Ramanujan's Summation says that the sum of all integers is -1/12... 1 + 2 + 3...=-1/12.  If we define group G to be group of all positive integers, then the group contains all positive integers. Since -1/12 is negative, and the group only contains positive integers, -1/12 is not an element of the group.  Therefore, Ramanujan's Summation is wrong.

I'm reading about zeta-function regularization in physics and I have some mathematical doubt.  I understand  that, since a sum of infinite terms is not well defined in a field, a series that is considered divergent in the  usual meaning  can have a ''value'', defined in some less conventional way.   The  is one of such ways that, as an example, assign the value $-\frac{1}{12}$ to the infinite series  using the fact that the zeta-function $\zeta(s)$ is the analytic continuation of the series $\sum_{n=1}^\infty n^{-s}$, and $\zeta(-1)=-\frac{1}{12}$.  But how we can be sure that there does not exists other possible ''regularizations'' that gives different values to the same series?   And, if more than one value does exist, there is some  criterion to select between them?  Or the zeta-function regularization is preferred only for physical motivations (because the experiments confirm its values)?  On the web I've found a lot of posts less or more reliable about this topic, someone knows a reference to a well defined axiomatic approach to the problem of the value of divergent series?


Picture this: I'm playing a , who have the Sunlight Sensitivity trait (Volo's, p. 119)     You have disadvantage on attack rolls and Wisdom (Perception) checks that rely on sight when you, the target of your attack, or whatever you are trying to perceive is in direct sunlight.   Now, I assume from that wording that a normal "bright light" isn't enough - has to be direct sunlight. Except then we get something like , which not only creates a giant mah lazor, it also creates actual sunlight. (PHB, p. 229)     For the duration, a mote of brilliant radiance shines in your hand. It sheds bright light in a 30-foot radius and dim light for an additional 30 feet. The light is sunlight.   So far so good, it sounds like standing next to (or being, come to think about it) the caster while he's doing his thing is a bad thing for my eyes.  Except now we come to the 's level 20 feature, Holy Nimbus (PHB, p. 86):     At 20th level, as an action, you can emanate an aura of sunlight. For 1 minute, bright light shines from you in a 30-foot radius, and dim light shines 30 feet beyond that.   Here, the light is also called sunlight, but it's in the portion of the rules generally reserved for the "fluff" of the rules - is it actally sunlight? Would it hurt my eyes? Is bear-hugging vampires a Devotion Oath paladin sport now?

The  has the Holy Nimbus feature at level 20:     At 20th level, as an action, you can emanate an aura of sunlight. For 1 minute, bright light shines from you in a 30-foot radius, and dim light shines 30 feet beyond that.   Is "aura of sunlight" a fluff text or is "an aura of sunlight" actually a sunlight in terms of a sunlight weakness?  For instance, can it prevent a 's Wail:     Wail. The banshee releases a mournful wail, provided that she isn't in sunlight.


I am in the process of developing an application (Quartz scheduler) where we have a job class which is responsible for actually executing the work and we need to tell/pass the name of the job class while creating a trigger in the Quartz scheduler.  I want to provide an extension point to all who want to use the API (beside the some generic jobs which I will provide as part of the API). The idea is to create an (marker) interface and if any one wants to declare their class as scheduler job class, all they have to do is, to (declare to) implement the interface.  I am not sure how I can find which classes are following the contract (by implementing the interface) so that I can show them to the user who want to schedule a trigger in the scheduler.  My requirement is not to load the classes at run time but to show user list of classes which implement the required interface so that user can select the class and class name can be passed to the scheduler. It's the Quartz scheduler which at the end will be responsible to create an instance of class.  Can any one suggest how I can achieve the above goal or is there any other better way to achieve what I am trying to do?  Edit  I went through the doc of  and it seems that for implementing a service one has to create a file in the META-INF folder with the name of the implementation class, which leads me to think that if the user of my API wants 20 different implementations, he has to put 20 entries in the file which for me seems a lot of extra work for the end user since each job class will be created for executing a specific job and there can be 100s of job classes.  Please correct me if my assumption is wrong.

Some time ago, I came across a piece of code, that used some piece of standard Java functionality to locate the classes that implemented a given interface. I know the functions were hidden in some non-logical place, but they could be used for other classes as the package name implied. Back then I did not need it, so I forgot about it, but now I do, and I can't seem to find the functions again. Where can these functions be found?  Edit: I'm not looking for any IDE functions or anything, but rather something that can be executed within the Java application.


How can I make the following case insensitive?  myString1.Contains("AbC")

Is there a way to make the following return true?  string title = "ASTRINGTOTEST"; title.Contains("string");   There doesn't seem to be an overload that allows me to set the case sensitivity.. Currently I UPPERCASE them both, but that's just silly (by which I am referring to the  issues that come with up- and down casing).  UPDATE This question is ancient and since then I have realized I asked for a simple answer for a really vast and difficult topic if you care to investigate it fully. For most cases, in mono-lingual, English code bases  answer will suffice. I'm suspecting because most people coming here fall in this category this is the most popular answer.  answer however brings up the inherent problem that we can't compare text case insensitive until we know both texts are the same culture and we know  what that culture is. This is maybe a less popular answer, but I think it is more correct and that's why I marked it as such.


I don't get any option in settings or elsewhere so I can change my profile pic and username. Why?

It would be nice to update the profile page from within the app.  Perhaps not many people update their profiles more frequently, but when required to do so, I would prefer to do it from the app instead of the mobile browser.


I have to prove:   An infinite subset of a denumerable set is denumerable.   I understand this has been asked before and I did take the time to read what was said there, but I do not understand still.   I have to prove this using other theorems about denumerable or countable sets, nothing too complex for this proof.

In my book, it proves that an infinite subset of a coutnable set is countable. But not all the details are filled in, and I've tried to fill in all the details below. Could someone tell me if what I wrote below is valid?  Let $S$ be an infinite subset of a countable set $T$. Since $T$ is countable, there exists a bijection $f: \mathbb{N} \rightarrow T$. And $S \subseteq T = \{ f(n) \ | \ n \in \mathbb{N} \}$. Let $n_{1}$ be the smallest positive integer such that $f(n_{1}) \in S$. And continue where $n_{k}$ is the smallest positive integer greater than $n_{k-1}$ such that $f(n_{k}) \in S$. And because $S$ is infinite, we continue forever. Now consider the function $\beta : \mathbb{N} \rightarrow S$ which sends $k \rightarrow f(n_{k})$.   So in order for $S$ to be countable, $\beta$ would have to be a bijection. $\beta$ is injective since if $f(n_{k}) = f(n_{j})$, then $n_{k} = n_{j}$ because $f$ is injective. We also can conclude $k = j$ because the various $n_{i}$ chosen were strictly increasing.   Edit: $\beta$ also needs to be surjective. So for every $r \in S$ there exists a $q \in \mathbb{N}$ such that $\beta(q) = f(n_{q}) = r$. We know that $f^{-1}(r) \in \{n_{1}, n_{2}, ..., n_{k} ... \}$, so we can let $f^{-1}(r) = n_{d}$. Thus $\beta(d) = f(n_{d}) = r$.


I'm trying to overlay an image on top of a shader to create the effect of having printed onto metal like so:    I'm using an Anisotropic shader for the underlying brushed metal and have UV Mapped a PNG (with alpha channel) for the printed portions. I've tried using a Mix and an Add shader to combine the two but it doesn't give the effect I'm after. Instead, it looks like the metal was stained with a translucent film, rather than over-printed with an opaque ink/paint.  Here's my shader so far:   How can I achieve this over-printed effect?

I'm trying to setup a image decal in cycles, and I can't figure how to setup the nodes to work fine. Does anyone know the solution?


The book has a college-age girl gets hired at a supernatural bookstore as a editor for a city guide, and involves zombies and other creatures. It also involves citywalkers who hear the personality/voice of the city itself.

I read it within the last 3-4 years in the United States in English, and I think it was a relatively new book at the time. The protagonist is a female, I think recently laid off from her job as a travel writer. She finds a notice on a messageboard (at a coffee shop?) for a local business looking for travel writers. She bulls her way into an interview despite them repeatedly telling her she's not suitable, and finds that the business caters to supernaturals. Long story short, despite her relative frailties and ignorance, she's engaged to build a guide to exploring the city when you're a vampire, a zombie, or the like. Most aspects of the supernatural are fairly traditional. Vampires need to drink blood and can hypnotize people with their gaze. Zombies are slow rotting corpses and eat brains (although there's a slight twist in that the brain-eating is an addiction of sorts and being without them results in them going on rampages to get their fix). I want to say that the human resources woman is a water-spirit of some sort.   Plot developments included the delivery of the zombie's brains being disrupted, nearly resulting in a rampage, a shadowy organization dedicated to killing the supernatural which the main character gets mixed up in, and a fortune-telling witch who favors the protagonist for being willing to buy her a coffee. The witch is somehow tied into the supernatural-slaying group, although I forget exactly how.  I'm pretty sure that it was set in a real-world city, maybe New York. The title might include the name of the city, and I think was entitled something like "Things to Do in Denver When You're Dead" (no, it's not that movie or book). The cover was mildly cartoonish and showed the protagonist walking down a street with some supernatural characters sprinkled in the background.


Suppose we have a random variable $y$ and a collection $(x_1,\dots,x_n)$ of $n$ random variables that are all uncorrelated: $\operatorname{corr}(x_i,x_j) = 0$ $\forall i \ne j$ and that all have the same correlation with $y$: $\operatorname{corr}(y,x_i) = \rho$ $\forall i$. Obviously, they can't all have correlation $1$ or $-1$ with $y$ and be uncorrelated at the same time, so there must be bounds.   This question came up when I was solving a different problem, finding the correlation between $y$ and the linear model $\hat{y} = X(X^\intercal X)^{-1}X^\intercal y$, where $X = (x_1,\dots,x_n)$ and $y,x_i$ are now thought of as $m\ge n$ random samples from the random variables. I found that if the random variables have mean $0$ and variance $1$, the expected value is $\operatorname{corr}(y,\hat{y})=\rho\sqrt{n}$, there's also a more complicated formula for the general case (can post if interested, wanna keep this post short).   This lead me to conjecture that the bounds for $\rho$ are $\left[-\frac{1}{\sqrt{n}},\frac{1}{\sqrt{n}}\right]$, now thinking about proving it for the general case.

There are three random variables, $x,y,z$. The three correlations between the three variables are the same. That is,  $$\rho=\textrm{cor}(x,y)=\textrm{cor}(x,z)=\textrm{cor}(y,z)$$  What is the tightest bound you can give for $\rho$?


When a user posts an answer to a question and uses "@user" the user to whom they refer doesn't get a Notification, unlike  which does alert the user about the post.  It would seem that if the answerer makes a point of writing @user in his answer (possibly referring to another answer or comment) that they intended to notify that person, otherwise they could have wrote the user's name without the at symbol.

Sometimes I want to refer to a specific user in an answer.  Something along the lines of      "From the answers of UserA and UserB I have crafted this super useful solution..."   Is there a shortcode creating a link to a user profile using the user name? Similar to the @ we have in the comments, but in an answer.


Original Post  I have been using Wine 1.6 for running several old Windows XP applications. Last night I tried to install a old win98 app and seem to have broken something.  I changed the "default" compatibility mode to "win98" in the Configure Wine window and exited out. The n tried to right click on the .exe file to use install wine application from the pop-up menu. Wine never launched the install.  When I tried to go back to "Configure Wine" it even failed to open and then to my shock I found that my other three windows XP applications that worked prior to this all failed to launch.  Doing some research I tried launching winecfg from the command line and it failed with an error with something about .idt failed to invoke.  So my question is how can I undo or fix my horrible mistake? Is there a way to force the wine mode back to winXP?  Edit to add following  Per a suggestion I tried winetricks winxp but nothing happened, it just hung & I got the following:  gerald@gerald-Vostro-200:~$ winetricks winxp wine cmd.exe /c echo '%ProgramFiles%' returned empty string   When i run winecfg, I got:  gerald@gerald-Vostro-200:~$ winecfg  modify_ldt: Invalid argument  modify_ldt: Invalid argument  modify_ldt: Invalid argument  modify_ldt: Invalid argument  modify_ldt: Invalid argument  ^C (I tried to cancle / close the hung up process)  err:ntdll:RtlpWaitForCriticalSection section 0x7bcc7be0 "loader.c: loader_section" wait timed out in thread 0024, blocked by 0009, retrying (60 sec)  ^C  err:ntdll:RtlpWaitForCriticalSection section 0x7bcc7be0 "loader.c: loader_section" wait timed out in thread 0025, blocked by 0009, retrying (60 sec)  ^C  err:ntdll:RtlpWaitForCriticalSection section 0x7bcc7be0 "loader.c: loader_section" wait timed out in thread 0026, blocked by 0009, retrying (60 sec)  err:seh:raise_exception Unhandled exception code c0000194 flags 0 addr 0x7bc367d1  err:ntdll:RtlpWaitForCriticalSection section 0x7bcc7be0 "loader.c: loader_section" wait timed out in thread 0024, blocked by 0009, retrying (60 sec)  ^C  err:seh:raise_exception Unhandled exception code c000013a flags 0 addr 0xf77d3430  gerald@gerald-Vostro-200:~$    UPDATE  Looking around in the FAQ I found "10.6. Every app I try to start crashes"    I was not able to recover my wine installation and had to remove it then reinstall.  All is good now.

I am looking for a step by step instruction to guide me in the ways of installing, configuring and debugging many of the issues new users have when dealing with Wine in Ubuntu.  What is the recommended way of installing Wine, some of the key issues that it has and how to solve them?  If I have a specific problem with an App in Wine, how do I go about solving it? What are the recommended steps to ensure that I can fix a problem related to an app I wish to use?


I have taken it granted that an action in the special relativity must be a lorentz scalar. However is there a fundamental reason for this requirement? I cannot think of a plausible reason for this question.

From Landau & Lifshitz The Classical Theory Of Fields it is said:     To determine the action integral for a free material particle (a particle not under the influence of any external force), we note that this integral must not depend on our choice of reference system, that is, it must be invariant under Lorentz transformations.   This seems understandable. But in comments on  Ján Lalinský says that "there is no good physical reason why action should be invariant". Further he suggests another Lagrangian than that given in L&L, namely, if we denote L&L Lagrangian as $L_0$, then the example could be $L_0+Cv_x$, which is clearly anisotropic. Clearly, the equations of motion must not change with this Lagrangian, because $Cv_x$ is a total time derivative (of $Cx$).  On the other hand, in  Luboš Motl says that "the invariance of the action follows from special relativity – and special relativity is right (not only) because it is experimentally verified. [snip] If $S$ depended on the inertial system, so would the terms in the equations $\delta S=0$, and these laws of motion couldn't be Lorentz-covariant".  How could I connect L&L and Luboš's arguments with Ján's example? Can both sides be simultaneously right? They seem to contradict each other.


I logged into Area 51, and now I can't find any way to delete my account. Is it only me, or does this happen with everyone?

I have accounts in Stack Overflow, Programmers, Unix & Linux and Area 51. I don't want to continue my Area 51 account, so I planned to delete my Area 51 account. I have performed the following steps to delete my account, but I couldn't!  Case 1     If your account has votes or posts do the following steps:         Edit the "About Me" section of your profile to say “please delete me”.   Contact the SE support to request deletion.      I edited my "About Me" section to "please delete me". When I contacted SE Support to delete my account, I couldn't make a request. I am getting the following error:  This operation is incomplete. please do it in main site.   For deleting Area 51 account, when I do it main site, in link for deletion column I gave the Area 51 link. It says that:  it is not valid link!   Case 2     If the account has not interacted with the site yet (votes or posts), click on the delete button on your user page next to the edit link.   I am not eligible for this case!  Then how to delete my Area 51 account? Any help is appreciated!


I'm trying to write a program which can run on my windows laptop to track its connectivity but one of the python packages I want to use needs to be run in a linux environment. That, itself, is not an issue though since windows now has official support for CLIs for OSe like Ubuntu; the issue lies in the fact that whenever I try to use this line of code  print(ThisIsAVariableToHoldMyString, end=" ") it just doesn't print. I know the line is being called through repeated tests of my method (I deleted some commented out others but needless to say I have done a lot of tests)  def AddToReturn(self, toadd, end = False):   #print(toadd)   #print(end)   if end:    print("last hash : "+toadd)    self.returnstring += self.returnstring + "last hash : "+toadd    return self.returnstring   else:    print(toadd, end="")    self.returnstring += toadd  and they always printed whatever I asked them to. Even the first non-commented print statement    print("last hash : "+toadd) works fine and I can see its output, the only one that isn't working is the one with end="" in it. Is this just me being an idiot or is it an actual issue with the windows ubuntu environment? I already tried flush=True.

How do I force Python's print function to output to the screen?


I am new to Typescript, Javascript, NodeJS and the entire ecosystem. I have some code i a project that is somethings like this. This is my ModuleA.ts const x = SomeObject1(); const y = SomeObject2();  export class ClassA() {          someMethod() {         console.log(x);         console.log(y);     }  }  ModuleB.ts import { ClassA } from "./ModuleA";  const a = new ClassA(); a.someMethod();  I am unable to understand how someMethod of ClassA can access x and y variables which are declared in ModuleA and not even exported.

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


Problem :  find the smallest natural number $n>1$ such that : $$n(n+1)(2n+1)=6m^{2}~~,m\in\mathbb{N}$$  I don't know the method to find $n$ but I try many time $$n=1,2,3,....,24$$ Then I find $n=24$ $$24.25.49=6.70^{2}$$ Another try : $$n\equiv r\pmod{6}~~,r=1,..,5$$ $n=6k$ then $k(6k+1)(12k+1)=m^{2}$ So $k,6k+1,12k+1$ is perfect square in same time I find $k=4$ so $n=24$ Also for all $n=6k+r$ I can't find $n$ ? So I'm going to see you solution Thanks!

This question comes from trying to see why 24 is the only non-trivial value of $n$ for which $$1^2+2^2+3^2+\cdots+n^2$$ is a perfect square. To this end, let $m,n \in \mathbb N$ be such that $1^2+2^2+3^2+\cdots+n^2 = m^2$, or $$n(n+1)(2n+1) = 6m^2.$$ When $n=24$ the left hand side is $24\times 25 \times 49$ and there are two things that make it work as a solution: $$7^2+1=2\times5^2$$ $$7^2-1=12\times2^2.$$ We can write these algebraically as $$x^2=2y^2-1$$ $$x^2=12z^2+1$$ and solve them simultaneously (with $x,y,z\in \mathbb N$).    These are instances of Pell's equation and each individually has an infinite number of solutions. How do we show there is only one (non-trivial) value of $x$ that is common to the solutions of both equations?


Look at the following code. Are they the same? Is there any difference? If yes what?      string f = textBox5.Text;     if (string.IsNullOrEmpty(f))     {         MessageBox.Show("string");     }     if (String.IsNullOrEmpty(f))     {         MessageBox.Show("String");     }   Edit: Is a null or empty string test exactly the same as null or empty String test?

Example (note the case):  string s = "Hello world!"; String s = "Hello world!";   What are the guidelines for the use of each? And what are the differences?


When I try to give a bounty to a deleted answer, a pop-up occurs:    Nope, I didn't try - I didn't dare to. But why is it not prevented (or rather, is it really not prevented)?  I read up  but the answer seems to focus more on why the answer got deleted rather than whether it is possible to give bounty to a deleted answer.

Minor UI glitch: The button to award a bounty is active on a deleted answer. Clicking on it results in the "THIS CANNOT BE UNDONE!" alert.         After confirming, I get the following error though:        So not a fatal bug, but still better not show the +50 next to deleted posts.


This issue has followed me over the years, every once in a while I resolved it, but I never found the one solution.  Most of the times, the issue is a missing wireless firmware, in the current instance .  I usually create the install drive with dd if=./debian.iso of=/dev/sdb.  Now in the past, I've tried to find the firmware file and copy it onto a USB flash drive. The first issues were:   I couldn't find the exact, required file (e.g. b43/ucode16_mimo.fw). I believe that  file once, but didn't work this time. The install medium is read-only, so I used a second USB drive, where I don't know if it's accepted or not. I have no clue where to place the files on the USB drive.. is it in /, /firmware/,  /lib/firmware or somewhere entirely else?   Lately I failed there and wasn't able to add the firmware during the setup, that's where I found the , which felt like a holy savior at this point.  But that didn't change a thing, I was prompted with the same error about missing firmware again.  TL;DR and my question:  How do I correctly add missing firmware during a Debian setup and where do I find the suggested firmware files?

I just installed Debian on laptop, it tells me  Some of your hardware needs non-free firmware files to operate. The firmware can be loaded from removable media, such as a USB stick or floppy. The missing firmware files are: iwlwifi-7265-9.ucode iwlwifi-7265-8.ucode If you have media available now, insert it, and continue. Load missing firmware from removable media?  Using minimal Debian iso and no mirror I was able to install terminal only. Two questions:  Where do I download these files?  How do I get Debian to recognize them once on flash drive? Grep?  Do I need to do special formatting or partitioning to flash drive?


Connecting to any debian installation via PuTTY  results in a very strange situation: I can have correct display of line drawing, but not for all programs.  In particular Midnight Commander and aptitude seem to belong to opposite camps: If one works the other does not.  Currently I have linux set to use utf8 (LANG=en_US.UTF-8) and PuTTY likewise (Window->Translation->{Remote character set: UTF8; Use Unicode line drawing}); in this situation mc works as expected and aptitude displays "lqqqk". if I reverse settings in PuTTY (wihout changing anything in linux) (Window->Translation->{Remote character set: ISO-8859-15; Use Unicode line drawing}); this time aptitude shows as it should and mc displays "ââ€â"; using other "Handling of line drawing characters" breaks mc and aptitude.  Other programs (e.g.: kernel menuconfig) seem to follow aptitude behavior.  What's going on "under the hood"? How do I fix this (if at all possible)?  UPDATE: I have been living with this problem (and NO solution to be found, I am aware of many other answers, but they so address only one half of the problem: mc). As stated above I am able to make mc work correctly and I thought I was able to make aptitude/kconfig work correctly... only I need two different settings for them.  To recap:   I have a plain, default debian server (no GUI) install (currently jessie, but this holds true for all releases)`. Locale is pretty standard:  $ locale LANG=en_US.UTF-8 LANGUAGE=en_US:en LC_CTYPE="en_US.UTF-8" LC_NUMERIC="en_US.UTF-8" LC_TIME="en_US.UTF-8" LC_COLLATE="en_US.UTF-8" LC_MONETARY="en_US.UTF-8" LC_MESSAGES="en_US.UTF-8" LC_PAPER="en_US.UTF-8" LC_NAME="en_US.UTF-8" LC_ADDRESS="en_US.UTF-8" LC_TELEPHONE="en_US.UTF-8" LC_MEASUREMENT="en_US.UTF-8" LC_IDENTIFICATION="en_US.UTF-8" LC_ALL=    I am using either the standard "xterm" setting or "putty" in Connection->Data->{Terminal-type string}; it makes no difference. Certain programs work, others not; if I fix the "not working" ones I contextually break the "working" ones. The "fix" consists in switching PuTTY Window->Translation->{Remote character set} from "UTF8" to "ISO-8859-15" and vice versa. Extreme case is aptitude which, I discovered, can't be fixed because it seems to use two different standards: if menu and scrollbar are displayed right then pop-ups are wrong, and vice-versa. Kernel configuration (make menuconfig) shows the same (wrong) behavior as aptitude. I include screenshots to explicate better (nothing is changed server-side).    This was taken from KiTTY with UTF8 setting; note scrollbar is displaying correctly (and also menu (F10) display ok, I did not feel like adding other images, but I can provide, if needed).   This was taken from KiTTY with ISO-8859-15 setting; note scrollbar is "wrong", but pop-up is correct (in this case also menu are garbled). Notice also the "kind" of mis-translation is different.   Please Note: the question is not (and never was) "How to make mc display line-drawing chars", but "How to have mc and aptitude/kconfig working in the same environment".

I discovered that when I do ssh to a machine using OS X 10.6 and use mc I do not see the .  This does not happen if I open terminal and start mc.  I'm connecting using putty configured to use xterm-color, configuraton that works just fine if I do ssh to a linux machine.  The mc from  OS X is version 4.7.0 (installed using macports).  What locale returns:   LC_CTYPE="C" <== ssh LC_CTYPE="UTF-8" <== Terminal.app    ssh: mc > display bits shows: 7-bit ASCII (changing does not help, it defaults to the same value) Terminal.app: mc > display bits shows: UTF-8  The environment shows TERM=xterm-color in both cases Terminal.app and ss but mc looks different.  I filed a bug to mc with this information at


Is it true that set of all real numbers under addition isomorphic to set of all complex numbers under addition

I think the answer is yes.   Sketch of the proof Consider $\mathbb{R}$ as a vector space over $\mathbb{Q}$. Let $\{e_\lambda:\lambda\in\Lambda\}\subset\mathbb{R}$ be its Hamel basis. Then $\{(e_{\lambda_1},e_{\lambda_2}):\lambda_1,\lambda_2\in\Lambda\}\subset\mathbb{R}^2$ is a Hamel basis of $\mathbb{R}^2$. Consider set theoretic bijection $i:\Lambda\to\Lambda\times\Lambda$ define map $\varphi:\mathbb{R}\to\mathbb{R}^2$ by its action on element of Hamel basis of $\mathbb{R}$ by equality $\varphi(e_\lambda)=(e_{i(\lambda)_1},e_{i(\lambda)_2})$. This is an isomorphism between $\mathbb{Q}$-vector spaces $\mathbb{R}$ and $\mathbb{R}^2$.  Question Could you tell me is this proof correct, and if it is not, where is the mistake?  EDIT: Thanks to GAJO we found that this proof is wrong. The correct one basis is  $$ \{(e_\lambda,0):\lambda\in \Lambda\}\cup\{(0,e_\lambda):\lambda\in\Lambda\} $$ So we had to look at bijections of the form $i:\Lambda\to\Lambda\coprod\Lambda$ and the desired linear operator is defined by equalities $\varphi(e_\lambda)=(e_{i(\lambda)},0)$ if $i(\lambda)$ lies in the first copy $\Lambda$ and $\varphi(e_\lambda)=(0,e_{i(\lambda)})$ otherwise.


My terminal choice has always been Guake, but at my job they have some Macs and I've started to use iTerm2 and I really love the split-functionality.  So I was searching for something similar in Ubuntu. I've tried with Guake + screen, but that is definitely not the same experience, because screen has to be executed as a command.  Yes, I could put it into my bash config, but if I split the screen I cannot move the scroll bar with the mouse (maybe there's a shortcut for this?). The other thing is that my bash config is completely screwed up with screen, I have a function to make an ls after each cd and another to show some info in my prompt when I enter a git repository.  Both don't work for me.  I really would like to know about a program with the iTerm2 functionalities for Ubuntu or, in the worst case, try to emulate them the most similar possible.

Is there an  (terminal application for Mac OS) equivalent for Ubuntu?  Amongst the many features it adds the one I'm after is the "hotkey window", where you can overlay/hide a translucent terminal window at the touch of a button on the keyboard.


I was unable to solve this particular question in my real analysis assignment and I am looking for help here.  Question: Let $x_1 =0$ and $x_2 =1$ and for n>2 define $x_n = (x_{n-1} +x_{n-2})/2$. Then which of following are true?  A ${x_n}$ is monotone B ${x_n}$ is Cauchy C Lim $n \to \infty $  $x_n=2/3$. I was unable to prove $x_n$ is Cauchy and monotone. All I could prove was that $|x_{n+1} -x_n|$=$ 1/(2)^{n-2}$  and I put n tends to infinity in recurrence relation to get limit but I am only getting that x=2x/2 . I am unable to prove/ doisprove any of the options. Can you please help?

Show that the sequence $a_1=1$, $a_2=2$, $a_{n+2} = (a_{n+1}+a_n)/2$ converges by showing it is Cauchy.   My work : Need to show that for every $\epsilon \gt 0$ there exist $N$ such that $n,m\ge N \implies  | a_n - a_m|  \lt\epsilon$. $$|a_n-a_m| = \dfrac{1}{2}|(a_{n-1} + a_{n-2}) - ( a_{m-1} + a_{m-2})|$$ I feel triangle inequality might be helpful here, but really not sure how to link it to the $\epsilon$. Appreciate any help...


How can we combine c# accessor declaration and initialization  List<string> listofcountries= new List<string>(); and  List<string>listofcountries {get;set;}   Is there a way to combine these to statements ?

How do you give a C# auto-property an initial value?  I either use the constructor, or revert to the old syntax.    Using the Constructor:  class Person  {     public Person()     {         Name = "Initial Name";     }     public string Name { get; set; } }   Using normal property syntax  (with an initial value)  private string name = "Initial Name"; public string Name  {     get      {         return name;     }     set     {         name = value;     } }   Is there a better way?


I've wrote a PHP-Script, and the execution requires sudo permission, because it executes some other system related stuff. So i've added this into the crontab -e but i can't see, that my script is running correctly.  Command:  */5 * * * * /usr/bin/php /srv/www/php/script.php && date > /srv/www/php/mylog.log   The only output is the date. No response from my script. It is executable (chmod a+x) and if i use the same command in the terminal as root, everything is okay. So it's up to crontab -e?  Also i made sure, that my cronjob is running (/var/log/syslog):  Oct 23 16:40:01 $MYMACHINE CRON[13797]: (root) CMD (/usr/bin/php /srv/www/php/script.php && date > /srv/www/php/mylog.log)   And this every 5 mins. Also my "mylog.log" always got the latest timestamp, so i guess, there's might be a problem with the script inside.  EDIT: I've created another test script to check, if the scripts getting executed or not. But the script was executed, so it's a problem inside the script.  I am trying to add dynamically IPs to an iptables chain:  #!/bin/bash value=`cat whitelist.txt` #echo "$value"  for i in $(echo $value | tr "," "\n") do   # process   /sbin/iptables -I teamspeakCommunication --src $i -j ACCEPT done   May you can see something weird?

This is a  about using cron & crontab.   You have been directed here because the community is fairly sure that the answer to your question can be found below. If your question is not answered below then the answers will help you gather information that will help the community help you. This information should be edited into your original question.  The answer for 'Why is my crontab not working, and how can I troubleshoot it?' can be seen below.  This addresses the cron system with the crontab highlighted.


In Machine learning we use activation functions to give non-linearity to the output of neuron. But what is the exact non-linearity in this context? How it differs in different activation functions(e.g. sigmoid, relu ...)?

Are there any reference document(s) that give a comprehensive list of activation functions in neural networks along with their pros/cons (and ideally some pointers to publications where they were successful or not so successful)?


I'm currently working on a pipe system in Java where many processors can write in it and read from it. The code compiles without any errors but when I try to run it, it throws me the following exception: Exception in thread "main" java.lang.NullPointerException     at Processor.main(Processor.java:42)  And here is my code so far:  class Pipe {     private float[] buffer;     private boolean buffer_blocked;  public Pipe() {     this.buffer = new float[10];     this.buffer_blocked = false; }  public synchronized void send(int chnl, float value) {     while (buffer_blocked) {         try {             wait();         } catch(InterruptedException e) {}     }     buffer_blocked = true;     buffer[chnl] = value;     buffer_blocked = false;     notifyAll(); }  public synchronized float receive(int chnl) {     while (buffer_blocked) {         try {             wait();         } catch(InterruptedException e) {}     }     return buffer[chnl]; } }  public class Processor { private static Pipe pipe;  public Processor() {     // empty constructor }  public static void main(String[] args) {     Processor P1 = new Processor();     Processor P2 = new Processor();     P1.pipe.send(0, 6.1f);         // write     float number = P2.pipe.receive(0); // read;     System.out.println(number); // should print 6.1 } }   I read something about that the array must not contain null pointers when it comes to setting values but I didn't use null pointers. I appreciate any kind of help, thanks in advance!

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Due to the wider information released about the  and the fact that a user's flag weight is now revealed to them (well, sometimes):  As one of the new moderators on SU I've notice that a pretty small subset of users do a lot of the really good flagging, so I wonder if there should be a new badge created to be awarded to users that manage to the reach the maximum weighting score (or a lower threshold, or maybe two badges for different score levels, etc - whatever makes the most sense in terms of current flag weights I guess).  This will give a small reward (as well as being responded to first, of course) to the users who really make an effort to help keep the sites clean, and will hopefully encourage the same positive behaviour in newer and current users who currently don't bother.  I also wonder if worthwhile modifing the Citizen Patrol badge to award it only after a user has a flag accepted as valid, not when they post a flag, although I can see this causing confusion (why didn't I get my badge posts, etc) without some very careful wording, so this isn't something I'm really pushing.

Because the , and (if I understood it right) you'll get less and less weight with every flag towards 750, I'd like to suggest two new Badges:   Sheriff (Silver): Achieved a flag weight of 700 Clint Eastwood or Marshal1 (Gold): Achieved a flag weight of 749   1: As suggested by .  Edit: I've started this bounty, because now that there are people actually getting a flag weight of 750 in multiple sites, don't you think it would be a good idea to implement this brilliant idea which is so popular with many users? Jeff? please?


I'm making a flying map where players are not allowed to touch grass, quartz, or leaves. If they do, I need them to be teleported to the start. How can I do that? By the way, this is 15w47c map.

I'm interested in negating fall damage with command blocks by giving players Resistance as they're falling. How can I use /testfor to tell whether a player is on the ground or in the air?


In a settlement, if I have one recruitment beacon, settlers don't come very often. If I add another one, will settlers come more often than if I have one?  .  NOTE:  I'm not sure if you actually can do more than one. I am asking this question to see if I should make another, or if it will be pointless.

I want to populate my settlements faster, is there any purpose in placing multiple recruitment radio beacons in them?


I spilled some milk on my MacBook Pro and immediately dried it, it seemed to only have been on the top and bottom. Then about 10 minutes later I played a movie and there was no sound. I then noticed a small amount of milk in the aux port so I sucked it out and turned it off and started drying it off (I turned it upside down and put it in front of my now barely warm fire place.) What should do for the sound to be normal?

Sadly, yesterday I've spilled some water on my MacBook Pro (El Capitan). Before you yell at me - it was closed, turned off and it wasn't a lot of water, the laptop was wet only on the top and under - not inside.  Today I've turned him on. At first battery wasn't recharging for some reason, but SMC reset fixed the problem.  At the first booting speaker was like talking to me, hard to explain but it was weird. Also only right speaker was "talking", despite the fact that only left side of the laptop was watered. Then there was no sound at all, not from the speakers, nor from the headphones. Also microphone's not working. USB ports are okay. The water was spilled from the left side of the laptop. I know this is hardware issue, and something's broken, but I want to be 100% sure. No it's not muted. I've also tried NVRAM reset a few times, but it doesn't fix the problem :(  There might be one factor, before spilling, my laptop "died" for the first time (battery energy ran off), but I doubt it's the case. (but hey, every info matters, right?)  It wouldn't be weird for me, if only left speaker wouldn't work, but built-in microphone not working is kinda weird in this case, isn't it?  I just want to ask you guys, what else can I check, before I'll be 100% sure it's dead inside?  I've plugged in external microphone - it's not working too.


I have few Terminal commands which i'm using so frequently,So i though to automate it to reduce the effort of copy-pasting the commands one by one in terminal and time.  I created a .command file for this but the issue with it is, it is only executing the first statement.  The first statement is connecting to a remote server and it needs a password , for that i usually copy-paste the password. When i changed it to a .command file after executing the first command it is requesting a password in a new window and further commands are not getting executed in the new window.  Does can anyone help/suggest to find a way to do this?  Below is the commands,  #!/usr/bin/expect set timeout 60 set host 111.111.111.11 set name root  set password **************  spawn ssh $host -l $name   expect {     "(yes/no)?" {         send "yes\n"         expect "password:"         send "$password\n"     }     "password:" {         send "$password\n"     } }  expect "#" # test whether login to host send "ssh-agent bash\n" send "ssh-add etlbi-master\n" send_user "Now you can do some operation on this terminal\n" send “ssh-add etlbi-master”   Getting the below error,Also not able to enter any commands on the terminal window.  Last login: Thu Jun 20 17:39:57 2019 from 111.111.111.11 root@Ubuntu-1689-xenial-64-minimal ~ # Now you can do some operation on this terminal usage: send [args] string     while executing "send “ssh-add etlbi-master”"     (file "/Users/sand/Documents/google/newtest.command" line 25) logout Saving session... ...copying shared history... ...saving history...truncating history files... ...completed.   [Process completed]   Note: i'm the admin.  Thanks in advance!

I'm using a series of commands for deploying my files to production. This is currently done manually.  Is it possible to make these commands into an executable file? So that I don't have to copy paste these commands each and every time.  When the first line is executed i.e., connecting to the root server, it will ask for the password and I have to paste the password: xxxxxxxxxxxxxx  ssh root@server pwd: xxxxxxxxxxxxxx ssh-agent bash ssh-add bi-master cd /home/trans/bimaster git status git pull git@bitbucket.org:xxxxxxxxx/bimaster.git master   Note : I'm the admin of the server, Since the project is been done by different teams as of now, we have decided to do manual deployment (cannot use Jenkins or any other tools for automated deployment), as we have to check the status of some files.


We gifted our daughter an all-expense paid trip to Europe, with the initial stop in London before going to the Schengen member states. Since Paris is the first planned entry to the Schengen countries, she applied with the French Embassy in Manila. She has a UK visa stamped in her passport. Since she is unemployed and we are paying for her full trip for a month, and I am also traveling with her, we have given our support letter addressed to the consul and our financial documents showing our capacity to pay for everything. After losing 2 straight pregnancies, we thought this will give her a break she needed plus she will be traveling with me and my husband will later join us. Her visa was refused by the French embassy for the following reasons:   The information submitted regarding the justification for the purpose and conditions of the intended stay was not reliable  Your intention to leave the territory of the Member States before the expiry of the visa could not be ascertained.    She submitted all her flight tickets, hotel accommodations, cruise confirmation and all documents that would show where she will be and that at the end of the trip she will be flying back to the Philippines. Although it was stated that she can appeal the refusal and the address to send the appeal was in France, will it be better to submit instead a new application rather than make an appeal? I don't know how long the response will be and we are scheduled to leave on May 1 from the Philippines. All her tickets and accommodations are paid since I am traveling with her. I am a US citizen so I don't need a visa.

Schengen refusal formulae can be difficult to understand sometimes.  Sometimes an applicant receives a refusal with:       Justification for the purpose and conditions of the intended stay was not reliable.     often accompanied by:       Your intention to leave the territory of the Member States before the expiry of the visa applied for could not be ascertained.   What is meant by this refusal reason?  What are they trying to say?


Let $R$ be the subgroup of $\mathbb{Z}^n$ generated by the rows of integer matrix $M$.  I want to show that $det M=0$ implies $\mathbb{Z}^n/R$ is infinite, and also that $det M\neq 0$ implies $|\mathbb{Z}^n/R|=|det M|$.  I know I must use the Smith normal form in some way, as that is what we have been studying.

I am aware of some theorem that says that if $M$ is non singular, $\det(M) \neq 0$, then: $$\mathrm{card}(\mathbb{Z}^n/M \mathbb{Z}^n)= |\det(M)|.$$ How does one prove this? Figured if I put in the context of the rational canonical form, this would help, but cant piece it together.  Thanks.  This result is mentioned in the first answer of this question:  .


how to close my laptop lid in ubuntu 18.04.2 without doing anything? i tried sudoedit /etc/systemd/logind.conf and also sudoedit /etc/UPower/UPower.conf

The issue is solved temporary using the method in this forum, but only if I have fresh boot, if i suspend my laptop and wake it again, Ubuntu will ignore my rules, and suspend when i close the lid.


Im trying to make a forest scene of a path and I want it to seem like the path is infinite or the path goes on for a very long time.  Im gonna also add trees to the side of the path and an HDRI for the sky.  I wanna know what I should set the camera settings and the plane size to so that the screen will be filled but appear to be infinite.  All help will be appreciated.  Thanks

I have already found one similar , however it doesn't correctly address what I am talking about. Please see , example to know exactly what I'm talking about. I have only found , and , but both use a curved plane to do the trick, which would work unless the object is to be rotated(in animation) to view from every angle.      Yes, again we could rotate the object instead of the camera but, what about a large array of object, that would really distort the scene and setting the camera accordingly would be very difficult.    Setting the camera at this angle would be good even for a large array of objects: , but what if we need a more acute view like this:  , (even if we set the world background color to white this would be impossible to actually blend if taking the lighting into account, as it would emit light and the edges of planes would be visible.)    I don't know if there is a workaround with the lightpath node with this to only make the area where the shadow falls visible. And I don't know how to take only the shadow information into the compositor to make this?    Primarily focusing two problems: 1) how to make such a world in cycles, infinite, only the shadow information and the object? 2) How to make such a world in cycles, infinite, only the shadow information and the object and a slight gradient in the infinite world?  Therefore, I resolved here.


This question was asked in a masters of mathematics exam for which I am preparing.  Compute $\int\limits_0^{\infty} \frac{x^{1/3}}{1+x^{2}} dx$.  I could only think of substituting $y^3 = x$ and that does not change much. Could somebody post a solution using residues or in ways besides here in this link?:  Edit : I am interested in the answers which use contour integration and residue calculus.

I want to compute this integral $$\displaystyle\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$$  What I did was the following. I substituted $x=t^{6}$, so that my $dx= 6t^{5} \ dt$ and so the integral changes to $$\int_{0}^{\infty} \frac{t^2}{1+t^{12}} \cdot 6 t^{5} \ dt =6 \cdot \int_{0}^{\infty} \frac{t^7}{1+t^{12}} \: dt$$  Now If I substitute $t^{4}=v$ then what I will be having is the following integral $$\frac{6}{4}\cdot \int_{0}^{\infty} \frac{v}{1+v^{3}} \ dv$$  Now I can write $1+v^{3} = (1+v) \cdot (1-v+v^{2})$ and so I have   \begin{align*} \int_{0}^{\infty} \frac{v}{1+v^{3}}\: dv &= \int_{0}^{\infty}\biggl[\frac{1}{3}\cdot \frac{v+1}{1-v+v^{2}} - \frac{1}{3} \cdot \frac{1}{1+v}\biggr]\: dv \end{align*}  Now the point is that the integral of $1/(1+v) \to \infty$, so I am not sure if this is the right way to do. Can anyone suggest anything?


How can I create a custom error message, without checking the return code of the last command everytime? I want to log an event to a log file, when the script succeeded or fails (anywhere in the script). Anything like this: # cat /var/log/myscript.log name: myscript | state: failed | date: 2021-01-18 name: myscript | state: succeeded | date: 2021-01-19  Regards

What is your favorite method to handle errors in Bash?  The best example of handling errors I have found on the web was written by William Shotts, Jr at .   He suggests using the following function for error handling in Bash:  #!/bin/bash  # A slicker error handling routine  # I put a variable in my scripts named PROGNAME which # holds the name of the program being run.  You can get this # value from the first item on the command line ($0).  # Reference: This was copied from <http://www.linuxcommand.org/wss0150.php>  PROGNAME=$(basename $0)  function error_exit {  #   ---------------------------------------------------------------- #   Function for exit due to fatal program error #       Accepts 1 argument: #           string containing descriptive error message #   ----------------------------------------------------------------       echo "${PROGNAME}: ${1:-"Unknown Error"}" 1>&2     exit 1 }  # Example call of the error_exit function.  Note the inclusion # of the LINENO environment variable.  It contains the current # line number.  echo "Example of error with line number and message" error_exit "$LINENO: An error has occurred."   Do you have a better error handling routine that you use in Bash scripts?


I previously changed my domain from www.visualstudiolearn.blogspot.com to www.visualstudiolearn.com.  I had around 300 posts with the previous domain name and most of them where showing up on Google. Now that I have changed my domain name the index status shows total indexed as 0 and when I go to the advanced tab it says 304 (not selected) and 217 blocked by robots.  Any ideas?

I recently switched my domain from  to , and added my new domain to my Webmaster Tools account. After a few days, I went there and checked the data, and I was a bit worried when I saw this:    How can I interpret this? Is Google really not indexing my site at all? I'm afraid that's the case, because when I google for it, only my old blogspot domain shows up!


I know that the order is meaningless.  But I want to adjust the order for readability.  Can not change the order of columns in the postgresql?  I am using postico for mac. Thanks.

Is it possible to change the natural order of columns in Postgres 8.1?  I know that you shouldn't rely on column order - it's not essential to what I am doing - I only need it to make some auto-generated stuff come out in a way that is more pleasing, so that the field order matches all the way from pgadmin through the back end and out to the front end.


In the sentence:  The cost overrun was due to a higher-than-budgeted consumption of electricity,  should higher-than-budgeted be hyphenated? It seems to me that it should definitely be hyphenated, given that the phrase is a compound adjective that precedes its noun. However, does that change when the last word is a participle?

Hyphenating an adjective composed of two words is, from what I understand, fairly straightforward: if the adjective is before the noun, it must be hyphenated      The three-eyed raven   Customer-centric organizations     (with some exceptions such as not hyphenating after adverbs ending in -ly)     A highly efficient team   But how would one apply this to create an adjective from a composed word or expression and an adjective or past participle ? The example that comes to my mind is the following sentence:     Your product is based on big data     Which of these two options, if any, should I use, and why?     A big-data-based product   A big data-based product    Reading this, I think the second option does not mean what I want it to mean (it means that the product is big and based on data, not based on big data). The first option seems to make more sense, but is it correct?


I am interesting in teaching myself General Relativity, since I only learned Special Relativity during my bachelor in Physics. Now, I have turned into math, but nevertheless I remember enjoying theoretical physics and in particular relativity, I know that G.R. is a beautiful mathematical construction. I know the basis of Differential Geometry (Riemannian, Pseudo-Riemannian, Banach manifolds and Lie groups). I ordered General Relativity by Robert M. Wand. But honestly, I found the notation to be very cumbersome.  I know physicists find it more useful to deal with tensors in general in terms of a coordinate system, but I myself feel more comfortable with the abstract definition knowing a priori how such tensor should transform (from chart to chart). Also, Einstein summation convention does not do too much for me, I often forget whether or not I was summing. So, is there a good book you could recommend me to learn the general theory of relativity? I am more interested in the foundations and fundamental principles than in the applied stuff (Black holes, gravitational lenses, etc.).

What are some good books for learning general relativity?


I'm looking for advice on the classic build vs buy question.   We need a new linux server to run Matlab computation on in our lab (academic). Matlab parallel computing toolbox licence allows up to 12 local workers so we are aiming at a 12 core server with 4GB memory per core (total of 48gb). The system will have an SSD for the OS and a raid-5 (4x2tb) for data.    I looked around and found a (relatively) cheap vendor, Silicon Mechanics, that offers a system to our liking (specs below) for $6732. However, buying the components from newegg cost only $4464!  The difference is $2268 which is 50% of the base cost. If buying from a company can be thought of as a sort of insurance, basically my premiums are of 50% of the base cost which to me sounds like a lot.   Of course any downtime is bad, but the work is not "mission critical", i.e. if it takes a few days to fix it when it breaks its no the end of the world. If it takes weeks to months then its a problem. If it breaks 2-3 times in 3 years, not too bad. If it breaks every month not good.   In term of build experience, I set up a linux cluster in grad school (from existing computers) and I build my home pcs but I never built a server before.   The server components I'm thinking about:   1 x SUPERMICRO SYS-7046T-6F 4U Tower Server Barebone Dual LGA 1366 Intel 5520 DDR3 1333/1066/800 ($1,050)  12 x Kingston 4GB 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10600) ECC Unbuffered Server Memory  ($420)  2 x Intel Xeon E5645 Westmere-EP 2.4GHz LGA 1366 80W Six-Core ($1,116)   4 x Seagate Constellation ES  2TB 7200 RPM SATA 6.0Gb/s 3.5" ($1,040)  1 x SAMSUNG Internal DVD Writer Black SATA ($20)  1 x Intel 520 Series 2.5" 180GB SATA III MLC SSD $300  1 x LSI LSI00281 PCI-Express 2.0 x8 MD2 Low profile SATA / SAS MegaRAID SAS 9260CV-4i Controller Card, $695

This is the  for "Should I build coomputing hardware myself?" questions.   I have put together countless PCs, but never a large server. The geek in me says build it, but the realist in me says let the manufacturer handle it when there is a problem. Ignoring the time penalty involved with the initial assembly time of a built one, which is a better solution? Have you ever run into a problem with a home build server that would have been solved easier/quicker/cheaper by going with a manufacturer? Are there any features that manufacturers give that aren't easily attainable with a home built server?


I've found a  asking if they are supported, and answers saying that it isn't, but there are suggestions about several different hacks. And even though the question is relatively old, it seems to still hold true.   But I'm wondering if this functionality is planned for any time soon?  And is there an actual reason they didn't want to support tables?

This is similar to:  and , but is slightly different. The other questions are asking more of a why question, not a please do this question. I am asking for a specific implementation of Markdown tables. I found  on making tables in Markdown using  or . The code to make a table looks like this:  | Left align | Right align | Center align | |:-----------|------------:|:------------:| | This       |        This |     This     | | column     |      column |    column    | | will       |        will |     will     | | be         |          be |      be      | | left       |       right |    center    | | aligned    |     aligned |   aligned    |   And the result is:   This is much different than , which says that Jeff doesn't want the <tr><td> tags allowed on the SE sites. This request has a specific feature request, as opposed to the other questions which don't really have a decisive yes/no answer.  Here are some specific posts that need this type of support:


This is a question that has bothered me for a long time and I haven't found an answer to anywhere. Imagine you have a steel rod balanced on a fulcrum, but not evenly balanced as shown in the picture below.    Now naturally the rod would tip over because of the uneven weight distribution but my question is what would be the net torque that is pulling the rod to the ground. Since this particular question is just one I came up with myself, I'm looking for an explanation rather than an answer. I believe this has something to do with net torque= Inertia x Angular acceleration, but I keep coming to dead ends. Thanks!

I've learned that the torque on an object is just $ \text{perpendicular force}\times\text{radius}$ and that has worked well for things like seesaws but it doesn't take into account the torque of the object itself!    In the picture the rod has a total mass of 5kg, and by definition the torque on the right is greater than that on the left.  $$T=Fr$$   I am supposed to solve the question     What distance to the left of the fulcrum (triangle supporting the rod) would I have to put a 3kg weight to balance the rod?     I've tried calculating the net torque $T_{net} = I\alpha$ but I don't really know how to approach this. I'm looking for an explanation more than an answer.


Find all $f$: $f(m^2+n^2)$=$f(m)^2+f(n)^2$ for all $m,n\in \mathbb{N_0}$ where  $f(1)>0$,  $f\in\mathbb{N_0}$ for all inputs I did $f(0)=2f(0)^2\implies f(0)=0$ $f(1)=f(1)^2\implies f(1)=1$ From this we can get $f(2)=2, f(4)=4$ etc. easily and also use some tricks like $f(2^2+1^2)=f(5)=5, f(4)=4$ so $f(3)=\sqrt{5^2-4^2}=3$ I tried using the parametrization of Pythagorean triples but am unable to prove that $f(7)=7$ Please help

Let $f:\mathbb{N}\cup\{0\}\to\mathbb{N}\cup\{0\}$ be a function which satisfies $f(x^2+y^2)=f(x)^2+f(y)^2$ for all $x,y \in\mathbb{N}\cup\{0\}$. It' easy to see that $f(0)=0$ and $f(1)=0$ or $f(1)=1$. Suppose let's assume that $f(1)=1$. Then it's very easy to see that $f(2)=2$ and since $f(2)=2$, we can see that $f(4)=4$ and $f(5)=5$ because $5=2^2+1^2$. To see $f(3)=3$, note that $$25=f(5^2)=f(3)^2+f(4)^2 \implies f(3)=3$$ One can even see that $f(6)=6$, $f(7)=7$ and so on. Is it generally true that $f(n)=n$ for all $n$?  Edit. If anyone wondering how $f(7)=7$ here is the way. Note that $f$ satisfies $f(n^2)=f(n)^2$. One can see that $$25^{2}=24^2+7^2 \implies 25^{2}=f(24)^{2}+f(7)^{2}$$ We have to show $f(24)=24$. For this note that $$26^2 = 24^2+10^2 \implies f(26)^{2} = f(24)^{2}+f(10)^{2}$$ But $f(26)=26$ because $26=5^2+1^2$ and $f(10)=10$ since $10=3^{2}+1^{2}$. In short if $n=x^2+y^2$ for some $x,y$ and $f(1)=1$, then we can see that $f(n)=n$.


What is the difference in meaning between these two questions:      who are you?   and      what are you?

I am often asked "Who are you?" and "What are you?", but I don't know the difference between these two questions.  Please explain it to me.


What does the phrase "happen to be" mean in the sentence:  Camera just happen to be recording this.

I saw  while in 1:19 Sec I have heard so:     "I happen to be pro-life"   What does it mean? I have tried to find it on some dictionaries (Cambridge, Oxford and Merriam Webster) and I didn't find the meaning.


My computer keeps asking me to update but there is no space, boot memory at 100%.  Have tried apt-get clean, sudo apt-get clean and sudo rm .xsessions-errors.   None of which work. Any suggestions greatfully received.  NB, I am NOT a computer whiz so baby steps PLEASE

My first issue was when I tried to apt-get update or apt-get upgrade. On upgrade I get the following error:  You might want to run 'apt-get -f install' to correct these. The following packages have unmet dependencies: linux-image-server : Depends: linux-image-3.2.0-27-generic but it is not installed E: Unmet dependencies. Try using -f.   I tried running apt-get install -f and this was the output(after saying yes on prompt)  (Reading database ... 186183 files and directories currently installed.) Unpacking linux-image-3.2.0-27-generic (from .../linux-image-3.2.0-27-generic_3.2.0-27.43_amd64.deb) ... Done. dpkg: error processing /var/cache/apt/archives/linux-image-3.2.0-27-generic_3.2.0-27.43_amd64.deb (--unpack):  failed in write on buffer copy for backend dpkg-deb during `./boot/System.map-3.2.0-27-generic': No space left on device  No apport report written because the error message indicates a disk full error                                                                           dpkg-deb:    error: subprocess paste was killed by signal (Broken pipe) Examining /etc/kernel/postrm.d . run-parts: executing /etc/kernel/postrm.d/initramfs-tools 3.2.0-27-generic   /boot/vmlinuz-3.2.0-27-generic run-parts: executing /etc/kernel/postrm.d/zz-update-grub 3.2.0-27-generic /boot/vmlinuz-3.2.0-27-generic Errors were encountered while processing: /var/cache/apt/archives/linux-image-3.2.0-27-generic_3.2.0-27.43_amd64.deb E: Sub-process /usr/bin/dpkg returned an error code (1)   I tried running apt-get autoremove and it gives me the same error as apt-get upgrade.  When I run df, I get this for /boot:  /dev/sda1                    233191     230297         0 100% /boot   So, I read elsewhere that I should try to purge old kernels. I checked for what kernels I had with:  $ dpkg -l linux-image-\* | grep ^ii ii  linux-image-2.6.38-13-server  2.6.38-13.52  Linux kernel image for version 2.6.38 on x86_64 ii  linux-image-3.0.0-13-server   3.0.0-13.22   Linux kernel image for version 3.0.0  on x86_64 ii  linux-image-3.0.0-14-server   3.0.0-14.23   Linux kernel image for version 3.0.0  on x86_64 ii  linux-image-3.0.0-15-server   3.0.0-15.26   Linux kernel image for version 3.0.0  on x86_64 ii  linux-image-3.0.0-16-server   3.0.0-16.29   Linux kernel image for version 3.0.0  on x86_64 ii  linux-image-3.0.0-17-server   3.0.0-17.30   Linux kernel image for version 3.0.0  on x86_64 ii  linux-image-3.2.0-24-generic  3.2.0-24.39   Linux kernel image for version 3.2.0  on 64 bit x86 SMP ii  linux-image-3.2.0-25-generic  3.2.0-25.40   Linux kernel image for version 3.2.0  on 64 bit x86 SMP ii  linux-image-3.2.0-26-generic  3.2.0-26.41   Linux kernel image for version 3.2.0  on 64 bit x86 SMP   When I try to remove the oldest with this:  $ sudo apt-get purge linux-image-2.6.38-13-server Reading package lists... Done Building dependency tree Reading state information... Done You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies: linux-image-server : Depends: linux-image-3.2.0-27-generic but it is not going to be     installed E: Unmet dependencies. Try 'apt-get -f install' with no packages (or specify a solution).   How can I free up or extend boot without messing up my installation?


I'm trying to design a 24V to 12V step down converter. Power efficiency is not that important to me, but I want to come up with the cheapest solution possible. I don't need isolation neither. So I though I would just come up with the simplest buck converter. Something like this    Sw2 would of course be an appropriate power MOSFET. Also the schottky diode is arbitrary, just used the first thing available in Circuit Lab.  Would such a simple buck converter be the cheapest solution for my application, and would it work, assuming that ripple is not a concern for my application?  EDIT: Second part of the question was if it works with such a simple feedback loop. There is a similar question which is already answered so I removed that part.  Thanks!

I am supposed to come up with some control schemes for the converter before understanding the standard PWM control scheme.   Isn't it just enough if the output of the converter is compared with a fixed reference voltage to drive the output to required voltage level? Although I'm not sure there is a lot more to it, this seems to work pretty well.   I've tried simulating this circuit with L,C and R values from an example.  Schematic:    The required output voltage is 6V. S2 is a voltage controlled switch, controlled by the output of comparator.    V2(green) is the output of comparator and V1(red) is the output of buck converter.


I have a Stamen Toner OSM background on a report am doing. It seems impossible to use "Print" or "Save as image" functions since the OSM is being projected wrong with 10 km or so.. Right now I'm taking screenshots from there as a work around but it feels kind of wrong?  Screenshot with correct OSM projection:   Save from print composer with wrong OSM projection: (Buffers should be located at the lower right corner

I'm having trouble with the OpenLayers Plugin of Qgis and the map composer:  If I create an OSM-background layer and if I want to export this, the OSM-Layer looks perfectly all right in the normal qgis program window. But in the map composer and after export the layer has shifted relatively to my other shape layers (EPSG:32633 - WGS 84 / UTM zone 33N).  The second thing is that the output resolution of the exported osm-layer is very, very poor.   A really bad way of getting around this whole trouble would be to increase the screen resolution and make a screenshot of the map composition window of qgis. But I don't think this would be very professional. It also would cause a lot of pain :)   I'm using Qgis 1.8.0-Lisboa under Linux. The openlayers plugin is version 0.92.


I'm writing a code to check for balanced brackets but I'm having a problem, probably with Java syntax. In the following code:  String s0 = "{{[[(()[])]{()}]}}}"; String[] s1 = s0.split(""); if (s1[0] == "{")     System.out.println("Ok"); else     System.out.println("Nope");   Why the comparison   s1[0] == "{"   is not true?

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


If the p-value is greater than 0.900, should  you reject $H_0$ at the 0.10 level?"

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests.  It seems that students easily learn how to perform the calculations required by a given test but get hung up on interpreting the results.  Many computerized tools report test results in terms of "p values" or "t values".  How would you explain the following points to college students taking their first course in statistics:   What does a "p-value" mean in relation to the hypothesis being tested?  Are there cases when one should be looking for a high p-value or a low p-value? What is the relationship between a p-value and a t-value?


8 rooks are randomly placed on different squares of a chessboard. A rook is said to attack all of the squares in its row and its column.  Compute the probability that every square is occupied or attacked by at least 1 rook.  The first step I took was to state that there are $64C8$ ways to decide how to place the 8 rooks on the chessboard. Next, I tried to experiment with a physical chessboard to see how this could be done. The only way I found that every square on the board can be attacked is if one rook is in either every horizontal row or every vertical row. Therefore, there are $2 * 8^8 - 2$ ways to place the rooks. To clarify, it is "-2" because the diagonals are counted twice.   Is there a case that I overlooked, or did I solve the problem correctly?  Thanks,  You Know Me......

In how many different ways can we place $8$ identical rooks on a chess board so that no two of them attack each other?  I tried to draw diagrams onto a $8\times8$ square but I'm only getting $16$ ways.  Does that sound right?  Thanks for the help!


I'm trying to remember a name of a book that took place on a spacecraft, with a hunchback character named Bartholomew. they notice a ship following them and eventually go investigate, the ship turns out to be full of booby traps. That's about all I can remember. thanks for any help.

The cover has a large Leviathan type ship on the front.   It is set in deep space as the people on said ship have been living there for generations. They come across an abandoned ship and set out to check it out. There are several traps but it seems to be a human ship and they even find a lone woman. Unfortunately she turns out to be an alien and attacks. They end up on a planet where a factory/warehouse is found to contain bodies, they think were eaten/experimented on by the aliens. I thought the book was called Leviathan but can't seem to find it anywhere. I seemed to be an older book from the golden age maybe even up into the 70's but I haven't had any luck yet. Any help I could get finding this would be great,thanks.


If I understand correctly, the action for a massive free particle is: $$ S = -mc^2 \int \mathrm{d}\tau = -mc \int \sqrt{g_{\mu\nu} \frac{\mathrm{d}x^\mu}{\mathrm{d}\lambda} \frac{\mathrm{d}x^\nu}{\mathrm{d}\lambda}} \, \mathrm{d}\lambda $$  and from this we can derive the geodesic equation. This action functional doesn't make sense for photons though, which have $m = 0$. So what is the action for photons?  I thought about replacing $mc$ with the quantity $\hbar k$ (which has the same units) but I'm not sure whether that makes sense, given that $k$ is not constant for a photon propagating through curved space-time. (On the other hand, it makes sense that there should be a single free parameter since the propagation of light in GR is independent of the photon's momentum. But if this is the correct action then how do we actually interpret the parameter $k$?)

For relativistic massive particle, the action is $$\begin{align}S ~=~& -m_0 \int ds \cr ~=~& -m_0 \int d\lambda ~\sqrt{ g_{\mu\nu} \dot{x}^{\mu}\dot{x}^{\nu}} \cr ~=~& \int d\lambda \  L,\end{align}$$ where $ds$ is the proper time of the particle; $\lambda$ is the parameter of the trajectory; and we used Minkowski signature $(+,-,-,-)$. So what is the action for a massless particle?


Let $A,B$ be connected subsets of the Real Numbers. Show that $A+B$ is a connected subset of the Real Numbers.

$A$ and $B$ are  two connected subset of $\mathbb{R}$ define $A+B=\{x+y:x\in A,y\in B\}$, then is $A+B$ also connected?  naturally I was thinking about two disjoint connected subsets of $\mathbb{R}$, say $A=[0,1]$ and $B=[4,5]$    then $A+B=[4,6]$? so is it ingeneral true?


I've used Blender for years but have never hopped on the forums. I am still new as I am very slow at this (all self-taught as I know many of us are).  I am sure this question has been asked elsewhere but I couldn't find it so is it possible to have blender respond so that when I click on an object in the viewport the object list hierarchy automatically goes to that object also?  Oh and also -- Seeing as how this is my first post I'll share an image of what I'm currently working on. I've only ever made 3 things before. A potato, a strawberry, and a sculpted demon looking thing that came out by pure mistake. This thing is getting so complex it is time consuming to keep going through the folders in the hierarchy to find the objects.  Anyway here is what I'm currently working on -- A starship hallway - Currently under red alert. I'm using it as a practice model to learn materials and textures. It will eventually have a door at the end of the hallway and you'll see the exterior of the ship and a planet out the port side windows.    Thank you everyone in advance.  I'll update everyone as this project goes along.

How can I jump to the selected object in the out-liner, I've got over 200 objects in my scene, all named cube.___ ... and I can't seem to find my selected object. How can I jump to it?


I have the following 2 equations and I have drawn their graphs.  $$\begin{cases}y=5+x-x^2\\ y=x+4\end{cases}$$  I have found intercepts as well.   The question is asking to find area between these 2 curves. I am not sure if I should take as a whole triangle?

Find the area enclosed between the curves $y=x^2$ and $y=60-7x$.  I am completely new at this but I have tried and I believe that it should be between the numbers $0$ and $60$ is this right?


I want to completely wipe a harddrive with Ubuntu on it, so I can put Windows back on it. How do I do that? I don't want to dual boot either, I just want to wipe the drive and put Windows on it. How do I do this? Thanks!  -Trace

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


I have submitted the paper to  after the stage "submitted to the journal" (14 days ) ,I have received the message that paper is assigned with current stage " Decision in process " in the same time , Is this can say anything about acceptenece or reject of my paper ?

What steps does a manuscript typically go through from submission to publication (or rejection) in a typical journal? How are these steps referred to, in particular by editorial systems, and how long do they each typically take?  Note that this question is about the typical situation and hence not about:   Journals with an atypical workflow, e.g. those that allow for an instantaneous reviewer–author interaction. Exceptional steps or rare occurrences such as withdrawal or .   This is a canonical question on this topic as per . Due to its nature, it is rather broad and not exemplary for a regular question on this site. Please feel free to improve this question.


Take $x^2=x+x+x+\cdots$ ($x$ times). Now differentiating both sides wrt $x$, we get:  $$2x=x.$$  This means $x=0$ or $2=1$.  How? Where did I go wrong?

Consider the following:   $1 = 1^2$ $2 + 2 = 2^2$ $3 + 3 + 3 = 3^2$   Therefore,   $\underbrace{x + x + x + \ldots + x}_{x \textrm{ times}}= x^2$   Take the derivative of lhs and rhs and we get:   $\underbrace{1 + 1 + 1 + \ldots + 1}_{x \textrm{ times}} = 2x$   Which simplifies to:   $x = 2x$   and hence    $1 = 2$.     Clearly something is wrong but I am unable pinpoint my mistake.


When a post is deleted and the notification comes through, it scrolls over the inline flag bar:    The entire post also seems to capture clicks instead of letting them get to the flag bar. Looks like someone got a z-index wrong...

There is a little bug that becomes visible when a page contains realtime-post-deleted-notification banners (that's the CSS classname of these red banners appearing on answers which just got deleted, see screenshot below) and you try to open the flag dialogue above them:    Obviously, the dialogue appears below the banners, which it clearly should not do. It also has no input focus, trying to interact with the dialogue fails and either closes it (clicking outside of the red banners) or reloads the page (clicking on the red banners).  The cause for this is simply the z-index ordering in the site's CSS. Relevant CSS snippets:  .realtime-post-deleted-notification {     position: absolute;     text-align: center;     z-index: 100; }  .popup {     display: none;     padding: 15px;     position: absolute;     z-index: 10; }   So the fix for this minor bug would probably be to raise the z-index of the popup class to something greater than 100.


My dedicated server can't handle more than 4Mbits/s of bandwidth. After that, the server don't ping anymore. My provider told me it's because my server isn't well configured.  When I look in the logs (syslog), I see that it's probably a syn flood on the port 8085. So I configure iptable to limit the connexion number per IP      iptables -I INPUT -p tcp -m connlimit --connlimit-above 50 -j REJECT --reject-with tcp-reset   and     iptables -A INPUT -p tcp --dport 8085 -m state --state NEW -m recent --name BLACKLIST --set   iptables -A INPUT -p tcp --dport 8085 -m state --state NEW -m recent --name BLACKLIST --update --seconds 10 --hitcount 10 --rttl -j DROP   I activated syn cookie :  echo "1" > /proc/sys/net/ipv4/tcp_syncookies echo "1024" > /proc/sys/net/ipv4/tcp_max_syn_backlog echo "1" > /proc/sys/net/ipv4/conf/all/rp_filter    To be sure, I installed fail2ban. But there isn't a huge trafic on this port...  Any idea ?  Thank you

This is a  about DoS and DDoS mitigation.   I found a massive traffic spike on a website that I host today; I am getting thousands of connections a second and I see I'm using all 100Mbps of my available bandwidth.  Nobody can access my site because all the requests time out, and I can't even log into the server because SSH times out too!  This has happened a couple times before, and each time it's lasted a couple hours and gone away on its own.  Occasionally, my website has another distinct but related problem: my server's load average (which is usually around .25) rockets up to 20 or more and nobody can access my site just the same as the other case.  It also goes away after a few hours.  Restarting my server doesn't help; what can I do to make my site accessible again, and what is happening?  Relatedly, I found once that for a day or two, every time I started my service, it got a connection from a particular IP address and then crashed.  As soon as I started it up again, this happened again and it crashed again.  How is that similar, and what can I do about it?


when i try ping google server takes only 30ms.   PING google.com (172.217.26.174) 56(84) bytes of data. 64 bytes from google.com (172.217.26.174): icmp_seq=1 ttl=56 time=31.2 ms 64 bytes from google.com (172.217.26.174): icmp_seq=2 ttl=56 time=32.3 ms   I did this from cochin,Kerala,India to a google server located in california, US. The minimum distance from this two places is 14,560 km.  So, light can do this two way trip in just 97ms.  (14,560 * 2 ) / c =~ 97ms   So how pinging google server can exceed the light speed? What is wrong in the assumptions/calculations?  EDIT  Hi i have found similar question here,   But ping does not shows any cdn domain there, also iplocation of server belongs to the US. If server located nearby why ping is not showing the that nearby ip address?

I just discovered very strange thing while testing my internet connection. My ping is smaller than it should be. For example ping time to Arizona State University is about 14ms.  eryk@eryk-pc:~$ ping www.asu.edu PING www.asu.edu.cdn.cloudflare.net (104.16.51.14) 56(84) bytes of data. 64 bytes from 104.16.51.14: icmp_seq=1 ttl=60 time=13.8 ms   I'm living in Poznań in Poland so my distance to Arizona State University in a straight line (very optimistic assumption) is about 10000 km. Considering the fact that ping time is a time for two directions (to the target and back to home). So my ping packet have to cross 20000 km distance. Speed of light is 300 000 km per second that is 300km per millisecond. So the smallest possible time to ping Arizona State University with my packet travelling at a speed of light is  20000/300=67ms   I have noticed similar results for servers located in Australia and some other States of America. Is my internet connection five times faster than light?


Consider $C([a,b])$, the vector space of continuous functions in $[a,b] \subset \mathbb{R}$ to $\mathbb{R}$. Let be $f \in C([a,b])$, we define $\|\cdot\|_1$ as follows: \begin{equation*}  \|f\|_1 =  \int_{a}^{b}|f(x)|dx  \end{equation*} I must show that $(C([a,b]), \|\cdot\|_1)$ is not a Banach space. This is my answer the which one is wrong according to my teacher. Consider the following counterexample. Let $c =2^{-1}(a+b)$ y $f_n:[a,b] \rightarrow \mathbb{R} \hspace{.1cm} \forall n \in \mathbb{N}$ with the following association rule and graph:  It's clear that $\{f_n\}_{n \in \mathbb{N}} \subset C([a,b])$. We will show that $\{f_n\}_{n \in \mathbb{N}}$ it's a $||\cdot||_1-Cauchy$ sequence. Let be $\epsilon > 0$ and $N = \displaystyle \left\lceil{ \frac{1}{2 \epsilon}}\right\rceil$, then: \begin{equation*}     ||f_n-f_m||_1 = \int_{a}^{b} |f_n(x)-f_m(x)|dx = \left| \frac{1}{2n}-\frac{1}{2m} \right| \leq \max \left\{ \frac{1}{2n}, \frac{1}{2m}\right\} < \epsilon, \hspace{.1cm} \forall n,m \geq N \end{equation*} So the sequence is $||\cdot||_1-Cauchy$, however though this sequence converges to the following limit function, the limit function is clearly discontinuous. Let be $f:[a,b] \rightarrow \mathbb{R}$: \begin{equation*} f(x) =      \begin{cases}         1 & \text{si $x \leq c$}\\         0 & \text{si $x > c$}     \end{cases} \end{equation*} Fixed $\epsilon_1 > 0$ and $N_1 = \left\lceil{\displaystyle\frac{1}{2 \epsilon_1}}\right\rceil$, then: \begin{equation*} ||f_n-f||_1 = \displaystyle\int_{0}^{1} |f_n(x)-f(x)| = \frac{1}{2n} < \epsilon, \hspace{.1cm} \forall n \geq N_1 \end{equation*} $\textbf{Now, the problem is that}$ (according to my teacher) I only have propose a discontinuous function wich is a limit of the sequence, this does not means that do not exits another continuous function wich is also the limit of the sequence. I understand the problem, but nothing comes up to me to solve this.

That's really embarrassing, however I need to ask it. I could not prove that the normed space    $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle $ is complete (as a metric space), where $\| f\|_1 = \int_0^1 |f(x)|dx$. I don't really know how to explicit a continuous functions as a limit of a Cauchy sequence. I tried to prove that the pointwise limit (of the Cauchy sequence) have just a finite number of discontinuities (I don't know if it's true) and then approximate it by a continuous function.  Thanks in advance.


What is preventing my objects from moving smoothly? Instead of moving slowly and precisely, the object moves by one unit    .

My cursor is moving by every selection by large increments!  Normally when I use Blender, I am able to select and move objects to any coordinate. Now, all of the sudden, when I select an object or mesh the selection moves by an inch or so in each direction.  How do I reset it to normal?


I have tried to research this .. could anyone answer why figures 1-9 are written as digits/numbers and then from 9 onwards they are typed in alphabetical form?

The junction has a stop sign on each of the four entrances.   The junction has a stop sign on each of the 4 entrances.   The first is preferred, for some reason, by many English texts. Why? I haven't seen this phenomenon in other languages.


If a commenter says some fact that I don't entirely agree with, I tend to reply. Sometimes we do not immediately come to a consensus and I can tell it has a good chance of creating a long back-and-forth dialogue.  Could I request a way to quickly create a chat room to continue the discussion? (similar to the button that appears after the dialogue gets rather long)  I tried creating it manually once, but it is so tedious to go over there, enter a description, and then post a link back to the new chat room, on the original comment discussion.  Perhaps this Move To Chat button appears earlier only when I reach a certain level of reputation? IDK, but it would be nice to pre-emtively prevent cluttering of the comments trail.

One of my sites has a persistent problem with comments -- chatty comments, proto-answers in comments, big long conversations in comments.  I suspect we're not the only ones with this problem.  While a conversation between two people will eventually trigger the "hey, you should do this in chat" notice, and while moderators can move comments to chat (after an auto-flag is raised), I'm looking for something that regular users can do, and sooner.  We currently ask people to , but the process is a little cumbersome:   You're on the site, on a specific post, and see a comment thread that's getting away from what comments are for. You leave the page or launch a new tab, navigate to chat, and find your way to "create a room".  You might or might not give this room a helpful name. Optionally you cut/paste existing comments there.  I include this theoretical step for the sake of completeness; it's not really a reasonable thing to expect. You go back to the post and write a comment linking to the chat room.   But the other commenters might just ignore you, might not even have privileges to chat, and have no easy way to move things there.  What can we do to make this easier?  It'd be great if we could at least create the room (with a canonical name pattern) and auto-generate the comment containing the link, all without leaving the post page.  A harder question is what to do about existing comments; we probably don't want any random user to be able to move a whole set of comments to chat, but there's something to be said for copying existing comments to the new chat room and then raising a moderator flag on the post so mods can review and decide whether to purge those comments.  (Ones that ask for clarification should remain, as usual, hence the need for human review.)  What can we do to make this process easier?


good day i am in the mid of creating a bike-frame-jig. the model is oriented at tanner w s jig:  see some the parts (here as Acronyms ) he is using: HT - Head Tube ST - Seat Tube TT - Top Tube DT - Down Tube BB - Bottom Bracket CS - Chain Stay SS - Seat Stay note: i found two or three very interesting "hacks" of Tanner W: see the following pictures: modifications made by Kristofer Henry a. HT Assembly - The standoffs sit 45 deg.    So here is the HT Assembly pretty much put together with the exception of the bottom "puck" holder and purge fittings. The standoffs sit 45 deg. back from the centerline of the extrusion. This allows me to have access to both sides of the HT/TT/DT area. I'll mount both standoff's on a rotary table and radius the ends to make my hands happy. Now that it is assembled, and I've had some time to stare at it long enough, I'm thinking I may change how the bottom standoff is mounted so it is fixed to the bottom of the extrusion and the whole assembly rotates off of it. Taking a measurement from the top of the main beam will enable an exact measurement to locate the bottom of the HT in space which will be nice..  and see the following discussion:  Francois Cau: What did you use for the pivot point of the extrusion part ? Is it just a simple screw ? (I'm trying to find a good/precise solutions for Rev2.0 of my jig...)  Kristofer Henry:  There is a shoulder bolt that rides on a pressed in bearing. It's pretty smooth and clamping action is good.  queston: - very very interesting .- Why did you change the standoff - with a 45 degree-skip?! Can you compare it with a standard - standoff another hack: by kolb-Rahmenbau.ch  he uses a very very big plate - see the right side  of the spine ...: the plate for the head tube assembly is very very big - much bigger than that one that Tanner W uses. i guess that this is much more precicely .. he can work with a lower degree of measurement-failures how do you see this !? what do you think !? What else do you like at this bike-frame-jig !? I think it is very very interesting - if we compare it with tanner ws jig!? look forward to hear form you

i am currently workin on the Bicycle-Frame-Building-Jig that is designed by tanner W at Instructables  which bottom bracket assemblies should i work out: The question is - which bottom bracket-assembly-types would you suggest!?which axles and dummy shells should i drill see  well at the moment i am musing bout the extras and features  what should i add which features should i add eg some dummy axles for the bottom bracket assembly - what do you suggest!?  i think as long as we can get a standard English bb in both 68 and 73, we should be fine. afaik: It's hard to deal with the press fit sizes because AFAIK nobody is selling facing/reaming tools for them. As far as i know: Paragon has a ton of bb shells available, so we could match what they sell. but I think the two most standard sizes will probably do for now. the tanner w fixture is adjustable for width, so we only need one set of blocks see here:  and also see the bottom bracket shells:  well at the moment i am musing bout the extras - what should i add ?


I'm just wondering Does Ubuntu sell the tablets or can I buy one with the right requirements and put Ubuntu on to it as the new operating system??

With the announcement of the Ubuntu Phone OS I'd like to know what phone (and tablet) models are supported at this time.  Note from foss & Oli: We are making this the master question for all future "Will this work on <insert random tablet/phone/device here>?!" questions


actually I want to install a Samsung galaxy s5 ROM on my micromax bolt a068 but I was not able to find such ROM for my device on the internet but now I found a s5 ROM for micromax canvas juice ant this device is almost similar to my device,only one the processor is not same I have a 1 GHz processor and it has a 1.3 GHz processor. so my question is that can I use that ROM for my device. is it safe to do so.  thankyou

I own a MicroMax A100. I want to install the latest version of a different ROM (Samsung or Nexus).  Is it possible? If so, can you tell me how?  If not, can I install a ROM made for a different device, but from the same manufacturer? For example, could I install a ROM for the MicroMax A110, which is the successor of A100?


for my dish tv set up box. I am using 5 volt 2amp ac/dc adapter instead of 1amp. Is it okay? Or harmful? That dealer said to me that I can use higher amp.  Please reply. ...

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.


When I use Chrome to listen to music, sometimes the volume suddenly goes down. Other sounds are just normal. This is the Windows Sound mixer shows:    The volume meter on Chrome has 2 indicators. I have no Skype or any communication application on at that time.  My Chrome version is "Version 36.0.1985.125 m" (newest up to now). Here is the extensions list:    What is the problem with Chrome? How can I fix it? It is quite annoying that I have to move the volume up everytime this happens.

I recently upgraded to Windows 8 from Win 7 64 bit and have started to encounter a strange issue. When I have any program running which plays sound, such as a game or spotify, after a random interval (usually around 5-10 minutes) the program sound will set itself really low.    If I Alt-Tab to the desktop and check the Mixer I can see that the Application volume has automatically set itself really low - the other volume levels (i.e. the Device speakers) stay the same.  I'm able to just set the application volume back to a reasonable level and it stays that way for another 5 - 10 minutes then goes quiet again.  My sound is Realtek High Definition Audio and my machine is an Acer Aspire 5738G if that helps in any way.  Any help much appreciated!


If $$a_{n+3}=-a_{n+2}+2a_{n+1}+8a_n $$ for $$ a_0=a_1=a_2=1.$$ Then prove that $a_n$ is a perfect square.

I would be happy if you let me know how to tackle this problem. Thanks.


I build a few models, each model will produce a normal distribution for the value of a future event. For example, model M1 will produce a normal distribution $n(30, 5^2)$, and the value of the future event observed is 24. Likewise,  M2-> $n(40, 10^2)$, observation: 35  M3-> $n(10, 2^2)$, observation: 20  How do I evaluate the underlying theory used to build M1, M2, M3?

The Kolgomorov-Smirnov test, Shapiro test, etc.... all reject the hypothesis that a distribution is normal. Yet when I plot the normal quantiles and and histogram, the data is clearly normal. Maybe because the power of the tests are high?   The sample size is around 650. So shouldn't at least one of these tests fail to reject the null hypothesis?  Results:             Kolmogorov-Smirnov    D          0.05031          Pr > D       <0.010            Cramer-von Mises      W-Sq       0.30003          Pr > W-Sq    <0.005            Anderson-Darling      A-Sq       1.66965          Pr > A-Sq    <0.005            Chi-Square            Chi-Sq  3250.43596     18   Pr > Chi-Sq  <0.001


SO i have a Bash Script like this and goal is to determine the path of an executable file and i want to print it, here is what i'm doing #!/bin/bash  exepath=which exe  echo "$exepath"  Now this instead of printing path its starting the exe file in my system, how do i print the path stored in exepath variable.

I want to assign the result of an expression (i.e., the output from a command) to a variable and then manipulate it – for example, concatenate it with a string, then echo it.  Here's what I've got: #!/bin/bash cd ~/Desktop; thefile= ls -t -U | grep -m 1 "Screen Shot"; echo "Most recent screenshot is: "$thefile;  But that outputs: Screen Shot 2011-07-03 at 1.55.43 PM.png Most recent screenshot is:   So, it looks like that isn't getting assigned to $thefile, and is being printed as it's executed. What am I missing?


So our program is suppose to have the user input a certain amount of money and then generate how much change they get (quarters, dimes, etc.) and after getting change back, the program asks the user to input whether they want to try again or not. Here is where the program doesn't seem to work and I need help. this is what I have so far:   package week14; import java.util.Scanner; public class VendingMachine {      public static void main(String[] args) {     Scanner input = new Scanner(System.in);      System.out.print("Enter a whole number 1-99.\n I will find a combination of coins\n that equals that amount of change: ");     int coins = input.nextInt();     String answer = "yes";     while (answer.equals("yes")) {                 if (coins >=1 && coins <= 99) {                     int quarters = coins / 25;                     int dimes = (coins%25) / 10;                     int nickels = ((coins%25)%10) / 5;                     int pennies = (((coins%25)%10)%5) / 1;                      System.out.print(coins + " cents in coins can be given as\n"+quarters+" quarters\n"+dimes+" dimes\n"+nickels+" nickels\n"+pennies+" pennies\n");                     System.out.print("Do you want to try again? ");                     answer = input.nextLine();                     answer = answer.toLowerCase();                       System.out.print("\nEnter a whole number 1-99.\n I will find a combination of coins\n that equals that amount of change: ");                     coins = input.nextInt();                 }else {                     System.out.print("Please enter between 1-99.\nEnter again: ");                     coins = input.nextInt();                 }                  if(answer.equals("no")) {                     System.out.println("\nThanks for using \"Change Maker\" program!");                     break;                 }          }     } }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I am new to python, so I expect that I am missing some basic knowledge of types here.  I am trying to create a string where I take a floating point number and replace decimal point with a string.  In doing so I tried calling a line of code that is equivalent to:  int(pow(10, 1)*(5.1%1)))   But if you run this code:  x = pow(10, 1)*(5.1%1) print(x) print(type(x)) print(int(x)) print(int(1.0)) print(type(1.0))   It returns:  1.0 <type 'float'> 0 1 <type 'float'>   I assumed there is a type problem here but they are both type float. So why does int(x) return zero but not int(1.0)?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


Prove that if $V$ is an inner product space, then $|\langle x,y\rangle| = \|x\| \cdot \|y\|$ if and only if one of the vectors $x$ or $y$ is a multiple of the other.   Given the hint: identity holds and $y \neq 0$, let $a=\frac{\langle x,y\rangle}{\|y\|^2}$, and let $z=x-ay$. Prove $y$ and $z$ are orthogonal and $|a|=\frac{\|x\|}{\|y\|}$. Then use Pythagorean theorem   I am not able to appreciate this hint, can someone explain the general idea behind this? especially why do we need a $z$ a have to prove $z$ and $y$ are orthogonal? Want the intuition to understand why to do this.

Prove that if $V$ is an inner product space, then $|\langle x,y\rangle| = \Vert x \Vert\Vert y\Vert$ if and only if one of the vectors $x$ or $y$ is a multiple of the other.  I am given a hint to let $a= \frac{\langle x,y\rangle}{\|y\|^2}$, and let $z = x - ay$, then prove $y$ and $z$ are orthogonal and $|a|= \frac{\|x\|}{\|y\|}$. I don't know how they come up with this, what was the original idea?