I lost access to my instance which I host on AWS. Keypairing stopped to work. I detached a volume and attached it to a new instance and what I found in logs was a long list of  Nov  6 20:15:32 domU-12-31-39-01-7E-8A sshd[4925]: Invalid user cyrus from 210.193.52.113 Nov  6 20:15:32 domU-12-31-39-01-7E-8A sshd[4925]: input_userauth_request: invalid user cyrus [preauth] Nov  6 20:15:33 domU-12-31-39-01-7E-8A sshd[4925]: Received disconnect from 210.193.52.113: 11: Bye Bye [preauth]   Where "cyrus" is changed by hundreds if not thousands of common names and items.  What could this be? Brute force attack or something else malicious? I traced IP to Singapore, and I have no connection to Singapore.  May thought is that this was a DoS attack since I lost access and server seemed to stop working. Im not to versed on this, but ideas and solutions for this issue are welcome.
I just checked my server's /var/log/auth.log and found that I'm getting over 500 failed password/break-in attempt notifications per day! My site is small, and its URL is obscure. Is this normal? Should I be taking any measures?
If you have an $m \times n$ matrix and the rows are linearly independent, are the columns linearly independent too?  I know that it's the case for $n \times n$ matrices. I've yet tried to think about it, and I think the answer is yes, for example the matrix: $\begin{bmatrix} 1 &amp; 2 &amp; 3 \\ a &amp; 2a &amp; 3c \end{bmatrix}$ has linearly dependent rows and columns, but I'm not sure that it works for every $m \times n$ matrix. Convert JavaScript string in dot notation into an object reference Finding a 2x2 Matrix raised to the power of 1000 Let $A= \pmatrix{1&amp;4\\ 3&amp;2}$. Find $A^{1000}$.  Does this problem have to do with eigenvalues or is there another formula that is specific to 2x2 matrices? This is a question in Ahlfors in the section on the argument principle: How many roots of the equation $f(z)=z^4+8z^3+3z^2+8z+3=0$ lie in the right half plane?  He gives a hint that we should "sketch the image of the imaginary axis and apply the argument principle to a large half disk."  Since $f$ is an entire function, I think I understand that the argument principle tells us that for any closed curve $\gamma$ in $\mathbb{C}$, the winding number of $f(\gamma)$ around 0 is equal to the number of zeros of $f$ contained inside $\gamma$.  How would you go about actually applying the hint though? I am having trouble figuring out what the image of a large half disk under $f$ would look like. Rolle's Theorem and the Mean Value Theorem Let $f\colon \mathbb{R} \to \mathbb{R}$ have derivatives of all orders. Suppose that $a &lt; b$ and that $f(a)=f(b)=f'(a)=f'(b) =0$. Prove that $f'''(c) = 0$ for some $c$ in $(a,b)$. First week of August in Scotland : What kind of clothes to pack? In a couple of weeks I will be going to Edinburgh, Scotland. I've been told that the weather is very unpredictable throughout the year. Can you suggest what I should pack as regards clothes? $x^y = y^x$ for integers $x$ and $y$ Mirror Modifier making ugly smoothing on mirrored faces The model is vivisected right down the middle along the z axis. The right leg is rendering funny and I assume if I can get that fixed everything else will fall into place. I tried flipping normals, changing shading types - can't think of anything else to do. How to make a bib entry appear also in the main document I have a reference which has a bib entry and appears in the bibliography. I want to be able to include the entire entry, exactly as it appears in the bibliography, somewhere else in the document.   Is there any way to do that other than to manually write it and format it to look similar? In logic, a semantics is said to be compact iff if every finite subset of a set of sentences has a model, then so to does the entire set.   Most logic texts either don't explain the terminology, or allude to the topological property of compactness. I see an analogy as, given a topological space X and a subset of it S, S is compact iff for every open cover of S, there is a finite subcover of S. But, it doesn't seem strong enough to justify the terminology.   Is there more to the choice of the terminology in logic than this analogy? I am unable to figure out simple solution to add "Bookman Old Style"  as a main font in my latex document. I have used below line but does not give me required font.  \usepackage{bookman}   Could not find any Simple correct answer for this. Pl. suggest how to do it.  I am using windows, pdflatex.  thank you If $AD$, $BE$, $CF$ are exterior bisectors then $D,E,F$ are collinear Let $ABC$ be a triangle and AD the exterior bisector of $\angle A$, $BE$ the exterior bisector of $\angle B$, $CF$ the exterior bisector of $\angle C$ where $D\in BC$, $E\in AC$, $F\in AB$.  Show that $D,E,F$ collinear. What are the reputation requirements for privileges on sites, and how do they differ per site? Formerly Reputation requirements compared. What are the reputation requirements for privileges on the various sites in the network? Also, how do reputation requirements for various privileges compare on different Stack Exchange sites? Specifically, the following types of sites:  Designed sites e.g. Stack Overflow, Ask Ubuntu, Gaming, etc. Public beta and non-designed sites Private beta sites  ...as well as any site-specific differences. If $z$ lies on the circle $|z-1|=1,$ then the value of $\frac{z-2}{z}$ is If $z$ lies on the circle $|z-1|=1, $ then the what is the value of $\frac{z-2}{z}$ ($z\ne 0 \ \text{and} \ 2$ ) is?  What I am aware of : the equation $|z-1|=1$ represent a circle with  centre $(1,0)$ and radius $1$. Also $$|z-1|=1 \implies (z-1)^2=1 \\ \implies  z^2-2z+1=1 \implies z(z-2) =0$$ $\implies z = 0; z =2 $ I think this is wrong.. please suggest thanks.. Ignored and watched tags seem broken For the longest time my ignored tags have been working but today they are not. They work on the home page but not the /questions page. However, if you choose the &quot;Gray out questions&quot; option then that fails. Arqade is the only site I've ever had a long-standing ignore list so I don't think I can blame cache. The same behavior seems to be exhibited on Stack Overflow but I added those ignore tags just moment ago so cache could be an issue. If it matters, I am using Chrome x64 v91.0.4472.77 on Windows 10 Via comments, this issue has been confirmed for Watched Tags as well. How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$? I'm about to prove that for any $a,b&gt;0$ and $n\in\mathbb{N},$ the inequality: $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$ holds.   By induction I get: $$\left(\frac{a+b}{2}\right)\cdot\frac{a^n+b^n}{2}$$ $$=\frac{1}{2}\cdot\frac{a^{n+1}+b^{n+1}+ab^n+ba^n}{2}$$ $$=\frac{1}{2}\left(\frac{a^{n+1}+b^{n+1}}{2}+\frac{ab^n+ba^n}{2}\right).$$  Now I have to prove that $$\frac{1}{2}\left(\frac{a^{n+1}+b^{n+1}}{2}+\frac{ab^n+ba^n}{2}\right)$$ $$\leq\frac{a^{n+1}+b^{n+1}}{2}$$ $$\Leftrightarrow a^{n+1}+b^{n+1}\geq ab^n +ba^n.$$ But I don't know how to prove that one, is it possible to be proved by induction ? Thank you. How does one actually show from associativity that one can drop parentheses? Ubuntu 14.04.5/16.04 and newer on AMD graphics I have 14.04.5/16.04 or newer and an AMD GPU. I'm not getting the performance I want, and some programs say they need things like OpenCL.  I've heard about fglrx, but if I try to install it on my machine, it breaks and I have no GUI.  Is there anything I can do to get my AMD card working to its full potential? I'm having a difficulty in finding one way car rentals from Alaska, which I can return in Seattle.  Do all the main rental agencies restrict such one-way rentals, as they involve crossing through Canada, before entering the lower 48 states? A relative of mine has received a multiple-entry UK visa for 2 years. Is there a particular limit on how many months in total per year she can stay in UK? The way I understand the current rule is that such visitors can enter UK as many times as they want as long as they do not stay for longer than 6 months per single visit. However, does this mean that if she stayed with us for 5 months and went back home for 1-2 months, she could come and stay for another 5 months? I heard that it is advisable to spend only 180 day per calendar year in UK and not more, but I could not find that rule in any official UK Home Office documents. Thanks in advance for any info about this.