I'm really confused now. I always thought that the differential notation $\frac{df}{dx}$ was just that, a notation.  But somehow when doing integration by u-substitution I'm told that you can turn something like this $\frac{du}{dx} = 2x\;$ into this $\;du = 2x\ dx$.  But how is that even possible? I understand that the notation comes from the fact that $\frac{du}{dx}$ actually means the limit of the difference in $u$ over the difference in $x$, with $\Delta x$ approaching $0$.  $$u'(x) = \frac{du}{dx} = \frac{du(x)}{dx} = \lim_{\Delta x\to 0} \frac{u(x+\Delta x)\ -\ u(x)}{(x+\Delta x) - x} = \lim_{\Delta x\to 0} \frac{u(x+\Delta x)\ -\ u(x)}{\Delta x}$$  So if $\frac{df}{dx}$ is just a notation for the limit mentioned above, then what is the underlying argument to say that you can treat $\frac{du}{dx}$ as if it were an actual fraction?  Appreciate the help =)

In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $dy/dx$ is not a ratio. Couldn't it be interpreted as a ratio, because according to the formula $dy = f'(x)dx$ we are able to plug in values for $dx$ and calculate a $dy$ (differential). Then if we rearrange we get $dy/dx$ which could be seen as a ratio.   I wonder if the author says this because $dx$ is an independent variable, and $dy$ is a dependent variable, for $dy/dx$ to be a ratio both variables need to be independent.. maybe?


Let $k$ be a field and let $A$ be an algebra over $k$. Denote by $End_A (A)$ the set of all endomorphisms of the regular $A$-module $A$ into itself. Fix $a \in A$, and define the A-module homomorphism $r_a : A \rightarrow A$ by $r_a(x) = x \cdot a$.  Clearly, $\{r_a: a \in A\} \subseteq End_A (A)$. But, is it true that moreover $\{r_a: a \in A\} = End_A (A)$? If so, how to show this?

Let $k$ be a ﬁeld and let $A$ be a $k$-algebra. Denote by $End_A(A)$ the set of all $A$-homomorphisms of the regular $A$-module $A$ into itself. Fix $a ∈ A$, and deﬁne the $A$-module homomorphism $r_a : A → A$ by $r_a(x) = x*a$.  $\\$ Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}  $\\$ Answer: $\\$ Obviously I can see that, for any $a$ we have $r_a$ is in $End_A(A)$, but how do I go about the other direction? Namely why is it that any endomorphism at all has this very simple form? I just don't see it...


I have got a serious doubt.  I have read, "yellow light from a low pressure sodium vapour is monochromatic"  How can it be monochromatic when yellow light is a combination of red and green primary colours?

What happens when secondary colors like yellow,green and magenta are passed through a prism? Will it split into its component colors(for example yellow split into green and red)?If yes why we are observing secondary colors in the visible spectrum obtained when white light(composite light) is passed through a prism?


My proof goes like this     For $n=2$ there are infinite solutions.   Let $x^2+y^2=p^2$ be one such solution.As there are infinite solutions, We can assume that $ p = q^3$ for some integer $q$.  Then after substituting,we get  $x^2+y^2=(q^3)^2$  $x^2+y^2=(q^2)^3$  We found a solution for $n=3$.Instead of $p=q^3$ we can put any power to q.Therefore we can find a solution for any value of $n$.  Is this correct proof or are there any loopholes in my proof or is there any more elegant proof

I was presented with the following problem:      Prove that there exist solutions to $x^2+y^2=z^n$ for all $n$, with $x,y,z, n \in \mathbb{N}$   I showed that by taking any Pythagorean triple $x^2+y^2=z^2$ and multiplying by $z^{2(n-1)}$ we get $(z^{n-1}x)^2+(z^{n-1}y)^2=(z^2)^n$, which allows me to generate solutions easily for any value of $n$. I managed to find several similar questions on this site, such as  concerning the specific case $n=3$. I notice that all of these questions take a similar approach and start with a Pythagorean triple and use it to generate general solutions.  Is there a way to prove the statement (or better yet provide solutions to the equation) without first relying on Pythagoras?


I want to get the variable name of an argument passed into a method. // Somewhere in the code int myNumber = 1; Method(myNumber);  ...  public void Method(int number) {     // Here I want to somehow get "myNumber" as well as access the value '1'. }  I haven't had any success finding an answer to this question. Many answers says no, but that is back when C# 6 was the latest version. Maybe there is a solution today? I imagine that passing by reference ref could be relevant, as that at least ensures that a variable is passed in the method, and not just the value.

Let me use the following example to explain my question: public string ExampleFunction(string Variable) {     return something; }  string WhatIsMyName = "Hello World"; string Hello = ExampleFunction(WhatIsMyName);  When I pass the variable WhatIsMyName to the ExampleFunction, I want to be able to get a string of the original variable's name. Perhaps something like: Variable.OriginalName.ToString()  Is there any way to do this?


i need a bus to run so it gives me a 1/2 chance of getting to point B faster than walking. The distance from point A to B is 1.5 miles. the speed of the bus is 25mph and the walking speed is 4mph  takes .375 hours to get by walking takes takes .06 hours to get by taking bus time difference is .3150 hours  The answer is 1.59 bus per hour but I am not sure how to get to this answer.....any help is appreciated!

i need a bus to run so it gives me a 1/2 chance of getting to point B faster than walking. The distance from point A to B is 1.5 miles. the speed of the bus is 25mph and the walking speed is 4mph   Distance = speed x time  Speed by walking 4 miles per hour Speed by bus 25 miles per hour Total distance= 1.5 miles Time it takes to go by walking (distance divided by speed) or 2 miles / 4 mph = 1/2 an hour or 30 mins. Time it takes to go by bus 2 miles / 25 miles per hour or 1/12.5th of an hour or 60/12.5= 4.8 mins.  The answer is 1.59busperhour but I am not sure how to get to this answer.....any help is appreciated!


I was just wondering if we should do obj = null after adding it into an array. Note that this is about a special case, read below.  First, let's consider class A like this:  public class A {     public void doSomething(B object) {         // some code here     } }   and class B like this:  public class B {     private final A a;     public B(A a) {         this.a = a;     }     public void aMethod() {         // Does something here         a.doSomething(this);     } }   Until now everything's ok. An object of type B can call the A's doSomething() method to edit the object based on some data there.  Now let's consider the following situation: the doSomething() adds the object B to an arraylist. Now which if these codes should I use:  public void doSomething(B b) {     arrayList.add(b);     b = null; } // or public void doSomething(B b) {     arrayList.add(b); }   In the first doSomething() we set the object to null, which means that the method caller becomes null. Well, that's OK to me as doSomething() call is the last statement I need to in my aMethod(). But is it good to do so?

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


Every PPA I'm trying to add on Ubuntu 20.10 fails to be added. For example, trying to add the neofetch PPA (ppa:dawidd0811/neofetch): $ sudo add-apt-repository ppa:dawidd0811/neofetch  gives me this: http://ppa.launchpad.net/dawidd0811/neofetch/ubuntu groovy release 404 Not Found [IP: 91.189.95.83 80]  The same happens for any PPA ppa:anything.

PPA seems to be constantly offline. Whenever I use sudo apt-get update, this error is shown:  W: Failed to fetch http://ppa.launchpad.net/ 404  Not Found   How do I fix these errors?


I am interested in a proof of very general theorem, well known:  Given a topological space $X$ and a dense subset $A$ (so it has nonempty intersection with any open subset of $X$), and if we are given two continuous functions $f, g$ which map $X$ to $Y$, where $Y$ is another topological space, Hausdorff, and $f(x) = g(x)$ for all $x$ in $A$, then for all $x$ in $X$ it holds $f(x) = g(x)$.

Specifically, $f = g$ on $S$, where $S$ is a dense subset of $X$. Is it true that $f = g$ on all of $X$? I'm quite sure that this holds true in the case where $X = \mathbb{R}$, but I don't think it holds true in general. Is this true? If so, could you provide a counterexample where $f \neq g$ on $X$?


I want to install Macaulay2 on Ubuntu 18.04. I followed the instructions  and for some reason its not working. Could anybody help me figure this out? So this is what I have:  Input    sudo apt-get install libblas3 libgfortran4 liblapack3 libquadmath0   Output:   Reading package lists... Done  Building dependency tree  Reading state information... Done  libblas3 is already the newest version (3.7.1-4ubuntu1).  liblapack3 is already the newest version (3.7.1-4ubuntu1).  libgfortran4 is already the newest version (7.4.0-1ubuntu1~18.04.1).  libquadmath0 is already the newest version (8.3.0-6ubuntu1~18.04.1).  0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   Input   wget https://faculty.math.illinois.edu/Macaulay2/Repositories/Ubuntu/dists/bionic/main/binary-amd64/Macaulay2-1.14-amd64-Linux-Ubuntu-18.04.deb   Output   Will not apply HSTS. The HSTS database must be a regular and non-world-writable file.  ERROR: could not open HSTS store at '/home/artus/.wget-hsts'. HSTS will be disabled.  --2019-10-30 13:51:17--  https://faculty.math.illinois.edu/Macaulay2/Repositories/Ubuntu/dists/bionic/main/binary-amd64/Macaulay2-1.14-amd64-Linux-Ubuntu-18.04.deb  Resolving faculty.math.illinois.edu      (faculty.math.illinois.edu)... 128.174.199.46  Connecting to faculty.math.illinois.edu   (faculty.math.illinois.edu)|128.174.199.46|:443... connected.  HTTP request sent, awaiting response... 200 OK  Length: 23695100 (23M) [application/octet-stream]  Saving to: ‘Macaulay2-1.14-amd64-Linux-Ubuntu-18.04.deb.7’   Macaulay2-1.14-amd64-Lin 100%[===============================>]  22.60M   425KB/s    in 59s   2019-10-30 13:52:25 (395 KB/s) - ‘Macaulay2-1.14-amd64-Linux-Ubuntu-18.04.deb.7’ saved [23695100/23695100]   Input   wget https://faculty.math.illinois.edu/Macaulay2/Repositories/Ubuntu/dists/bionic/main/binary-amd64/Macaulay2-1.14-common.deb   Output   Will not apply HSTS. The HSTS database must be a regular and non-world-writable file.  ERROR: could not open HSTS store at '/home/artus/.wget-hsts'. HSTS will be disabled.  --2019-10-30 13:53:27--  https://faculty.math.illinois.edu/Macaulay2/Repositories/Ubuntu/dists/bionic/main/binary-amd64/Macaulay2-1.14-common.deb  Resolving faculty.math.illinois.edu (faculty.math.illinois.edu)... 128.174.199.46  Connecting to faculty.math.illinois.edu (faculty.math.illinois.edu)|128.174.199.46|:443... connected.  HTTP request sent, awaiting response... 200 OK  Length: 21834554 (21M) [application/octet-stream]  Saving to: ‘Macaulay2-1.14-common.deb.7’   Macaulay2-1.14-common.de 100%[===============================>]  20.82M   946KB/s    in 43s   2019-10-30 13:54:19 (499 KB/s) - ‘Macaulay2-1.14-common.deb.7’ saved [21834554/21834554]   Input   M2   Output   M2: command not found   Note: I am using the linux subsystem in windows 10 (not sure if that makes any difference). I would really appreciate any help since I've been trying to install this for over a week and it doesn't seem to work for some reason.

I am unable to install Macaulay2. I am following the guideline given in the website . I have added the repository in the sources list (see the attached screenshot). I have installed the key from the link above. Now when I search for the package with apt-cache search macaylay2 I get nothing.   I have also looked at the answer to  but I don't think that will work either, please help.


Light spoilers ahead, be advised.   I killed Kellogg in the main story and had the Brotherhood of Steel arrive in the Prydwen. Paladin Danse became a companion and I was tasked to wipe out a castle full of super mutants. Now I've dismissed Danse and I'm fairly certain I send him to Boston Airport. When I glance at the map, both the Airport and the ship have one person living there. Though when I look around, I can't find him. Anybody know where I can find him? Or what area, where to look for?   I'm on PC, though would like to avoid using commands, if possible.

Keeping track of where everyone is is hard.  I could be out in the wasteland while Dogmeat will let me know he found something. That's great, but then it's a chore trying to find him a lot of times. Sometimes, he'll even run ahead and attack enemies and I'll lose sight of him. Only if I leave an area sufficiently far enough, he'll come back and meet with me which isn't always possible. I know I can listen out for him but visual indicators would be better. But none of this works if I sent him to a settlement but needed to find him and he hasn't returned yet.  Is there anything we can do to make locating companions in the world easier?


I need to verify string whether the string is image file name.  $aaa = 'abskwlfd.png';  if ($aaa is image file) { echo 'it's image'; else { echo 'not image'; }   How do i do that? It will chck 100 images, so it should be fast. I know there is a filetype verification method, but I think that's slow.. What about preg_match? Is it faster? I'm not good at preg_match.  Thank you in advance.

This is a question you can read everywhere on the web with various answers:  $ext = end(explode('.', $filename)); $ext = substr(strrchr($filename, '.'), 1); $ext = substr($filename, strrpos($filename, '.') + 1); $ext = preg_replace('/^.*\.([^.]+)$/D', '$1', $filename);  $exts = split("[/\\.]", $filename); $n    = count($exts)-1; $ext  = $exts[$n];   etc.  However, there is always "the best way" and it should be on Stack Overflow.


I want to charge my tablet on the wall. And I have a charger behind the tablet and connected 2 wires to vcc and gnd, the same pins as usb female, it turns out that I can't have more than 10 mA. If I connect with usb cable I get values like 2000mA. Shouldnt it be the same? Is it because of the shield? Should I short the shield to GND?

I have powerbank that provides 5v (presumably regulated) power, as typical of most usb interface powerbanks. I have been trying out my powerbank with different phones. It works on all except one. I have tried it with various USB cables, making sure I didn't overlook anything foolish. Then, I looked at the AC adapter of the phone that it didn't seem to be compatible with. The adapter read: 5.4v DC output. The device's official website or manual doesn't tell me what the input voltage should be. So I have the following questions   Is the fact that the device's AC adapter creates a DC 5.4v output enough to assume that, this is the correct voltage for my cell phone? If 5.4v is the input voltage, then when I attempt to power it with a 5v power bank, am I hurting it? Thus far, it just seems to be non-responsive when I try this. It seems another explanation is polarity mismatch. I'm aware that laptops have a polarity correction feature, which could explain why I can charge this phone via my laptop. Is there any other way to tell if polarity is an issue, given that I don't have access to detailed product information (unless the official website is updated, or something)   So that's the gist of it, I'm not sure why my powerbank isn't charging my phone. And I'm having difficulty troubleshooting the underlying problem by myself. Any tips big or small will be appreciated.


I have third party iframe widget component on my page. This is all I have as an HTML string in the body of my page. This iframe brings some custom button with style set by that widget.jsp. Chrome inspector doesn't show anything else except <iframe> component. But FireFox shows that button inside <iframe> with style class ".button"  <iframe src='https://www.xxxxxxxx.com/aaa/bbb/widget.jsp?par1='TEST%20BUTTON'></iframe>     So how do I override that .button style class?

I have a simple page that has some iframe sections (to display RSS links). How can I apply the same CSS format from the main page to the page displayed in the iframe?


Recently I have been chewing on a bit of a paradox in my mind, and I'm trying to figure out what I'm doing wrong. I am not in high school anymore, I have just graduated from college, and I haven't actively done any non-CompSci related math in a long time aside from youtube videos. So, I'm sorry if this question is really basic, I am versed in this kind of stuff, I am just having problems googling the answer to this one.  Alright, so back in middle school Algebra we learned $(b^n)^m = b^{nm}$. What I'm wondering is, say b is a negative number raised to an odd power. Couldn't we write it in such a way that the answer is always positive?  $b^n$ where $b$ is negative and $n$ is odd. Can't we always write it in the form $(b^2)^{n/2}$. Following the order of operations we can evaluate the parenthesis first, get a positive number, and from there it's a positive number raised to a positive, rational exponent. Which is always positive. Yet, if you did the expansion of the exponents, the answer is clearly negative.  My googling of this property of exponents hasn't led to anywhere that stipulates that this property is only valid when $b > 0$, and from my point of view it's a very trivial question, so what am I doing wrong here?

On Math SE, I've seen several questions which relate to the following. By abusing the laws of exponents for rational exponents, one can come up with any number of apparent paradoxes, in which a number seems to be shown as equal to its opposite (negative). Possibly the most concise example:  $-1 = (-1)^1 = (-1)^\frac{2}{2} = (-1)^{2 \cdot \frac{1}{2}} = ((-1)^2)^\frac{1}{2} = (1)^\frac{1}{2} = \sqrt{1} = 1$  Of the seven equalities in this statement, I'm embarrassed to say that I'm not totally sure which one is incorrect. Restricting the discussion to real numbers and rational exponents, we can look at some college algebra/precalculus books and find definitions like the following (here, Ratti & McWaters, Precalculus: a right triangle approach, section P.6):      The thing that looks the most suspect in my example above is the 4th equality, $(-1)^{2 \cdot \frac{1}{2}} = ((-1)^2)^\frac{1}{2}$, which seems to violate the spirit of Ratti's definition of rational exponents ("no common factors")... but technically, that translation from rational exponent to radical expression was not used at this point. Rather, we're still only manipulating rational exponents, which seems fully compliant with Ratti's 2nd property: $(a^r)^s = a^{rs}$, where indeed "all of the expressions used are defined". The rational-exponent-to-radical-expression switch (via the rational exponent definition) doesn't actually happen until the 6th equality, $(1)^\frac{1}{2} = \sqrt{1}$, and that seems to undeniably be a true statement. So I'm a bit stumped at exactly where the falsehood lies.  We can find effectively identical definitions in other books. For example, in Sullivan's College Algebra, his definition is (sec. R.8): "If $a$ is a real number and $m$ and $n$ are integers containing no common factors, with $n \ge 2$, then: $a^\frac{m}{n} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$, provided that $\sqrt[n]{a}$ exists"; and he briefly states that "the Laws of Exponents hold for rational exponents", but all examples are restricted to positive variables only. OpenStax College Algebra does the same (sec. 1.3): "In these cases, the exponent must be a fraction in lowest terms... All of the properties of exponents that we learned for integer exponents also hold for rational exponents."  So what exactly are the restrictions on the Laws of Exponents in the real-number context, with rational exponents? As one example, is there a reason missing from the texts above why $(-1)^{2 \cdot \frac{1}{2}} = ((-1)^2)^\frac{1}{2}$ is a false statement, or is it one of the other equalities that fails?    Edit: Some literature that discusses this issue:   Goel, Sudhir K., and Michael S. Robillard. "The Equation: $-2 = (-8)^\frac{1}{3} = (-8)^\frac{2}{6} = [(-8)^2]^\frac{1}{6} = 2$." Educational Studies in Mathematics 33.3 (1997): 319-320. Tirosh, Dina, and Ruhama Even. "To define or not to define: The case of $(-8)^\frac{1}{3}$." Educational Studies in Mathematics 33.3 (1997): 321-330. Choi, Younggi, and Jonghoon Do. "Equality Involved in 0.999... and $(-8)^\frac{1}{3}$" For the Learning of Mathematics 25.3 (2005): 13-36. Woo, Jeongho, and Jaehoon Yim. "Revisiting 0.999... and $(-8)^\frac{1}{3}$ in School Mathematics from the Perspective of the Algebraic Permanence Principle." For the Learning of Mathematics 28.2 (2008): 11-16. Gómez, Bernardo, and Carmen Buhlea. "The ambiguity of the sign √." Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. 2009. Gómez, Bernardo. "Historical conflicts and subtleties with the √ sign in textbooks." 6th European Summer University on the History and Epistemology in Mathematics Education. HPM: Vienna University of Technology, Vienna, Austria (2010).


If I have 2 cameras in my scene, and I want to render images from both the cameras simultaneously and not one after the other, is that possible ?   One alternate option I was thinking of doing was open two blend files and render image from one camera in each blend file simultaneously. But my doubt is can it be done in the same blend file?

I have baked a fluid simulation that runs for 300 frames.  I have 3 cameras, one from the left side, one from the right side, and one from the top.  Can I render a sequence of 900 frames where the first 300 are rendered from the simulation from the left camera, then it uses the same simulation and does the next 300 frames from the right camera, then uses the same simulation for the final 300 frames from the top camera?


In RPM, there is a (much maligned, but nonetheless it is there) field called EPOCH, used to override a version stream with lower numbering.  It is a source of constant trouble, but in the cases where it is needed, EPOCH is often the only way to go.  Does the DEB package format have a similar field?

I have just noticed that Wine (and a number of other packages) have shifted their versioning scheme to something like:  1:1.6.2-0ubuntu3   I understand everything after the 1:... But what does the 1: refer to?  It doesn't seem to mirror the major version. Looking at a list of pending upgrades, there are versions like: 2:4.1.3... and there are plenty of packages without the #: prefix.  What's going on?


What is the best flash building alternative for Adobe flash or Macromedia flash ?

First, thank you in advance for any help that you can give a recent transplant from Windows to Ubuntu. I have a question that I have been seeking the answer too but I draw a blank at every turn.  I design websites, free of charge, for nonprofit organizations that are just starting and do not have the resources to hire a design firm. I am in need of a flash/swf editor and compiler. I had a program that I used with the awful previous O/S, however WINE would not run the program.   Thank you in advance for any help that you can offer. Since I do not earn a dime for doing this, I would prefer if the program was open source, however any suggestions are greatly appreciated.


Using cycles, how would I go about making text that is UV mapped onto a surface (in this case a book cover) have a gloss while the remaining part of the image stays matte? The text needs a kind of foil finish with the white being matte paper. Can the mesh be selected with the image, or is there a better way?

I have a skyscraper building but I only want the glass in the texture to be glossy.  How would I accomplish this?    Ok, I have done a test and here are the results.  Here is the original:   here is an adjusted image


My flag limit is increasing day by day. I haven't noticed before how many flag I can raise. But since I am noticing it is increased a lot. In last week, I have raised above 200 helpful flags.   I have noticed to increase it from 36. Daily it is increasing by 1. Now it is reached to 40.  Is it good/ bad? On what basis, flag limit is getting increasing daily?

Looks like flagging has been affected by releases today. Are these intended effects?   Higher daily limits (appear doubled for me, flagging of posts limit also doubled).  Explained by Shog9 below. Soft comment deletion  - e.g. for "accept rate" obsolete comments - it does in fact work, but the immediate feedback is gone.  This is fixed now. Has the throttling rate changed?  Seems possible to repeated flag without waiting 5 seconds.  If it was broken, it isn't anymore. Old soft deletions that were neither categorised as "helpful" or "declined" have all become "helpful".   If limits have been updated, can we get the new formula published? Not changed, as confirmed by Shog9.


I got a PC with the following configuration:  Intel Core2Duo 2.6Ghz 4GB of RAM DDR2 667 Nvidia 7200GS 256mb  The graphics card is the weak point of my computer. I tried to install Ubuntu 14.04 but the graphics effects we're running very slow, although the rest was working well. Now I installed Lubuntu and everything it is running ok but I think it is too simple, I would like a distribution more like Ubuntu.  What Ubuntu distribution can you recommend me for my configuration ?  Thanks in advance.

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


I have a form with an input file, I want the user to upload a sql file, read it with php and import it to my database  My form code is

          <input type="file" accept=".sql" class="form-control" name="sql">

          <button type="submit" formaction="upload_sql.php" style="margin-top:8%" class="btn btn-primary" name="upload_sql">Upload</button>

   But I don't know how to import that file into my database, I tried with "mysql -u root -p database < file.sql"

I'm creating an installation script for an application that I'm developing and need to create databases dynamically from within PHP. I've got it to create the database but now I need to load in several .sql files. I had planned to open the file and mysql_query it a line at a time - until I looked at the schema files and realised they aren't just one query per line.  So, how do I load an sql file from within PHP (as phpMyAdmin does with its import command)?


I have two counter realizations seems identical (for me), here is my code:    var fakeCounter = function() {     var i = 0;     return function() {         return i++;     } };  // And  var counter = (function() {     var i = 0;     return function() {         return i++;     } }());  // And here the confusion:  console.log(fakeCounter()()); // 0 console.log(fakeCounter()()); // 0 console.log(fakeCounter()()); // 0  console.log(counter()); // 0 console.log(counter()); // 1 console.log(counter()); // 2     So, the first counter doesn't work, while the second does. And I can't get why, because counter() is equal to fakeCounter()() on my mind. Can someone clarify that?

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.


I'm trying to set a variable conditionally in Ruby.  I need to set it if the variable is nil or empty (0 length string).  I've come up with the following:  variable = id if variable.nil? || (!variable.nil? && variable.empty?)   While it works, it doesn't seem very Ruby-like to me.  Is the a more succinct way of expressing the above?

Is there a better way than the following to check to see if a string is nil OR has a length of 0 in Ruby?  if !my_string || my_string.length == 0   return true else   return false end   In C# there's the handy  string.IsNullOrEmpty(myString)   Anything similar to that in Ruby?


By definition, a sequence of functions $f_n$ converges to $f$ almost everywhere in a set $D$ if $m(\left\{x\in D \text{ such that } f_n(x) \text{ does not converge to } f(x)\right\}) = 0$ where $m$ is the Lebesgue measure. My question here is how do we relate this kind of definition to uniform convergence? Can we show by example that almost everywhere convergence doesn't imply uniform convergence? In other words, an example of a sequence of functions that converges almost everywhere but does not converge uniformly, and why it fails to converge uniformly.

I've been trying to think of a simple example of a sequence of sets $f_n$ that converge almost everywhere to $f$ but not almost uniformly to $f$. Suppose $f$ is the zero function for the sake of simplicity.  The problem I'm having is that almost everywhere means that the set of values where $f_n$ does not converge to $0$ has measure $0$. But this just seems like a special case of almost uniform convergence which means that we can remove a set of arbitrary small measure from the domain and we will have uniform convergence on the remainder.  So is there some simple example that illustrates the difference between these two modes of convergence?


"Under this directive, any and all Jedi leadership must be executed for treason against the Republic. Any soldier that does not comply with the order will also be executed for treason." Clone Commander Rex to his men during the implementation of Order 66 From Wookiepedia   So, we know what order 66 basically says by a quote of Commander Rex. But I was not able to find the original order 66 the way it was implemented into the clones head. I presume it was more, i.e. more detailed, than kill all Jedi leadership for treason against the Republic. So, does the original formulation of the order exist? Even though it was implemented in a chip, IMHO somebody had to formulate it before it could be added (and if necessary programmed) into the chip.

As we know, "" led the clones to try to kill all the Jedi.  But what was the wording of the order itself?  Was it simply "kill all Jedi", or was it more complicated?


I have an object - "training" , which has a master detail relationship with an object - "Employee". I am writting a trigger on training such that when a new training record is created for an employee, it should create an object called "Log" which should copy a field of employee into a field in "Log" object:  for(trainig__c training: trigger.new){  List<Log__c> newtransLog = new List<Log__c>();         Transaction_Log__c log = new Transaction_Log__c(Job_Level_Name__c=training.Employee__r.Job_Level_Name__c);         newtransLog.add(log); } Insert newtransLog;   What I am trying to do is - get a value of field from Employee record and assign it to a field in Log record. But this seems to be not working, I am getting a blank value for Job_Level_Name__c  in the Log record  PS - Not sure how I shall query the parent fields inside the for loop? How do I do the query and assignment in this case?

I'm sure this has been addressed before but I can't seem to find the answer. In a trigger on a record, aside from the actual fields on the record, what do I have access to? The parent info? that record's children? Do you just add the fields by re querying in your handler?


After the latest episode, I have some doubt about what can kill a White Walker and why.  We know, as a fact, that both Valyrian Steel and dragonglass can kill White Walkers, and they have in common being forged by dragon fire, which I initially thought was the reason they had this power.  In the latest episode, though,      we see the Night King stand untouched in one of the arguably strongest breaths of dragon fire, made with the sole purpose of killing him   That scene gives me lots of doubt.      if dragon fire cannot kill White Walkers, why should things forged with it do it? We can argue Valyrian steel has been enchanted in the forging process, but weapons made from dragonglass have clearly not been, yet they have been shown to kill White Walkers. Why can't the dragon fire kill the White Walkers?

In the S08E03 episode of Game of Thrones, we see Daenerys on her dragon standing against the      Night King    and the dragon throws flames at them.  This character survives without harm (even smiling a little). How is that possible?      This should kill even regular people. But he is a White Walker. It should be even deadlier for him.


I graduated from PhD almost 2 years ago and I am a full time assistant professor in another country.  A paper of mine was accepted recently (main paper of the thesis).   1- Now my supervisor asks me to use my old affiliation (i.e. the university I studied) because she thinks I have completed the thesis while I was there. I received financial help for my PhD which I have acknowledged in the paper. I responded that I am legally bound to my new university and I could not do that. Am I supposed to do that?  Btw. both my supervisors are included as co-authors (with their affiliation which matches my old university).  2- Now again she asks me to at least put my old university's name first. I am the main author (and honestly have done all of the work. My two supervisors read my work, gave comments and possibly corrected English mistakes).  If I am the main author, the correct format requires me to mention my own university first. If I just change the order of affiliations list (a. old university, b. my university) and still keep my name as first author (my name *b), is that acceptable?  3- What is your suggestion for the remaining papers that come out of the thesis?

If research was done and paper was mostly written at institute A, but then it finally got accepted while the author moved to institute B, say, 3 years later. Should the affiliation of the author be   Only Institute A: because 95% of the support was from here, and work was done here Both Institute A and B: in some sense, both institutes supported the work Only Institute B: this is where the author is affiliated at the moment   related:


As a native speaker, this sounds correct:     There are a number of cows in that field.   whilst this sounds totally wrong:     There is a number of cows in the field.   But arguably the second form might be technically correct, because "a" indicates "a number" is singular.  Some examples support this hypothesis: "There is a collection of cows in that field."  Whilst others contradict it: "There are a lot of cows in that field."  Can you confirm which is correct, and is there a good justification which can be generalised to other situations?

Possible Duplicate:             There is a large number of labourers who want to migrate to Japan for work.   I type this sentence in a word processor, and it reports an error that "is" should be "are" (subject-verb agreement).  I doubt this is a valid error. Could anyone confirm this?


I have $200 in $5 & $10 denominations. They are all 2001 series. I would like to exchange them for EUR. Are they still valid?

I received from my Dad 150 American Dollars about 12 years ago. I never have thought to change this money but a few days I tried change it in a currency exchange in Sydney and the guy didn't change it because the series are old.     What do I have to do to change this money?


It's easy to find good recommendation for books here for any subject other than analytic geometry ,therefore I'd like to ask for any suggestion of analytic geometry books ,the only  charactrestic I'm looking for is a somewhat visual expostion.

Hi my course specifically talks about :  Cartesian and Polar Coordinates in 3 Dim, second Degree eqns in 3 vars, reduction to canonical forms, straight lines, shortest distance between 2 skew lines, Plane, sphere, cone, cylinder, paraboloid, ellipsoid,hyperboloid of one and two sheets and their properties.  This is merely indicative, and I would really like if the book talks about these (atleast) and some more. Would appreciate if it contained solved examples and exercise problems as well  Help Much Appreciated, Soham


I know there are different posts about changing PhD, but with such an important decision I would like to ask the same question but including the details of my personal situation.  I am in the first year of my PhD (now starting the 8th month). I did my masters in my home country, Spain, where I did research in computational protein dynamics although my background is about computational chemistry at atomistic level (Quantum Mechanics). I really enjoyed my masters, but I decided to look for a PhD position in quantum chemistry again. I got this position in Stockholm University. I though I would enjoy it, but after 7 months I am not enjoying at all, I do not trust my own research and my interests are moving far from this field. The thing that my group is the only computational group of the whole department is also a big point, because all other groups are experimental and this make me feel quite isolated.  I already had a talk with my boss, where I expressed all my concerns and where we agreed to look for new things. He was really open-minded and comprehensive, and I will try my best for the next months to see if the change fits me. However, my apathy feeling is still present and I think I should start considering the possibility of changing PhD. Do you think I must change only considering this personal feelings? In the past I was really passionate in science, but this feeling of apathy is keeling me. I want to make clear that there is not any problem with my boss or my group mates (all of them are really fantastic), just with myself and my motivation.  Any opinion and advise is welcome

I am a third year (starting fourth year in the fall) PhD student in mathematics. I've passed all qualifying exams and am currently doing research. As far as I can tell, I am not doing poorly. I have the good fortune of having a great advisor, being in a very supportive department, and having friends and family who genuinely care about my success.   The fact is research is hard. It appears to consist primarily of staring at a problem for days and days and days without getting anywhere. Sometimes, rarely, I do figure something out and that feels wonderful, but the overwhelming majority of my time appears to be spent banging my head against a mostly figurative wall. I am not complaining about the material being hard, and I am not averse to putting in hard work, but I get frequently discouraged when I realize the vast volumes of mathematics that I yet know nothing about (and probably never will). It's very hard to quantify progress - in particular, there are too few tangible returns after too many hours worked. I find myself thinking along the lines of "Oh, if only someone actually smart were thinking about this problem they would have solved it in moments" and so on.   I've talked about this to some number of people; here is some advice I have received:   Take a day off. Putting in hours upon hours of trying things doesn't magically lead to a solution, particularly if the brain is tired and just wants to sleep. Have a hobby. Since math research doesn't exactly provide instant gratification, a hobby might provide some instead.  Talk to other graduate students. Realize that many graduate students go through this.   I'm interested to know how other folks have dealt with being discouraged as a graduate student. Does it get better with time and experience? Is this a sign that research is not for me and that I should seriously consider a life outside academia?


Looking for stock prices from 2000 to 2010 for Yahoo stock which is now Altaba (AABA).  Believe it may be defunk now.  Yahoo finance doesn't show historical prices for delisted or the old name for a stock.  Need to find cost basis for taxes

With services like Google Finance or Yahoo Finance it is very convenient to find the historical stock price metric of a listed company, but if the company is not listed, I can't find the data.  For example, I want to see the price metrics for Macromedia, which had been listed in 1993 on NASDAQ (MACR), then acquired by Adobe in 2005. How could I find its historical price metrics?


I have a simple class: class MyClass():          ...           def function(self):         return self.transform(**self.kwargs)              def transform(self, **kw):         ''' main '''         return 1  I tried to override the transform method, but when it's called by the function method it fails. def t(self, **kw):     return 2  instance = MyClass() instance.transform = t instance.function()  > missing 1 required positional argument: 'self'  weird right? I thought the self. denotes that it's passing the self in as the first argument automatically...? So it works if I don't include self. def t(**kw):     return 2  instance = MyClass() instance.transform = t instance.function()  > 2  But that means my t function can't access any of the attributes of the object. Can you help me? Of course I could create a new class that derives from MyClass, but I don't want to. Any other way to inject a method to an object that can access the objects memory?

I've read that it is possible to add a method to an existing object (i.e., not in the class definition) in Python.   I understand that it's not always good to do so. But how might one do this?


I'm currently amateur-ok at UV unwrapping, but I want to learn how I can straighten UV islands and be able to organize them better, but I haven't found any good resources. Does anyone know a good one?

Since asking for tutorials, videos, resources, links to other content or downloads is considered off topic here, this is a specifically created Community Wiki which gathers resources for Blender and it has been approved by the .  Just write in the appropriate answer/section. If you have concerns, questions, post a  question, so we don't clutter the comments, but you can link your meta question from the comments.  Questions regarding such resources are not allowed anymore, except for very specific and on topic requests (ask on  if you're unsure about your question). Follow the instructions made in the question about how to post, what can be posted, etc.  Learning             Assets    (also see: )   Reference Images/Blueprints (also see: )    Tools    (also see: )      Other   Special Interest ()     Also see the .


Noting  on a 1000 qubits quantum computer had me wondering...  Does the number of qubits nonlinearly change the speed/rate at breaking a SHA256 hash?  If someone makes a say 10,000 qubit processor, does this speed up cracking the hash more than 10 times (linearly) faster?

can search an unordered list of length $N$ in time $\sqrt{N}$  on a quantum computer. Applied to cryptography, this means that it can recover n-bit keys and find preimages for n-bit hashes with a cost of $2^{n/2}$. But the basic version of Grover's algorithm is sequential. Each iteration uses the output of the previous iteration as input. I don't see an obvious way to parallelize the algorithm. Reducing the number of iterations significantly reduces the success probability more than linearly. If the algorithm is inherently sequential, building a bigger computer won't speed up the attack, limiting its impact. $2^{80}$ sequential cipher invocations looks pretty hard to achieve to me. On the other hand, $2^{80}$ parallel cipher invocations is already on the edge of feasibility today using classical computers. Assume an attacker using a quantum computer is limited to $T$ timesteps with $T<\sqrt{N}$, so they can't run Grover's algorithm with the optimum number of sequential steps. What's the cost for finding a preimage/recovering a key? What is the average cost per-break if they have multiple targets?


I have two text files. One file has startdatetime and second file have enddatetime.  file 1 data(startdate-time):  2019-01-08 04:14:59 2019-01-08 04:16:57   file 2 data(enddate-time):  2019-01-08 04:15:50 2019-01-08 04:17:02   I need Unix script which will perform operation on endtime - starttime (only on time). Example for first entry it should perform:  04:15:50 - 04:14:59   and give result in seconds (for this example, it should print total difference seconds)

I've seen many questions and examples showing how to calculate the difference in two times by converting the times to epoch, and then converting the difference in seconds... However, what is the best way to calculate the difference in time that may span over several days in a $DAY days, $HOUR, hour(s), $MIN minute(s), and $SEC second(s)?  For my purpose, I'm using the date format, date +"%m/%d/%y %T" (08/17/18 09:03:31).  Let's say my first date is 08/15/18 16:22:05, and the second is 08/17/18 09:03:31. How can I calculate the difference by echoing "The difference is 1 day(s), 16, hours, 41 minutes, and 26 seconds."  But also, with the same script, how can it recognize if the time difference is less than a day to not report "The difference is 0 day..."?  EDIT: I have a mostly working script below, however, there's a lot going on in order to preserve proper formatting. Everything seems to work aside from the appropriate spaces and commas depending on if a value equals zero...  The idea is that it should format it with "and" in the appropriate spot when removing values that equal "0"...  So, all values:     02:05:23:44     2 days, 5 hours, 23 minutes, and 44 seconds  No hours:     02:00:23:44     2 days, 23 minutes, and 44 seconds  No seconds:     02:05:23:00     2 days, 5 hours, and 23 seconds  I had it so close awhile ago, but with certain readings, it'd break. Any help on formatting how I'd like? The script is also a long-mess... Any help cleaning it up would be nice. I'd like to see how to make it more efficient.  #!/bin/bash TIME1="08/17/2018 11:36:40" TIME2="08/17/2018 12:37:41" SEC1=`date +%s -d "${TIME1}"` SEC2=`date +%s -d "${TIME2}"` DIFF=`expr ${SEC2} - ${SEC1}`  CONVERTTIME() {   ((d=${1}/86400))   ((h=(${1}%86400)/3600))   ((m=(${1}%3600)/60))   ((s=${1}%60))    #DAYS   if [ $d -eq 1 ]; then     DAYLABEL=day   else     DAYLABEL=days   fi   DAYCOMMA=", "   if [[ $d -gt 0 || $h && $m && $s -eq 0 ]]; then     DAYCOMMA=""   fi   DAYTEXT="$d $DAYLABEL$DAYCOMMA"   if [ $d -eq 0 ]; then     DAYTEXT=   else     if [ $h -eq 0 ]; then       DAYTEXT="$d $DAYLABEL$DAYCOMMA"     fi   fi   #HOURS   if [ $h -eq 1 ]; then     HOURLABEL=hour   else     HOURLABEL=hours   fi   HOURCOMMA=", "   if [[ $h -gt 0 || $m && $s -eq 0 ]]; then     HOURCOMMA=""   fi   HOURTEXT="$h $HOURLABEL$HOURCOMMA"   if [ $h -eq 0 ]; then     HOURTEXT=""   else     if [ $m -eq 0 ]; then       HOURTEXT="$h $HOURLABEL$HOURCOMMA"     fi   fi   #MINUTES   if [ $m -eq 1 ]; then     MINLABEL=minute   else     MINLABEL=minutes   fi   MINCOMMA=", "   if [[ $m -gt 0 || $s -eq 0 ]]; then     MINCOMMA=""   fi     MINTEXT="$m $MINLABEL$MINCOMMA"   if [ $m -eq 0 ]; then     MINTEXT=""   else     if [ $s -eq 0 ]; then       MINTEXT="$d $MINLABEL$MINCOMMA"     fi   fi   #SECONDS   if [ $s -eq 1 ]; then     SECLABEL=second   else     SECLABEL=seconds   fi   SECTEXT="$s $SECLABEL"   if [ $s -eq 0 ]; then     SECTEXT=""   fi    ANDHOUR=   ANDMIN=   ANDSEC=   if [[ $d && $h && $m && $s -gt 0 || $d && $h && $s -gt 0 || $d && $m && $s -gt 0 || $h && $m && $s -gt 0 || $d && $s -gt 0 || $h && $s -gt 0 || $m && $s -gt 0 ]]; then     ANDSEC="and "   else     #days hours AND minutes     #days AND minutes     #hours AND minutes     if [[ $d && $h && $m -gt 0 || $d && $m -gt 0 || $h && $m -gt 0 ]]; then       ANDMIN="and "       else       #days AND hours       if [[ $d && $h -gt 0 ]]; then         ANDHOUR="and "       fi     fi     fi   echo -e "$DAYTEXT$ANDHOUR$HOURTEXT$ANDMIN$MINTEXT$ANDSEC$SECTEXT" } echo echo "TIME DIFFERENCE: $(CONVERTTIME $DIFF)" echo


I am trying to prove:  Suppose $f$ is bounded and continuous on $[0, 1]$. For any $n \in \mathbb{Z}^+$, define $$||f||_n = \left(\int_0^1|f(x)|^n \, dx\, \right)^{1/n}$$ Then, $\lim_{n \to \infty} ||f||_n \ge \max\{|f(x)|:x \in [0, 1]\}$.  I found the following proof:  Let $\epsilon>0$ and $\max\{|f(x)|:x \in [0, 1]\}$. Then, $M-\epsilon<M$ which means that there exits a $a \in [0, 1]$ such that $|f(a)| \ge M-\epsilon$. Since $f$ is uniformaly continuous on $[0, 1], \exists \delta>0$ such that for all $x \in (a-\delta, a+\delta)$, we have $|f(x)|> M-\epsilon$. Now, let $\delta_1=\{\delta, 1/2\}$ which implies that $2\delta_1 \ge 1$. Hence,  $$\int_0^1|f(x)|^n \, dx = \int_0^{a-\delta_1}|f(x)|^n \, dx+ \int_{a-\delta_1}^{a+\delta_1}|f(x)|^n \, dx+\int_{a+\delta_1}^1|f(x)|^n \, dx \ge \int_{a-\delta_1}^{a+\delta_1}|f(x)|^n \, dx\ge \int_{a-\delta_1}^{a+\delta_1}(M-\epsilon)^n\, dx$$ Thus, $$\int_0^1|f(x)|^n \, dx \ge |M-\epsilon|^n \cdot 2 \delta_1 \ge M-\epsilon^n$$ and the rest of the proof is rather trivial. Now, I am highly skeptical of this proof. For instance, the above proof seems to erroneously assume that $M-\epsilon \ge 0$. Also, how does the definition of uniform continuity imply that $|f(x)|> M-\epsilon$? Is there a way to fix this proof? Can someone please suggest how this can be proven (without using any concepts from measure theory)? If someone can show how $|f(x)| \ge M$, I can complete the rest of the proof from there.

Let $(X,B,\mu)$ be a complete measure space,Show that $$\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}, \quad \forall f \in \bigcup_{p} \bigcap_{p \leqslant q<\infty} L^{q}$$ So,$\lim _{q \rightarrow \infty}\|f\|_{q}$ , $\|f\|_{\infty}$ are equal-norm with space $ L^{\infty} \cap\left(\bigcup_{p} \bigcap_{p \leqslant q} L^{q}\right)$. Case 1: $m(X)<\infty $.It's easy to prove that. Case 2: $m(X)=\infty $. I have no idea about it,And I started to doubt the correctness of this conclusion. Can somebody give me a hint for this problem or just give an example to prove that this is a wrong conclusion when $m(X)=\infty $. Thanks in advance.


Example: I have some pictures with size about 3 MB, and want them to have a size about 1020 KB. I don't know is there some option on Ubuntu or I do that with some editor, so can you help me?   My current way is to cut them, but that is not very useful. :(  Maybe this is not a question for this site, but I don't know where to ask.

I have 5,000 images which I need to compress (to display on my website).  I am new to Ubuntu. So what do I do?


I always thought, an electron could not pass through a hole, with a diameter, which is smaller than its wavelength. Just like microwaves could not pass through a metal mesh with small holes, but visible light could.   The other day I came across a video of a series of lectures on Quantum Transport, in which during a Q&A, it is mentioned, that if one shrinks the chamber in front of electrons to be smaller than the wavelength, quantum effects would be more sensible, and it is implied, that the electrons pass through. Here is the time-coded link to that video:    My question, which is an abstract one, is if an electron can really pass through a hole or a chamber, with a diameter smaller than the wavelength. If yes, how, and does it have to do with quantum tunneling? What would be the mathematics, explaining this phenomenon? I would be grateful, if you could provide a concrete explanation about my question.

I was wondering this for quite a long time now. Let's say you have a water wave (like ripples, not the ones you see during tsunamis) with wavelength 10 m. Imagine you put a boundary with an opening of 1 m. Will diffraction be observed? According to my research, no. But, then, what would be seen?


In a multi-threaded environment, is a class's static block guaranteed to finish before other static methods (in the same class) are called?  I don't mean in the event that the static block itself calls some other static method. In order to clarify, we can use the following code block.  Can an outside class start two threads, both of which call OurClass.doSomething(), and one them will begin executing before the static block finishes?  public class OurClass {      static {     // does something that takes a long time     }      public static void doSomething() {     // can I be called before the block has finished?     } }

Let's say I have some Java code:  public class SomeClass {     static {         private final double PI = 3.14;         private final double SOME_CONSTANT = 5.76;         private final double SOME_OTHER_CONSTANT = 756.33;     }    //rest of class }   If a thread is initializing SomeClass's Class object and is in the middle of initializing the values in the static block when a second thread wants to load SomeClass's Class again, what happens to the static block?  Does the second thread ignore it assuming it's already initialized even though the first thread is not done? Or does something else happen?


Is $$\sum_{i\in I_1} a_i + \sum_{i \in I_2} b_i$$ or $$\prod_{i\in I_1} a_i \cdot \prod_{i \in I_2} b_i$$ confusing or bad math? Should I rather use $j$ for indexing the $b$'s?

The title says it all (I'm referring to the case, when writing for example an article to be published or something similar - something where the writing itself should also be of quality).  Example: "Let $A_1,A_2,\ldots,A_n$ be subsets of a set $L$ and $f:L\rightarrow L$. Then define $B=\cup_{i=0}^n A_i$ and $C=\cup_{i=1}^{\infty} f^i (A_2)$, where $f^i$ is $f$ iterated with itself $i$ times."  So (in this example), would it be a problem to use $i$ twice as an index variable the ranges over different sets ? Or is it ok to think of $i$ as being define like a (lets do a computer-science analogy) "local variable", that is only used to create the object "in" which it is defined ($B$ for example) and after the object is created, the variable is "freed" again (so it can be used again to define $C$) ?  If it is NOT okay to do that, when is it allowed to use the same symbol again, after its first use ? After half a page ? After two pages ? In index-heavy proofs one would very soon have finished all letters commonly used as indices, of one would always have to use a different letter. And indexing sets with letters like $x$ or $f$ seems even worse style to me (ok, maybe there are areas in math, in which this would be common practice, but I don't know any).


When I look at  using Firefox, my layout changes to fullscreen instead of a central column, which is common on the SE sites.  I'm using Firefox 58.0.2 (32-bits).  When I'm logged in on the same account using Edge, for example, it just looks fine.

This is just... wrong. Chrome latest, just started now.  It only seems to be happening on SO, I checked several other SE sites.


How many roots does the equation $f(z)=z$ have in the circle $|z|<1$ if for $|z|\leq 1$, $f(z)$ is analytic and satisfies $|f(z)|<1$?  My idea:  I figured I could do this pretty easily using Rouche: Consider $|z|=1$, and let $g(z)=z$, then $|f(z)-g(z)|=z-z=0<1=|g(z)|$.  So, since $g$ has only $1$ root in $|z|<1$, then so does $f$. I just feel like I am missing something.  In particular, can I define $g$, and use it, in the way I did? Any thoughts are greatly appreciated!  Thank you.

Let $f$ be analytic on the closed unit disk centered at the origin and $|f(z)| < 1$ for $|z| = 1$. Show that $f$ has exactly one fixed point inside the open unit disk. That is, there exists a unique number $z_0$ with $|z_0| < 1$ such that $f(z_0) = z_0$. We must prove 1 there exists at least on solution, 2 there is at most one solution.  1) Having problems with at least one solution. 2)By definition a is a fixed point if f(a) = a. Assume that f has more then one fixed point a,b and that a


I have initialized all my classes correctly although not shown in the code. I have tested if the source of the error was in my textfield but it wasn't. the "s" in the MainForm class is the initialization of the Sqlstatement class. There is one error here which is shown in the code below  my new_user class  public new_user() {     initComponents();      try{          mf = new MainForm();      }catch(Exception e){         e.printStackTrace();     } }private void save_user_btnActionPerformed(java.awt.event.ActionEvent evt) {                                                    try{         user = uname_input_txt.getText();         pass = pass_input_txt.getText();          //ERROR HERE         if(mf.search_for_dupe_user(user) == true){             JOptionPane.showMessageDialog(null, "Username not available");         }else{             mf.new_user(user, pass);             JOptionPane.showMessageDialog(null, "New user added.");             this.dispose();         }     }catch(Exception e){         JOptionPane.showMessageDialog(null, e.getMessage());         e.printStackTrace();     } }   There is one here too which is shown in the code.  my main_form class  public void new_user(String user, String pass)throws SQLException{     try{         s.new_user(user, pass);     }catch(Exception e){         e.printStackTrace();     } }  public boolean search_for_dupe_user(String user)throws SQLException{     boolean result = false;     try{          //ERROR HERE         if(s.search_for_dupe_user(user) == true){             result = true;         }else{             result = false;         }    }catch(Exception e){        e.printStackTrace();    }     return result; }   my sqlstatement class  public void new_user(String user, String pass)throws SQLException{     try{         stmt = conn.prepareStatement("insert into users (user_num, username, password) values(null,'"+user+"','"+pass+"')");         stmt.execute();     }catch(Exception e){         e.printStackTrace();     } }  public boolean search_for_dupe_user(String user)throws SQLException{     boolean result= false;     ResultSet rs = null;    try{         rs = statement.executeQuery("select username from users where username='"+user+"'");          if(rs.next())         {            result = true;         }          else         {            result = false;         }    }catch(Exception e){        e.printStackTrace();    }     return result; }   my stacktrace     java.lang.NullPointerException       at MainForm.search_for_dupe_user(MainForm.java:3151)       at new_user.save_user_btnActionPerformed(new_user.java:129)

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?


My only question is what is faster for the browser to render?  An image as a background-image or the same image as a simple <img src=".">

In what situations is it more appropriate to use an HTML IMG tag to display an image, as opposed to a CSS background-image, and vice-versa?  Factors may include accessibility, browser support, dynamic content, or any kind of technical limits or usability principles.


I would like to jump to next feature in my attribute table. I know this is possible with the "print composer" using "atlas".   Is there any possibility to jump to the next feature in my attribute table using the standard QGIS canvas?

I have to check all the elements on a layer and I'm looking for an easy way to go through all of them. One option would be to open the attribute table and just always click on the next line and then "move to selection". I would prefer an option where I just click on an arrow or use a shortcut and QGIS just jumps to the next element, so that I don't have to be aware of not missing a line and just needing half the amount of clicks. Is there anything like that in QGIS?


I need to prove that for every natural number n, there exists an intermediate extension E of A/Q with [E:Q]=n, being A the algebraic closure of Q (the field of all complex numbers that are algebraic over Q) and deduce that A/Q is not finitely generated. Could you give me any hint? Thank you in advance.

Problem: Consider the subfield $$E = \mathbb{Q} \big(\left\{\sqrt[n]{2} \mid n \in \mathbb{N} \setminus \left\{0\right\} \right\} \big)$$ of $\mathbb{R}$. Prove that $[E: \mathbb{Q}]$ is not finite.  Attempt: I proved that $E$ is algebraic over $\mathbb{Q}$. Because let $u \in E$. Then there is a $n \in \mathbb{N} \setminus \left\{0\right\}$ such that $u = \sqrt[n]{2}$. Then $f(x) = x^n - 2 \in \mathbb{Q}[x]$ is the minimal polynomial of $u$ over $\mathbb{Q}$ such that $f(u) = 0$. Hence $E$ is algebraic over $\mathbb{Q}$.  I now want to prove the degree of extension is not finite. I assume it is finite. Suppose then $[E: \mathbb{Q}] = k \in \mathbb{N}$. I don't know how to derive a contradiction from this.   I know that if $u$ is algebraic over $\mathbb{Q}$ and $f$ is the minimal polynomial of $u$ over $\mathbb{Q}$, then $[\mathbb{Q}(u) : \mathbb{Q}] = \deg(f)$.   Help/suggestions are appreciated.


I am running Windows Server 2012 R2.  When I run Process Explorer (as Administrator) I can see that the System process is listening on port 443. More specifically, it shows the following:        Protocol: TCPV6   LocalAddress: [0:0:0:0:0:0:0:0]:443   Remote Address:    [0:0:0:0:0:0:0:0]:0   State: LISTENING      There is no entry for TCP 443, only for TCPV6.  In my running services, I have checked for all the usual suspects mentioned in the other posts concerning this issue. Below you can find an overview of the services running on this system:  Application Experience Application Host Helper Service Application Information Background Intelligent Transfer Service Background Tasks Infrastructure Service Base Filtering Engine ccmsetup Certificate Propagation COM+ Event System Cryptographic Services DCOM Server Process Launcher Dell SupportAssist Service Dell Update Service DHCP Client Diagnostic Policy Service Diagnostics Tracking Service Distributed Link Tracking Client Distributed Transaction Coordinator DNS Client DSM Essentials DA Service DSM Essentials Host Service DSM Essentials Task Manager DSM SA Connection Service DSM SA Data Manager DSM SA Event Manager DSM SA Shared Services File Server Resource Manager Group Policy Client IKE and AuthIP IPsec Keying Modules IP Helper IPsec Policy Agent Local Session Manager Microsoft iSCSI Initiator Service Microsoft Software Shadow Copy Provider Modular Disk Storage Manager Agent Modular Disk Storage Manager Event Monitor Netlogon Network Connections Network List Service Network Location Awareness Network Store Interface Service Plug and Play Power Print Spooler Remote Desktop Configuration Remote Desktop Services Remote Desktop Services UserMode Port Redirector Remote Procedure Call (RPC) RPC Endpoint Mapper Security Accounts Manager Server Shell Hardware Detection Smart Card Device Enumeration Service SNMP Service System Event Notification Service System Events Broker Task Scheduler TCP/IP NetBIOS Helper Themes TSM Client Scheduler User Access Logging Service User Profile Service Volume Shadow Copy Windows Connection Manager Windows Event Log Windows Firewall Windows Font Cache Service Windows Management Instrumentation Windows Modules Installer Windows Remote Management (WS-Management) Windows Sync Share Windows Time Windows Update WinHTTP Web Proxy Auto-Discovery Service Workstation   Other analysis options that I have tried:   netstat -ao: This shows the same information as Process Explorer. System with PID 4, is listening on port 443 wmic process: PID 4 is System... no further information. Opening a browser to localhost:443, or a raw PuTTY session doesn't work.   Any suggestions are welcome...

I am having problems starting my Apache server, because port 443 is already in use.  It turns out, the system process (PID 4) uses the port 443. I don't have IIS installed, the services.msc shows (predictably) no Exchange server running, nor WWW-Services, nor IIS. I have no idea how to find out what service uses that port, short of just disabling each service one after the other, and I am not even sure that would help.  I would be grateful if someone could point me towards how I can get my SSL port back, thank you :)  P.S.: Of course "just switch Apache to another port for SSL" would solve the problem of not being able to start Apache. But I'd still like to know what is so insistent about hogging port 443. :)    I by now took the 'hard route' and disabled services one after the other. It turned out that the "Routing and RAS" service was the culprit.  Thank you all for the valuable input and the new tools in the combat against "WTF does my system do now?".


I have 2008 iMac and OS X El Capitan on it. I will make bootable USB drive for my friend, but I can't. I format my USB as Mac Os Extended and GUID parition map, then I downloaded InstallMacOSX.dmg file from apple; double click on it and I have installmacosx.pkg. (I can't find The El Capitan installer to the /Applications folder). I click on this package and I have an ALERT: "OS X v10.11.6 is already installed on this computer. Use the Updates page to install the 10.11 update or if you would like to download the full OS X installer click Continue". I click continue and have to select destination disk, but when I select my external USB drive, I have the message: "OS X can't be installed on this disk. macOS isn't installed". Can you help me?

My old mac's hdd died. It's dead. So I got a ssd and installed it in the macbook.  Now how do I get El Capitan on there? I find lots of tips online that speak of creating a bootable USB drive from the Capitan installer. But I can't download the El Capitan from the appstore because the mac has got nothing to boot from.  On my newer macbook running Catalina, I also cannot download El Capitan from the appstore because it doesn't show up when searching for it.  What I did download is El Capitan's InstallMacOSX.dmg via   But now I need to run/open this on the old mac with the fresh ssd.  I feel I'm stuck in a loop. I need a working OS to install an OS.....  Who can help me out here?


I'm wondering where on StackExchange I could ask for how other people interpret a specific license agreement and also whether people have rejected to agree to the specific liencese agreement because of certain aspects within it.  It would be very helpful to gain insights from other people's view on the specific service agreement in order to decide whether or not to agree to the license and start using the service.  The specific service I'm interested in is . Their  states in section 3.2 that:     You hereby grant Company an irrevocable, non-exclusive, royalty-free, transferable license, with rights to sublicense, to use, reproduce, modify, display, perform and create derivative works of the Applications, the Content and the Brand Features and Marks for the sole purpose of allowing the Company to provide the Company Software and the Services to You.   For me it is very important that the content I would put into my Firebase database would remain mine and that it would only be used by/accessible to those that I explicitly grant access.  The license agreement says that I would grant Firebase the right to use the content (which is something I do not wish to agree to), but on the other hand it also says that Firebase is only granted to do so for the sole purpose of providing the service to me.  I'm confused by this and would appreciate any sites that I can ask questions about this issue.

Is it appropriate to ask questions about software licenses/licensing on ? Or is the appropriate place  ? Or is there no appropriate site currently and we should suggest such a site on ?


Probably published late 1970s or early 1980s. A large group of people are organized into a small city that is in a huge contraption that has to keep moving around the earth after some apocalyptic event. They might call the conveyance "Earth City." They have to keep pulling up track behind and placing it in front to proceed.   They are following electromagnetic pulses in the earth's crust that provides motive power for the thing.   The direction in which they are heading is called "up future," whilst the direction from which they have come is called "back past." Any ideas would be much appreciated.

I read a very special book a few years back. We follow a boy who lives in a world where, if one moves far enough in a direction, that person gets distended and changed in size.   The boy works on laying tracks for the train, on which his city is. The city has to continually keep moving or it also will get squashed.   It's like a world like if one end is pinched and then dragged out like a piece of rubber string or bubble gum.   The book is not older than 10 years I think.  Hope I was clear enough...


I have this issue with some form fields in Firefox and using the adwaita-dark theme. In some webpages where the field background is white, you cannot read the text because it is also white.   This question was edited in order to clarify that this kind of wording of the question might help people who are not familiar with what a GTK+ theme. I also thing that the wording will help to get more hits through search engines. If it's still considered a duplicate, I'll accept it.

I have a dark GTK theme installed in my Ubuntu 10.10 install and a persona installed for Firefox that I also like.  The problem is that Firefox is using my dark GTK theme for items like buttons and text fields on common web pages, and this commonly creates unreadable menus, text areas, and buttons.  (white text on white backgrounds, or black text on black buttons).  I don't want to change either theme, because they look great in every other application, and I don't want to have to do something crazy to my Firefox install like use custom user scripts or CSS overrides.   All I want to do is tell Firefox to stop using my GTK theme completely. This appears to be what Google's Chrome browser does and it makes the most sense by far.   How can web developers possibly work around all the possible GTK themes out there?


For example when integrating by substitution one would write dx=2u.du. In this what does the dx mean and why do we get it in equations like the above? What i am basically asking is why does x=u^2 mean that dx=2u.du where do the du and dx come from??

$dx$ appears in differential equations, such us derivatives and integrals.  For example, a function $f(x)$ its first derivative is $\dfrac{d}{dx}f(x)$ and its integral $\displaystyle\int f(x)dx$. But I don't really understand what $dx$ is.


Let $\{a_n\}$ be a sequence satisfying $\forall m,n\in\Bbb{N}:0\leq a_{m+n}\leq a_m+a_n$. Prove that $$\lim_{n\to\infty}\frac{a_n}{n}$$ exists.   At first I tried to do it with some $\epsilon-\delta$. We wish to prove that there exists some $L$ such that $\forall\epsilon>0:\exists n_0\in \Bbb{N}:n>n_0\Rightarrow|\frac{a_n}{n}-L|<\epsilon$. Which then got me to something like this:$$-\epsilon\cdot n<a_n-Ln<\epsilon\cdot n$$ which got me nowhere and I didn't find a way to make use of the inequality given.  The sequence is obviously bounded below but non-decreasing, which tells me nothing. I don't see any way to use this fact to prove the existence of given limit. Any useful tips, hints appreciated.

Let $\{a_n\}_{n=1}^\infty$ be a positive sequence of real numbers such that $a_{n+m} \leq a_n + a_m.$  Prove that $\lim_{n\to\infty} \frac{a_n}{n}$ exists by showing that $\lim_{n\to\infty} \frac{a_n}{n} = \inf_{n \geq 1} \frac{a_n}{n}.$   A similar question has been posted previously, see  , and I have found that this is the general result of "Fekete's Subadditive Lemma" for sequences, but I am unhappy with the few proofs I've seen.  Perhaps the clearest one I have found is  , but this seems a bit tricky for what is expected on this qualifier question.  We are given a hint "treat $\liminf$ and $\limsup$ separately".  Does anyone know of a more direct way to show that this limit exists?


I am wondering which data cleaning steps should be performed if you want to re-fine a BERT model on custom text data. Which steps should be performed? Does it make sense to perform a stemming or lemmatization if it has not been applied to the initial training of the BERT Base/Large model?

This might be silly to ask, but I am wondering if one should carry out the conventional text preprocessing steps for training one of the transformer models? I remember for training a Word2Vec or Glove, we needed to perform an extensive text cleaning like: tokenize, remove stopwords, remove punctuations, stemming or lemmatization and more. However, during last few days I have had a quick jump into transformer models (fascinated btw), and what I have noticed that most of these models have a built-in tokenizer (cool), but none of the demos, examples, or tutorials are performing any of the these text preprocessing steps. You may take  for instance, there are no text preprocessing involved for the demos (maybe it is just a demo), but at  the whole sentences are passed without any cleaning: texts = ['I really love the Netflix original movies',          'this movie is not worth watching'] predictions = learner.predict_batch(texts)  The same is true for the  by HuggingFace. Or many tutorials that I have looked at (take  or ). I can imagine that depending on the task this might not be required, e.g. next work prediction or machine translation and more. More importantly I think this is part of the contextual-based approach that these models offer (that is the innovation so to say) that are meant to keep most of the text and we may obtain a minimum but still good representation of the each token (out of vocabulary word). Borrowed from  by HuggingFace:  Tokenisation BERT-Base, uncased uses a vocabulary of 30,522 words. The processes of tokenisation involves splitting the input text into list of tokens that are available in the vocabulary. In order to deal with the words not available in the vocabulary, BERT uses a technique called BPE based WordPiece tokenisation. In this approach an out of vocabulary word is progressively split into subwords and the word is then represented by a group of subwords. Since the subwords are part of the vocabulary, we have learned representations an context for these subwords and the context of the word is simply the combination of the context of the subwords.  But does that hold true for tasks like multi-label text classification? In my use case the text is full of not useful stopwords, punctuation, characters and abbreviations and it is multi-label text classification as mentioned earlier. And in fact the prediction accuracy is not good (after a few rounds of training using ). What do I miss here?


I have a laptop with a 1TB HDD which is divided into two drives, C & D. The C drive is used for Windows 10. I am installing Ubuntu on the D drive, but at the time of creating swap and root partitions I am not getting an option to create a home partition.   How can I create a /home partition during installation?

I'd like to see the full How-To on how to use manual partitioning during Ubuntu installation. The existing guides (at least those I found here) cover only automatic part and leave untouched the manual part (or extremely short and contain no pictures).  I'd like to cover such situations:     If your disk contains other systems:


I have a MySQL table called mst_order_details and it has column (order no) and it can be same order no it more time.  Each order number have related technique column I want to concat technique column according to order no  mst_order_details table :  order no   Technique ------------------------- 1           heat_seal 1           laser_cut 1           oil_filter 2           diamond cut 2           diamond cut   Output should be like this :   order no    Technique ---------------------------------------------  1          heat_seal/laser_cut/ oil_filter  2          diamond cut

Using MySQL, I can do something like:  SELECT hobbies FROM peoples_hobbies WHERE person_id = 5;   My Output:  shopping fishing coding   but instead I just want 1 row, 1 col:  Expected Output:  shopping, fishing, coding   The reason is that I'm selecting multiple values from multiple tables, and after all the joins I've got a lot more rows than I'd like.  I've looked for a function on  and it doesn't look like the CONCAT or CONCAT_WS functions accept result sets.  So does anyone here know how to do this?


How to force nautilus and gedit (and practically all program's windows on ubuntu) to always remember their window position? When i start another nautilus window, it is randomly placed on different positions of desktop. I dont wanna that. I work on 16:9 monitor, with one document window on left and nautilus/gedit on right, it really annoys me to reposition every time i start new window or run new instance of nautilus/gedit.  I use ubuntu 12.04.3 lts.

When I log in Ubuntu, I would like all windows opened at previous session (terminal and Firefox mainly) to be re-opened automatically at the same size and position.  How to proceed?


I want to open a Admin activity when the defined admin e mail signs in, without using role based auth. I've tried the below but it keeps opening the profileActivity when I sign in with the admin@admin.com e mail, could anyone assist? Edited to include the full code. I'm trying to firstly check if the user trying to log in is registered and if they are, do they have an admin e mail address, if so, take them to the admin area, if not, take them to the profile area. Thanks  progressBar.setVisibility(View.VISIBLE);     mAuth.signInWithEmailAndPassword(email, password). addOnCompleteListener(new OnCompleteListener<AuthResult>() {         @Override          public void onComplete(@NonNull Task<AuthResult> task) {             String loggedInUserEmail = mAuth.getCurrentUser().getEmail();             String adminEmailAddress = "admin@admin.com";             progressBar.setVisibility(View.GONE);             if(task.isSuccessful() && (loggedInUserEmail.equals(adminEmailAddress))) {                 finish(); // finish activity                 Intent intent = new Intent(MainActivity.this, adminActivity.class);                 intent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);                startActivity(intent);              }                if(task.isSuccessful()) {                 finish(); // finish activity                 Intent intent = new Intent(MainActivity.this, ProfileActivity.class);                 intent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);                 startActivity(intent);               }               else             {                 Toast.makeText(getApplicationContext(), task.getException().getMessage(),Toast.LENGTH_SHORT).show();             }         }     });

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?


Why does [1, 2, 3].map((x) => Math.max(x)) return [1, 2, 3]  yet [1, 2, 3].map(Math.max) returns [NaN, NaN, NaN] ?  I would have thought since [1, 2, 3].map(Number) returns [1, 2, 3], the same would true for using Math.max in the same way.  Especially since Math.max(3) == Number(3).

From the :  [1,4,9].map(Math.sqrt)   will yield:  [1,2,3]   Why then does this:  ['1','2','3'].map(parseInt)   yield this:  [1, NaN, NaN]   I have tested in Firefox 3.0.1 and Chrome 0.3 and just as a disclaimer, I know this is not cross-browser functionality (no IE).  I found out that the following will accomplish the desired effect. However, it still doesn’t explain the errant behavior of parseInt.  ['1','2','3'].map(function(i){return +i;}) // returns [1,2,3]


Sometimes when I remote into my computer, I can get in and see everything and drive the mouse for a few seconds -- then the screen goes black and just sits there.   Anyone seen this before and know the reason or how to fix?

After connecting from my home via remote desktop, both my screens are black when I arrive at work. The only thing I can see is a mouse pointer on one of the screens. I then seem to have only two choices: rebooting or working from a remote desktop connection, which works fine.  It did happen every time I tried last week.  However, I did the same from my laptop in a meeting room today, and I didn't have any problem.


template<class T> class CData{ public:     T::Buffer GetBuffer() = 0; }  class CAudio : public CData<CAudio>{ public:     struct Buffer{}; }   How can I implement a functionality like this?  This throws: error C2061: syntax error: identifier 'BuffData' error C2334: unexpected token(s) preceding '{'; skipping apparent function body error C2039: 'BuffData': is not a member of 'CAudio'

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


How to update to the latest Python version in Ubuntu? I tried sudo apt-get install python3 but it says that the current (3.3.1) is already the latest.

How can I install a different version of Python using apt-get?  Obviously I realise I can install using the source tar ball, however I would prefer not to install from source and instead use the package manager, as that's what it's there for. Surely somewhere reputable builds .deb files for the latest Python releases (why python.org don't is beyond me) that I can reference.   What do I need to do to reference them and what issues might it create when upgrading to the next version?  If there is no way except for building from source, is there a (pseudo) package that I can can install that will provide all of the dependencies needed without having to find and install each individually? So that I don't get:  The necessary bits to build these optional modules were not found: _bz2                  _curses               _curses_panel       _dbm                  _gdbm                 _lzma               _sqlite3              _ssl                  _tkinter            readline              zlib


Is there any way I can find all the default installed packages for a given Ubuntu version, like Xubuntu 16.04.3 x86? I'm not talking about the list of the packages currently installed on the system but the packages which you'll find installed after a clean install.

I am developing an offline installer for all versions of Ubuntu, and I need Ubuntu's default installed packages list. Is there a way to get this information from any server (web server)? Any script to fetch any Ubuntu version's default installed packages list.  I will give the Ubuntu version, and the script will fetch the packages list.  Note: I need at least a server address. I can write a script for this.


I am getting intrigued by this question that I don't have the sufficient knowledge to answer it, I've looked up when black holes collide "non-directly" but that doesn't really apply to my question nor if its possible to do this.  I know that slight deviations of their trajectories would cause them to spin on each other or slingshot them but what would happen if we accelerate them at near light speeds and collide them both directly to their centers of mass?   Since black holes are massive their inertias would be huge, where would all this inertia go?   Or would the black holes disintegrate each other under the extreme conditions (they shouldn't)?   Or something else?  For reference, these black holes are equally massive and aren't spinning rotationally.

Assume two uncharged non-rotating black holes traveling straight at each other with no outside forces acting on the system. What is thought to happen to the kinetic energy of these two masses when they collide?  Is the excess energy lost through gravitational radiation?  What would the effect of these gravity waves be on matter or energy that they encounter?


When I connect with the Terminal on Mac, I see:  root@example:~#   How can I change the value of example ?  Is it the hostname ?  Thanks.

Currently it is:   michael@Castle2012-Ubuntu-laptop01:~/Dropnot/webs/rails_v3/linker/spec/controllers$   Outside of renaming my machine and directory structure...  How could I make it be something more like:  michael:controllers$


I have installed Ubuntu 13.10 in my samsung laptop,everytime i boot up the system it starts with full screen brightness which is quite annoying in the night.  Is there a way to fix this problem so that the brightness remains at a level which i set before shutting down the system ?

The brightness of my laptop is reset to max on every restart. I tried the solution provided at  but had no luck.   This command   cat /sys/class/backlight/acpi_video0/max_brightness   Returns   cat: /sys/class/backlight/acpi_video0/max_brightness: No such file or directory   Then I found that I don't have a folder named acpi_video0, but a folder called intel_backlight:    Every time I increase or decrease the brightness using the brightness control keys, the values in brightness and actual_brightness get updated.  Is there any method I could follow to set the brightness to a fixed value on every boot and vary it as and when I need it using the brightness control keys?


I'm submitting an mathematics article concerning research that was done entirely while I was an undergraduate at University A.  This August I will be a graduate student at University B.  The only funding I received came from NSF through a ten week program at University C at the very beginning of the project, after which I finished the research on my own while attending University A.  On the other hand, while University B has nothing to do with the publication, it is the most up to date institution as far as contact information goes.  Should I put University A or University B as my affiliation (or both)?

I am moving from one job to another (postdoc to tenure track) this summer and I have papers in several stages of being written, these go from handwritten notes with all the necessary arguments to under revision at a journal. All the papers will have my new contact information put on them but where is the line for changing affiliation? It seems obvious to me that the one that is still in the handwritten notes stage will get the new affiliation and that the ones under revision won't. So somewhere in between is a line.   Where is it?  There are some similar questions so far (see  and  but they do not seem to be quite the same situation since I am not changing fields and the appointments are not concurrent.


The University of Illinois Department of Physics article  states that the acceleration due to gravity is the same no matter the mass of the object.   However if an object, say for example the moon, were falling to the Earth, gravity would have to pull harder to speed it up the same. Would the acceleration of gravity be the same?  My question is not the same as  because I'm asking about acceleration of gravity, I'm asking if heavier objects would fall slower, not faster. So, wouldn't they fall slower because gravity has to pull harder?  Side note: Let's just say we also ignore the effects the other question mentions.

The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half. The halves clearly can't then fall more slowly just by being sliced in two.  However, I believe the answer is that when two objects fall together, attached or not, they do "fall" faster than an object of less mass alone does. This is because not only does the Earth accelerate the objects toward itself but the objects also accelerate the Earth toward themselves. Considering the formula: $$ F_{\text{g}} = \frac{G m_1 m_2}{d^2} $$  Given $F = ma$ thus $a = F/m$, we note that the mass of the small object doesn't seem to matter as when calculating acceleration the force is divided by the $m$ term, its mass. However, this overlooks that the force is actually applied to both objects, not just to the smaller one. The acceleration on the second, larger object is found by dividing $F$, in turn, by the larger object's mass. The two objects' acceleration vectors are exactly opposite, so closing acceleration is the sum of the two:  $$ a_{\text{closing}} = \frac{F}{m_1} + \frac{F}{m_2} $$  Since the Earth is extremely massive compared to everyday objects, the acceleration imparted on the object by the Earth will radically dominate the equation. As the Earth is $\sim 5.972 \times {10}^{24} \, \mathrm{kg} ,$ a falling object of $5.972 \, \mathrm{kg}$ (just over 13 pounds) would accelerate the Earth about $\frac{1}{{10}^{24}}$ as much, which is one part in a trillion trillion.  Of course in everyday situations, we can for all practical purposes treat objects as falling at the same rate because of this negligible difference—which our instruments probably couldn't even detect. But I'm hoping not for a discussion of practicality or what's measurable or observable, but what we think is actually happening.  Am I right or wrong?  What really clinched this for me was considering dropping a small Moon-massed object close to the Earth and a small Earth-massed object close to the Moon. This made me realize that falling isn't one object moving toward some fixed frame of reference, but that the Earth is just another object, and thus "falling" consists of multiple objects mutually attracting in space.


I am running Ubuntu 18.04.1 LTS and I am having issues to install the ecrypt-utils app. See the output below:  ubuntu@ubuntu:~$ sudo apt install  ecryptfs-utils Reading package lists... Done Building dependency tree        Reading state information... Done Package ecryptfs-utils is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'ecryptfs-utils' has no installation candidate   Any help is much appreciated.

When I try to install any package through the command line, I get an error.   $ sudo apt-get install <package> Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package <package>   Can anyone help me on this?


I have qbittorrent installed.  When I click on a magnet link with Firefox it prompts me what program to use to open it.  I would love to use qbittorrent, but it is not listed there.  I search for it and it is not there.  I have qbittorrent installed and open, currently running.  This is frustrating as hell.  Why isn't it there?  Why can't I just open the file that I would of had downloaded an hour ago if I were on windows?  Why is such a simple thing so complicated in ubuntu?

The key /desktop/gnome/url-handlers/magnet in gconf-editor is missing.  How do I assign magnet links to use qbittorrent?  It would be really nice if it were easy to set url handlers. I always struggle with this when doing a fresh install. I would like to set subl:// to open sublime text 2 too.  EDIT: I would like it to work regardless of the application I'm using to activate the link. I'm using Chrome, but IMO the OS (Ubuntu) should be handling links that an application doesn't know how to handle - which it does, so how would one configure this?  EDIT2: This post details how to make the text editor in VIM handle vim:// urls, perhaps this can be applied to to magnet links. i.e create a desktop shortcut defining a MimeType handler then refreshing the cache. (Can't try right now as I'm using 12.04).


while read wholeline do   echo ${wholeline} --outputs John Jones   #grab all the lines that begin with these values   #grep '^John Jones' workfile2   --works, prints contents of workfile2 where the 1st matches   grep '^${wholeline}' workfile2  # --does not work. why? it should be the same result. done < workfile1  workfile1 contains the value John Jones at the beginning of the line in the file.  workfile2 contains the value John Jones at the beginning of the line in the file.  How can I change that second grep statement so that it works? It is picking up nothing.

I could see that certain patterns in the GNU Grep can be enclosed within brackets and certain others need not be. For example, matching the beginning of a word works only if it is enclosed within quotes.  user@host:~/Desktop$ grep -E '\<H' test Hello World user@host:~/Desktop$ grep -E \<H test   [test contains the string Hello World]  But matching end and beginning of file works without dollar:  user@host:~/Desktop$ egrep d$ test Hello World   Why is it so? And what is the rule?


I can't find the exact original, but I have attached an image identical to the original.  Edit:   Originalish:   Getting the original image is next to impossible. However the image I proved is about 95% like the original detail and colour wish, excluding the location.  Tip: to save the images download the whole page and then copy the image from the files. This only applies to the first link which has download disabled. The last link will have a download button.

I found this photo on a flickr page and was wondering how to create those colours and what seems to be some kind of coloured filter added on top.  Subject images;    Similar unedited Image:   It's next to impossible to find an identical photo due to the secrecy amongst us planespotters in involved, in getting exclusive photos.  I have been told lightroom and Photoshop were used to create this effect.


I would like to compare ciphertext based on the order assumed on the message space.  So, do you know if there exists some encryption scheme with the follow property:  Let $c_0 = E(m_0)$ and $c_1 = E(m_1)$ for all $m_0$ and $m_1$ in the message space. So,  $$c_0 \leq_C c_1 \Leftrightarrow m_0 \leq m_1$$  Note that I used $\leq_C$ instead of $\leq$, because the partial order relation on the ciphertext space may be different from the partial order of the message space.  For example, if I have $c_0$ and $c_1$ such that $c_0 = E(-3)$ and $c_1 = E(103)$, I would like to know that $c_0 \leq_C c_1$ without knowing the clear texts $-3$ and $103$.  If something is unclear, just let me know.  Thank you.

Order-preserving encryption (OPE) is, apparently, a method of encrypting data so that it's possible to make efficient inequality comparisons on the encrypted items without decrypting them.  I've been coming across this term in various places (including ) lately, but I have no idea how such encryption schemes are supposed to work.  Any obvious methods I can think of to allow such comparisons on encrypted data would result in catastrophic security failure.  Certainly, I assume that OPE must involve some kind of security tradeoff compared to traditional encryption, but given that it seems to be actively  and , it seems that it must be possible to implement in a way that retains at least some level of useful security.  I just don't see how.  Given that  didn't turn up any convenient Wikipedia articles or other popular summaries of OPE, I figured I'd try asking for one here before diving into the academic literature.  (At worst, I may try to answer my own question later, if nobody else beats me to it.)  So, to summarize, my question is: How does order-preserving encryption work, and what security properties does it provide?


I want to prove the below:  $$\sum_{i=1}^n f_i^2 = f_n \times f_{n+1}$$  The example of $n = 1$ is trivial:  $$\begin{align} \sum_{i=1}^1 f_i^2 &= f_1^2 \\ &= 1^2 \\ &= 1 \times 1 \\ &= f_1 \times f_2 \end{align}$$  And working through $n=2$:  $$\begin{align} \sum_{i=1}^2 f_i^2 &= f_1^2 + f_2^2 \\ &\stackrel{?}{=} f_2 \times f_3 \end{align}$$  Using the definition of a Fibonacci number, I can work backwards from $f_2 \times f_3$:  $$\begin{align} f_2 \times f_3 &= (f_{2-1}+f_{2-2}) \times (f_{3-1}+f_{3-2}) \\ &= (f_1 + f_0) \times (f_2 + f_1) \\ &= f_1f_2 + f_1f_1 + f_0f_2 + f_0f_1 \\ &= f_1f_2 + f_1^2 \end{align}$$  Since $f_2 = 1$, $f_1f_2 = f_2f_2 = f_2^2$, thus $f_2 \times f_3 = f_1^2 + f_2^2$.  But how could I generalize this for any $n$ and not show examples for $n=3$, $n=4$, etc?

The definition of a Fibonacci number is as follows:  $$F_0=0\\F_1=1\\F_n=F_{n-1}+F_{n-2}\text{ for } n\geq 2$$   Prove the given property of the Fibonacci numbers for all n greater than or equal to 1. $$F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$$  I am pretty sure I should use weak induction to solve this. My professor got me used to solving it in the following format, which I would like to use because it help me map everything out...  This is what I have so far:  Base Case: Solve for $F_0$ and $F_1$ for the following function: $F_nF_{n+1}$.  Inductive Hypothesis:  What I need to show: I need to show $F_{n+1}F_{n+1+1}$ will satisfy the given property. Proof Proper:  (didn't get to it yet)  Any intro. tips and pointers?


I have a set of points on a 2D surface and need to build a heatmap. However, I also need to smooth out the density/distribution by applying some sort of kernel (Gaussian kernel, for example).  I Know what Gaussian distribution is, and I have no idea, how mathematically apply the Gaussian kernel to the points on 2D so I can get a smooth distribution or density of points. I know there are functions in Wolfram to do that, but this is more like a research problem, so I need to understand the THEORY of it. Let's say, I am a theory person, and I am NOT in needs of programming. I just need to understand the underlying math of it, why it is still   Can someone, please, explain to me, possibly with an example? Or take me to a website that I can read about it?   I'd much appreciate that.  Thanks

I have a set of points on a 2D surface and need to build a heatmap. However, I also need to smooth out the density/distribution by applying some sort of kernel (Gaussian kernel, for example).  I Know what Gaussian distribution is, and I have no idea, how mathematically apply the Gaussian kernel to the points on 2D so I can get a smooth distribution or density of points. I know there are functions in Wolfram to do that, but this is more like a research problem, so I need to understand how this is done.  Can someone, please, explain to me mathematically how this is done, and possibly with an example? Or take me to a website that I can read about it?  I'd much appreciate that.  Thanks