Using Danny Pak-Keung Chan's answer I've tried to do the supremum case. We want to show if $s_{n} \leq t_{n}$ then $\limsup s_{n} \leq \limsup t_{n}$ Let $n\geq N$ be arbitrary and let $k \geq N$ be arbitrary. Then $s_{k} \leq t_{k} \leq \sup_{m \geq n}t_{m}$. Thus $\sup_{m \geq n}t_{m}$ is an upper bound of the set $\{s_{n}, s_{n+1}, \dots ,\}$ therefore $\sup_{m \geq n}t_{m} \geq \sup_{m \geq n}s_{m}$. Define $S_{n}:= \sup_{m \geq n}s_{m}$ and $T_{n}:= \sup_{m \geq n}t_{m}$. Then we have $S_{n}$ and $T_{n}$ are decreasing. Hence $S_{n} \leq T_{n}$. Therefore $\lim_{n \to \infty}S_{n} \leq \lim_{n \to \infty}T_{n}$. Hence $\limsup s_{n} \leq \limsup t_{n}$

This is half of Theorem 3.19 from Baby Rudin. Rudin claims the proof is trivial. What I've come up with so far doesn't seem trivial, however, and is probably also wrong (my problem with it is pointed out below). This makes me wonder whether I'm overlooking some useful fact and/or using an unprofitable approach.  Theorem. If $s_n \leq t_n$ for $n \geq N$, where $N$ is fixed, then  $$ \liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n. $$  Proof. Suppose that $s_n \leq t_n$ if $n \geq N$, but that  $$ \liminf_{n \rightarrow \infty} s_n > \liminf_{n \rightarrow \infty} t_n. $$  Let $E_s$ denote the set of all subsequential limits of $\{s_n\}$, and let $E_t$ denote the set of all subsequential limits of $\{t_n\}$. Then  $$ \inf E_s > \inf E_t. $$  This implies that there exists some $x \in E_t$ such that $\inf E_s > x > \inf E_t$, since otherwise $\inf E_t$ would not be the greatest lower bound of $E_t$. Hence some subsequence of $\{t_n\}$, say $\{t_{n_i}\}$, converges to $x < \inf E_s$.  Lemma. (from Rudin) If $x < \liminf_{n \rightarrow \infty} s_n$, then there exists an integer $N$ such that if $n \geq N$, then $s_n > x$.   By the lemma, there exists an integer $N_0$ such that if $n \geq N_0$, then $s_n > x$.   Now, let $\epsilon = \inf_{n \geq N_0} \{s_n - x\}$. This is where I think my proof breaks down. Can't $\epsilon$ be zero? Then, since $\{t_{n_i}\}$ converges to $x$, there exists an integer $N_1$ such that if $n_i \geq N_1$, then $|t_{n_i} - x| < \epsilon$. But this means that, if $n_i \geq \max\{N, N_0, N_1\}$, we have both  $$ s_{n_i} > t_{n_i}, $$  as well as $s_{n_i} \geq t_{n_i}$, a contradiction.


It had been him and Nina that had decided years ago. Now it was her who had to clean up their mess.   or     It had been he and Nina that had decided years ago. Now it was she who had to clean up their mess.   Which is correct

Overheard on an elevator today,     I didn't realize it was him.   Corrected by the know-it-all,     He.  "I didn't realize it was he."   The know-it-all then went on a rant about how everybody is a dolt for not knowing that.  I swear I have never heard this before in my life.  Is the know-it-all correct?    If so, why is "I didn't realize it was he," grammatically correct?  What rule makes "him" incorrect here?


I have three branches. Master is the production's branch. Staging for testing and Dev for development. How do I merge only specif commits into master from staging branch? I don't always need to merge all differences.

I'm using Git on a new project that has two parallel -- but currently experimental -- development branches:  master: import of existing codebase plus a few modifications that I'm generally sure of exp1: experimental branch #1 exp2: experimental branch #2  exp1 and exp2 represent two very different architectural approaches. Until I get further along I have no way of knowing which one (if either) will work. As I make progress in one branch I sometimes have edits that would be useful in the other branch and would like to merge just those. What is the best way to merge selective changes from one development branch to another while leaving behind everything else? Approaches I've considered:  git merge --no-commit followed by manual unstaging of a large number of edits that I don't want to make common between the branches.  Manual copying of common files into a temporary directory followed by git checkout to move to the other branch and then more manual copying out of the temporary directory into the working tree.  A variation on the above. Abandon the exp branches for now and use two additional local repositories for experimentation.  This makes the manual copying of files much more straightforward.   All three of these approaches seem tedious and error-prone.  I'm hoping there is a better approach; something akin to a filter path parameter that would make git-merge more selective.


Assuming I am opening an iTerm window with the following AppleScript:  tell application "iTerm"             set win1 to (create window with default profile)         repeat until exists win1             delay 0.01         end repeat         tell current session of current tab of current window             write text "watch -n1 " & "'"  & "kubectl get pods | grep -i " & input & "'"             split horizontally with default profile             split vertically with default profile         end tell   What code snippet should I use so that win1 gets maximized (as in clicking on the green window button)?  edit: regarding the proposed solution indicated in the question that is supposed to be duplicate, I have changed my snippet as follows:      tell application "iTerm"             set win1 to (create window with default profile)         repeat until exists win1             delay 0.01         end repeat         tell application "System Events"             perform action "AXZoomWindow" of (first button whose subrole is "AXFullScreenButton") of (first window whose subrole is "AXStandardWindow") of (first process whose frontmost is true)         end tell         tell current session of current tab of current window             write text "watch -n1 " & "'"  & "kubectl get pods | grep -i " & input & "'"             split horizontally with default profile             split vertically with default profile         end tell   However this now opens a new terminal window and no further command executes.

Based on , I wrote the following Applescript which would allow me to click the green (zoom) button at the top-left corner of an window. I want to apply the script to MacVim and others which have the green button as "AXFullScreenButton". But, running the script makes the window to FULL SCREEN rather than a "maximized" window. Can anyone tell what is wrong?  tell application "System Events"     key down option     click (first button whose subrole is "AXFullScreenButton") of ¬              (first window whose subrole is "AXStandardWindow") of ¬             (first process whose frontmost is true)     key up option     set frontApp to (name of first application process whose ¬             frontmost is true) as string end tell tell application frontApp to activate


I don't understand why Animax stopped showing Naruto: Shippuden in India. I want to know what happened when Naruto was killed by Sasuke and how exactly he got a son.  Why did Animax stop broadcasting Naruto: Shippuden in India?

Animax Asia suddenly stopped airing new episodes of Naruto Shippuden in India as of January 30th 2014. As I am a Naruto fan, I was upset to see it cancelled. What was the reason it stopped airing?


Im having 2 lists. Looping list2 and checking if list1 elements exists in list2 or not.But my below code is checking for only exact match and not considering upper case or lower case elements like Date, CIRCUIT  list1 = ['circuit', 'Date', 'common', 'discover'] list2 = [('id-23', 'po'), ('id-24', 'date'),('id-25', 'CIRCUIT'), ('id-26', 'discover')]  for i, a in list2:     if a in list1:         kia = i,a         print(kia)   Output im getting is ('id-26', 'discover')  expected output should be ('id-24', 'date'), ('id-25', 'CIRCUIT'), ('id-26', 'discover')

How can I do case insensitive string comparison in Python?  I would like to encapsulate comparison of a regular strings to a repository string using in a very simple and Pythonic way. I also would like to have ability to look up values in a dict hashed by strings using regular python strings.


I would like to be able to apply and edit a material to objects I have create using python script. I am using the cycles render engine but can't find a way to get this to work.  I've tried a bunch of the answers already given in other threads but none of them seem to work.  I would like to: create and apply a new material for each object and adjust the colours using rgb, using nodes or otherwise.  Sorry if this is a stupid question, I'm very new to blender scripting!

How can I define the different properties of an Cycles/Eevee material? Such things as glossy, glass, diffuse, RGB-color, emissive via python scripting?


I am a beginner in Blender, I know how to use the basic commands but don't have much experience creating models. I am trying to create a circle of ribbon-like DNA with the base pairs detached in the center like this, except with a few caveats.  The base pairs should be able to freely rotate around the "vertical" axis, and somehow I can control the loop so it can writhe/contort (like go from a circle to an "eight"). Could anyone please help me figure out how to do this or point me to some resources that could help?

First time asking a question here, and I'm really new to Blender. Hopefully you'll forgive me for asking really dumb questions.  So I want to do a neat little "beginner project" animation that involves unravelling a double helix. The issue is, how can I create a double helix mesh? Using edit mode? Or some modifier that I'm not aware of? And if so, how can I "un-twirl" it?  Any help is much appreciated!


Is a submodule of a free module also free ? For me it looks natural that yes, but in my course it's written that it's only true for a module over a PID and I don't really understand why. Any example ?

Assume $A$ is a nontrival submodule of a free $R $-module, where $R $ is a ring.   Is it true that $A $ is also free?


Starfleet personell obviously uses a lot of software (e. g. LCARS) on their vessels, stations, handheld and wearable devices.  Thus, it would seem to me that there must be a lot of software engineers and developers in Starfleet, that develop and maintain all this software. However, none of the main characters calls themselves a software engineer.  Are there any known software engineers in Starfleet? Where are Starfleet's software engineers?

Star Trek, for being a show about the distant future and extraordinarily high-tech equipment, sure seems to be lacking a lot of computer programmers.   With technology as complex as it is, where are all the starship-based computer programmers responsible for preventing AI malfunctions aboard ships like the Enterprise?    More specifically, we hear plenty of references to having to 'program in' certain things - Picard is dismayed in "All Good Things" that the past Enterprise doesn't yet have an Earl Grey Tea program, and we see plenty of holodeck programming going on, but is all of this programming done explicitly by the crewmember who just wants a cup of tea or a nice stroll along a sandy beach?    In short: Are there any actual dedicated computer programmers in any Star Trek series or movie?  Even one example of a person with such a job would satisfy.


I want to start using QGIS. I have worked in ArcGIS but I would like to start learning QGIS online.   Any suggestions for good online courses (hopefully free or not very expensive)?

I wish to familiarize myself with the capabilities of QGIS up to and beyond QGIS version 3.0.   Can you recommend some good web resources and tutorials that would show me QGIS' capabilities?   I am interested in both using QGIS through its GUI and in developing applications using QGIS.


Why do cosmic bodies such as planets, stars, satellites revolve? What made them to revolve after the formation of universe?

The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons.  Where has all the angular momentum come from? Why is it so natural?  I was also thinking do photons spin? we always think of the wave as a standard 2d sin wave but could this rotate in 3d? What implications would this have?   And what about spacetime how does all the spinning effect?  This has always been avoided in all lectures and classes I ever went to.


I installed many apps through Terminal. I notice that my storage had 120GB left and I installed 1 GB app then I uninstalled it and I got 119.5GB left. Where is my 500MB??? so my storage keeps decreasing day by day I've tried apt-get purge  to remove compeletely but my storage's still the same I've been using Ubuntu for 2 days so please help

For example, de-fragmenting, disc cleanup, or stuff like that?


When I install Cuda it says "no supported version of visual studio was found. Some of the CuDa toolkit won't work properly" do I have to download the whole visual studio or  there is a zip file around

I have been advised to download cuda and I downloaded nvidia cuda version 6.5,yet the cycle compute showed none. what should I do?  Help me please.  I'm using windows 7  im trying to enable graphics card nvidia geforce 320


My previous attempt at proof did not work as I thought and so I decided to try again. Please bear in mind that this is not a duplicate of my old proof. If you look at the other one you will see that this examines the parity of the equation, something the previous attempt does not do. This time I have based my attempt on induction rather than algebra.  To begin with, I examined the equation: $$ A^3 + B^3 = C^3$$ Where $A$, $B$, $C$ $\in \Bbb Z$ and $A$, $B$, $C > 0$. We can also assume that $A, B, C$ are the lowest solutions. Therefore, $A^3, B^3, C^3$ are co-prime.   Examining this, we should be able to draw conclusions on each term's parity. In this form, we could have: $$(1)EVEN + ODD = ODD$$ $$(2)ODD + ODD = EVEN$$ $$(3)EVEN + EVEN = EVEN$$  However, equation $3$ is not possible as we know that $A^3, B^3, C^3$ are the lowest solutions possible and are co-prime. Therefore, we are left only with $1$ and $2$.    My previous attempted solution involved rewriting the equation in terms of $A^3$: $$A^3 + xA^3 = C^3$$ Here $x$ is either an integer, irrational or fraction. If it is an integer we get: $$(1+x)A^3 = C^3$$ Since $x \in \Bbb Z$, $x+1 \in \Bbb Z$. Therefore, $\sqrt[3]{x+1} \in \Bbb Z$ and $\sqrt[3]{x} \in \Bbb Z$. The only possible integer solution to this is $x = 0$. However, this would mean that $B^3 = 0$.  Therefore, $x$ is irrational or a fraction. If $x$ is irrational, $B^3$ will be irrational.  Therefore, $x$ is a fraction.  We can now represent this in the equation: $$A^3 + \frac{p^3}{q^3}A^3 = C^3$$ Where $p,q \in \Bbb Z$. The reason the fraction can be represented as such is because that is the ratio of $A^3$ to $B^3$. Even if $p^3$ and $q^3$ did share factors they could be simplified to still be cubes. (For example, $\frac{64}{8} = 8$.)  Simplifying this further we get: $$(qA)^3 + (pA)^3 = (qC)^3$$  We shall begin by analysing $qA$. We know from earlier that this is either odd or even. If we assume it is even, then either: $$\frac{A}{2} \in \Bbb Z , \frac{q}{2} \notin \Bbb Z$$ or $$\frac{A}{2} \notin \Bbb Z , \frac{q}{2} \in \Bbb Z$$  or $$\frac{A}{2} \in \Bbb Z , \frac{q}{2} \in \Bbb Z$$  Analysing $pA$, we can see from before that $pA$ must be odd. Therefore: $$\frac{A}{2} \notin \Bbb Z , \frac{p}{2} \notin \Bbb Z$$ This means we can compare this with the other possible parities of $A$ to give:  $$\frac{A}{2} \notin \Bbb Z$$ $$\frac{p}{2} \notin \Bbb Z$$ $$\frac{q}{2} \in \Bbb Z$$  Substituting this all into our equation gives us: $$(EVEN)^3 + (ODD)^3 = (EVEN)^3$$ $$EVEN + ODD = EVEN$$  This clearly is incorrect and so our original assumption, that there are integer solutions to the below is incorrect. $$A^3 + B^3 = C^3$$  Q.E.D. (Hopefully.) Is this correct? I cannot find anything wrong with it unlike my previous one. Thank you.

So I have spent some time thinking about Fermat's Last Theorem and about how to come up with a proof for certain cases of n. To begin with I took n = 3.  $$A^3 + B^3 = C^3 (A,B,C \in \mathbb {Z})( A,B,C ≠ 0)$$ We can assume that $A<B<C$. Because of this we can rewrite this as: $$A^3 + xA^3 = C^3$$ We now have three possibilities: $x$ is an integer, $x$ is an irrational, or $x$ is a fraction.  If $x$ is an integer then $x$+1 and $x$ must be cubes. The only numbers which satisfy this are $x$ = 0. However, this means $B^3 = 0$.  $x$ cannot be irrational because then $C^3$ is irrational. Therefore $x$ is a fraction.  We can represent this now as: $$A^3 + \frac{p}{q}B^3 = C^3 (p,q \in \mathbb {Z})(GCD(p,q) = 1)$$ This means $\frac{p}{q}$ is actually a cube over a cube. Therefore $p$ and $q$ are cube numbers.  However, $1 + \frac{p}{q}$ is also a cube. Therefore $\frac{p+q}{q}$ is a cube over a cube. Hence: $$\sqrt[3]{p} ,\sqrt[3]{q}, \sqrt[3]{p+q} \in \mathbb {Z}$$  We can now create another variable $v$ for $p+q$. Therefore, $$p+q = v$$ (Where $\sqrt[3]{v} \in \mathbb {Z}$)  Now we must deal with $\frac{p}{q}+1$. Since this is a cube we can write this as: $$\frac{p}{q} + 1 = \lambda^3$$ Since $p$ and $q$ are co-prime and in simplest form, $\lambda$ and $\lambda^3$ are also fractions in simplest form. Rearranging, we get: $$p = q(\lambda^3 - 1)$$  Substituting this into $p+q=v$, we get: $$q+q(\lambda^3 - 1) = v$$ $$q\lambda^3 = v$$  Since $\lambda^3$ is a fraction, we can express it as $\frac{D^3}{E^3}$. Hence: $$qD^3 = vE^3$$  However, because $v$ is a cube, $vE^3$ is also a cube. Therefore $\lambda^3$ doesn't have to be a fraction. This is a contradiction, and so there can be no integer solutions for $p$ and $q$. Subsequently, there can be no integer solutions for A,B,C in: $$A^3 + B^3 = C^3$$.  If anyone could point out the problem in this and what you think of it it would be greatly appreciated. Thank you.


I get that Earth was easier to defeat in post WW3 21'st century, but what would the borg gain? I mean there is no Federation or technology to speak of. Other than script writers thinking that it might be fun to have Picard and crew fight the borg in a time travel movie, what is the big gain for the borg?

If the Borg found Earth in 20 century or early 21st century, such as 2015, would they assimilate humanity? If they thought Earth is too primitive to their use, would they just leave Earth alone for later, kill everyone on it, or forget about Earth?


note: the first set of three dots in the title is definitely three separate dots, and the second is one character when I select it during editing. However viewing the posted in Safari both select as a single character.  I sometimes write explicitly three periods in a row "..." in a text field in TextEdit or in Keynote when discussing a bit of code or script, (e.g. X[..., 1] in Python puts a 1 in the last axis of a multidimensional array) and either Keynote or macOS says "Oh, I'm going to change what you typed to something you probably wanted instead" and converts it to X[…, 1] I would like my laptop to stop doing that, in Keynote and basically anywhere! How can I do this? macOS 10.15.6 "Bonus points" for sharing how to stop it from putting periods at the ends of anything it thinks might be a sentence.  I have found that on a case-by-case basis I can stop and undo what is already done, but I just want to suppress this behavior from the beginning.

Every time i write ... in a text editor like TextEdit or Coda, Lion has started replacing it with a single Ellipse character, which doesn't encode to HTML. This started after I upgraded to Lion and happens across multiple programs. This persists in the latest Big Sur betas. Any idea how to stop it?


I have a gaming chair with a speaker built into it and I lost the cord for it.  I managed to find an old xbox 360 cord that fit it but it’s 24V. The chair turns on with the 24V cord but I’m trying to find out if the higher voltage is hurting it.

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


I'm wondering why this differential equation, $xy'= 1$ has no solution on the interval $I:−1 < x < 1$ per Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard, page 29: example 4.22.  From my understanding, this differential equation should have a solution as long as $x ≠ 0$.  It's "family" of solutions would then look like, $y = log|x| + c_1$ (which is given in the book), and seems to be defined for all $x ≠ 0$ as well.  What am I missing here?

Here is the ODE equation $xy' = 2y$. A book states that the interval where it makes sense doesn't include $0$. Can you explain why? As to me, I think it is defined everywhere.  This problem is from the book "Ordinary Differential Equations - Harry Pollard, Morris Tenenbaum". The exact problem states: "Prove that the functions in the right-hand column below are solutions of the differential equations in the left-hand columns. (Be sure to state the common interval for which solution and differential equation make sense.)"  $xy' = 2y$ and $y = x^2$ with the answer $x \neq 0$


I am quite sure I saw this somewhere on SE but I couldn't find it. How to evaluate $$\int_0^{\frac{\pi}{2}}\frac{\sin^3(x)}{\sin^3(x) + \cos^3(x)}dx$$  I already have  $$\int \frac{\sin^3(x)}{\sin^3(x) + \cos^3(x)}dx+\int\frac{\cos^3(x)}{\sin^3(x) + \cos^3(x)}dx = \frac{\pi}{2}$$  Ideally I would like to have something like $I_1 + I_2 = \frac{\pi}{2}$ and $I_1 - I_2 = \text{something}$. But   $$\int \frac{\sin^3(x)}{\sin^3(x) + \cos^3(x)}dx-\int\frac{\cos^3(x)}{\sin^3(x) + \cos^3(x)}dx=?$$  I tried to play around with even and odd functions' property. The problem is that $\sin^3(-x) + \cos^3(x) = -\sin^3(x) + \cos^3(x)$.

Evaluate the integral $$\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\, \mathrm dx.$$  How can i evaluate this one? Didn't find any clever substitute and integration by parts doesn't lead anywhere (I think).  Any guidelines please?


y'all..well, i created an another user and then changed the password for it, but after i tried to log in by that new user account it said that password is wrong, yea seems like i have entered an wrong password with the beginning. oh also i set that account as an admin but disabled that account. i can't log in with that account also whenever i command on terminal it says something means like that it's not the admin account so you can't command anything.. what should i do to about my password? really need to fix it immediately. HELP me

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


I'm brand new to this site so please be kind. It has always struck me as odd to declare one's love for the very 1st time to another by saying, "I'm in love WITH you."  The brief definition I found for WITH was the Oxford one; accompanied by.  Which means both people would be in love with each other.  Why not just say "I love you?"  Does anyone know where the expression came from?

I'd like to learn the etymology of using the preposition with in the phrase in love with somebody. For me it doesn't make much sense because with seems to imply something that is shared by two people, something symmetrical wherein the phrase only states that one person has romantic feelings towards another. In Polish, we say być zakochanym w kimś which directly translates to be in love in somebody, which, at least to me, seems to make much more sense.  Why do we use/What is the etymology of using with in the phrase in love with somebody?


Say you make a cake after having wanted to make it for a long time. You say, "I finally got around to making this cake." and then you say "I have wanted to make this cake since/for so long." Has the sentence in boldface been constructed correctly? What about, "I have been wanting to make this cake for so long?"

Which of these is grammatically correct?       1. a) He has been working under my direct supervision since the last two years           1. b) He has been working under my direct supervision for the last two years            2. a) He has not met her since a very long time        2. b) He has not met her in a very long time    Which of the above are correct? Are all of them correct? My friend says 1.b and 2.b are correct, but I am not sure. Or is this an American English and British English thing? (He mostly goes by American English)


When we speak about 4096- or 2048-bit RSA keys, what part of the key is this number of bits? The public key comprises both the modulus and the public exponent, and the strength of the key can also be seen as depending on the length of the prime factors. Which of these is the "4096-bit" part?

I have implemented a key pair generation scheme for RSA algorithm. I have taken the length of private key exponent as RSA key size, but then I've got to know that RSA key size is the size of the modulus $n$. Is it wrong to take RSA key size as the size of the private key exponent?  To generate a private key of 1024 bits, I increase the size of private key exponent regardless the modulus $n$.


Find all incongruent solutions to $x^2 \equiv 23 \pmod{77}$  Using the Chinese Remainder Theorem, I obtained $x^2 \equiv 23 \pmod{7}$ and $x^2 \equiv 23 \pmod{11}$. For $x^2 \equiv 23 \pmod{7}$, the answers are: \begin{align} x \equiv 3 \pmod{7} \\ x \equiv 4 \pmod{7} \end{align} For $x^2 \equiv 23 \pmod{11}$, the answers are: \begin{align} x \equiv 1 \pmod{11} \\ x \equiv 10 \pmod{11} \end{align} But the solutions for $x^2 \equiv 23 \pmod{77}$ are: \begin{align} x \equiv 10 \pmod{77} \\ x \equiv 32 \pmod{77} \\ x \equiv 45 \pmod{77} \\ x \equiv 67 \pmod{77} \end{align} Why are my answers not the same as the solutions? Can someone help me with this? Thanks!

I understand what the Chinese remainder theorem is. However I am not sure how to apply it to my question. Can someone explain please?


Recently I've been working with a cluster monitoring tool (ganglia) which aggregates system metrics from /proc/* on each machine.   How is the data in /proc/* gathered? Who writes the data there? How often is the data updated? Can I tune the way it is gathered so that it is more accurate?

How frequently is the proc file system updated on Linux? Is it 20 milliseconds (time quantum)?


Type this in the console of your browser:  9999999999999999==10000000000000000  It says they are equal, why?

Is this defined by the language? Is there a defined maximum? Is it different in different browsers?


Is it possible to reset and re-select the skills that I want my followers to have?  I want my Templar to be able to heal more, so I would like to change the skills that I originally selected for him.

I didn't like the skill I chosen for the first follower I found. Is it possible to respec his skill later on?


What would be the most frequent/common way of telling the time when the minute is between 01 and 09? Is there any difference between BE and AmE?  5:03 ->   1) five oh three  2) five three   3) three past five

I don't know if this is a good question. But as far as I know, and as I do it, American English also say "after" other than "past" in expressing times.   For example, a quarter after six instead of, a quarter past six as in British English.  The other difference I know, so far, is that the British use dots to separate "hour" and "minute" in digital times like "08.35" while Americans use a colon e.g; "08:35".  So is what I know, so far, correct? Or are there any other differences that I don't know about?


When I do an apt-get update, I get this message at the end:  E: Unable to parse package file /var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_trusty_universe_i18n_Translation-en (1) E: Problem opening /var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_trusty-updates_main_binary-amd64_Packages E: The package lists or status file could not be parsed or opened.   Originally, the problem referring to "Translation" wasn't showing, it was only the one referring to "AMD64 packages". So I did a little web surfing and came across a possible solution. I did this:   sudo rm /var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_trusty-updates_main_binary-amd64_Packages   And after than the "Translation" Errors came.   Help?

Everytime I sudo apt-get update it always not complete and will say in the end  E: Read error - read (5: Input/output error) E: The package lists or status file could not be parsed or opened.   Same goes, when I try to install something and do sudo apt-get install <some app>  What should I do ? I admit, that my drive has bad sectors, could that be the reason? Is there anything else I can do?


Given a convergent sequence $(x_n)\rightarrow 2$, I am asked to prove $(1/x_n)\rightarrow 1/2$ without the use of the algebraic limit theorem.   Here is what I have tried: Let $\epsilon>0$ be arbitrary. We must prove that $|1/x_n-1/2|<\epsilon$. Observe that $$|1/x_n-1/2|=\frac{|x_n-2|}{2|x_n|}$$ and we can make $|x_n-2|$ as small as we like. However, I'm not sure how to choose $N$, and what to do with the $|x_n|$ in the denominator.

We know that for all $\varepsilon > 0$, there exists an $N \in \mathbb{N}$ such that $\lvert x_n - 2 \rvert < \epsilon$ for all $n \geq N$, and we want to show that for all $\varepsilon' > 0$, there exists an $N' \in \mathbb{N}$ such that $\left| \frac{1}{x_n} - \frac{1}{2} \right| < \epsilon'$ for all $n \geq N'$.  Let $\varepsilon = \varepsilon' - \frac{3}{2}$. Then by the triangle inequality, we have $$\left| \frac{1}{x_n} - \frac{1}{2} \right| \leq \left| \frac{1}{x_n}\right| + \left| -\frac{1}{2}\right|.$$  Because we proved earlier that $x_n > 1$ for all $n \geq N$, we know that $$\left| \frac{1}{x_n}\right| + \left| -\frac{1}{2}\right| < \left| x_n\right| + \left| -\frac{1}{2}\right|.$$  By the triangle inequality again, we know that $$\left| x_n - \frac{1}{2}\right| \leq \left| x_n\right| + \left| -\frac{1}{2}\right|.$$  Note that $\left| x_n - \frac{1}{2}\right| = \left| (x_n - 2) + (2 - \frac{1}{2})\right|$, so we get $$\left| (x_n - 2) + (2 - \frac{1}{2})\right| \leq \left| x_n - 2\right| + \left| 2 - \frac{1}{2}\right|.$$  Then we have $$\left| x_n - 2\right| + \left|2 - \frac{1}{2}\right| < \varepsilon + \frac{3}{2} = \left(\varepsilon' - \frac{3}{2}\right) + \frac{3}{2} = \varepsilon',$$ so $\frac{1}{x_n} \rightarrow \frac{1}{2}$.  I just realized that I don't know how to make sure that $\varepsilon' - \frac{3}{2}$ is a positive number. How can I do this?


This is one of my homework problems:  Let $C$ be the Cantor set and $\mu$ be the uniform measure (with the usual Cantor distribution). Find $\int x^2 d\mu$.  I tried finding the value by using symmetry property, and failed, unsurprisingly. I also tried to use Fubini's theorem by setting $\int x^2 d\mu=\int_{0}^{1} \int_{0}^{x} 2t dx d\mu$, but I think it does not simplify the problem.  So what should I deal with it?

Calculate the integral $$\int_{[0,1]}x^2d\mu_F$$ where F is the cantor function. Use the following hints about the cantor function:  $F(1-x)=1-F(x)$ $F(\frac x 3)=\frac{F(x)}{2}\quad\forall x\in[0,1]$ $F(0)=0$   I thought that $$\int_{[0,1]}x^2d\mu_F=\int_{[1,0]}(1-x)^2d\mu_{F}=\int_{[0,1]}x^2d\mu_{1-F(x)}$$ but here I'm stuck and I don't know how to continue calculating this integral. Furthermore, how do we use the second and third properties when given the cantor function above?


Can someone help me prove this. It is a proof of the sum and difference of the greatest common denominator.  Given: x and y are integers with a GCD of 1.   Prove: that the GCD of x + y and x − y is either 1 or 2.

Suppose $a, b \in \mathbb{Z}$, $a > b$, and $\gcd (a,b) = 1$.  What can be said about $\gcd (a+b,a-b)$?  Is it true in general that $\gcd (a+b,a-b) \leq 2$?


some paragraph some paragraph   I ask for the difference between this two tags.

What's the difference between <b> and <strong>, <i> and <em> in HTML/XHTML? When should you use each?


Here is where the code is throwing the error:  public class ArrayPila<E extends Bebidas> implements Pila<E>{   private static final int TAMAÑO=5;   private E []arP;   private int tope;    public ArrayPila() {     arP=(E[]) new Object[TAMAÑO];     tope=-1;           } }   I'm just creating a generic stack with a type of object (created in another class) and it gives me:   Exception in thread "AWT-EventQueue-0" java.lang.ClassCastException: [Ljava.lang.Object; cannot be cast to [Lmis.java.clases.Bebidas;     at mis.java.estructuras_de_apoyo.ArrayPila.<init>(ArrayPila.java:13)     at mis.java.miformulario.VentanaP.<init>(VentanaP.java:67).   Could you please help?

Due to the implementation of Java generics, you can't have code like this:   public class GenSet<E> {     private E a[];      public GenSet() {         a = new E[INITIAL_ARRAY_LENGTH]; // error: generic array creation     } }   How can I implement this while maintaining type safety?  I saw a solution on the Java forums that goes like this:  import java.lang.reflect.Array;  class Stack<T> {     public Stack(Class<T> clazz, int capacity) {         array = (T[])Array.newInstance(clazz, capacity);     }      private final T[] array; }   But I really don't get what's going on.


I am not a mathematician, but I study it for fun.  I know that Cantor showed that the infinite set of the real numbers is larger than the rationals since the real numbers are uncountable and the rationals are countable.  The real numbers include rational and irrational numbers and the irrational numbers are uncountable.  Is the set of irrational numbers smaller than the set of real numbers, the same size, or does this question not make sense?  Thank you!

I know and I have proved more than once that the set of irrational numbers ($\mathbb{I}$) is uncountable, but now I'm given to solve this problem:   Show that $|\mathbb{I}|=|\mathbb{R}|$,  How can I do that?  Do I need to assume the Continuum Hypothesis in order to that statement to be true?  Thanks


I have got the enum  enum ProgramID {     A = 0,     B = 1,     C = 2,     MIN_PROGRAM_ID = A,     MAX_PROGRAM_ID = C,  } CurrentProgram;   Now, I am trying to increment CurrentProgram like this: CurrentProgram++, but the compiler complains: no 'operator++(int)' declared for postfix '++' [-fpermissive]. I think there IS such an operator that increments "enums", but if there is not, how do I get the successor of one of these values?

I just noticed that you can not use standard math operators on an enum such as ++ or +=  So what is the best way to iterate through all of the values in a C++ enum?


I'm working on a classification problem and I have a very high F1 baseline of 85%. I have trained three classification models and I want to know which one is the best. How I can do so?  I tried two ways:   To compare each model against the baseline using paired t-test. So I have tests like:  baseline vs. model 1 | baseline vs. model 2  | baseline vs. model 3   That tells me that only model 1 is significantly higher than the baseline and so I concluded that model 1 is the best. Is this a valid methodology given that usually classification models are compared against baselines? To compare all models in one fell swoop with one-way ANOVA. So entered the information of modals 1-3 AND the baseline with gave me a p-value of 0.02 indicating that there is a difference in means. Yet, with a post pairwise test, there is no significance between any of the pairs.   Which method is the correct one?

I'm working on a classification problem and I have a very high F1 baseline of 85%. I have trained three classification models and I want to know which one is the best. How can I do so?   I tried two ways:   To compare each model against the baseline using paired t-test. So I have tests like:    baseline vs. model 1 baseline vs. model 2 baseline vs. model 3   That tells me that only model 1 is significantly higher than the baseline and so I concluded that model 1 is the best. Is this a valid methodology given that usually classification models are compared against baselines?  To compare all models in one fell swoop with one-way ANOVA. So I entered the information of models 1-3 and the baseline which gave me a p-value of 0.02 indicating that there is a difference in means. Yet, with pairwise post-hoc tests, there is no significance between any of the pairs.   Which method is the correct one?


As the title states: PCA is an autoencoder with one hidden layer with linear transfer functions.  Can someone explain this sentence to me? I understand that if you want to map something into lower dimensional space then PCA has essentially perfectly optimized this procedure. With this understanding, if an autoencoder has a loss function that aims to find the best representation in lower dimensional space (say dimension H) then PCA that takes H rank basis vectors will produce the exact same result as the autoencoder?   Which of these is quicker and a better approach?

Both PCA and autoencoder can do demension reduction, so what are the difference between them? In what situation I should use one over another?


I am migrating a site hosted on on Drupal 7.22, apache 2.2.22aa and php 5.6.9 from one linux server to another lunx server. I did a back up of mysql and apache htdocs folder and extract it on the destination server. But when I lunched the page on the server, I am getting the following error:      Fatal error: Class name must be a valid object or a string in .../common.inc on line 7924   I enabled the debug as below  /*  * Get the entity controller class for an entity type.  */ function entity_get_controller($entity_type) {   $controllers = &drupal_static(__FUNCTION__, array());   if (!isset($controllers[$entity_type])) {     $type_info = entity_get_info($entity_type);     $class = $type_info['controller class'];      // add debug.     if(gettype($class) == 'string' || gettype($class) == 'object') {       $controllers[$entity_type] = new $class($entity_type);     } else  {       print_r(debug_backtrace());     }     $controllers[$entity_type] = new $class($entity_type);   }   return $controllers[$entity_type]; }   Now I am getting the error as   Array ( [0] => Array ( [file] => ../includes/common.inc [line] => 7891 [function] => entity_get_controller [args] => Array ( [0] => node ) ) [1] => Array ( [file] => ../modules/node/node.module [line] => 952 [function] => entity_load [args] => Array ( [0] => node [1] => Array ( [0] => 15 ) [2] => Array ( ) [3] => ) ) [2] => Array ( [file] => ../modules/node/node.module [line] => 971 [function] => node_load_multiple [args] => Array ( [0] => Array ( [0] => 15 ) [1] => Array ( ) [2] => ) ) [3] => Array ( [file] => ../includes/menu.inc [line] => 593 [function] => node_load [args] => Array ( [0] => 15 ) ) [4] => Array ( [file] => ../includes/menu.inc [line] => 761 [function] => _menu_load_objects [args] => Array ( [0] => Array ( [path] => node/% [load_functions] => a:1:{i:1;s:9:"node_load";} [to_arg_functions] => [access_callback] => node_access [access_arguments] => a:2:{i:0;s:4:"view";i:1;i:1;} [page_callback] => node_page_view [page_arguments] => a:1:{i:0;i:1;} [delivery_callback] => [fit] => 2 [number_parts] => 2 [context] => 0 [tab_parent] => [tab_root] => node/% [title] => [title_callback] => node_page_title [title_arguments] => a:1:{i:0;i:1;} [theme_callback] => [theme_arguments] => a:0:{} [type] => 6 [description] => [position] => [weight] => 0 [include_file] => ) [1] => Array ( [0] => node [1] => 15 ) ) ) [5] => Array ( [file] => ../includes/menu.inc [line] => 472 [function] => _menu_translate [args] => Array ( [0] => Array ( [path] => node/% [load_functions] => a:1:{i:1;s:9:"node_load";} [to_arg_functions] => [access_callback] => node_access [access_arguments] => a:2:{i:0;s:4:"view";i:1;i:1;} [page_callback] => node_page_view [page_arguments] => a:1:{i:0;i:1;} [delivery_callback] => [fit] => 2 [number_parts] => 2 [context] => 0 [tab_parent] => [tab_root] => node/% [title] => [title_callback] => node_page_title [title_arguments] => a:1:{i:0;i:1;} [theme_callback] => [theme_arguments] => a:0:{} [type] => 6 [description] => [position] => [weight] => 0 [include_file] => ) [1] => Array ( [0] => node [1] => 15 ) ) ) [6] => Array ( [file] => ../includes/menu.inc [line] => 1755 [function] => menu_get_item [args] => Array ( ) ) [7] => Array ( [file] => ../includes/menu.inc [line] => 1770 [function] => menu_get_custom_theme [args] => Array ( [0] => 1 ) ) [8] => Array ( [file] => ../includes/common.inc [line] => 5292 [function] => menu_set_custom_theme [args] => Array ( ) ) [9] => Array ( [file] => ../includes/bootstrap.inc [line] => 2212 [function] => _drupal_bootstrap_full [args] => Array ( ) ) [10] => Array ( [file] => ../index.php [line] => 25 [function] => drupal_bootstrap [args] => Array ( [0] => 7 ) ) )

"Fatal error: Class name must be a valid object or a string in C:\xampp\htdocs\uc\includes\common.inc on line 7506"  The error above showed up unexpectedly. I was adding a "Long text" field to a content-type, but when I expected to be brought to a saved field configuration page, I instead got a Fatal error on every page.  I had a look at includes\common.inc:  /**  * Get the entity controller class for an entity type.  */ function entity_get_controller($entity_type) {   $controllers = &drupal_static(__FUNCTION__, array());   if (!isset($controllers[$entity_type])) {     $type_info = entity_get_info($entity_type);     $class = $type_info['controller class'];     $controllers[$entity_type] = new $class($entity_type); // Line 7506   }   return $controllers[$entity_type]; }   However, I just don't understand Drupal at a low enough level to understand the relationships between these variables and functions.  I also searched Drupal for people with a similar problem:  (1)  who claims that I have to install the submodule "Relation Endpoints Field", but searching Drupal, .  (2) :  DELETE FROM cache; DELETE FROM cache_filter; DELETE FROM cache_menu; DELETE FROM cache_page; DELETE FROM watchdog;   (via , misleading name, I know.)  Clearing those tables from the cache did not help.  (3) And another user . Because I can't find a module specifically pertaining to old search facets, I went into MySQL system table, and marked the Search module's line with a 0 status, indicating to stop loading the module altogether.  On that same link as (3), one user suggested enabling the , so I dropped all the tables, imported the latest stable .sql, and installed the module, but after recreating the problem (trying to add a field to a content-type), that as well concluded fruitless.  Still, the problem remains  The Fatal error shows up on every page, making the site completely non-functional. Any help or direction would be immensely appreciated. Thank you for looking.


Windows 10 has an extensive collection of lock screen photos, many of which have  here on Travel.SE.  Is there a website which lists the location of all of these photos? I imagine Microsoft has purchased an official license, so they should have a record about the photographer and the place where the photo was taken.


Prove that for any positive integer $n$, $$ 2\sqrt{n+1}-2 \leq 1 + 1/\sqrt{2} + 1/\sqrt{3} + .... + 1/\sqrt{n}\leq 2\sqrt{n}-1 $$  the middle part can be expressed as a sum. of $1/\sqrt{x}$ from 1 to $n$, which leads to a $Hn^{0.5}$. Im not sure how that helps.  I tried differentiating both end functions and found they are both increasing.. But it doesn't seem to help much... help pls

Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound.


I am looking at a plot of likelihood against parameters for a Bernoulli context (i.e. finding the p of a coin facing heads) and am comparing it to the equivalent plot for a log likelihood one. I notice that the peak is a lot sharper for likelihood. I understand that using log likelihood is a lot easier for us to solve and less computationally expensive, since we are no longer dealing with variables in the power. Does this mean that we incur a tradeoff of getting a less certain, i.e. higher variance for our estimate?

I'm trying to understand at a deeper level the ubiquity of log-likelihood (and perhaps more generally log-probability) in statistics and probability theory.  Log-probabilities show up all over the place: we usually work with the log-likelihood for analysis (e.g. for maximization), the Fisher information is defined in terms of the second derivative of the log-likelihood, entropy is an expected log-probability, Kullback-Liebler divergence involves log-probabilities, the expected diviance is an expected log-likelihood, etc.    Now I appreciate the many practical and convenient reasons.  Many common and useful pdfs are from exponential families, which leads to elegantly simplified terms when log-transformed.  Sums are easier to work with than products (esp for differentiating).  Log-probs have a great floating point advantage over straight probs.  Log-transforming a pdf often converts a non-concave function into a concave function.  But what is the theoretical reason/justification/motivation for log-probs?  As an example of my perplexity, consider the Fisher information (FI).  The usual explanation for intuiting the FI is that the second derivative of the log-likelihood tells us how "peaked" the log-likehood is:  a highly peaked log-likelihood means the MLE is well-specified and we are relatively sure of its value, while a nearly flat log-likehood (low curvature) means many different parameter values are nearly as good (in terms of the log-likelihood) as the MLE, so our MLE is more uncertain.   This is all well-and-good, but isn't it more natural to just find the curvature of the likelihood function itself (NOT log-transformed)?  At first glance the emphasis on the log-transform seems arbitrary and wrong.  Surely we are more interested in the curvature of the actual likelihood function.  What was Fisher's motivation for working with the score function and the Hessian of the log-likelihood instead?  Is the answer simply that, in the end, we have nice results from the log-likelihood asymptotically? E.g., Cramer-Rao and normality of the MLE/posterior.  Or is there a deeper reason?


Does there exist a differentiable function $f: \mathbb R \to \mathbb R$ such that its derivative $f'$ is nowhere continuous ?

Could someone give an example of a ‘very’ discontinuous derivative? I myself can only come up with examples where the derivative is discontinuous at only one point. I am assuming the function is real-valued and defined on a bounded interval.


So I rendered the animation png sequence, then I plugged the render results into the denoiser node and then in the composite node. But it only denoise the last frame of animation. How can I actually get the rendered png seq denoised? ?

After enabling Denoising Data pass, there are now two image outputs:  Image Noisy Image  Which should I use with the Denoise node?  doesn't cover it.


\documentclass[a4paper]{report}  \usepackage{mleftright} \usepackage{amsmath} \usepackage{amssymb} \usepackage{braket}  \begin{document}  \begin{align} \langle \hat{\widetilde{S_{\hat{a}}}}^{\, \, \, \mleft( 1 \mright) } \hat{\widetilde{S_{\hat{b}}}}^{\, \, \, \mleft( 2 \mright) } \rangle_{\ket{ss}} & = \langle \mleft( \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \hat{\mathbb{I}}^{ \mleft( 2 \mright) } \mright) \mleft( \hat{\mathbb{I}}^{ \mleft( 1 \mright) } \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \mright) \rangle_{\ket{ss}} \nonumber \\ & = \langle \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \rangle_{\ket{ss}} \, . \end{align}  \end{document}   produces the following output:   In fact, it creates a bunch of errors which seem to be due to using nested expressions of \widetilde, \hat, and such via the amsmath package. Curiously, those errors do not show up in my overall document.  Anyway, the same output is produces and as you can see, sigmas somehow show up at the S symbol although they are only used later in the line ...  Also, the equation reference parenthesis are right of the page limit in my overall document, which may not be so obvious here.  I tried the same thing without \mleft( and such, but I like it better this way.  EDIT: After properly reading the question that egreg linked to, this is what comes closest to the desired result for me:  \documentclass[a4paper]{report}  \usepackage{mleftright} \usepackage{amsmath} \usepackage{amssymb} \usepackage{braket}  \newsavebox{\accentbox}  \newcommand{\compositeaccents}[2]{%   \sbox\accentbox{$#2$}#1{\usebox\accentbox}}  \begin{document}  \begin{align} \langle \compositeaccents{\hat}{\widetilde{S_{\hat{a}}^{\mleft( 1 \mright) }}} \compositeaccents{\hat}{\widetilde{S_{\hat{b}}^{\mleft( 2 \mright) }}} \rangle_{\ket{ss}} & = \langle \mleft( \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \hat{\mathbb{I}}^{ \mleft( 2 \mright) } \mright) \mleft( \hat{\mathbb{I}}^{ \mleft( 1 \mright) } \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \mright) \rangle_{\ket{ss}} \nonumber \\ & = \langle \mleft( \hat{a} \cdot \vec{\hat{\sigma}}^{ \mleft( 1 \mright) } \mright) \otimes \mleft( \hat{b} \cdot \vec{\hat{\sigma}}^{ \mleft( 2 \mright) } \mright) \rangle_{\ket{ss}} \, . \end{align}  \end{document}   The sigmas have disappeared but through use of the saveboxes, the S operators look somewhat different than in other instances in the document, but it's good enough for me.

On  I've noticed a strange problem with nested \tilde and \breve commands, when amsmath is used.  In this code the X appears also in the output of the second and the third formula:  \documentclass{article} \usepackage{amsmath} \begin{document} \[ \breve{\tilde{X}} \] \[ \breve{\breve{{T}}\breve{{v}}} \] \[ \tilde{{\tilde{T}}{\tilde{v}}} \] \end{document}     If I don't load amsmath, the code works fine. This seems to be a bug in amsmath. How can it be solved?


A student prepares for an exam by studying a list of 12 problems. She can solve 9 of  them. For the exam, the instructor selects 7 problems at random from the 12 on the list  given to the students. What is the probability that the student can solve 5 of the 7  problems on the exam?   I am really confused by this problem. My first initial thought was to do:  (5 chose 7)(7 chose 0)/ (12 chose 7)  I am not 100% sure about this though.


I remember watching a series in the 80s about a car.  It wasn't Knight Rider and I don't think it was Automan.  It was a cop or detective-type guy who had a car which, when it went round corners, did so at right angles.  He always dreaded getting in the car, and when the car went round the corner he was thrown up against the window inside.  My brother and I always watched it but it wasn't on for long... and everyone I ask thinks I'm nuts!  Any ideas?

I remember one scene where the alien got shot. He pulled up his shirt and a blue grid (on black background) was there instead of regular skin, which then healed him.  The Movie "Starman" comes to mind, but I distinctly remember it as a TV-show, not a movie.


I'm trying to create an alert box to show some info, with background color and an icon to the left. With the help of this  I've figured out to come up with this: \documentclass[letterpaper,12pt,twoside]{report} \usepackage{graphicx} \usepackage{xcolor} \definecolor{warningbackground}{RGB}{252,226,158}  \usepackage{floatflt} \newcommand{\alertwarningbox}[1]{     \centering     \colorbox{warningbackground}{\parbox{400pt} {             \vskip 10pt             \begin{floatingfigure}[l]{50pt}                 \includegraphics[scale=1.0]{AlertWarning.pdf}             \end{floatingfigure}             #1             \vskip 10pt         }     } }   \newcommand{\alertwarning}[1]{     \vskip 10pt     \begin{floatingfigure}[l]{50pt}         \includegraphics[scale=1.0]{AlertWarning.pdf}     \end{floatingfigure}     #1     \vskip 10pt }  \begin{document}     Text...     \alertwarning{         Warning message Warning message Warning message Warning message Warning message Warning message Warning message Warning message Warning message  Warning message  Warning message .      }      Text...      \alertwarningbox{         Warning message Warning message Warning message Warning message Warning message Warning message Warning message Warning message Warning message  Warning message  Warning message .       } \end{document}   But, as you can see in the picture, when I put the picture and the text inside a colorbox, the content gets aligned to the right. How can I center the box? Or What is correct way to do this task.

I am writing an Article in LaTeX.  Please suggest me how to create a highlight boxes like the ones shown below in LaTeX:


How can I find out how many system are connected to the local network and how can I get all IP and mac address of these systems. Is their any command/package to show the IP details? Can I use this command/package in our Firewall(IP Corp onLinux OS) to block unauthorized systems?

How can I list all  and their associated  of the machines connected to my local network (LAN)?


Let $\theta$ be a parameter and $\hat{\theta}$ be an estimator for $\theta$.  I understand that the MSE of $\hat{\theta}$ can be decomposed into its bias and variance. That makes sense. What I don't see is where there is a trade off. A trade-off would suggest that all estimators have the same MSE and you can only get less variance by incurring higher bias and vice versa.  Can you please explain the mathematics behind it?

I'm trying to understand the bias-variance tradeoff, the relationship between the bias of the estimator and the bias of the model, and the relationship between the variance of the estimator and the variance of the model.               I came to these conclusions:                We tend to overfit the data when we neglect the bias of the estimator, that is when we only aim to minimize the bias of the model neglecting the variance of the model (in other words we only aim to minimize the variance of the estimator without considering the bias of the estimator too)       Vice versa, we tend to underfit the data when we neglect the variance of the estimator, that is when we only aim to minimize the variance of the model neglecting the bias of the model (in other words we only aim to minimize the bias of the estimator without considering the variance of the estimator too).   Are my conclusions correct?


I'm trying to schedule a batch file to run at start up. Here is my command:  schtasks /create /tn test /tr c:\simple.bat /sc onstart   simple.bat only writes the current time to a file:  time /t > now.txt   The task is created without issues, I see it when listing tasks via schtasks (it has status ready) and in the Task Scheduler Library in windows.  When running the batch file manually, everything is fine. However, when restarting, I see the batch is not running (no output file with the updated time) and when looking at the output of schtasks I see the status has changed to "Could not start":  TaskName                                 Next Run Time          Status          ======================================== ====================== =============== test                                     N/A                    Could not start   Any ideas? Thanks.

I wanted to run a .bat file in Windows task scheduler, so I opened it, added a new task, browsed to the bat file, and... nothing happened.   So I changed the timing to see if it'll run, and it didn't. Next I right-clicked on the task and chose "run", it didn't run. The file itself is only one line, basicly backups a folder to a another location. It runs fine when not in the scheduler.  When I asked on  they first said to come here and the other guy said to write:  cmd.exe /C completepathtobatchfile argstobatchfileifany   So I wrote:   cmd.exe /C k:\backup.bat    and it didn't work. What do I have to change to make it work?


What is the correct response to the following question: Ten divided by five is not two?  1) Yes, it is.  2) No, it is.  Intuitively I would say "Yes, it is", but then I thought about it in the following way:  If one asks "Ten divided by five is two?" I would say "Yes, it is", but if the person asks "Ten divided by five is not two?" then I would say "No, it is".  So I think my intuitive answer is wrong, but I am not sure.

I faced a problem to answer a negative question, for example, when someone asks you:      Don't you have any money?   It's a yes/no question but how should one answer the question without ambiguity?  When you answer "yes", does it mean "yes, I don't have any money"? or the other way "Yes, I do have money"? the questioner may think you are agreeing to the negative, that yes, you do not have any money.  I know it's better to answer with "on the contrary" but is it possible to answer yes or no?


Is there a shortcut (key combination) in emacs to repeat the second last command? Or third last command and so on? I know that Ctrl + x +  z   can be used to invoke the last command, but could not find a key combination for others!

Frequently, I've dug into apropos and docs looking for something like the following only to give up to get back to the task at hand:  (repeat-last-command)  do the last C- or M- command I just executed (to be rebound to a fn key)  or sometimes the related:   (describe-last-function)  what keystroke did I just mistakenly issue, the effect of which I'd like to add to my bag of tricks. describe-key is close, but requires knowing what I typed.   Am I simply asking too much from my trusty sidekick?


Can two distinct users legally and ToS-compliantly use the same Windows 10 machine simultaneously (i.e. both being logged in)? If it helps, allow for remote connections.  An ideal answer would be supported by documentation in case the answer is "No".

A friend asked me if it is possible to have two screen/keyboards/mouse connected to one computer, and allowing two users to use the computer as if they where using two different computers (one sessions for each input/output)  Is it possible?


In terminal, I find this and it does not respond well to my orders, what should I do?     To run a command as administrator (user "root"),    use "sudo <command>".    See "man sudo_root" for details.   This message is found in the beginning of terminal.

I've downloaded a driver for a video card (*.run) and tried to install within a terminal. When I started the installation process I got this error: ERROR: nvidia-installer must be run as root. I'm logged in with my own profile.


On my workstation using several browsers, JavaScript's new Date().toString() method returns a string such as:  Thu Aug 15 2019 17:34:40 GMT-0500 (Central Daylight Time)   I'm interested in how it knows about "Central Daylight Time"?  I know how to get the offset (e.g. -300) using , but I don't see any documented approach to get the named time zone.  Is parsing the output of toString() really the best approach?

Is there a standard way for a web server to be able to determine a user's timezone within a web page?   Perhaps from an HTTP header or part of the user-agent string?


My Original question:     When I run sudo su my zsh prompt changes back to Bash. How can I make Zsh the default shell for the root user?   My answer about duplicate :  The question about when a post is considered as duplicate is debating here :   I quote the first paragraph of the first answer :      Most opinions I have seen about this say that questions are duplicates, not answers. Therefore, questions should only be closed as a duplicate when they are the same, not because the answer to one is also the answer to the other.   And then the first words after :      I, however, disagree.   You are free to see the post to read the arguments of this user.  I personally, as "most opinions" think that questions are duplicates and no answers because i had never find an answer to my particular question with the post :   And what a coincidence the user that i quoted is one of the users who marks my post as duplicate.   I tried to defend myself but probably in bad way. So please stop down vote my post and please understand that perhaps some people just want to extend already default shell to all users and others want make a particular shell to be default. This is not the same search and i think this can help the community.

Is there a way to set fish as the default shell in ubuntu netbook remix? I put in my .bashrc to run fish, which works fine, but ubuntu recognizes it as fish running inside bash, which means that when I try to close the shell it warns me that a task is still running.  It doesn't pop up as a new application, so I can't pin it to my bar like a normal app.


My work is 17 km (10.5 miles) from home and I am wondering if it's possible to commute daily by bike. I live in the Netherlands so the roads are bike-friendly. Google predicts it takes 52 minutes (one-way).Do you think it's an accurate prediction?  I am 25 years old, weigh 80 kg (176 pounds or 12.5 stone), and I am 183 cm (6 foot 0 inches) tall.

Currently, on every other day I commute to work which is a distance of 18km each way. I enjoy this ride but next year I may be moving to a place which will be about 35km from work. Questions:  1) Would it still be reasonable to commute this kind of distance each way once I have moved?  2) Google maps estimates that this distance would take 2 hours to complete. Would it be possible (depending on the bike and fitness) to do this distance in about an hour?


This may seem like a pretty basic question, but I am struggling to find a nice way of expressing $(1+x+\cdots+x^{n-1})^2$ where $n\in\mathbb{Z}_{\geq 2}$. Plugging in some numbers yields a clear pattern,  $(1+x+\cdots+x^{n-1})^2=1+2x+\cdots+nx^n+\cdots+2x^{2n-3}+x^{2n-2}.$  However, I can't seem to find a formal expression of this, or a proof. Can anyone point me in the right direction?

Question: What is an easy or efficient way to see or prove that   $$ 1+2a+3a^2+\cdots+na^{n-1}+(n+1)a^n+na^{n+1}+\cdots+3a^{2n-2}+2a^{2n-1}+a^{2n}\tag{1} $$   is equal to   $$ (1+a+a^2+\cdots+a^n)^2\tag{2} $$   Maybe this is a particular case of a more general, well-known result?   Context: This is used with $a:=e^{it}$ to get an expression in terms of $\sin$ for the .  Thoughts: I thought about calculating the coefficient $c_k$ of $a^k$. But my method is not so obvious that we can get from $(1)$ to $(2)$ in the blink of an eye.  $\mathbf{k=0}$ : clearly $c_0=1$.  $\mathbf{1\leq k\leq n}$ : $c_k$ is the number of integer solutions of $x_1+x_2=k$ with $0\leq x_1,x_2\leq k$, which in turn is the number of ways we can choose a bar $|$ in $$ \underbrace{|\star|\star|\cdots|\star|}_{k\text{ stars}} $$ So $c_k=k+1$.  $\mathbf{k=n+i\quad(1\leq i\leq n)}$ : $c_k$ is the number of integer solutions to $x_1+x_k=n+i$ with $0\leq x_1,x_2\leq n$, which in turn is the number of ways we can choose a bar $|$ in $$ \underbrace{|\star|\star|\cdots|\star|}_{n+i\text{ stars}} $$ different from the $i$-th one from each side. So $c_k=(n+i)+1-2i=n-i+1$.


Here is the question $f:X \rightarrow Y$ and $g: Y \rightarrow Z$ are functions and $g \circ f$ is surjective, is $g$ surjective?  My proof: If $g \circ f$ is surjective than $\forall z \in Z \; \exists x \in X \; \mid (g \circ f)(x)=z  $ Suppose $f$ is surjective, than $\forall y \in Y \; \exists x \in X\; \mid f(x)=y$. By def. of $(g\circ f)(x)=z$ we have $g(f(x))=z$ and since $f(x)=y$ than we have $g(y)=z$ which implies surjectivity therefore $g$ is surjecive.  Is this the correct way to prove that $g$ is surjective? Or can I not assume surjectivity on $f$

The Problem:  Let $X, Y, Z$ be sets and $f: X \to Y, g:Y \to Z$ be functions.  (a) Show that if $g \circ f$ is injective, then so is $f$.  (b) If $g \circ f$ is surjective, must $g$ be surjective?  Where I Am:  So, I really have trouble with these, for some reason. I can draw pictures and make sense of the problems, but writing down proofs is very difficult for me.   Basically, for (a), I ended up with some complicated statement involving an implication implying another implication and then tried to derive a contradiction. It just got so convoluted that I couldn't make sense of it anymore, and I know there's a quick, elegant way to show it.  For (b), I know that $g$ need not be surjective. Once again, though, proving it directly from definitions has given me a bit of a headache.  Any help here would be appreciated. Thanks in advance.  The Proofs!  Ok, I did it. Thanks for the help, everyone! Let me know if there's anything wrong with these proofs, or if they could bet any better.  (a) Suppose $f$ is not injective. Then $$ f(x_1)=f(x_2) \implies x_1 \ne x_2 \text{        }(*).$$ Let $f(x_1)=y_0=f(x_2)$ and let $g(y_0)=z_0$. Then $$ (g \circ f)(x_1) = (g \circ f)(x_2) = g(y_0) = z_0. $$ Since $g \circ f$ is injective, $$ (g \circ f)(x_1) = (g \circ f_2) \implies x_1 = x_2. $$ However, this contradicts $(*)$. Therefore, $f$ must be injective.  (b) Suppose $g$ is not surjective. Then  $$ \forall y \in Y, \exists z \in Z \text{ such that } g(y) \ne z \text{         }(**).$$  Since, $g \circ f$ is surjective,  $$ \forall z \in Z, \exists x \in X \text{ such that } g(f(x)) = z \text{       } (***). $$  Let $f(x) = y$. Then,  $$ g(f(x)) = g(y) = z. $$  Because of $(***)$, this is true for all $z \in Z$, which contradicts $(**)$. Therefore, $g$ must be surjective.


In the film Star Wars: The Force Awakens we learn that Kylo Ren      Is Anakin Skywalker's grandson, his predecessor    We also learn that he was trained by       Luke Skywalker   Surely his master would have told him about his predecessor, how he was seduced by the Dark Side and how he eventually returned to the Light Side of The Force?   And yet we hear him say he wants to finish what his predecessor started.  What does Kylo Ren know?

It seems Kylo has an obsession of Darth Vader and has an interest in the dark side because of it.   Does he not realize that Darth Vader turned good and helped destroy the Empire (Spoilers?)? I feel like Kylo would've seen how much better the Light Side was as it was able to turn Vader from the Dark Side if he had known this.


In my theme’s preprocess node function i’m trying to create a new variable by combining 2 existing fields, both of which are text strings.  pseudo code is this:   $teachers_name = $firstname + $lastname;  When looking at a print out of the Teacher object using Devel, i see the field first name is an array, structured like this…  field_first_name     und         0             safe_value ‘Lisa’   but so far it’s not working at all. i’m not accessing the variables correctly.   function myTheme_preprocess_node(&$variables){     if($variables['type']=='teacher') {         $variables['teachers_name'] = $variables['field_first_name’][‘und’][0]    [‘safe_value’];     }   how can i access the text string of field 'first name'? thanks!

Im sure this is an easy question, just not for me because of lack of experience with the Drupal preprocess hooks. I am removing the standard "Read More" links from my content. I want the ability to replace them with a css button. I can do that, the tricky part come when I want to use a FIELD from the CONTENT TYPE, as the name for the button.   function bootstrap_preprocess_node(&$variables) {   unset($variables['content']['links']['node']['#links']['node-readmore']);     $variables['newreadmore'] = t(' '.$readmoretext.' ',    array(     '!title' => $variables['node_url'],   ) ); }   My question is how can i HOOK into the node and retrieve the field for my variable $readmoretext  Thanks!


I looked at this beautiful picture for 3 hours, and I would really like to how to this with tikz. If someone have an idea.

Say I want to include geometry graphics such as the following in a document:   I don't merely want to import preexisting figures, I want to be able to draw my own corresponding to a solution I may write up. Is there a package or something that allows one to do this relatively easily?


My dataset contains a single class, which has noisy examples. Up to now I have been converting this to a binary classification problem and using logistic regression, however this does not feel correct, as the negative class has data which is not truly part of a single class, it is just not in the "positive" class. I stumbled upon and tried  with little success (in terms of classification performance). What are some possible techniques for learning the distribution of just one class? Am I formulating the problem in the correct manner? My specific dataset are document vectors created by a doc2vec model. EDIT: Adding more information based on comments. The task is to classify webpages that will be relevant for certain advertisers based on past performance. We have a positive class, where we know there was a positive interaction. I have been training an LR model based on this positive interaction and a sample of pages where no interaction occurred. EDIT 2: Again based on the comments I would like to provide a simpler contrived example to see if my thinking about this is wrong. Let's say we want to classify webpage as being about football, we could:  train a classifier of football VS non-football train a model to learn the distribution of football and treat all other articles as outliers  Is the second option an incorrect way of framing this problem?

I have to deal with a text classification problem. A web crawler crawls webpages of a certain domain and for each webpage I want to find out whether it belongs to only one specific class or not. That is, if I call this class Positive, each crawled webpage belongs either to class Positive or to class Non-Positive.  I already have a large training set of webpages for class Positive. But how to create a training set for class Non-Positive which is as representative as possible? I mean, I could basically use each and everything for that class. Can I just collect some arbitrary pages that definitely do not belong to class Positive? I'm sure the performance of a text classification algorithm (I prefer to make use of a Naive Bayes algorithm) highly depends on which webpages I choose for class Non-Positive.  So what shall I do? Can somebody please give me an advice? Thank you very much!


Prove that $$ \left( \frac{a+b+c\cdots k}{n} \right) ^{a+b+c \cdots k} \lt a^a b^b c^c \cdots k^k $$ We can prove that $$ (1+x)^{1+x} (1-x)^{1-x} \gt 1$$ (if $x \lt 1$) and from there by assuming $x = \frac{u}{z}$ and then $u+z =a$ and $u-z =b$ we will have $$ \left( \frac{a+b}{2}\right)^{a+b} \lt a^a b^b$$ but how to extend this result upto $n$ number of terms?

If $a_1,\dots,a_n$ are all unequal positive quantities, then prove that: $$\prod_{i=1}^n a_i^{a_i} > \left(\frac{\sum_{i=1}^n a_i}{n}\right)^{\sum_{i=1}^n a_i}$$ No other conditions are given. I tried to solve it using logarithms, but I could not understand how can I prove $${a_1\log a_1}+{a_2 \log a_2}+\dots+{a_n\log a_n} > {(a_1+\dots +a_n)}  \left(\log(a+\dots+a_n)-\log(n)\right)$$ And please tell me, is there any standard method to solve this kind of problems?


I tried using the result that if p is the least prime dividing the order of G, then any subgroup of index p is normal in G. So a subgroup H of order 3 is normal in G. Then, if there was a normal subgroup K of order 2 then G=HK. But how do I get a contradiction?

Prove that every non-abelian group of order $6$ has a non-normal subgroup of order $2$. Use this to classify groups of order $6$.   I proved that every non-abelian group of order 6 has a nonnormal subgroup of order 2, but then how can I use this to classify groups of order 6?


I made a city that I need to export into unity, I am unable to get with the textures.

I used node textures in a mesh I exported to .FBX.  I then imported it into Unreal Engine 4 and it didn't import any textures; I clicked the Upload Textures option in Unreal Engine.  Is there something I'm doing wrong or is it Blender?


I want my h3 element to be vertically centred within the div element. I tried several solutions but any of those didn't work. Could anyone figure it out for me where I am doing wrong? Below is my html and CSS code snippet. HTML:

This is a text

  CSS: #test{     height: 100px;     background-color: cadetblue;     text-align: center; } #test_h3{     vertical-align: middle; }    #test{     height: 100px;     background-color: cadetblue;     text-align: center; } #test_h3{     vertical-align: center; }

This is a text

I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. I found some solutions, but all of them are missing Internet Explorer 6 support.
Div to be aligned vertically
   How can I center a div vertically in all major browsers, including Internet Explorer 6?


I am looking for a summary term for a collective of groups. Specifically, I would like to make a general statement that people are nested in groups, which in turn are nested in (?).   Some examples to illustrate:   Students are nested within classes (groups), which in turn are nested within a school (?).  Students are nested in sorority chapters (groups), which in turn are nested within a sorority (?).  Employees are nested in departments (groups), which in turn are nested within an organization (?).    I can summarize classes, departments, and sorority chapters with the summary term "group".   I have tried summarizing schools, sororities, and organizations with the summary terms "collective" and "society", yet I am not satisfied with either.    "Collective" appears to imply a common goal. While departments in an organization likely pursue a common goal (e.g., improve company performance), I feel the term "collective" draws away attention from the fact that departments may also have competing interests. I am thus looking for a more neutral term than "collective". "Society" seems unsuitable because its meaning is already : "A society is a group of people involved in persistent social interaction, or a large social grouping sharing the same geographical or social territory, typically subject to the same political authority and dominant cultural expectations." All people I talked to therefore found it confusing to refer to an organization as society.    Edit 1. I am hoping to find a term that is intuitive and descriptive. For example, I find that collective has an intuitive meaning (collection of items/people). While I like super-group, I feel the term does not convey the same intuitively graspable description for people who never encountered this term in mathematics.   Edit 2. Subgroup appears more intuitively graspable. However, I would like to start at the group level and find an overarching term from there (rather than going from group to subgroup).

To expand on the title slightly: all of the groups to which an item belongs directly or indirectly? That seems to make "parent groups," my first choice, ill-fitting.   The key concept here is membership, but that term generally refers to the items in the group, not the groups themselves.  A bit more explanation:  An item's relationship to a group may be direct or indirect because groups are hierarchical. The term would describe all of the relevant groups in the hierarchy.  An example:  Fuji is an apple. Apples are fruit. Fuji belongs to apples and fruit.  The phrase I need to construct is along the lines of: Fuji and "the groups to which it belongs."  Edit  As Barrie pointed out, my example involves categorical relationship, but that won't necessarily be the type of membership I'm referring to. The membership is arbitrary and changeable.  Edit 2  My example caused more confusion than good. The best metaphor for what I'd like to express is: a child has parents and grandparents, who are collectively his ancestors. I want to say: a user has groups and (super?) groups, which are collectively _?_.


I am learning the wildcards.  I see that  ls *[0-9]* would list all the files/directories with numbers in its names so shouldn't ls *[^0-9]* list all the files/directories without numbers in the middle of its name? I see that some of the files that command listed has numbers.   file1.txt and file1~ were the once that were listed.

ls -d *e* prints out all files containing an "e" somewhere in it. But the opposite, ls -d *[!e]* does not seem to work. Why exactly is that?  is it because ls takes * as its own argument and expands all the files?  I understand I can do: ls -d !(*e*) (in Bash with extglob set, or in ksh).


I wasn't sure, so I looked it up, and it would seem it's specific to single words.           1.) the derivation of a word.   Synonyms: word origin, word source, derivation, origin.      2.) a chronological account of the birth and development of a particular word or element of a word, often delineating its spread from one language to another and its evolving changes in form and meaning.   Synonyms: word history, word lore, historical development.      3.) the study of historical linguistic change, especially as manifested in individual words.   Obviously the following sentence would be easily understood, but is it technically correct?  Or is there a better way to ask the following question?  “What is the etymology of the Baseball term 'meat hand'?”  As in a first-use, or how the phrase came to be, or what made it popular – etc.  What I think of as “etymology”, but perhaps that word is more technical, and specific to the linguistic breakdown and origins of individual words.

I have always heard the term used in referring to a single word. When browsing questions on this site, I've seen it used applied to entire phrases, and have suppressed the compulsion to edit them and replace the term with origin.


everyone. Recently, I have been learning how to develop a function to delete a pointer safely. However, something weird happened when I made my safe_delete() code shown below. #include <iostream> using namespace std;  template <class T> void safe_delete(T* ptr) {   delete ptr;   ptr = NULL; }  int main() {   int var = 10;   int* ptr = &var;   safe_delete<int>(ptr); }  Running the code in repl.lt (I am afraid that it might cause a memory leak), here is what I get: munmap_chunk(): invalid pointer exited, aborted  What does the above error mean? I currently guessed that munmap_chunk() is some function used in the implementation of delete. The above source code is taken from stack overflow's answers. Something is weird. I just added templates to the function, which I believe is correct. Can anyone tell me why is this error happening?

Ignoring programming style and design, is it "safe" to call delete on a variable allocated on the stack?  For example:     int nAmount;    delete &nAmount;   or  class sample { public:     sample();     ~sample() { delete &nAmount;}     int nAmount; }


Let $S_n = \sum_{i = 1}^n \frac{i^k}{n^{k+1}} $ . For what values of $k$ the series $S_n$ is convergent and what is the value of convergence ? I'm really unable to understand $S_n$ because I haven't seen any series which is similar to that , so applying tests isn't possible for me . Also I've searched over the internet but didn't find any useful result .

By considering:  $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^1}{n^{2}} = \frac 1 2$$ $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^2}{n^{3}} = \frac 1 3$$ $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^3}{n^{4}} = \frac 1 4$$  Determine if this is true: $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}} = \frac 1 {{m+1}}$$  If it is, prove it.  If it is not, evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{{m+1}}$.


I understand that when an EC2 instance is stopped and restarted, the IP address associated with the instance may change, and that to avoid this, one should assign an Elastic IP to the instance. However, I did not know this from the start, so right now I have a running EC2 instance that does not use an Elastic IP. I would like to transfer the current IP address to a new EC2 instance in the same region but a different availability zone (I want to keep using this current IP address because it is whitelisted in many external places, and whitelisting a new IP address may be difficult). Is that somehow possible?

I currently have an ec2 "t2.nano" instance up and running. I would like to switch to a "t2.micro". In order to do that, I need to stop the instance. But I would lose my IPv4 address in the process. And I do not want that (because I have several ssh tunnels up and running from rasps in the wild that are currently hard coded to connect to this IPv4 address). I decided to create an Elastic IP address. But I understand that by creating an Elastic IP address and assigning it to my current ec2 instance, I would lose my current IPv4 address too. Is it possible to create an Elastic IP address from the current IPv4 address of my ec2 instance? If so, how can I do this operation?


I bought a new VPS and using WHM i created a cpanel account. After doing some research about why are the emails were going on spam without any reasons and by this i mean :   1. No blacklisted IP,  2. No blacklisted hostname,  3. Normal emails with only text, not html,  4. SPF, DKIM and PTR records configured .   If there is any other reasons for this please help me .

This is a  about how to handle email sent from your server being misclassified as spam.  For additional information you may find these similar questions helpful:                    Sometimes I want to send newsletters to my customers. The problem is, that some of the emails get caught as spam messages. Mostly by Outlook at the client (even in my own Outlook 2007).  Now I want to know what should be done to create "good" emails. I know about reverse lookup etc., but (for example), what about a unsubscribe link with an unique ID?  Does that increase a spam rating?


E: dpkg was interrupted, you must manually run 'dpkg --configure -a' to correct the problem.  E: _cache->open() failed, please report.

I was running an upgrade with the apt-get command, and it was taking an exceptionally long time because half way through my ISP hit me in the face with their fair usage policy.   After sitting outside & watching the rain for awhile my electronics regained consciousness, so I went back to complete the upgrade and my terminal scolds me with   "E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to correct the problem."   The last bit of legible info was all this:  Installing (ri/RDoc) documention for (stuff and such) ERROR:  Could not find a valid gem 'watobo-0.9.8.724.gem' (>= 0) in any repository rm: cannot remove `watobo-0.9.8.724.gem': No such file or directory  Setting up metasploit (4.3.0-bt1) ... Upgrading Pre-Existing Installation... /opt/metasploit/postgresql/scripts/ctl.sh : postgresql  (pid 1191) already running prosvc is running metasploit is running [*] [*] Attempting to update the Metasploit Framework... [*]   So on it goes for miles, talking about gem caches, rubies, & stuff I wish I had. All up until:  A    lib/gemcache/ruby/1.9.1/gems/state_machine-1.1.2/gemfiles/active_record-2.1.2.gemfile.lock   ...and there it has sat, all night.    If I stop it, will I still get the dpkg error (on the off chance that I won't), or if so what do I need to to resume using apt-get commands and its Super Cow Powers?


I am writing a module that gives this option to users to put comment on each paragraph.  So I have added a new field to my comment table, called "paragraph_id".Also in comment form I have added a new field which asks users which paragraph do they want to put comment on.  I have done some changes to node.tpl.php. This is part of it:  <div class="content clearfix"<?php print $content_attributes; ?>> <?php   // We hide the comments and links now so that we can render them later.   hide($content['comments']);   hide($content['links']);   $paragraphs = explode("
",render($content));   $number = count($paragraphs);   if($teaser){      print render($content['links']);    }   if($page){           $node_number=$node->nid;    print render($paragraphs[0]);   for ($i=1;$i<$number;$i++) {      print render($paragraphs[$i]);        Put comment for Paragraph <?php echo $i?>
          <?php      }    ?>   <?php print render($content['comments']['comment_form']);   so you can see that there is a link under each paragraph that when they click on it, it will take them to the comment form. So now I want to show the comments that belong to each paragraph under that paragraph.  When I use this:   krumo($content['comments']['comments']);  This is part of what I see:     ...(Array, 11 elements)    #sorted(Boolean ) TRUE    22(Array, 13 elements)    26(Array, 13 elements)    25(Array, 13 elements)    28(Array, 13 elements)   when I check the comment table, I find out that 22,26, 25, .. are cid numbers from comment table. And if I click on for example 22, this is part of what  I will see:      #pre_render(Array, 1 element)     #entitly_type(String, 7 characters ) comment     #bundle (String, 20 characters ) comment_node_article     links (Array, 4 elements)     #view_mode (String, 4 characters ) full     #theme (String, 21 characters ) comment__node_article     #comment (Object) stdClass     #node (Object) stdClass     #language (String, 2 characters ) en     #prefix (String, 24 characters )      #weight (Integer) 0     #children (String, 1520 characters ) <div class="comment comment-by-node-author comm...     #printed (Boolean) TRUE   And if I click on #comment, this is what I will see:       cid (String, 2 characters ) 22       pid (String, 1 characters ) 0      nid (String, 2 characters ) 22      uid (String, 1 characters ) 1      subject (String, 1 characters ) 1       hostname (String, 9 characters ) 127.0.0.1       created (String, 10 characters ) 1410041425    changed (String, 10 characters ) 1410041423     status (String, 1 characters ) 1     thread (String, 3 characters ) 01/     name (String, 6 characters ) gbi222     mail (String, 0 characters )     homepage (String, 0 characters )     language (String, 3 characters ) und     **paragraph_id (String, 1 characters ) 1**   So for each paragraph , I need to check the paragraph_id and if the number of the paragraph number is equal to the paragraph_id, show that comment under that paragraph.  so after print render($paragraphs[$i]); in my code, write:         if($i==($content['comments']['comments']['22']['#comments']->paragraph_id))            show the comments that its cid is 22.   So now my questions are:  1) How can I say that if the above equality is true, show the comment subeject, author, body, ... for that comment?Because if I write:  $content['comments']['comments']   it will show all the comments.  2) In this example I knew the cid number of that comment, which was 22, so what can I write instead of '22', in           if($i==($content['comments']['comments']['22']['#comments']->paragraph_id))  so it means like  any number, so it will do that comparison for all the comments(with their cid number)?

In node.tpl.php, I have done some changes, like creating an array of paragraphs:      $paragraphs = explode("
",render($content));   So, I have a for loop for showing the paragraphs, like:  $number = count($paragraphs); if($page){   print render($paragraphs[0]);   for ($i=1;$i<$number;$i++)       {          print render($paragraphs[$i]);        Put comment for Paragraph <?php echo $i?>
 <?php  } ?>     <?php print render($content['comments']); ?> <?php }?>   As you can see I want to create a hyperlink under each paragraph, so when user click on it, they can put comment on the paragraph, But right now, when they click on the hyperlink, it will  jump to the end of the page, which has the comment form.  If you check the CommentPress website, in the right column, you can see for example, it is said: 5 Comment on Paragraph 1, and when you click on it, it will show the comments and the comment form under that link, I want to have the same thing, I mean, when users click on the link under each paragraph, the comment form displays under that link instead of jumping to the end of the page.


I have recently changed the title of my website and whenever I search it I get the previous one only but on search with the specific keywords change I have recently made I get the correct output which I have changed Why is that and will I get punished for this? And is it possible to remove the old one and replace it with the new one

I changed the title and meta description of a web page.  It got re-indexed but still it shows in search results with the old title.  Why would this happen and how would we resolve it?


I want to have a text box oriented at an arbitrary angle. I know that I can rotate a text box relative to a current orientation, but can I specify the angle of the final orientation? I know that this information exists in Illustrator because if I turn smart guides on and perform a free rotation, a context box tells me the current angle. I would like to be able to do the same thing for a line.

I have a "rotation" issue with Illustrator. I've rotated some shape which has no horizontal component which I could align to guide, so I have no idea how to rotate the shape back to 0 degrees. In the case of multiple shapes (I've rotated letters) I have a problem to align them back.  Any suggestions to solve the problem?  AI CS6


Could someone please clarify the difference between these seemingly interchangeable groups? (quantitative,qualitative) vs (discrete,continuous).   Obviously they are not, but I cannot seem to pinpoint the reason why they are different inside my head. I am only a freshman college student so forgive my ignorance.  It would seem that discrete is kind of similar to qualitative, where as continuous is kind of similar to quantitative.  Are (quantitative,qualitative) and (discrete,continuous) just synonyms for each other or is (discrete,continuous) a subset of (quantitative)

One thing that has always tripped me up when trying to learn new methods in statistics is understanding what type of features/variables can this method be applied to.  The variable types that especially trip me up are   Discrete Continuous Categorical Nominal Ordinal   What are some examples and simple explanations of these and other commonly used variables types.


When I run sudo apt-get update  I get this error:     **404  Not Found [IP: 91.189.95.83 80]**     Err:5 http://in.archive.ubuntu.com/ubuntu focal InRelease                                Could not connect to in.archive.ubuntu.com:80 (2403:8940:ffff::f). - connect (113: No route to host) Could not connect to in.archive.ubuntu.com:80 (103.97.84.254), connection timed out     Err:6 http://in.archive.ubuntu.com/ubuntu focal-updates InRelease       Unable to connect to in.archive.ubuntu.com:http:     Err:7 http://in.archive.ubuntu.com/ubuntu focal-backports InRelease       Unable to connect to in.archive.ubuntu.com:http:     Reading package lists... Done     E: The repository 'http://ppa.launchpad.net/webupd8team/java/ubuntu focal Release' does not have a Release file.     N: Updating from such a repository can't be done securely, and is therefore disabled by default.     N: See apt-secure(8) manpage for repository creation and user configuration details.`  Please help to fix it.

I just installed a fresh version of Ubuntu 19.10 today, and the first thing I decided to do was to install GNU Screen, using sudo apt-get install screen. my output was: Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package screen  I figured the package archives were not quite updated as it was a clean install so I tried sudo apt-get update. This is what I got: Get:1 http://security.ubuntu.com/ubuntu eoan-security InRelease [97.5 kB]       Err:2 http://au.archive.ubuntu.com/ubuntu eoan InRelease   Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Could not connect to au.archive.ubuntu.com:80 (202.158.214.106), connection timed out Err:3 http://au.archive.ubuntu.com/ubuntu eoan-updates InRelease      Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Err:4 http://au.archive.ubuntu.com/ubuntu eoan-backports InRelease   Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Fetched 97.5 kB in 31s (3,106 B/s) Reading package lists... Done Building dependency tree        Reading state information... Done All packages are up to date. W: Failed to fetch http://au.archive.ubuntu.com/ubuntu/dists/eoan/InRelease  Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Could not connect to au.archive.ubuntu.com:80 (202.158.214.106), connection timed out W: Failed to fetch http://au.archive.ubuntu.com/ubuntu/dists/eoan-updates/InRelease  Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) W: Failed to fetch http://au.archive.ubuntu.com/ubuntu/dists/eoan-backports/InRelease  Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) W: Some index files failed to download. They have been ignored, or old ones used instead.  I'm really not sure why it would be doing this, other than maybe some first-use hiccups? The computer is definitely connected to the internet, as I am writing this from that machine, and I have tried running the commands after rebooting and it still gives the errors. I can't seem to be able to connect to au.archive.ubuntu.com at all. ping au.archive.ubuntu.com just sits there without a response. If anyone could help, that would be great! If any extra information is required I'd be happy to edit it into the question.


Please stop marking this question as a duplicate, it's not a duplicate. Thanks. Consider the sequence of a, followed by \x1b[D ("cursor back"), followed by b. This would produce an output of just b.  I am looking to experiment with and create TUI applications (examples: less, vim), e.g. using ncurses style libraries or with raw application of escape sequences. I've found that as a tmux user, tmux offers a very useful capture-pane feature which could be a good basis for a test framework that can use this as a form of "screenshot" functionality for test verification purposes. For example, rather than manually testing the output for correctness and, say, establishing a test that runs the program under test for a specific window size and then comparing the output with a rigid string compare, I could instead run it under tmux through a wide range of window dimensions and check the rendered state to satisfy requirements in a practical way. Anyway, the point is that this seems to be the only way I know of to "resolve" a terminal byte stream into a terminal screen buffer. As great and versatile as tmux is, I'm somewhat hoping for a tool that provides this specific capability. Since I read some more today about what ptys are and how they work , it does seem to me that this aspect of the system is in the purview of the terminal emulator, and something like tmux is rather unique in that it has to do it while not being a GUI application (which is a plus here).

I am creating a terminal application that writes stuff to the terminal. And in order to test it, I really should test what's actually displayed in the terminal. Is there a way to read the data that's actually displayed in the terminal somehow?   The terminal must be some file somewhere or something, so there must be some way to read what's there.  cat /dev/tty   seems to give me a stream of data that's in there..But I don't want to see key strokes, just what I have written.


I tried to discuss two cases when $m$ is even and odd. By discussing both cases, $m$ must be odd, and by using the fact that every odd perfect square is congruent to $1$ modulo $8$.  It is clear that $n=3$ and $m=3$ is a solution, and it seems that it is the only one? I tried to prove that the equation admits one solution, but I failed.  Can I get some help, and thanks in advance.

Suppose $k\in\mathbb N$ and suppose $2^k+1=u^2$ and $2^k-1=v^2$ for some $u,v\in\mathbb N$. I have to prove that the first case implies $k=3$ and the second case implies $k=1$. Also, for the second case it is hinted to use the fact (lemma) that if $n$ is odd, then $n^2\equiv1 \pmod 8$, but I suppose it could be used for the first one as well. My progress so far:     First question:      Suppose $u$ is even, then $u=2t$ for some $t\in\mathbb N$, thus $u^2=4t^2=2^k+1$. Notice that two divides the left hand side of the equation, therefore it also divides the right hand side. Since it divides $2^k$ for any $k\ge1$, it must also divide $1$, contradiction. So $u$ is odd and therefore $u^2\equiv1\pmod 8$. Thus there exists an $m\in\mathbb Z$ such that $u^2=8m+1=2^k +1$. Thus $2^k=8m$, therefore $k\ge3$.   I am stuck at this point, however. I suppose setting $k>3$ and finding a contradiction would be a possible method, but I do not know what $k>3$ actually has to offer to solve this problem. No other method I think of gets me anywhere, either. I guess I could try to show that $2^k+1$ cannot be a square for $k>3$. Perhaps I could use the fact that $u^2-2^k=1$ or that $\gcd(u^2,2^k)=1$.     Second question:      The same reasoning can be applied to show that $v$ has to be even. Therefore, according to the lemma proposed above, $2^k-1=v^2\equiv1\pmod 8$. This implies $2^k\equiv2\pmod 8$. For any $k\ge3$ there exists some $t\in \mathbb N$ such that $2^k=8t$, therefore $2^k\equiv0\pmod 8$, which leads to a contradiction. Checking for $k=1,2$ leads to the conclusion that $k=1$ is the only possibility.   I think I have actually figured out this proof while writing down the progress I already have made, but for the sake of completeness and to check it's correctness I will leave it here.