Compute the complexity of the following Algorithm?
Big O, how do you calculate/approximate it?
Why is sum of squared residuals non-increasing when adding explanatory variable? In my econometric textbook(Introductory Econometrics) covering OLS, the author write, "SSR must fall when another explanatory variable is added."  Why is it? Ubuntu in VirtualBox wants to install on every boot Let $f: \Bbb C \to \Bbb C$ be an entire (analytic on the whole plane) function such that exists $\omega_1,\omega_2 \in \mathbb{S}^1$, linearly independent over $\Bbb R$ such that: $$f(z+\omega_1)=f(z)=f(z+\omega_2), \quad \forall\,z\in \Bbb C.$$Prove that $f$ is constant.   The intuition seems clear to me, we have the three vertices of a triangle given by $0$, $\omega_1$ and $\omega_2$. All points in the plane are one of the vertices of that triangle under a suitable parallel translation. The constant value will be $f(0)$, fine. Throwing values for $z$ there, I have found that $$f(n\omega_1) = f(\omega_1) = f(0)=f(\omega_2) = f(n\omega_2), \quad \forall\, n \in \Bbb Z.$$  I don't know how to improve the above for, say, rationals (at least). Some another ideas would be:   Checking that $f' \equiv 0$. I don't have a clue of how to do that. Write $w = a\omega_1+b\omega_2$, with $a,b \in \Bbb R$, do stuff and conclude that $f(w) = f(0)$. This approach doesn't seem good, because I only have a weak result with integers above. Finding that $f$ coincides with $f(0)$ on a set with an accumulation point. This seems also bad: the set on with $f$ coincides with $f(0)$ by which I found above is discrete.    Nothing works and this is getting annoying... And I don't see how analyticity comes in there. I'll be very thankful if someone can give me an idea.  (On a side note.. I know that this title is not informative at all. Feel free to edit if you come up with something better.) Changing Vim indentation behavior by file type Could someone explain to me in simple terms the easiest way to change the indentation behavior of Vim based on the file type? For instance, if I open a Python file it should indent with 2 spaces, but if I open a Powershell script it should use 4 spaces. Exit strategies for "chameleon questions" I'm not sure if there's already an existing term for this, so I'm inventing my own. (tl;dr: I call them &quot;chameleon questions&quot; because they change every time you submit or edit an answer.  If you're already intimately familiar with the phenomenon, please skip past the first set of bullet points to where I ask for recommendations.)  I think many of us have experienced this on occasion:  You open up a narrow-looking question, usually dealing with some specific error message.  The question probably contains a snippet of sloppy but not quite awful code; code indicating that the author, typically a new/low-rep user, possibly a , doesn't really know what they're doing.  I'm not trying to be condescending here, they're probably very intelligent and hardworking, but in this specific case, they're clearly in way over their head.  However, as a question, it's not really too bad.  The goal and problem are both clearly stated.  The code is formatted (sort of).  Mort was polite and checked their spelling.  The question looks answerable, although from a rep perspective* it's an obvious dead-end, it's had maybe 3 views in the past 30 minutes.  So you decide, you know what, this person took the time to write up the question properly, they deserve an answer, put on your good citizen hat and throw them a bone.  You slog through the ugly code, find the offending line, direct their attention to it and explain why it's wrong and how it needs to be fixed.  Later, they leave a comment saying that yes, that was indeed the problem and your answer helped them fix it (great!).  Oh, but, now there's another problem (uh-oh...). Something else is broken.  After letting out a long sigh, you read the comment and/or edited question, roll up your sleeves, and write up Take 2, hoping that's the end of it.  And of course it's not the end.  Now maybe the error is gone, but it's not doing what it's supposed to.  If you're anything like me, your patience is now starting to wear thin. It's lousy code and you didn't volunteer to help them rewrite their whole app.  And of course, the question still only has 12 views, and nobody has upvoted either the question or your answer, including the person you're helping, so this is turning out to be a genuinely thankless task in all respects.  Welcome to &quot;Family Tech Support&quot;, Web 2.0 Edition.   * Which is of course just an arbitrary number that none of us care about. Not really, anyway. Not very much, at least.  So, here's where I get to my question.  At this point, do you:  Leave a comment, stating as politely as possible that you've done your best to help them answer the original question they asked, and if they have a new problem then they should start a new question?  (I did this once, and actually ended up with an accept, but I felt kind of guilty afterwards, I don't think anybody answered their 2nd question).  Bite the bullet and edit your answer a 3rd, 4th, 5th time, however many times it takes to resolve their issue, knowing full well that they may not even remember to accept the answer once you're done? (I may work for free on SO, but that doesn't mean my time is worthless.)  Just abandon the question, hoping that it will force Mort to start thinking for himself?  Something else?   I've tried all three of the above and none of them ever quite feel right. I do want to help, but at the same time there are a lot more &quot;lucrative&quot; questions I could be answering. And I don't mind spending a lot of time on an answer either, if the question is interesting or important to me, but debugging is dull work. I'd prefer not to reference specific questions here; I'm pretty sure that this is a shared experience, and my objective isn't to point fingers at &quot;misbehaving&quot; members.  I'm more looking for some practical advice on how to dig myself out of these pits of despair. Anybody have any other ideas? Is the function Riemann integrable? If yes, obtain the value of $\int_0^1f(x) \ dx$      $f(x) = \begin{cases} \frac {1}{n},  &amp; \frac{1}{n+1}&lt;x\le\frac{1}{n}\\ 0, &amp; x=0 \end{cases}$   My attempt  $f$ is bounded and monotonically increasing on $[0,1]$. Also, $f$ has infinite discontinuities but only one limit point. Therefore $f$ is Riemann integrable. Now, to calculate the integration  $\int_0^1f(x) \ dx=\int_{1/2}^{1}1 \ dx + \int_{1/3}^{1/2}\frac{1}{2} \ dx + \int_{1/4}^{1/3}\frac{1}{3} \ dx+...$  $=\sum_{n=1}^\infty \frac{1}{n^2}-\frac{1}{n}+\frac{1}{n+1}$  How do I proceed from here? How do I calculate these summations? I know $\sum \frac{1}{n}$ is $\log 2$, but not the other two summations. I have a text file abc.txt and its contents are:     /lag/cnn/org/one.txt    /lag/cnn/org/two.txt    /lag/cnn/org/three.txt   If I use:  $ tar -cvf allfiles.tar -T abc.txt   I'm getting the tar of files in the list. Similarly is it possible to copy those files in abc.txt to a folder?  I tried this:              $ cp --files-from test1.txt ./Folder   But it is not working. Word for giving animal characteristics (esp. physical ones) to humans I am writing a paper about Art Spiegelman's Maus, specifically the metaphor that Spiegelman creates by depicting his obviously quite human characters with the heads of various animals, or a couple times animal masks. The metaphor is used at times to bestialize/animalize the acts of the Nazis and, in some cases, to show the arbitrary nature of the classes/groups/divisions they and others applied to human beings.  I considered "chremamorphism," but this describes the attribution of the characteristics of an object to, or the objectification of, a human. I also considered "animalize" and "bestialize," but those describe some of the effects that can be produced by Spiegelman's metaphor, not the metaphor itself - in many scenes in the book, the characters are extremely human, and I think that the negative or degrading connotations of these words makes them inappropriate for this use. Nor do "anthropomorphism" or "personification" fit, because Spiegelman is not applying human characteristics to animals but the other way around. None of the words that I can think of quite fit.  What is a word that accurately describes Art Spiegelman's depiction of obviously human characters as having animal body parts or wearing animal masks in the comic book Maus? Why didn't the basilisk bite in Chamber of Secrets destroy the Horcrux? As the title asks, why didn't the basilisk bite received in the Chamber of Secrets destroy the Horcrux inside the bitten person?   Yes, I know Fawkes quite quickly healed the bite wound with his phoenix tears, but when Harry used the basilisk fang to destroy Tom Riddle's diary the destruction of that Horcrux was immediate. When Ron hit the locket with the Sword of Gryffindor, it was destroyed immediately. Although the destruction of the ring occurred off-page, Dumbledore used the Sword of Gryffindor to destroy it, so presumably, like the locket, it was gone right away. Nagini died straightaway when Neville decapitated her. The destruction of the Hufflepuff cup happens off-page. The diadem seems to have been destroyed by Fiendfyre immediately as well, as when Harry examined it outside the Room of Requirement it was already leaking a blood-like substance, and then it cracked in half. When Voldemort hit Harry with Avada Kedavra in the forest, Harry woke up in limbo with the last fragment of Voldemort's soul - that awful flayed baby-like being - separated from him immediately.   Is there a logical/canon-based explanation for why the fragment of Voldemort's soul residing in Harry wasn't destroyed upon Harry being bitten by the basilisk?  NOTE: I've read the HP Wiki's entry on Horcruxes; however, I find the HP Wiki to be inconsistent in its accuracy, so I'm hesitant to accept the Wiki's explanation on the matter. I'd prefer an explanation constructed from information in the books or a statement by JKR, or the like. 'Sorry' as a replacement for 'Excuse me'? Is it ok to say 'sorry' where you otherwise would use 'excuse me'?  Example: "Sorry, but could you show me the way to the next train station?" Nth derivative of $x^x$ A few days ago, I was wondering about a series expansion for $$f(x) = \  x^x$$ so I tried taking a couple derivatives. From these I was able to guess at some formulas for the general coefficients of the first few terms of the nth derivative as well as the last term (where I put the terms of the derivative in the order  $$f^{(n)}(x) = c_1x^x + c_2x^{x-1} + c_3x^{x-2}\ + \ ... \ +\ c_nx^{x-(n-1)}$$  Please let me know if there is a general formula for the coefficients as a function of n. In my own fooling around, I found that $$\ln(x)+1$$ appears quite a bit, so I called this $a$ in my work. Since I would like to center my expansion at $1$, and this expression evaluated to $1$, at $x=0$, I was interested in writing my formulas as functions of $n$ and $a$. I found that you get something of the form (this could very well be completely incorrect):  $$f^{(n)}(x) = ax^x + a^{n-2}{\binom n2}x^{x-1} + a^{n-4}(3{\binom n4}-a{\binom n3})x^{x-2}\\ + a^{n-6}(15{\binom n6}-10{\binom n5}a+2{\binom n4}a^2)x^{x-3}\ + \ ... \ +\ (-1)^n(n-2)! \ x^{x-(n-1)}$$  An interesting property that seemed to recur for the various coefficients was  that once I found a recursion formula for the coefficient in question and plugged in my initial value, it always seemed to be the same as taking the integral of the previous coefficient with respect to $a$. That is to say, if I plugged in the nth coefficient (a polynomial of $a$) into my recursion formula for the $(n+1)$th coefficient, this gave me the same result as integrating. In general, as reflected by the few coefficient formulas above,  the formula for the coefficient of $$x^{x-c}$$ where c is an integer such that $$0\le c&lt;n$$ "Stabilized" to a polynomial of a with c terms after the first few applications of the recursion formula. This stabilization occurred when $$n=2c$$ Also, as a direct result of the tentative and incomplete formula I have written above, the first nonzero-value for the coefficient of $$x^{x-c}$$ is $$(-1)^{c+1}(c-1)!$$ and appears in $$f^{(c+1)}(x)$$ If these various properties are indeed true, can anyone explain why this would be the case? I am aware that this function can be expanded using the expansion for $$e^x$$ with $$x\ln(x)$$ in the exponent. This does not strike me as particularly enlightening (let me know if I'm missing something). I am most interested in the coefficients on the binomial coefficients, since these are the only things that stand between me and a general formula for the coefficients (since the form is quite standard). These are: $$1$$ then $$3,-1$$ then $$15, -10,2$$The sum of these coefficients should also give the nth derivative evaluated at zero since $$f(1) = 1$$ and $$a(1) = 1$$  Anyway, please let me know what you think! I am currently stuck due to an inability to brute force my way any further and a complete lack of cleverness. My knowledge of mathematics is quite elementary, so please explain any higher level concepts if they are necessary to explain this problem. How does linear regression use the normal distribution? What is the capacity of this circuit? I simply can't figure out what the capacity of this circuit is.  I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in series... The Maximum possible order for an element $S_n$ In iPhone, you can easily change the default ringtone (Settings → Sounds → Ringtone) and set a custom ringtone for individual people (Contacts → [some person] → Edit → Ringtone).   But can you set a custom tone for a group of contacts? (E.g. "family" or "workmates".)  I think that would be handy—and quite basic functionality, so to speak—but I couldn't find a way to do this through the iPhone UI. Is it possible at all (without jailbreaking)? How do I execute for a player wearing armor with a colored name I am working on a command block contraption on my server that involves armor giving you certain potion effects.  /execute if entity @p[nbt={Inventory[{Slot:100b,id:"minecraft:leather_boots",tag:{display:{Name:"{\"text\":\"Frog Boots\"}"}}}]}] run effect give @s jump_boost 1 1 true  However, it only works if the boots are named in an anvil. How would I write the command if I wanted to test if the player was wearing boots named "Frog Boots" in bold and green text? I think it's something like  this: (Fedora14/bash)  #!/bin/bash  for i in {0..10..1}; do echo -e "$i"'\c' echo -e "\n\r" sleep 1 done   But it doesn't work. Purpose: like this, but without the "clear":   #!/bin/bash  for i in {0..10..1}; do echo -e "$i" sleep 1 clear done   So a counting script that doesn't deletes the whole screen to output +1 number, instead it only deletes the line, where the counting is, so that there could be ex.: a beatifull "progress bar".. Combining the first and second law of thermodynamics we can get the following equation  $$TdS=dU-P_{ext}dV$$  First question: Is this equation applicable for irreversible processes such that that $dS≠\dfrac{dQ}{T}$?  Second question:If the system temperature $T_{sys}$ is smaller than the surrounding temperature $T_{sur}$, which temperature should we put in the equation?   I have this question because sometimes people use $T_{sur}$ instead of $T_{sys}$ (e.g. , ) but the equation is supposed to describe changes in the system. A water pipe from sea level to beyond the atmosphere If a pipe extended from just above the ocean floor to outside the atmosphere, would water be sucked up it by the vacuum beyond the atmosphere? If a hole was made in the pipe, above sea level, how would that affect the flow of water? Would it stop it completely? Installing Broadcom Wireless Drivers