Runge Kutta 4th order for system coupled equations-how to do?
Solving a system of ODEs with the Runge-Kutta method
Javascript add js libraries by code Stack Overflow has successfully borrowed at least one XBox feature (Achievements).  I'd like to see another feature borrowed as well. Let's say I'm playing Halo online and another player is being a bigot.  I have the option to add him to a list of ignored users.  After doing that, all the racist things he says will never be heard through my headphones anymore. Now, on Stack Overflow, I'd like the ability to add a user to a list of ignored users.  This would hide all of that user's comments, and maybe his questions and answers as well (not sure if hiding questions/answers is necessary). This serves multiple purposes:  It would make it easy for users to avoid other users' flamebait. It would give users a more appropriate response to flamebait. The ability to start flame wars would be reduced, since fewer users would see those comments. Users would now have an incentive to be more diplomatic, as there is now a negative consequence to the behavior (the silent treatment). Administrators could review which users are the most often ignored, which would be a strong indication that someone should be  or even locked out of their account. Administrators wouldn't have to spend as much time dealing with complaints about abusive users, since users would have a better way to respond.    makes a good point in a comment to an answer, that I thought should get more visibility:  I had a problem, reported it and got the response &quot;not bad enough to do anything about, sorry&quot;. Which is kind of true, because the only options available to the mods are the nuclear one (penalty box) and the zero-effect one (do nothing). We need a middle ground option where abuse can be handled for you without also being handled for everyone. Can I use apt-get or aptitude to install software to non standard location? Comparing and contrasting, p-values, significance levels and type I error I was wondering if anybody could give a concise rundown as to the definitions and uses of p-values, significance level and type I error.  I understand that p-values are defined as "the probability of obtaining a test statistic at least as extreme as the one we actually observed", while a significance level is just an arbitrary cutoff value to gauge if the p-value is significant or not. Type I error is the error of rejected a null hypothesis that was true. However, I am unsure regarding the difference between significance level and the type I error, are they not the same concept?  For example, assume a very simple experiment where I flip a coin 1000 times and count the number of times it lands on 'heads'. My null hypothesis, H0, is that heads = 500 (unbiased coin). I then set my significance level at alpha = 0.05.  I flip the coin 1000 times and then I calculate the p-value, if the p-value is > 0.05 then I fail to reject the null hypothesis and if the p-value is &lt; 0.05 then I reject the null hypothesis.  Now if I did this experiment repeatedly, each time calculating the p-value and either rejecting or failing to reject the null hypothesis and keeping a count of how many I rejected/failed to reject, then I would end up rejecting 5% of null hypotheses which were in actuality true, is that correct? This is the definition of type I error. Therefore, the significance level in Fisher significance testing is essentially the type I error from Neyman-Pearson hypothesis testing if you performed repeated experiments.  Now as for p-values, if I had gotten a p-value of 0.06 from my last experiment and I did multiple experiments and counted all the ones that I got a p-value from 0 to 0.06, then would I also not have a 6% chance of rejecting a true null hypothesis? Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$ What punctuation should follow after a list introduced by a colon? The whole department: John, Jeff, Jean, and the accountant [?] were thrown into jail. Hyphen or no hyphen when modifying an adjective with a quantity? I have a sentence which has an object that is described with an adjective:     We need to inform our interested patrons of this change.   If I modify "interested" with "more" or "less", do I connect the words with a hyphen or not?  Example sentence:     We need to inform our less-interested patrons of this change.     Also, please let me know if I have not used the correct terms for sentence parts in this question. Is it possible to remove a terminal command? For example, if there was a command call lookup (not an alias), how would I go about removing it? How do I calculate the power consumed by a lightbulb? The following is an old qualifying exam that I cannot solve:  Suppose $f$ is holomorphic on the punctured unit disk and $ \frac{f '}{f} $ has a simple pole at $0$.  Show that $f$ does not have an essential singularity at $0$. Add air resistance to projectile motion I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals.  This is what I have so far:  If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, a_x = 0, a_y = -9.8$, and time will be 0,1,2,3... and so on.  Using these equations on every second you can find the plot will be a bell shaped with the highest point being ~ 325 m at about 600 seconds:   $$ x = x0 + (v_{0x})t + 1/2((a_x)t^2) $$ $$ y = y0 + (v_{0y})t + 1/2((a_y)t^2) $$  Usually in physics, we are taught in perfect condition with no air resistance. But what if there was air resistance? How would it affect this problem? How can i add it to my calculations and see what the difference is? Current Configuration: I have two SQL Servers, which are connected by the failover mechanism, meaning one is primary and one is secondary. I restarted both services on both servers sequentially. On the secondary server, all the databases are in the &quot;Synchronizing&quot; state. AG replication mode is synchronous. It has been 12hr it's still showing &quot;Synchronizing&quot; state. What I did so far to resolve Drop the database from the secondary server and remove the database from AG group on the primary server and add it back. Any insight on this, I am using SQL Server 2017. Who should I be damage buffing as Mercy generic function with a "has property X" constraint? uwsgi errno 24 too many open files on CentOS / nginx How can one motivate the relativistic momentum? Motivating the non-relativistic momentum $$\mathbf{p} = m\mathbf{v}$$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and should be proportional to velocity (how fast and to where it is moving). Now, in Special Relativity the momentum changes. The new quantity of motion becomes $$\mathbf{p} = \dfrac{m\mathbf{v}}{\sqrt{1-\dfrac{v^2}{c^2}}}$$ Or, using $\gamma$ the Lorentz factor $$\mathbf{p} = \gamma(v) m\mathbf{v}$$ where I write $\gamma(v)$ to indicate that the velocity is that of the particle relative to the frame in which the movement is being observed. The need for this new momentum is because the old one fails to be conserved and because using the old one in Newton's second law leads to a law which is not invariant under Lorentz transformations. So the need for a new momentum is perfectly well motivated. What I would like to know is how can one motivate that the correct choice for $\mathbf{p}$ is the $\gamma(v)m\mathbf{v}$. There are some arguments using the mass: considering a colision, requiring momentum to be conserved, transform the velocity and then find how mass should transform. Although this work, it doesn't seem natural, and it is derived in one particular example. On my book there's even something that Einstein wote saying that he didn't think it was a good idea to try transforming the mass from $m$ to $M = \gamma(v)m$, that it was better to simply keep $\gamma$ on the new momentum without trying to combine it with the mass. So I would like to know: without resorting to arguments based on transformation of the mass, how can one motivate the new form of momentum that works for special relativity? I understand that when I press and release the power button on the top of my iPhone or iPad, it stays on but turns off the screen.  Whereas if I press and hold the power button, a "slide to turn off" control appears on the screen.  Sliding this, as I was told, does turn the unit off, but it does so by suspending the RAM to disk (flash memory, actually.) So, when turning on the iPhone or iPad, it isn't so much rebooting the OS as it is resuming it from flash storage.  How to force the OS to completely reboot on these devices? I stumbled upon a question given like:  Let $m$ and $n$ be two integers such that $m \geq n \geq 1$.   Count the number of functions $$f: \{1, 2, · · · , n\} \to \{1, 2, · · · , m\}$$ of the following two types:  (a) strictly increasing; i.e., whenever $x &lt; y, f(x) &lt; f(y)$, and  (b) non-decreasing; i.e., whenever $x &lt; y, f(x) \leq f(y)$.  I tried in the following way.  For (a). We can say $f(n)&gt;f(n-1)$ AND $f(n)&gt;f(n-2) \ldots f(n)&gt;f(1)$ (total $n-1$ elements)  Similarly for $f(n-1)&gt;f(n-2), f(n-1)&gt;f(n-3) \ldots f(n-1)&gt;f(1)$ (total $n-2$ elements)...  and $f(2)&gt;1$  Like this $$(n-1) + (n-2) + \ldots + (1) = \frac{n(n-1)}{2}$$  Is this correct?  For (b). Since there's equality, it will be $$n + (n-1) + ... (1) = \frac{n(n+1)}{2}$$  Is my approach correct? Any help is appreciated. Thanks in advance. How can I keep track of a decimal number that indicates the current paragraph's place in a logical hierarchy and print it in the margin of each paragraph?  (To yield a numbering in the style of Tractatus Logico-Philosophicus).  \def\on{} \def\down{} \def\up{}  \on This is the first paragraph, paragraph number 1.  \on This is paragraph number 2.  \down This is paragraph number 2.1  \down 2 This is 2.101  \up This is 2.11  \down 2.111  \up 3 3  \bye   If \down is starred, begin with zero.  If \up is followed by an integer, it should take it as an argument, unless there is a newline between \up and the integer.  An indefinite number of decimals should be possible.  PS.  I apologize for changing the question after (2) answers have been given, but I realize I failed to appreciate a feature of Wittgenstein's numbering: the last decimal is never 0.  Therefore, \down &lt;n&gt; is better than \down*, as now demonstrated above.  I think the 0 is supposed to indicate an additional level of unimportance. How to generate multiple maps where one highlighted attribute changes? I have a layer that contains counties within the state of Washington.    I need to build one map (jpg) for each county.  For that specific map all counties will show as light grey, but the specific county will be green, and the file name will be the county name.