Mods: Please note that this question is specifically about a server that is managed via cPanel and WHM, which makes it different than the .  The past month, my personal web server has received thousands of these notices. Please note, my server is primarily managed by WHM/cPanel, although I have root ssh, ftp and other traditional access points.   These attacks started by attempting root, but have since progressed to attempting user accounts where I am not certain how they even guessed the correct usernames (albeit wrong passwords).   Is there a way to prevent these kinds of attacks from happening?  Also, here's the number of auto-bans listed just today and some smattering of IP address sources - the attack times for past month are basically around 6:30 am east coast time to 11 pm:
I'm running an SSH server on my personal computer. The log had many people(or bots?) repeatedly trying to log in to my server (that is before I changed the default port), which made me a little freaked out. I was worried about their dictionary attacks or brute force password guessing.  But then if you type wrong password (or wrong username), the server waits for about 2 seconds before it asks for password again. So an attacker can try one password per 2 seconds. So I concluded that these attacks aren't that great a threat (as long as your password does not consist of dictionary words.) Am I correct?
Can an abstract class have a constructor?  If so, how can it be used and for what purposes? Differential equation: autonomous system This isn't homework. I have no idea what theorems I should be looking at to solve this. Guidance, partial and total solutions are all welcomed.     Let $f$ be a locally lipschitz function in an open set $G\subseteq \Bbb R^n$. Consider the autonomous system $y'=f(y)$.      Let $y(x,\xi)$ be the value at point $x$ of the maximal solution that satisfies the initial condition $y(0)=\xi$.         Prove that the domain of $y(\cdot, y(s, \xi))$ is $I-s$, where $I$ is the domain of $y(\cdot ,\xi)$.   Prove that for all $s, t$ such that $y(s, \xi)$ and $y(t+s, \xi)$ exist, then $y(t,y(s,\xi))$ also exists and $y(t,y(s,\xi))=y(t+s, \xi)$.   If $y$ is a maximal solution and there exists $T&gt;0$ such that $y(0)=y(T)$ and $f(y(0))\neq 0$, then $y$ is a periodic solution and not constant.   If $y$ is a solution whose domain is $(a,+\infty)$, if $\eta:=\lim _{x\to +\infty}y(x)$ and $\eta \in G$, then $f(\eta)=0$.      EDIT  I found an alternative solution for 3. Please check my proof and give feedback in comments:  let $u$ be the restriction of $y$ to $[0,T]$, now let $\overline u$ be the periodic extension of $u$ to $\mathbb R$. It is easy to see that $\overline u$ is a solution to the given differential equation. But since $f$ is locally lipschitz, $\overline u$ must coincide with $y$ wherever they are both defined. Since $y$ is a maximal solution, it must be $\overline u$, so $y$ is defined on $\mathbb R$. Bound for the correlation of three random variables Short-lived sci-fi series with a former astronaut turned superhero (or maybe a police officer?) using his spacesuit for his "powers" Plot Details/Summary I only watched an episode or two of this one, so I can't recall a whole lot about it.  The protagonist is a former astronaut of some sort, who makes it his mission to clean up the crime in his city.  He might have been a police officer in his &quot;new life&quot; or he might have decided to become a sort of quasi-superhero.  In either case, I distinctly recall his space suit being the gimmick that makes him an effective crime fighter in the show.  I seem to recall the protagonist being a young, dark-haired man, and I think he had a friendship or an alliance with a young woman (maybe a fellow cop, or someone from the space program?).  I don't think there were alien beings in the show.   The criminal threats were all quite terrestrial, IIRC. Timeframe and other Publication Details This was a syndicated tv show I saw on American television, probably around the late 90s to early 2000's.  I believe the show was filmed in Canada, though I'm not certain.  I don't think it lasted very long - it was pretty dreadful.  I can say for certain the show is not Space Cop or Gerry Anderson's Space Precinct. How to move apps from internal to external storage? Whether the sequence $\{x_n-y_n\}$ converge or not. Given, $\{x_n\}$ and $\{y_n\}$ are two real valued sequences such that $\lim_{n\to\infty} (x_{n}^{3}-y_{n}^{3})=0 $ Then is it always true that $\lim_{n\to\infty} (x_n-y_n) =0 $ ? I tried by splitting $ (x_{n}^{3}-y_{n}^{3}) $, but that didn't help as $\lim_{n\to \infty} (x_{n}^{2}+x_{n}y_{n}+y_{n}^{2}) $ can be $0$ or non zero or doesn't exist. Does installing many programs really slow down Windows? Man clones himself to have the clone do things he doesn't enjoy I read a short story about four years ago and can't remember the title or author. The only thing I know is that it is relatively old -- like Huxley or Asimov era. Can anyone help me?   The basic synopsis is this: a man clones himself and has his clone do the parts of his life that he doesn't enjoy. He deceives his wife about this; she doesn't know he has a clone. Whenever the man and the clone are both home, the clone is locked in the "toolbox" in the basement. The clone starts to treat the man's wife better than he had previously. His wife starts to fall in love the clone, and the man decides he needs to get rid of the clone. When he tries to do so, the clone overpowers the man and locks him in the toolbox in the basement!  I'm hoping to share this story with my English class this school year. Any help is appreciated! Can people PLEASE spell out their slang acronyms I am quite proficient with the keyboard and try to only use the mouse when necessary. Given that context I was very familiar with the shortcut keys in MS Outlook 2003 and never needed to use the mouse to use that product. Now my company has recently upgraded to MS Outlook 2010 and I am finding it impossible to operate it without having to use the mouse. In particular replying to meeting requests with the old shortcut keys no longer seems possible.   I have held down the ALT key and sometimes it shows some shortcuts on the ribbon but this seems to be limited to ALT+H which tends to alternate between designating "Accept" and "Tentative" without any keys for the other options. Also as this appears to switch between "Accept" and "Tentative" one can't even use this consistently without first having to check what it means for each particular instance.  Any help with this would be greatly appreciated! $\sqrt{1-x^2}$ is not a rational function If $k$ is a field in which $1 + 1 \neq 0$, prove that $\sqrt{1-x^2}$ is not a rational function. Hint. Mimic the classical proof that $\sqrt{2}$ is irrational   It seems rather odd to discuss the square root function in the context of an arbitrary field, but here goes nothing!  Proof:   Suppose that $\sqrt{1-x^2}$ is a rational function in $k(x)$. Then there exist polynomials $p(x)$ and $q(x) \neq 0$ that are relatively prime with $\sqrt{1-x^2} = \frac{p(x)}{q(x)}$; clearly we may take $p(x) \neq 0$. Then $1-x^2 = \frac{p(x)^2}{q(x)^2}$ or $q(x)^2(1-x^2) = p(x)^2$, which says $q^2 | p^2$, and since $q | q^2$, we can infer $q | p^2$. Moreover, since $p|p^2$ and $(p,q)=1$, then $pq|p^2$ or $q|p$, which contradicts the fact that the polynomials are relatively prime. Hence $\sqrt{1-x^2}$ cannot be a rational function.    How does this sound? Aside from the problem of discussing $\sqrt{~~}$ in the context of an arbitrary field, I am worried about not using the fact that $1+1 \neq 0$, at least not explicitly. Where exactly is this assumed used, if at all?  EDIT:  Suppose that $q(x) =1$, and let $f(x) = a_n x^n + ... a_1 x + a_0$. Then $1-x^2 = f(x)^2$. If $x=0$, $1 = a^2_0$ and therefore $a_0$ must be a unit. Letting $x=1$ we get $0 = (a_n + ... + a_1 + a_0)^2$; and letting $x=-1$ we get $0 = (-a_n - ... - a_1  + a_0)^2$. Since we are working in a field, there can be no nonzero nilpotent which means that $a_n + ... + a_1 + a_0$ and $-a_n - ... - a_1  + a_0$ are both zero. Adding the two equations together yields $2a_0 = 0$, and since $1+1 \neq 0$, $a_0 = 0$ which contradicts the fact that $a_0$ is a unit.   How does this sound?  Another attemtpt:  If $f(x)^2 = 1-x^2$, then $2 = \deg(f^2) = 2 \deg (f)$ implies $\deg(f) = 1$. Yet if $x=-1$, we get $f(-1)^2 = 1 - 1 = 0$ and therefore $f(-1)=0$ since there are no nonzero nilpotent elements in a field; similarly, $f(1)=0$. Since $1+1 \neq 0$, $f$ has two distinct roots in $k$ yet is only a $1$-st degree polynomial, a contradiction. I own a 2016 Macbook (with the USB-C charging) - at the time and in response to all of the reports of poor cables and poor chargers, I bought a meter so I could see what the throughput of my cables/chargers was. However, having run some tests I'm now not sure what to consider normal / what is harmless to the battery.   For all tests I used an original Apple C-C cable - though was able to replicate with two third party cables I own.  I have the original Apple block charging at 14.3 V / 1.99 A and a third party block that charges the same.  Another third party block which advertises USB PD and 3 A is currently charging at 20 V / 1.43 A  I've done some research online but I can't find any articles that indicate what a normal USB PD output is relative to the devices that connect to it and would appreciate any guidance / assistance.   TL;DR: Have Apple charger which charges at one voltage/amperage. Bought several others advertised at PD which are higher voltage, lower amperage. Not sure what is 'safe', or 'fast', or does least overall damage to battery. I am interested in publishing a GML file as a WFS. I don't want to use a database like PostgreSQL. What would be the rough steps I need to do for that? I like to use open source software (geoserver). I don't have much experience. I am just looking for a rough guide what kind of software I should look into and which step follows which step.. Where does the extra kinetic energy of the rocket come from? Consider a rocket in deep space with no external forces. Using the formula for linear kinetic energy $$\text{KE} = mv^2/2$$ we find that adding $100\ \text{m/s}$ while initially travelling at $1000\ \text{m/s}$ will add a great deal more energy to the ship than adding $100 \ \text{m/s}$ while initially at rest: $$(1100^2 - 1000^2) \frac{m}{2} \gg (100^2) \frac{m}{2}.$$ In both cases, the $\Delta v$ is the same, and is dependent on the mass of fuel used, hence the same mass and number of molecules is used in the combustion process to obtain this $\Delta v$. So I'd wager the same quantity of chemical energy is converted to kinetic energy, yet I'm left with this seemingly unexplained $200,000\ \text{J/kg}$ more energy, and I'm clueless as to where it could have come from. EM with Binomial How can you encode a string to Base64 in JavaScript? I have a PHP script that can encode a PNG image to a Base64 string.  I'd like to do the same thing using JavaScript. I know how to open files, but I'm not sure how to do the encoding. I'm not used to working with binary data. Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite. I have seen another post for this same question but it never got an answer. Since I am fairly new, I can't comment on other's posts, therefore I am creating a new one. The question states:  If a, b, and c are positive integers, prove that if $(a + b + c) | (a*b*c)$, then $a+b+c$ is composite.  I do not really know how to approach this.  The link to the post with the same question is: If we have a real valued function $f$ continuous at some point $a$, is it necessarily true that $f$ is Riemann integrable on the interval $[a - \delta, a + \delta]$ if a $\delta &gt; 0$ exists? How to read such figures with % as "up (by) 120%" and "increased (by) 120%". Do they mean the same? Automatically capitalise the first word in each sentence