infty} a_k$ be an arbitrary convergent series that also converges absolutely.  Then $\sum_{k=1}^{\infty} a_k \in \mathbb{C}$ and $\sum_{k=1}^{\infty} |a_k| \in \mathbb{R}$. Let $\{b_k\}$ denote a rearrangement of the $\{a_k\}$.  That is, we have that $\{a_k\} = \{b_k\}$ yet $a_i = b_i$ needn't hold. We will first show that $\sum_{k=1}^{\infty} b_k$ converges absolutely (immediately implying it converges non-absolutely).  We will use the Cauchy Criterion on the partial sums of $\sum_{k=1}^{\infty} |b_k|$ to demonstrate this. First let $\epsilon &gt; 0$. Consider that since $\sum_{k=1}^{\infty} |a_k| \in \mathbb{R}$, we have that $\exists N_1 \in \mathbb{N}$ s.t. for all $N_1 &lt; m &lt; n$ we have   $$ \sum_{k=m}^n |a_k| \le \epsilon. $$ Now let $0 &lt; N_2$ be large enough s.t $\{a_1, \ldots , a_{N_1}\} \subseteq \{b_1, \ldots , b_{N_2}\}$.  Let $M &gt; max\{N_1, N_2\}$.  Let $M &lt; m' &lt; n'$.  Then since $\{b_k\} - \{b_1, \ldots , b_{m'}\} \subseteq \{a_{N_1}, a_{N_{1}+1},  a_{N_{1}+2} \ldots\}$, we will have that   $$ \sum_{k=m}^n |a_k| \le \epsilon \implies \sum_{k={m'}}^{n'} |b_k| &lt; \epsilon. $$ Then we have that   $$ \left| \sum_{k={m'}}^{n'} |b_k| \right| = \sum_{k={m'}}^{n'} |b_k| &lt; \epsilon $$  so that since $\epsilon$ was arbitrary, we have obtained that   $$ \left| \sum_{k=1}^n |b_k| - \sum_{k=1}^m |b_k|  \right| = \left| \sum_{k=m}^n |b_k|  \right| \rightarrow 0 $$  so that via the Cauchy Criterion for Convergence  we have that $\sum_{k=1}^{\infty} |b_k|$ converges to some  value in $\mathbb{R}$ as desired. Then it follows that $\sum_{k=1}^{\infty} b_k$ is absolutely convergent (and hence also just convergent).   $\square$ Why does English spelling use silent letters? If all derivatives of $f$ are uniformly bounded by a common constant and $f(1/n) = 0$ for all $n$, is $f$ identically zero? $$ f: \Re \longrightarrow \Re \ \in C^{\infty} \\ \exists \ L&gt;0: \ \forall x \in \Re, \forall n\in N \\ |f^{(n)} (x)| \le L \\ f(\frac{1}{n})=0 \ \forall n\in N \\ f(x) \equiv 0  $$  Good morning,  Can you give me an help to make this proof?  This is my thought:   $\lim_{n \rightarrow +\infty } \dfrac{1}{n}=0=\theta$ $f(\theta)=0$ $f^{(n)} (\theta) =0\\f(x)=\sum_{k=0}^n \dfrac{f^{(k)}(x-\theta)^k}{k!}$  $f$ is analytic, the rest of Taylor's expansion is 0, because the derivatives are bounded, $f$ is null.   I have thought this reasoning, but I have difficulties to demonstrate part 3. Can you help me?  Is there any mistake?  Can I use an easier way to make the proof?  Thanks. centos: using epel repository on a server machine Are there any downsides in enabling epel repository on a server machine or is it something every sysadmin does? Suppose a particle only influenced by gravity is going from point a to point b on an x,y plane. Is there an equation in which the particle takes the longest amount of time, yet still makes it to point b? I know the equation for brachistochrone is the parametric for an inverted cycloid, yet I'm not sure of the opposite. For reference, I am a high school student wanting to try this for a research project. I really only need to know whether this has already been done or not, but attempted solutions are obviously appreciated. Why is OpenJDK 10 packaged as openjdk-11-*? While looking to compile OpenJDK from source, the newest General Availability version () insists on OpenJDK 9 or 10.  JDK 11, however, is not due to be released until .    However, to my surprise, when I do apt search openjdk the result is:  ... openjdk-11-jdk - OpenJDK Development Kit (JDK) ... openjdk-8-jdk - OpenJDK Development Kit (JDK) ...   No OpenJDK 9 or 10!  And wait, is that OpenJDK 11?  Maybe a Beta release?  Nooo....  So I looked at apt show openjdk-11-jdk:  Package: openjdk-11-jdk Version: 10.0.1+10-3ubuntu1 ...   Why has OpenJDK 10 been packaged as openjdk-11-*?? Is static HTML the fastest? If I am talking to somebody about a certain group of people in the third person, and then want to refer to the person I am talking with as one of those people, which do I say?     One of them were you      One of them was you. Replace preg_replace() e modifier with preg_replace_callback I'm working in Lee's book on topological manifolds and have gotten stumped on the first question in chapter 5, the chapter on cell complexes.  The problem is:   Let $D$ and $D'$ be two closed cells not necessarily of the same dimension.     Show that any continuous map $f:\partial D \to \partial D'$ can be extended to a continuous map $F:D \to D'$ such that $F(Int \; D) \subseteq Int \; D'$. Given points $p \in Int \; D$ and $p' \in Int \; D'$, show that $F$ can be chosen so $F(p) = p'$. Show that if $f$ is a homeomorphism then $F$ can be chosen to be a homeomorphism.   I proved the first part roughly as follows: First suppose $D$ and $D'$ are convex and each contain $0$ in their interior (in their respective ambient spaces).  Then every element other than $0$ in $D$ can be expressed uniquely in the form $\lambda q$ where $q \in \partial D$ and $\lambda\in (0,1]$ (an equivalence relation on the chords connecting $0$ to boundary points partitions $D- \{0\}$).  I then define the map $F(\lambda q) = \lambda f(q)$ which is continuous since if $\lambda_n q_n \to \lambda q$ in $D$ then $F(\lambda_n q_n) \to F(\lambda q)$.  Lastly $\lambda q \in Int \; D$ implies $\lambda &lt;1$ and so $\lambda f(q)$ is an interior point of $D'$ since $f(q)$ is a boundary point and $D'$ is convex.    Now if we suppose $D$ and $D'$ are arbitrary closed cells there are homeomorphisms $g_1: \overline{\mathbb{B}^n} \to D$ and $g_2: \overline{\mathbb{B}^m} \to D'$ (where possibly $m=n$) then we have that $g_2^{-1}\circ f \circ g_1$ is a continuous map between the boundaries of two closed balls and so by the first part can be extended to a continuous map $F:\overline{\mathbb{B}^n} \to \overline{\mathbb{B}^m}$.  The mapping $g_2 \circ F \circ g_1^{-1}$ is a continuous map that satisfies the desired claim.    My issue is that parts 2 and 3 don't seem (to me at least) to follow that easily from the proof I constructed.  Maybe my proof is wrong and I'm not seeing it, but more likely I think that I'm missing the spirit in which Lee is intending for us to approach this problem. I have some files with TikZ graphics that have suddenly changed appearance since I upgraded to PGF-2.10.  Here is a minimal example:  \documentclass{minimal} \usepackage{tikz} \begin{document} \pgfversion\par \begin{tikzpicture} \draw[blue] plot[domain=-1:1] (\x,{\x^2 + \x^3}); \draw[xshift=4cm,blue] plot[domain=-1:1] (\x,{(\x)^2 + (\x)^3}); \end{tikzpicture} \end{document}   In PGF 2.00 I had this:    while in 2.10 I have this:    The one on the left in PGF 2.10 looks like the graph of y=x^3 but could also be y=x^3 + x|x|.   This has been  on sourceforge and  on the pgf-users mailing list.  Although I haven't checked myself yet, the bug remains open and some of the commenters below report that problems still exist in the CVS version.   Geoffrey Jones notes the bug is in the 2.00 CVS version:     Hi Matthew, not an answer, just an FYI   that's too large for the comment box.   My compile of your code through pgf   v2.00 produces the result you see with   v2.10, above:       I.e., the difference you observe seems   to pre-date v2.10.   There is a workaround by inserting parentheses.  But since I have so many old lecture files I'd rather find a solution that doesn't involve rewriting my TikZ code.  And I'm squeamish about using the CVS bleeding edge code even if it were fixed, since I don't want to introduce other problems.  Ideally I'd like a simple patch that I can stick at the preamble, or just fix one file in the PGF distro. The disk that contains Ubuntu on my computer is 115GB in size.  When the disk was 114.7GBfull.  I started deleting some files here and there to free up around 5GB.  But I noticed the disk was 114GB filled again. I thought it was some cache or swap thingy so didn't give it much thought and went ahead and freed around 40GBby shifting some media files out of the disk.  I have a notification in an hour or so that the disk is full yet again!! 40GB!!! All gone!  So I debugged the problem down to the /var/log/syslog file which was initially definitely less than 20GB. I know this because /var folder was 17GB before I cleared the memory.  /var/log/syslog file is currently 55.9GB!  Could someone be so gracious to explain this anomaly? Is this a bug? Or am I affected with some malware or virus? I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude.  This appears to be the opposite of this question ().  I have already looked into the haversine formula and think it's approximation of the world is probably close enough.  I am assuming that I need to solve the haversine formula for my unknown lat/long, is this correct? Are there any good websites that talk about this sort of thing? It seems like it would be common, but my googling has only turned up questions similar to the one above.  What I am really looking for is just a formula for this. I'd like to give it a starting lat/lng, a bearing, and a distance (miles or kilometers) and I would like to get out of it a lat/lng pair that represent where one would have ended up had they traveled along that route. I need to find out the modular inverse of 5(mod 11), I know the answer is 9 and got the following so far and don't understand how to than get the answer. I know how to get the answer for a larger one such as 27(mod 392) but am stuck because they are both low numbers.  11=5 (2)+1  5=1 (5)