In every coloring in two colors of the edges of $K_{10} $ there are at least 20 monochromatic triangles.   Can anyone give me a hint of how to approach this? I have no idea..

Say $K_n$ is a complete graph of $n$ nodes, and every edge is either blue or red. I'm trying to find $T_n$, which is the lower bound for the number of monochromatic triangles in $K_n$ (monochromatic meaning triangles whose 3 edges are of the same color).  I'm trying this approaches:   A. Let $v_i$ a vertex in $K_n$. This vertex belongs to $\binom{n-1}{2} $ different triangles. Let $r$ be the number of red edges that $v_i$ belongs $b$ the number of blue edges. Of course,  $$r + b = n-1$$ So, the number of non-monochromatic (dual/stereo-chromatic?) triangles is $r \cdot b$, and so our bound would be (for vertex $V_i$)   $$T_n \le \binom{n-1}{2} - r \cdot b$$  Question is - how do I know when $r \cdot b$ is the maximal possible number? Also, this would give me the upper bound, how do I find the lower bound?  Thanks in advance!


I know there are other ways I can do this, but I'm a little curious about this anyway.   Basically, I have a breadboard that's mounted on a typical base that has the typical three posts I can hook power to. I want to operate one pair of power rails at 12V and one pair at 5V. And I have one 12V AC adapter and one 5V AC adapter But remember, I have 3 posts on this thing, red, green, black.  My thought is, I can hook the red up to 12V+ and the green up to 5V+ and put both grounds from these power supplies on the same black post?  Then I can wire jumpers from the posts to the rails. Is this kosher? Or does each AC adapter need to use its own ground? Do the grounds need to be isolated, or is ground, ground even if you're using different voltages?  It isn't lost on me I could do this a million other ways, but sharing a ground could be handy, but I haven't seen it done anywhere. Not sure if that's a sign or if I just haven't looked in the right place.  Thanks for any help!

As I'm relatively new to the electronics world, I was wondering if you can connect multiple  ground terminals (corresponding to several different voltage outputs) to the same ground. Or do they each need their own?  In my case I have 5 lines, one 12V, one 3.3V, two 5V and one variable from a 12V in using a  voltage regulator that already has its own ground. So I'm guessing that each would need its own ground, but it is never bad to ask.


I got stung by bees in animal crossing new leaf and None of the people have offered medicine. I don't know how to upgrade nookling junction. If anyone has gotten medicine from the following please tell me:  Walt, Bruce, Pietro, Alice, Derwin, Bluebear, Frobert, or Diana.  Where am I supposed to get the medicine for my bee stings?

I know it is possible to be stung by bees in Animal Crossing: New Leaf.   I learned that the hard way when I was trying to find my furniture tree. Now, I have an eye swollen shut and all of my towns people are making fun of me. They're all being kind enough to inform me that I need Medicine, but they seem to be enjoying themselves at my expense too much to tell me where to actually find the Medicine.  Where can i get medicine? I'd really like it if my townspeople stopped making fun of me.


I have and article document in latex. In this document, I have set \lhead in the header of doc. But as my doc is about many themes, I was wondering if I could change \lhead contain dynamically?

I'd like to modify the contents of my headers and footers - e.g., to display the current chapter and/or section title or to change the pagination alignment. How can I do that? I've noticed the packages  and scrpage2 (part of the -bundle) - are they interchangeable, or are there situations where I should prefer one package to the other?


Let $X$ a random variable with density $f_X(x)=\frac{1}{2}x,x\in [0,k]$. For it to be a density $k=2$. Now I have to find the cdf of $Y=X(2-X)$. To apply $f_Y(y)=f_X(x)|\frac{dy}{dx}|$ with $|\frac{dy}{dx}|=2-2x$ I have to find the transformation of $Y$, and I obtain $x=\pm \sqrt{2x-y}$. I consider only the positive solution because $x>0$, but remains $x$ under the square root. What is the inverse transformation of $Y$?

Suppose that the continuous random variable $X$ has probability density function  $f_X(x)=\begin{cases}\frac{1}{2}x & \text{if } 0<x<2\\0&\text{otherwise}\end{cases}$  Let $Y=X(2-X)$. Calculate $P(Y>y)$ and hence find the probability density function of $Y$.  So far I have tried expressing $P(Y>y)$ as $P(X(2-X)>y)$ but the quadratic inside has me stuck. Sorry - I am revising for an exam and it has been a long time since I have answered questions like this.


I have a bunch of files that I don't need. I'm wondering what's taking up all the space. I am tempted to almost format the laptop and start fresh.  What can I do to find out what is taking up all the disk space in my Macbook?

Every few days I get notices on my MacBook that it's running or run out of hard drive space. Curiously, restarting the computer will enable me to recover gigabytes of space (this past time, it was able to recover about 2.2GB). However, I can't identify anything in my personal activity that consumed that space.  It's possible that it's a rogue iTunes podcast or a huge software update that my Mac is automatically downloading - would either of these reclaim the space upon a restart?  One possibility that I can think of is that FileVault has some sort of disk leak, allocating but not freeing files. Does this make sense? Is there a tool that I can run to determine where this space is going? Assuming it is FileVault, should I try to disable it? What's the best way to turn of FileVault on a nearly full computer?


Occasionally an answer could solve (or help solve) an asker's problem - and hence be accepted - but may not be beneficial to the community. In cases where the answer is simply too specific, this can be harmless (and often another responder will leave a more generalisable answer). But occasionally an accepted answer may actually be a bad idea for many users (even though it was helpful to the asker of the question). A fairly strident example  - note the comments on the accepted answer (basically it introduces a security vulnerability). In cases as pronounced as this, is it inappropriate or discourteous to drop a comment on the question suggesting another answer be accepted? Or is it expected that readers should always view several answers to minimise the risk of going by sub optimal information?

I'm wondering what the etiquette is for suggesting that a user accept a different answer to their question.   A recent example: shortly after the OP posted the question, an answer was posted and quickly accepted. The answer was technically correct, but was short and low-quality. 45 minutes later another answer was posted, which was lengthy, thoroughly explained the answer to the question, and was just an all-around good answer. The accepted answer has only 1 upvote, and the other answer 5. So clearly there is community consensus regarding which is the better answer; it is not only my opinion driving this question. The problem is that, even though the better answer has more upvotes, it will never rise above the accepted answer when being displayed.  So my question is this: I would like to comment on the question and suggest that the OP change their accepted answer, as the other answer is far superior and I would prefer visitors to the site view excellent content to poor. It is of course their choice, and I would word the suggestion politely, but I'm not sure if it is proper etiquette to advise a user on which answer I think should be accepted. In this case this was actually the OP's first question on the site, which adds another layer of complexity, but I think the etiquette should probably be the same regardless. So, can anyone please advise me on the SE guidelines for such situations? Can I politely prod the OP, or do I need to just leave it alone? (To clarify, none of the answers in question are mine.)    I attempted to find an answer to this question before posting it; the closest I came was , which is related but not a duplicate.


I have recently been typesetting a Quranic Mashaf using a combination of XeLaTeX, bidi, and polyglossia. I am generally pleased with the results so far, but after reviewing Idris Samawi Hamid's work in ConTEXT and the development of the Husayni font, I believe that's the direction I'd like to move in.  But I'm unclear if Husayni is complete yet? The last reference I could find is in the article  which dates back to 2012, and at that time the font was still under development. I wrote to Professor Idris  recently but haven't heard back yet.  Could anyone provide a "minimal working document" that illustrates the use of Husayni?  Lastly, as a computer programmer, and the idea of being able to program TeX in a language like Lua seems very appealing. However, I'm unclear how mature LuaTeX and the rest of the stack that Professor Idris uses actually is, or whether it's missing features that will soon frustrate me and make me want to go back to XeLaTeX? Any advice from someone who's been down that road would be greatly appreciated.

I would like to typeset a line of Arabic using ConTeXt and the . I can see the lfg files located here:   /usr/share/texmf/tex/context/fonts/husayni.lfg /usr/local/context/tex/texmf-context/tex/context/fonts/mkiv/husayni.lfg   However, nothing I try can actually get a simple document rendering properly (although I was able to get the same line of Arabic rendering with ConTeXt and the Amiri font). After Googling around a bit, the issue may lie in a file husayni.ttf, which is referenced in  and , but which isn't found on my system.  Was this file never released? Is the font not meant to be used, or have I made a mistake in my setup?


i have downloaded the jdk file having the tar.gz extension.I am using a 64 bit pc.but i don't understand how to install the javac compiler and how to set the path in Ubuntu 15.04.if anyone can give me step by step process please.

I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7?


I have Samsung A5, SM-A500H. Android version 5.0.2. Latest version of SE android app on Google Play Store.  If I ask a question, you answer, I receive a notification on my phone that you answered, I click on the notification, I see this        So it doesn't load correctly, I have to go back and click on the notification icon from within the app for it to open correctly.

When I receive a message on an SE post, I get a notification like this:    If I double tap this notification, the SE application opens, but my feed is empty approximately half the time. It looks like this:    If I refresh the feed (slide from the top), the feed does refresh and shows the new notification.   The notification, above, leads to  comment.  I haven't figured out the pattern yet, but this occurs roughly half the time I open a notification. It's occurred for chat messages, comments and answers - but not consistently. I have received notifications for the same post (for example, the two comments after the one linked above) that do not show an empty feed. But, a chat message barely 10 minutes later will show the empty feed again.  I am utilizing the beta app - version 1.0.72 on Android 5.0.1.


A friend of mine is planning to come to London in April but she knows that her French ID expires while she is here. As far as the French authorities is concerned an expired ID card is still valid for the next 5 years. Will she have problem at Immigration at Gatwick airport when she goes back to France?

I am French. Can I enter Britain with an expired French identity card ?


I have a division 4/3 which produces 1.33333333... I am storing the result in java double and I want to round this result to 1.34. How can this be done in Java ?  import java.text.*; import java.math.RoundingMode; public class HelloWorld{       public static void main(String []args){        DecimalFormat decimalFormat = new DecimalFormat("#.##");      decimalFormat.setRoundingMode(RoundingMode.HALF_UP);       String dd =decimalFormat.format(1.33333333);       System.out.println(dd);      } }   Works with (Math.ceil(1.333333 * 100) / 100.0) but not with DecimalFormat

What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -> 0.91239 0.912300 -> 0.9123   What is the best way to achieve this in Java?


Currently, to approve or reject an application, user need to click this highlighted button from image (1), then it will redirect user to page image (2). User need to click highlighted text to go to approval page image (3). Button from image (1) is not a standard page. It is URL. Highlighted text from image (2) is from flows, and page image (3) is a approval process. What I want is, once user click on highlighted button from page image (1), it will bring user to page image (3). May I know how to do that?

I want to remove a few steps in the approval process. You may refer to the images that I attached here. The actual process, once user click return shipment approval/reject button from page 1, page 2 will come out, user can click either yes or no. Then user will go to page 3, then after click on Approve/Reject Record, page 4 will come out. What I want to do is, once user click on page return shipment approval/reject button from page 1, the user will go to page 4 directly without go to page 2 or 3. Is there any idea on how to do that?


I have these automatically changing wallpapers active on my work laptop (not activated by me) and I think the vast majority is at least high quality, some are brilliant and a few I just adore.  What is the source of these images?  I'd definitely like to download or even buy some of them.

Where, or what format, are the images used by Windows 10 when logged out or in lock-screen?  I searched the entire drive for *.jpg, *.bmp, *.png, and *.tif but the one I was looking for did not appear.  At first glance, , although not exactly a duplicate, appeared to have the path I wanted.  But when I went there, the pre-login image was there, but the lock-screen image was not.  (And contrary to the claim in that answer, the files there did have extensions.)  UPDATE: I just did a lockscreen, and got an image that IS in that directory, but earlier today, it was consistently an image of an interesting footbridge that is not in that directory.


I am a citizen of St.Vincent and Antigua, I have a USA visa in my St.Vincent passport but I will be holidaying in the USA but I want to go over to Canada, can I use my Antigua passport to go to Canada because Antiguans don't need a visa for Canada. So my question is can I go into the usa on my St.Vincent passport then leave the usa on my Antigua passport for Canada?

I was just wondering if you have two passports (a Chinese one and an Australian one), and you booked your airline ticket with the Chinese one, will you have to show both of your passports or just one?  The thing is, on my Chinese passport, it has my birth name, but then when I became an Australian citizen, I legally removed my Chinese name and replaced it with my English name. So I don't know whether I should just show the passport officials the one that I booked the airline ticket with.


How can I install Adobe flash player on 18.04 LTS? I have tried downloading it from the Adobe Flash official site where I select the Ubuntu/Debian version, but it says chose an application to open the download link, and the only option that appears is Apt-URL. When I select it I get a popup saying     the channel bionic partner is unknown    Enabling the partner repository doesn't help.  How can I install Adobe flash on 18.04?

Even though I have the latest Adobe Flash player 11.2 for Linux in Firefox -   - a particular online flash game still requests that I update to the latest flash player.  I've tried this online game on my laptop (Windows 8 with Flash Player 11.8) and it has no problems.  Is there a way to trick Ubuntu or this game into thinking Flash Player 11.8 is "installed"?


How does memory gets allocated for string literal in c and do we need to free it? EG  char *k="hello world";   where does this string gets stored and how does it gets de-allocated?

Is a string literal in c++ created in static memory and destroyed only when the program exits?


I am wondering about the "double possessive" I have been reading about.  I have a couple of sentences as an example:  He’s a new client of Jane and Kevin’s and a close childhood friend of Steven O’Neill’s.   I thought that the above sentence was correct, because it sounds natural to use the apostrophe S to me, in the same way that we say "he's a friend of mine."  However, I have heard people criticize sentences such as that one above as having a "double possessive" because of the OF as well as the apostrophe S.  Is the above sentence correct or should it be:  He’s a new client of Jane and Kevin and a close childhood friend of Steven O’Neill.  Thank you - any help would be greatly appreciated.

As  shows, we nearly always use the possessive form of personal pronouns for friend of mine/his/ours/etc.  But when it comes to actual names, we prefer  without the possessive apostrophe. That preference is even more marked with, say, . Not that I think the usage itself is particularly American - it's much the same with .  Personally, I find friend of him grates. In general I've no strong feelings either way as to whether it's friend of Peter or friend of Peter's (though I deplore the possessive in ), but in line with many others, I really don't like the possessive in relation to things like countries.  Why is this?   Edit: Noting an apparent "progression" (pronoun -> person -> nation) marked by reduction in use of the possessive, I checked at a finer "granularity". NGram shows that although it does occur,  virtually "flatlines" against friend of mine. But the bias reduces through of you, of us, and by the time I get to  it's much less extreme. There seems to be something "egocentric" about the double possessive.  Presumably when babies learn to speak, they soon notice that possessive pronouns, possessive apostrophes, and the word "of", all do the same job. Parents would correct a child who says "of mine's", but probably wouldn't even notice the same "redundancy" in "of Peter's". Younger speakers are unlikely to even be talking about something "of America's". Perhaps as we mature we tend to discard the "double possessive" for the more "distant" things that only adults are likely talk about, but we keep it for "closer" people because that's how we spoke when we were younger.  EDIT2 I note that I'm a great fan of him is vanishingly rare compared to ...fan of his, but with ...fan (of John) the double possessive occurs far less often than ...friend (of John's). Usage seems to be affected by the noun before "of" as well as the one after it. This is getting complicated...


Is it expected a fail, attempting to install Ubuntu Touch on an Android Tablet other than Galaxy or Nexus?  Thanks

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


When reading through other people's code I often wonder if there is a quick way to find the definition of a particular command argument. For example: Let's say I know what some_command does, but I don't know what the -x argument means. man some_command will certainly provide the answer, but scrolling through manual pages to find an obscure argument can be time-consuming. Is there a quicker solution? Thanks!

Whenever I search the manpages, I'm almost always trying to find out what's going on with a specific flag. For example, when searching the man pages for  I was searching the for -f flag. I'm not sure how to say, quickly get to the flag which is here:  OPTIONS    General options        -f FORMAT, -r FORMAT, --from=FORMAT, --read=FORMAT   and filter out stuff like:  iconv -t utf-8 input.txt | pandoc | iconv -f utf-8              or  pandoc -f markdown -t latex hello.txt   I've tried searching for /-f, and I've looked at  and tried (^|\s)-f($|\s\) but it was invalid. So I'm wondering how do you quickly search less for "only the flag -f"?  Would love your thoughts or some other tool that you use to quickly go through documentation


This is my code, which doesn't work:  \documentclass{article} \usepackage{tikz} \begin{document} \tikz \node {start\linebreak{}stop}; \end{document}   The \linebreak command doesn't work. In order to make it working I have to say \node[text width=5em]... Is there any other method to make it working, without explicit specification of the node text width?

How can I insert a line break in a TikZ node? Simply putting \\ where I want the break doesn't work (see MWE).  Is there a way to make lines break automatically at some specified width?  And can I control the alignment of the text (left, right, centered, justified)?  \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node {First line\\second line}; \end{tikzpicture} \end{document}


The iOS app has an icon that gets me a list of SE sites. I have scrolled slowly through the entire list on my iPad, and Expatriates is not there:      With Patrick's suggestion, I typed "expat" into the search box and they appeared, but they do not appear otherwise.  So, it seems to be a bug, but it is not, as explained in the accepted answer (and in the edited title).  Version 1.6.6.2

Stack Overflow seems to have abandoned us iOS users! Look:    What has happened?!   App Version: 1.6.6.2 Device: iPhone 5s (Global) OS Version: Version 10.3.2 (Build 14F89)


Let $A$ be an $m \times n$ matrix. Show that $Null (A) \subseteq Null(A^TA)$ if and only if $Null(A^TA)  \subseteq Null(A)$.   I can not really come up with the idea how to show that. Can someone help me? I would really appreciate that.

$A$ is an $n\times m$ matrix and $AA^{T}$ is a symmetric real matrix.  Also, we have: $\operatorname{rank}(AA^{T})=r\stackrel{?}{=}\operatorname{rank}(A)$.  Let $Q= \begin{Bmatrix} q_1,...,q_{n-r} \end{Bmatrix}$ be a basis for the Null space of $AA^{T}$. i.e. $AA^{T}q_i=0$, show that $A^{T}q_i=0$. I guess one proof can be that the Null space for $A^{T}$ is a subspace for Null space for $AA^{T}$, then the question would be why $\operatorname{rank}(A)=\operatorname{rank}(AA^{T})$?


I have a view into which I am pulling properties of vehicles, such as tire size, engine capacity, color, number of doors, etc. This data is stored in multiple tables but I have simplified the data into my view.  What I am trying to achieve is to join this view to my main vehicle table so that I can select the various properties as columns in a single row.  My view:  Vehicle_ID  Property     Value 1           Doors        2 1           Engine Size  2 liter 1           Tire Size    50cm 1           Color        Blue 2           Doors        4 2           Engine Size  3 liter   And my main vehicle table:  Vehicle_ID  Description  Date_Bought  Owner_ID 1           BMW M3 Sport 2000/12/23   1 2           Audi A5 3XL  2015/03/19   1   So what I would like to get out is something like  Vehicle ID  Description   Date_Bought   Doors   [Engine Size]  [Tire Size]  [Color] 1           BMW M3 Sport  2000/12/23    2       2 liter        50cm         Blue   My overall SQL knowledge is fairly limited, I'm pretty good with JOINS and stuff, but the logic of the PIVOT command and its syntax completely escape me.

My table is like this:  Sitecode    Month  Amount --------    -----  ------ XX          Jan     1000 XX          Jan     3000 XX          Apr     3000 XX          Apr     1000   What I want is, to show the result something like this:  Sitecode    MonthJAN   MonthAPR --------    --------   -------- XX          4000       4000


I need to get the IOS 10.2 IPSW to install on my iPod Touch to jailbreak it, but there is no JB for IOS 10.3.2, which I recently downgraded to from IOS 11. How can I get it to install?

I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this?


Is there any 'canonical' way to resolve hostname to IP, that should work on (almost) any Linux distribution?  I'm recently stuck with debugging of Docker container based on ubuntu:16.04 image. There is no ping, no ip, no dnslookup or anything else. Of course apt-get install is not possible as well, because logging as root is not available as well.

How do I get a remote host IP address if I don't have ping, and don't have any bind utilities like dig, nslookup, etc?  I need an answer that does not include 'install X' or 'use sidecar container'. I am looking for something that relies on nothing more than bash and the basic shell commands.


I have a slide that has some items and then underneath I have a figure, which is define as tikzpicture, while I want to point some arrows from items to the figure. The problem is that now both the figure and the items start from the center of the slide, and basically the figure is on top of the items. Any ideas how to solve this?  \documentclass{beamer} \usepackage{tikz} \usetikzlibrary{positioning,tikzmark}  \begin{document}  \begin{frame}{Test} \begin{itemize} \item Item 1 \tikzmark{a} \item Item 2 \tikzmark{b} \item Item 3 \tikzmark{c} \item Item 4 \end{itemize} \centering \begin{tikzpicture}[remember picture,overlay]     \node {\includegraphics[width=0.8\textwidth]{my-picture}};     \foreach \i/\j in {(0.5,0.66)/a} \draw [cyan,->] ({pic cs:\j}) -- \i; \end{tikzpicture} \end{frame}  \end{document}   The resulting layout should look like this sketch:

I'm creating a presentation in Beamer, and I have a slide that consists of a few items, and then underneath is a picture. And I want to draw arrows from the items to the picture underneath. How can it be done? Currently, I have just this.  \documentclass{beamer} \begin{document}  \begin{frame}{Test} \begin{itemize} \item Item 1 \item Item 2 \item Item 3 \end{itemize} \includegraphics[width=1\textwidth]{picture} \end{frame}  \end{document}   I was wondering whether TikZ can help here? But how?


A while ago, the following question was posted by the OP, who requested for help in proving the following inequality: Let $a,b,c,d$ be positive reals such that $a+b+c+d=1$. Prove that: $$\frac{a^3}{b+c}+\frac{b^3}{c+d}+\frac{c^3}{a+d}+\frac{d^3}{a+b} \ge \frac{1}{8}.$$  I have added the extra condition that $a,b,c,d$ must all be positive reals, since the given inequality by itself would not hold otherwise, as another user has pointed out in the comments. Since the original post has been closed (in all fairness to the OP, the condition of positive reals could be implied, especially if this was a competition math problem), I decided to open a new post in order to provide a possible solution for the OP, as well as inquire if there are other possible means to prove this inequality. My solution involves AM-GM, so it would be nice to see other methods that work as well.

If $a,b,c,d$ are positive real numbers such that $a+b+c+d=1$,show that                          $$  \frac{a^3}{b + c} + \frac{b^3}{c + d} + \frac{c^3}{d + a} + \frac{d^3}{a + b} > \frac 1 8$$


According to the chapter II.1 in "Quantum Field Theory in a Nutshell" by A. Zee, Dirac was trying to write down the relativistic wave equation linear in spacetime derivative.  The author stated that     The equation is supposed to have the form "some linear combination of $\partial_\mu$ acting on some field $\psi$ is equal to some constant times the field." Denote the linear combination by $c^\mu \partial_\mu$. If the $c^\mu$'s are four ordinary number, then the four-vector $c^\mu$ defines some direction and the equation cannot be Lorentz invariant   What I do not understand is the last part of this statement. If $a_\mu$ and $b_\mu$ are four-vectors, it is obvious that $a_\mu b^\mu$ must be Lorentz invariant. Why can it not be true in this case since both $c_\mu$ and $\partial_\mu$ are also four-vectors?

I have a question about the following passage on pg. 89 of Zee's QFT in a nutshell:     At first sight, what Dirac wanted does not make sense. The equation is supposed to have the form "some linear combination of $\partial_\mu$ acting on some field $\psi$ is equal to some constant times the field." Denote the linear combination by $c^\mu\partial_\mu$. If the $c^\mu$'s are four ordinary numbers, then the four-vector $c^\mu$ defines some direction and the equation cannot be Lorentz invariant.   The simplest equation I can construct that he is referring to is  $$(c^{\mu}\partial_{\mu}-m)\phi(x)=0, $$  for $m>0$. Taking $\phi(x)\rightarrow\phi(\Lambda^{-1}x)$, and $c^{\mu}\rightarrow\Lambda^{\mu}_{\ \ \nu}c^{\nu}$. Then, the left term transforms like   \begin{align*} \Lambda^{\mu}_{\ \ \nu}c^{\nu}(\Lambda^{-1})^{\sigma}_{\ \ \mu}\partial_{\sigma}\phi(\Lambda^{-1}x) &= \delta^{\sigma}_{\ \ \nu}c^{\nu}\partial_{\sigma}\phi(\Lambda^{-1}x)\\ &=c^{\sigma}\partial_{\sigma}\phi(\Lambda^{-1}x). \end{align*}  Then, we have that   $$ (c^{\sigma}\partial_{\sigma}-m)\phi(\Lambda^{-1}x)=0.$$  But doesn't this show that the equation is Lorentz-invariant?


Let $$f(z) = \frac{1-e^{2iz}}{z^2}$$ and let R > r > $0$ Find $$\int_{-\infty}^{\infty}\frac{sin^2(t)}{t^2}dt$$ using $$\int_{\gamma}f(z)dz = 0$$ where $\gamma=L(-R,-r)\oplus - S(0,r)\oplus L(r,R) \oplus S(0,R)$ I have found that f(z) has a singularity at $0$ with a pole of order 1  and that Res(f,0)= -2i. where can I go from here?

$$\int_0^{+\infty} \Big(\frac{\sin t}{t}\Big)^2 \ dt=\frac{1}{2} \int_{-\infty}^{+\infty} \Big(\frac{\sin t}{t}\Big)^2 \ dt=\frac{1}{2} \Big\rvert \Big\rvert \frac{\sin t}{t} \Big\rvert \Big\rvert_2^2 $$    Plancherel theorem:  $$2 \pi \Big\rvert \Big\rvert f \Big\rvert\Big\rvert_2^2=\Big\rvert \Big\rvert  \mathscr{F}(f)  \Big\rvert\Big\rvert_2^2$$    $$p_2(x)=\begin{cases} 1 \qquad x \in [-1,1] \\ 0 \qquad x  \notin [-1,1]    \end{cases}$$  $$\frac{1}{2} \Big\rvert \Big\rvert \frac{\sin t}{t} \Big\rvert \Big\rvert_2^2=\frac{1}{2} 2\pi \Big\rvert \Big\rvert \frac{1}{2} \ p_2 \Big\rvert \Big\rvert_2^2=\frac{\pi}{2} $$    Is there any other method to calculate this integral?  Thanks!


I'm following this tutorial to build a user login system within Flask using Python 2.7.    I have this Flask application structure.  flaskapp/ └── app/         ├── user/         │      ├── __init__.py         │      ├── static/         │      ├── templates/         │      ├── forms.py         │      ├── routes.py         └── runserver.py   Within the tutorial, it has me edit this file.  app/intro_to_flask/routes.py   Within that file you have this code.  from user import app from flask import render_template, request, flash from forms import ContactForm from flask.ext.mail import Message, Mail  mail = Mail() . . . # @app.route() mappings start here   I get this error.  ImportError: cannot import name app   That being said, I cannot do from user import app. I've tried:  from . import app   I don't really know how to explain the question here, but I am editing a python file within the user directory that is trying to import an outer directory within itself? How can you possibly do from user import app if the app directory does not live within the user directory? What am I missing here?  Within the runserver.py, I'm able to do it because I assume runserver.py lives in the app directory. I cannot do it in routes.py though.  If I cannot import app, I cannot define routes within Flask as such:  @app.route('/') def index():     return "Testing route!"

Imagine this directory structure:  app/    __init__.py    sub1/       __init__.py       mod1.py    sub2/       __init__.py       mod2.py   I'm coding mod1, and I need to import something from mod2. How should I do it?    I tried from ..sub2 import mod2 but I'm getting an "Attempted relative import in non-package".  I googled around but found only "sys.path manipulation" hacks. Isn't there a clean way?      Edit: all my __init__.py's are currently empty    Edit2: I'm trying to do this because sub2 contains classes that are shared across sub packages (sub1, subX, etc.).  Edit3: The behaviour I'm looking for is the same as described in  (thanks John B)


Being a student of English language I'm confuse should I use singular or plural with number greater then 1?   For example, please consider and guide if I'm wrong in my use:     I'm a 5 years experienced accountant   or it should be:     I'm a 5 year experienced accountant

Recently, while skimming through an article I came across a sentence which is as follows.  The five minute walk will connect you with life.  My rationale says it should have been "five minutes" and not "five minute". Kindly advise where am I going wrong?


a^2 + b^2 = c^2   what is the demonstration of this rule with triangle which has 90 deg? can be proofed using geometry?

Today we learned about Pythagoras' theorem. Sadly, I can't understand the logic behind it.  $A^{2} + B^{2} = C^{2}$    $C^{2} = (5 \text{ cm})^2 + (7 \text{ cm})^2$  $C^{2} = 25 \text{ cm}^2 + 49 \text{ cm}^2$  $C^{2} = 74 \text{ cm}^2$ ${x} = +\sqrt{74} \text{ cm}$  Why does the area of a square with a side of $5$ cm + the area of a square with a side of $7$ cm always equal to the missing side's length squared?  I asked my teacher but she's clueless and said Pythagoras' theorem had nothing to do with squares.  However, I know it does because this formula has to somehow make sense. Otherwise, it wouldn't exist.


If I have object that is heavy, I can pull it with rope but cannot push it. Why? What breaks the symmetry of the system? I can push or pull anything if I choose, so why is the push possibility not possible?

First of all, I have a confusion about the definition and idea of Tension. For example, in my Physics Textbook, the idea of tension is written like this: "Let's say there is a wire with a cross-section area of A and its length is $L_o$. If I hang the wire from a point and hang a weight of W on the other end of the wire, it will generate a repulsive force of T. This T is called the Tension Force." For me, this only explains to me what force will we call tension force, but it doesn't quite explain to me what is exactly this Tension force or where it originates from. Also, I have been doing pulley problems (Figuring out the acceleration of weights hanging from pulleys)  by first labeling all of the tension forces by $T_1$, $T_2$, and then doing some math with them to get my answer. But It bugs me that I am using these tension force values without even knowing where they came from or what they are. My idea was, maybe Tension force comes from the intermolecular bonds between the molecules of the rope, rubber or wire, etc. But even then, I have some different situational questions. For example:  Why you can't push a rope, copper wire against a wall?  What happens when I pull on two ends of a wire with 2 different forces?  Does the force increase proportionally to the applied force? Why does the wire break after a certain amount of force is exceeded.?  Does the idea of tension apply to everyday objects,(for example, a coffee mug, glass pane, etc). If it does, can I use something like a heat map or 3D equation to describe the tension in every point of the object? [Edit: more concisely, is there a mathematical way to show the various amounts of tension forces on a 2D (like a metal sheet) and 3D objects (like a football ) instead of a 1D object(like a string)].  If I take a metallic object like a paperclip or a thin wire. I can bend It multiple times and it eventually breaks into two pieces. I used to do this to pull of capacitors from old circuit boards. But does it happen with things like ropes or paper? If not, why it doesn't happen? ( Maybe it has something to do with intermolecular forces and the various internal stresses?)  Let's say I have an iron bar and I have thrown it out into space. Does that iron bar have equal stress distribution or still uneven or will the stress on all points become zero? (Is there even such thing as zero stress?)


When I try to run the algorithm it gives me this error:     Traceback (most recent call last): File   "C:/OSGEO4~1/apps/qgis/./python/plugins\processing\algs\grass7\Grass7Algorithm.py",   line 411, in processAlgorithm Grass7Utils.executeGrass(self.commands,   feedback, self.outputCommands) File   "C:/OSGEO4~1/apps/qgis/./python/plugins\processing\algs\grass7\Grass7Utils.py",   line 372, in executeGrass for line in iter(proc.stdout.readline, ''):   File "C:\OSGEO4~1\apps\Python37\lib\codecs.py", line 322, in decode   (result, consumed) = self._buffer_decode(data, self.errors, final)      UnicodeDecodeError: 'utf-8' codec can't decode byte 0xe8 in position 50: invalid continuation byte

I try running the v.clean tool using QGIS 3.4. As input I use a vector line layer (I checked the validity and everything is fine), but running the algorithm I get the following error:  Traceback (most recent call last): File "D:/Programme/OSGeo4W/apps/qgis/./python/plugins\processing\algs\grass7\Grass7Algorithm.py", line 415, in processAlgorithm Grass7Utils.executeGrass(self.commands, feedback, self.outputCommands) File "D:/Programme/OSGeo4W/apps/qgis/./python/plugins\processing\algs\grass7\Grass7Utils.py", line 372, in executeGrass for line in iter(proc.stdout.readline, ''): File "D:\Programme\OSGeo4W\apps\Python37\lib\codecs.py", line 322, in decode (result, consumed) = self._buffer_decode(data, self.errors, final) UnicodeDecodeError: 'utf-8' codec can't decode byte 0xf6 in position 81: invalid start byte  Execution failed after 0.50 seconds   Since it is says it is a decoding error I checked the encoding and it is encoded in UTF-8.  Does anybody know how to solve the error?


Given two independent random variables $X$ and $Y$ and two measurable functions $g$ and $h$, how do we show that $g(X)$ and $h(Y)$ will also be independent?

Is the claim that functions of independent random variables are themselves independent, true?   I have seen that result often used implicitly in some proofs, for example in the proof of independence between the sample mean and the sample variance of a normal distribution, but I have not been able to find justification for it. It seems that some authors take it as given but I am not certain that this is always the case.


I'm generating this HTML on .cs side :

         Product	         Price	         Destination	         Updated on

         Oranges	         100	         + On Store	         22/10

         	         120	         City 1	         22/10

         	         140	         City 2	         22/10

   And by calling the controller with Ajax I add the HTML to the page like this :   $.ajax(       url:"/MainController/HTMLGenerator",       success : function (data) {       $('#mydiv').html(data); })   I also have this JS code to toggle rows :   $(".toggler").click(function(){      $('.cat'+$(this).attr('zzz')).toggle(); });   But no matter what I do, I couldn't get the link working. I guess it happens because HTML is generated at the backend. I don't know how to solve this though. Thanks in advance.

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I made web application in Visual Studio 2010 with sqlite database which is located on the desktop (data source path in connection string points to a desktop). Now I want to add the database in my project so I can publish it, but when I change connection string (just database name) it cannot see the database.  If someone knows please tell me if these kind of things are common and what can I do to add the database in the project with working connection string? Am I missing something?  Here are connection strings:  working:  data source = "C:\Documents and Settings..........\dbBookStore.db; Version = 3";  not working:  data source = "dbBookStore.db; Version = 3"; (it says sql error login or missing database no such table)  not working:  data source = "~/dbBookStore.db; Version = 3"; (it says unable to open database file)  Errors are thrown when I click the Login button.  And here is the code:  namespace BookStore {  public partial class BookStoreMaster : System.Web.UI.MasterPage {     string connectionString;      protected void Page_Load(object sender, EventArgs e)     {          connectionString = @"Data Source = dbBookStore.db; Version = 3";     } protected void btnLogin_Click(object sender, EventArgs e)     {          using (SQLiteConnection con = new SQLiteConnection(connectionString))         {              SQLiteCommand com = new SQLiteCommand("select Username, Password from                 tblUserAccount where Username=@username                    and Password=@password", con);              com.Parameters.AddWithValue("username", txtUsername.Text);             com.Parameters.AddWithValue("password", txtPassword.Text);             con.Open();             SQLiteDataAdapter dap = new SQLiteDataAdapter(com);              System.Data.DataSet ds = new System.Data.DataSet();              dap.Fill(ds);              if (ds.Tables[0].Rows.Count == 1)             {                 Session["username"] = txtUsername.Text;                 Session["password"] = txtPassword.Text;                 Response.Redirect("BooksPage.aspx");             }              con.Close();         }      }

Wanting to deploy my project on different servers I would prefer to be able to specify a connect string using a relative path. I can't seem to get that to work and want to know if there is some trick to it...?


I own a Nikon D5300 body, but wish to upgrade to a Pro FX body in future (not any time soon).  Between  and , I prefer to buy the former, but at the same time, skeptical about my purchase decision.  The reasons I'd like to choose the former are:   The former is a lot cheaper I don't want to spend for what I won't need if I upgrade. I believe all Pro FX bodies have AF motor built inside the body. Hence, SWM in 'AF-S' lens is redundant The former is a bit lighter (~30gms) The former is dimensionally a bit smaller The optical performance, especially the Bokeh are    The reasons I hesitate before making the purchase are:   The later is said to have a better build quality (How better is the later compared to the former?) The former has an aperture ring which I am not at all familiar with (Is there any drawback of having an aperture ring apart from making the look of the lens messy?) The focus ring of the former turns when you focus. You can't touch it without disabling autofocus first   Can anybody please clarify my doubts? Apart from the points I have highlighted, is there any other major/minor concern which I have failed to take care of?

Recently, Nikon announced their , as revamp of the old 50mm f/1.8D. :     The main difference between this new   "nifty fifty" and the almost   decade-old ƒ1.8D is that it has an   autofocus motor inside. This means you   can use it with any current or recent   Nikon SLR. The older lens lacks this   motor and is instead driven by one in   the camera, which cheaper bodies don't   have.   I currently use a Nikon D80 (and I don't plan on changing that any time soon), and I've been considering getting such a lens. Is there any difference between the D and the G lenses when used on a D80? I believe that the D one works just as well, since D80's have internal autofocus motors - is that right?  Besides the autofocus motor aspect, is there any other big difference between them? Since the D is priced at around $120 and the G at $220, should I just get the D?


I am trying to install a build tool on my Mac called ; however it seems the word "please" is already aliased to "sudo" and I don't know where that alias is being set.  I'm using  which means I have a ~/.zshrc file instead of a ~/.bashrc file. But I can tell you that nowhere in my ~/.zshrc file nor in my ~/.bash_profile file are any aliases being set on the word "please."   Still, when I type please in the terminal I see this:  usage: sudo -h | -K | -k | -V usage: sudo -v [-AknS] [-g group] [-h host] [-p prompt] [-u user] usage: sudo -l [-AknS] [-g group] [-h host] [-p prompt] [-U user] [-u user] [command] usage: sudo [-AbEHknPS] [-C num] [-g group] [-h host] [-p prompt] [-u user] [VAR=value] [-i|-s] [<command>] usage: sudo -e [-AknS] [-C num] [-g group] [-h host] [-p prompt] [-u user] file ...   And when I type which please it just says this:  please: aliased to sudo   Are there other locations I'm not thinking of where aliases can be defined? How do I get rid of this annoying alias?

I have an alias which is predefined by an oh-my-zsh plugin.  -> % alias gcm gcm='git checkout master'  I'd like to remove it, i.e. I'd like alias | pcregrep "\bgcm\b" return 1. I've tried with alias gcm='' but after that the alias is still existent.


SOLUTION:  As the user Chili555 noted in the comments, I did what was said in :  sudo -i echo "options rtl8723be ant_sel=2"  >  /etc/modprobe.d/rtl8723be.conf exit   and it worked when rebooting    Original post:  First of all, I am very new to Ubuntu, so please ask for more data if it is needed.  I recently installed Ubuntu 16.04 on a dual boot with Windows 10.  I tried connecting to Wifi, but only some appear. For example, I can perfectly connect to my mobile hotspot, but my home wifi is not even listed with the available ones.  I tried many methods found online, but none seemed to work, si I write this question.  Firtly, after making sure drivers were installed, I tried restarting the nerwork-manager by typing:  sudo service network-manager restart   But this did not work at all, so I tried the fix to stop the mac address changes, changing   wifi.scan-rand-mac-address=no   in the file /etc/NetworkManager/NetworkManager.conf  However, this also did not work.  I ran lspci and it returned the following:  00:00.0 Host bridge: Intel Corporation Device 5904 (rev 02) 00:02.0 VGA compatible controller: Intel Corporation Device 5916 (rev 02) 00:04.0 Signal processing controller: Intel Corporation Skylake Processor Thermal Subsystem (rev 02) 00:08.0 System peripheral: Intel Corporation Sky Lake Gaussian Mixture Model 00:14.0 USB controller: Intel Corporation Sunrise Point-LP USB 3.0 xHCI Controller (rev 21) 00:14.2 Signal processing controller: Intel Corporation Sunrise Point-LP Thermal subsystem (rev 21) 00:16.0 Communication controller: Intel Corporation Sunrise Point-LP CSME HECI (rev 21) 00:17.0 SATA controller: Intel Corporation Sunrise Point-LP SATA Controller [AHCI mode] (rev 21) 00:1c.0 PCI bridge: Intel Corporation Device 9d10 (rev f1) 00:1c.4 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port (rev f1) 00:1c.5 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port (rev f1) 00:1f.0 ISA bridge: Intel Corporation Device 9d58 (rev 21) 00:1f.2 Memory controller: Intel Corporation Sunrise Point-LP PMC (rev 21) 00:1f.3 Audio device: Intel Corporation Device 9d71 (rev 21) 00:1f.4 SMBus: Intel Corporation Sunrise Point-LP SMBus (rev 21) 01:00.0 Display controller: Advanced Micro Devices, Inc. [AMD/ATI] Topaz XT [Radeon R7 M260/M265] (rev 83) 02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101/2/6E PCI Express Fast/Gigabit Ethernet controller (rev 07) 03:00.0 Network controller: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter   so I knew my network controller was RTL8723BE. I the added   SUSPEND_MODULES="RTL8723BE"   to the file /etc/pm/config.d/config (I found this solution online, as well.)  The last step I've tried is to type  iw reg get   It returned:  country ES: DFS-ETSI     (2400 - 2483 @ 40), (N/A, 20), (N/A)     (5150 - 5250 @ 80), (N/A, 23), (N/A), NO-OUTDOOR     (5250 - 5350 @ 80), (N/A, 20), (0 ms), NO-OUTDOOR, DFS     (5470 - 5725 @ 160), (N/A, 26), (0 ms), DFS     (57000 - 66000 @ 2160), (N/A, 40), (N/A)   and then I typed  sudo nano /etc/default/crda   it returned  # Set REGDOMAIN to a ISO/IEC 3166-1 alpha2 country code so that iw(8) may set # the initial regulatory domain setting for IEEE 802.11 devices which operate # on this system. # # Governments assert the right to regulate usage of radio spectrum within # their respective territories so make sure you select a ISO/IEC 3166-1 alpha2 # country code suitable for your location or you may infringe on local # legislature. See `/usr/share/zoneinfo/zone.tab' for a table of timezone # descriptions containing ISO/IEC 3166-1 alpha2 country codes.  REGDOMAIN=   As the last line seemed incompleted, I edited at the end  REGDOMAIN=ES   I rebooted, but it still does not work. At this point I am pretty desperate, because I can't seem to find any solution, and because I know my hardware is working (I can connect to other Wifis) and the network works (I can connect using Windows in the same PC)  Note: if any further information is needed, please let me know so I can add it

I installed Ubuntu 17.10.1 on my HP Pavilion x360 convertible, and my wi-fi connection was very weak.  I tried to install this driver from GitHub called rock.new_btcoex, but it didn't work.  What else can I try?


US domestic flight. I lost my passport and my flight is in 2 weeks. I have IDs like Student ID, but no other government ID. I am registered with TSA PreCheck though. Would it be possible to still fly without valid government ID, if they can compare fingerprints/do some other sort of check? Edit: I also have a photo of the passport.

I need to fly domestically within the United States. The only ID I have is an expired USA passport.  Can I use that to pass T.S.A.?  Can I use it as ID?


How to prove the equality of the two defintions of $e$? $$\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n=\sum_{n=0}\frac{1}{n!}$$  There are answers in other questions like this: $$\begin{aligned} \lim_{n\to \infty}\left(1+\frac{1}{n}\right)^n &= \lim_{n\to\infty}\sum_{k=0}^n \frac{1}{k!} \prod_{m=0}^{k-1}\left(1-\frac{m}{n}\right)\\ &=^?\sum_{k=0}^\infty\left[\frac{1}{k!}\lim_{n\to\infty}\prod_{m=0}^{k-1}\left(1-\frac{m}{n}\right)\right]\\ &=\sum_{k=0}^\infty\frac{1}{k!} \end{aligned}$$ However, I think this operation of limits is wrong. For example, $\lim\limits_{n\to\infty}\sum\limits_{k=1}^n\frac{1}{n}=1$ and $\sum\limits_{k=1}^\infty\lim\limits_{n\to\infty}\frac{1}{n}=0$.

How to prove that the following definitions of $e^x$ are equivalent, with as simple tools as possible and without any knowledge of $e$ or logarithms ?  $$\sum_{n=0}^{\infty} \frac{x^n}{n!}=\lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n$$  Also preferably, prove that this is $a^x$ for some real number $a>0$.


I want to redirect non-www URL to www URL in WordPress.  I added code for the redirect but I see that I only redirect URL internally but not accessible from the externally. I redirect to apache default page  I added coed in .htaccess.  <IfModule mod_rewrite.c>     RewriteEngine On     RewriteCond %{HTTP_HOST} !^www\. [NC]     RewriteRule ^(.*)$ http://www.%{HTTP_HOST}/$1 [R=301,L] </IfModule>   Not work externally. I also set www in secure/non-secure URL.  Does have any solution?

This is a  about Apache's mod_rewrite.   Changing a request URL or redirecting users to a different URL than the one they originally requested is done using mod_rewrite. This includes such things as:   Changing HTTP to HTTPS (or the other way around) Changing a request to a page which no longer exist to a new replacement. Modifying a URL format (such as ?id=3433 to /id/3433 ) Presenting a different page based on the browser, based on the referrer, based on anything possible under the moon and sun. Anything you want to mess around with URL   Everything You Ever Wanted to Know about Mod_Rewrite Rules but Were Afraid to Ask!  How can I become an expert at writing mod_rewrite rules?   What is the fundamental format and structure of mod_rewrite rules? What form/flavor of regular expressions do I need to have a solid grasp of? What are the most common mistakes/pitfalls when writing rewrite rules? What is a good method for testing and verifying mod_rewrite rules? Are there SEO or performance implications of mod_rewrite rules I should be aware of? Are there common situations where mod_rewrite might seem like the right tool for the job but isn't? What are some common examples?   A place to test your rules  The  web site is a great place to play around with your rules and test them. It even shows the debug output so you can see what matched and what did not.


I'm trying to convert some .png files I have into a movie using ffmpeg. I'm using the tutorial:    The files have names Image001.png, Image002.png, ..., Image500.png, and Image501.png. I manually installed ffmpeg this morning from their website, so I don't have to do step 1. I then proceed to run:  cd Downloads cd python-meep cd Images   Where both my images and my folder containing the manually downloaded ffmpeg are located. Next, I type:  ffmpeg -qscale 5 -r 20 -b 9600 -i Image%03d.png movie.mp4   To my surprise, this is the error message I get:  ffmpeg: command not found   What's going on here? Any suggestions would be appreciated. Thanks!  P.S. Could be relevant that I'm using Ubuntu 14.04.

I'm on OSX Snow Leopard.  Here's the full contents of grr.sh:  #!/bin/sh  echo wow   When I try to run it from terminal:  $ grr.sh -bash: grr.sh: command not found $ /bin/sh grr.sh wow $ sh grr.sh wow $ bash grr.sh wow   Okay. Fair enough. I'll give it executable permission, then try again:  $ chmod +x grr.sh $ grr.sh -bash: grr.sh: command not found $ chmod 755 grr.sh $ grr.sh -bash: grr.sh: command not found   Hmmm. Maybe it'll work if I use bash explicitly? I'll change the file's contents to:  #!/bin/bash  echo wow   And I get the exact same results. What could I have broken?!  One last thing! In case you're curious...  $ which sh /bin/sh


My question is when one say two cohomology rings are isomorphic, does the degree of generator matters?  Here is a motivating example:   $H^*(RP^{\infty}, \mathbb Z_2)\cong \mathbb Z_2[\alpha]$ with $|\alpha|=1$, and $H^*(CP^{\infty}, \mathbb Z_2)\cong \mathbb Z_2[\beta]$, with $|\beta|=2$, but if we define map between two cohomology rings by sending $\alpha$ to $\beta$, it is clearly a ring isomorphism. But we know that the two spaces even don't share the same cohomology groups. So, I have a doubt on definition of isomorphism between cohomology rings.

For $\mathbb{R} P^{n}$ we have,   $$ H^*( \mathbb{R} P^2 ; \mathbb{Z}_2) \cong \mathbb{Z}_2 [ \alpha ] / (\alpha^3)$$   where $|\alpha|=1$.   Let us assume there exists $X$ such that,   $$ H^*( X ; \mathbb{Z}_2) \cong \mathbb{Z}_2 [ \beta ] / (\beta^3) $$   but $| \beta |=2$.   Then the rings have the form, $a_0 + a_1 \alpha + a_2 \alpha^2$ and $b_0 + b_1 \beta + b_2 \beta^2$.   So as polynomials these rings look the same except for the condition given on the variables  $\alpha$ and $\beta$.   How does the dimension of $\alpha$ and $\beta$ come into play when viewing the polynomial rings?   I think, naively, I would assume these space are isomorphic and that dimension doesn't add any strong information about the structure of the spaces.


I think just about anyone who has studied Einstein or relativity has heard of the cosmological constant. He added it so that his equation would return an universe that is static. Of course, the universe is expanding but the cosmological constant is actually correct. So, my question is, what does the cosmological constant actually do in the equation? How does it affect the result? And lastly, what does this mean or represent in the universe?

I have read about cosmological constant given by einstein in universe in nutshell as well as in general and special relativity. But still I am not able to understand the aim to use it or to introduce it. Can someone explain in brief.


Is there an elegant way to have performant, natural sorting in a MySQL database?  For example if I have this data set:   Final Fantasy Final Fantasy 4 Final Fantasy 10 Final Fantasy 12 Final Fantasy 12: Chains of Promathia Final Fantasy Adventure Final Fantasy Origins Final Fantasy Tactics   Any other elegant solution than to split up the games' names into their components    Title: "Final Fantasy" Number: "12" Subtitle: "Chains of Promathia"   to make sure that they come out in the right order? (10 after 4, not before 2).  Doing so is a pain in the a** because every now and then there's another game that breaks that mechanism of parsing the game title (e.g. "Warhammer 40,000", "James Bond 007")


I had installed a the TeX editor kile from the official Ubuntu PPA. It came together with a bunch of dependencies, TeXlive among them. The provided TeXlive version however is from 2015 and thus quite old, buggy and outdated. I removed all texlive* components manually by means of dpkg -r --force-all and reinstalled a more recent version of texlive via the official texlive installer (install-tl). Works like a charm so far.  Other than apt, which now insists on reinstalling the old texlive because of that unsatisfied dependency. How can I tell apt to permanently ignore that missing dependency in the future and behave as if it were installed (which it actually is, just not through apt)?

I installed program (call it, for example,progA) by building it from source code, and then finally calling sudo make install and sudo ldconfig.   However, it seems apt-get hasn't gotten the memo, because when installing progB, which depends on progA, apt-get recommends I also install progA. Why is this, and what could I do?


In a recent question I asked about finding parts for my old 1960s electrical panel. I've given up on finding parts, and this new question is about replacing it with a new, modern panel:  One of the lugs burned up in my house's service panel. It was installed when the house was built in 1963. The lug is integral to the panel, and the panel is no longer available. I've looked for used panels of that model -- a GE TRX2012F -- but did not find any. So I'm told I need a new service panel.   I want to do the replacement myself. I've done minor DYI electrical work but nothing this involved. I'm reading and watching what I can find on replacing electrical panels. Can anyone offer answers to any of my questions below?  1) First, any suggestions on what panel to choose? The current one is installed flush in an unfinished stud wall. But surface-mount on top of the studs sounds fine to me too. There is about 14.5" between the studs, and they are about 3.5" deep. There is no real limit on height except that some bolts for the meter pipe extend into the wall about 6 - 7 inches above where the feeder wires come out of the wall from the meter.  2) Next, should I expect to reuse the breakers, or do I need new ones? If new ones, can you suggest what I need?  3) Regarding the fat black wires running from the breaker at the upper left down to between breakers below -- would I be duplicating that, or is that done differently in today's panels?  4) I'll need to know how to shut off the power to the panel box. If I understand correctly that would be done at the meter. And since the meter is locked by the power company, I believe that would mean calling them and asking them to turn it off, then asking them to come out and turn it back on when I'm done. Is that correct?  5) Are there any other components, or any special tools, I'll need?  Thanks! Pictures below:              More pictures:

What are my options to replace an old service panel?   We had a terminal get burned up in our old 1960s GE (TRX2012S if it matters, it's a split-bus/rule-of-six panel).   The tech who looked at it said the part is no longer available, but that if I could find another old service panel just like it, he could swap in the part. Otherwise, it's going to be $2,000+ to replace it with a modern service panel, which also requires getting up to modern code, which involves a lot of other stuff.   EBay and Google isn't showing any direct replacements (or the flush-mount TRX2012F).    What other options would there be to replace the panel internals?  Are the screw mounting holes compatible with modern GE panel internals? Is the main breaker separable and could that be changed alone?    Enclosure dimensions are about 20.5" x 12". Front panel dimensions are about 22.25" x 14".  UPDATE:    I'm looking at information on replacing the breaker box myself. As the homeowner I wouldn't be required to update anything else to get up to code. Does this sound like a good idea? I've done minor electrical DYI work but nothing this involved.  PICTURES:            More pictures:


So I'm trying to artificially enhance a 3D objects look to look more 2D, by having certain parts of the geometry shift in specific positions when the camera is facing those faces/vertices from specific angles to it.   To explain in an easier to word and grasp way: Think of a random character When the camera is facing from the left, the characters eyes look up and smiles, When camera is facing from the front character has closed eyes and frowns Etc  However when the character is faced from the front, but the head is turned to the side so that the characters face is viewed from the left, the behavior for the face displays the animation/position displacement for "camera on the left" while the body (the parts faced from the front) would display the position displacement/animation behavior for "camera facing the front" If this makes any sense?

Let's say (for the sake of simplicity) that this cube with two blue sides is my character...   and the shape key in question raises a few vertices on top.   Whenever the camera views either Blue side, I'd like the shape key to activate regardless of world orientation through the use of a driver. The problem is, I have no idea how to get values I need (or which values I need to begin with) in order to automate this.   TL;DR - I'd like the mesh of a character I have to deform when viewed from the side much like what was done in Land of the Lustrous     *Note: While I do have some experience with coding, I've never used python. Layman's terms would be greatly appreciated. Thank you for your time!    UPDATE: In response to @Leander's post  Would it be possible to have this script work with multiple characters on the same camera? Let's say I have character "Cube2" with shape key "Key 2", would simply adding variables like below accomplish this?  import bpy import mathutils  cam = bpy.context.scene.objects['Camera'] obj = bpy.context.scene.objects['Cube']  # ----------------------------- # Adding Cube2  obj2 = bpy.context.scene.objects['Cube2']  # -----------------------------   def drive_shapekey(scene):     obj_mat = cam.matrix_world.inverted() * obj.matrix_world      obj_eul = obj_mat.to_euler('XYZ')     cam_vec = obj_mat.to_translation().normalized()     obj_vec = mathutils.Vector((0.0, 1.0, 0.0))     obj_vec.rotate(obj_eul)     difference = cam_vec.dot(obj_vec)      key1 = obj.data.shape_keys.key_blocks["Key 1"]     key1.value = difference    # ----------------------------- # Adding Cube2 properties and shapekey 2  def drive_shapekey2(scene):     obj2_mat = cam.matrix_world.inverted() * obj2.matrix_world      obj2_eul = obj2_mat.to_euler('XYZ')     cam_vec2 = obj2_mat.to_translation().normalized()     obj2_vec = mathutils.Vector((0.0, 1.0, 0.0))     obj2_vec.rotate(obj2_eul)     difference2 = cam_vec2.dot(obj2_vec)      key2 = obj2.data.shape_keys.key_blocks["Key 2"]     key2.value = difference2  # -----------------------------   pre_handlers = bpy.app.handlers.scene_update_pre [pre_handlers.remove(h) for h in pre_handlers if h.__name__ == "drive_shapekey"] pre_handlers.append(drive_shapekey)   # ----------------------------- # Not sure if this'll work, but we'll see  [pre_handlers.remove(h) for h in pre_handlers if h.__name__ == "drive_shapekey2"] pre_handlers.append(drive_shapekey2)  # -----------------------------


On  we get a number of questions that end up closed that belong on other sites. I read on here that they will be migrated under certain circumstances. If those are not met, however, and the question receives 5 close votes from users, how do I then migrate the question to another site? In the past I have been reopening the question and then closing and migrating it. It seems like there should be a better way.  FWIW,  is an example.

Sometimes a question gets closed as off-topic (not-migrated) while there is another site where the question is on-topic.  If a moderator wants to migrate the question, the moderator needs to reopen the question and then reclose it as off-topic and migrate the question.  It would nice if a moderator can migrate questions closed as off-topic without going through this process of reopening/reclosing.


So, I want to use WhatsApp on my computer. The first step to do that is to... "open WhatsApp on my phone"? Huh? The whole point is to use a computer. Not "phone". I have no "phone". That's why I want to use WhatsApp on my computer!  This isn't the first time I've seen this nonsense. Apparently, I can't do anything anymore using an actual computer. If I already had this "WhatsApp" on my "phone", why would I be looking at a page for running it on my computer?

I've been using WhatsApp on my Android Smartphone. That phone is now broken, and until I have a new phone capable of running the WhatsApp App, I'm now using my older "non-smart" phone. My SIM card works well with it, but I can only do phone calls and SMS.  I have a couple of desktop/laptop PCs available, running Windows 7, 10, and Ubuntu. So what exactly are the steps - installation(s) of additional software, use of a WhatsApp service for this kind of matters, ... to be able to have my WhatsApp account work with a "PC interface"? I can have my phone turned on at any time, but it is really old. No Android, no WhatsApp App.  Note that before I've been using WhatsApp Web from time to time, which needs the smartphone to be powered on and online, which I currently can't do. I can currently only use plain old mobile services with my mobile number: calls and SMS.


I tried installing Google-Chrome-Stable on Ubuntu 16.04 from the graphical interface following instructions on  ... but it hung (waiting to install). Next I tried using terminal commands as per instructions but also failed. So I tried purging/removing all Google-Chrome-Stable files and got this:  (my-user-name)@(DELL)Inspiron-3451:~$ sudo apt-get purge google-chrome-stable E: Type 'wget' is not known on line 44 in source list /etc/apt/sources.list E: The list of sources could not be read.   Also a "no entry" icon appears on my laptop tool bar.  How do I purge all the Google-Chrome-Stable files in this situation?  I considered reinstalling Ubuntu 16.04 but cannot boot from flash drive (no CD on laptop) because I had fiddled with BIOS settings to boot from flash drive to upgrade from Ubuntu 14.04. F2 and F12 for boot options no longer appear now when I start computer; it apparently boots direct from Ubuntu. I had finally managed to upgrade to 16.04 using 'About This Computer' interface after missing dependencies were installed.  I have limited skills using terminal commands and usually only follow instructions as I find them in Ubuntu websites. Please help me out.  Thank you very much.

Every once in a while I see users having issues to update due to errors like this:  E:Type 'ain' is not known on line 1 in source list /etc/apt/sources.list.d/some-ppa.list'   with varying types/line numbers/source list files (often after removing a PPA).  How can such an error be fixed?


I have a module with a view and some other functionality. I want to give site managers the ability to change the filter on the view (this isn't an exposed filter) but not give access to change the view.  I know how to make a form for the module but what would I use to get the information from the view and return the information.  I assume it is one of these:

I want to add/modify a filter criteria programmatically.   For example, for a view, I added an "Email Address" filter whose value is needed to change dynamically, it is needed to set to the current logged in user's email id.   How to achieve that? Please see attached image for more details. Please help.


On the bash prompt one, three or more slashes (/,///,////, ...) are treated as a single slash, whereas two slashes (//) are left as is:  12:07 $ cd / 12:07 $ pwd / 12:07 $ cd // 12:07 $ pwd // 12:07 $ ls bin  boot  cdrom  dev  etc  home  initrd.img  lib  lib64  lost+found  media  mnt  opt  proc  root  run  sbin  srv  sys  tmp  usr  var  vmlinuz 12:07 $ cd /// 12:07 $ pwd / 12:07 $ ls bin  boot  cdrom  dev  etc  home  initrd.img  lib  lib64  lost+found  media  mnt  opt  proc  root  run  sbin  srv  sys  tmp  usr  var  vmlinuz   Usual suspects' versions:  12:07 $ bash --version GNU bash, version 4.3.11(1)-release (x86_64-pc-linux-gnu)  12:20 $ dpkg-query -s coreutils | grep Version Version: 8.21-1ubuntu5

I'm working on a python script that passes file locations to an scp subprocess. That's all fine, but I'm in a situation where I may end up concatenating a path with a filename such that there's a double '/ in the path. I know that bash doesn't care if you have multiple file separators, but I'm wondering how exactly that is rectified. Is it bash that strips extra /s or does it really not matter ever?  I ask because it will save me several lines of code to check for extra /s while concatenating. I know it's not a big deal, but I'm curious as well. I have a bash script that has the line cd //usr (instead of cd /usr), which seems to imply there might be a significance to using multiple /s in a path


Why in the second case the spacing is correct and not in the first ?  Maybe not fully correct in the second between + and u ?    \documentclass[xcolor=dvipsnames]{beamer}     \begin{document} \begin{frame} \begin{equation*} 5 \only<1>{\textcolor{red}{+}}6+7 \end{equation*}    \begin{equation*}           \frac{\partial u}{\partial t}= \only<1>{\textcolor{red}{+u(n,t)}u(n+1,t)}\only<2>{u(n,t)\textcolor{red}{u(n+1,t)}} -u(n,t)u(n-1,t)   \end{equation*}  \end{frame}  \end{document}

One can use the command such as \textcolor[rgb]{1.00,0.00,0.00}{boundary} to color the word "boundary" in a document.   Here is my question:  How to color the math symbols in $$? For example, can one turn $C^{2}$ into red in LaTeX?


I have followed this    But when I try   qmake --version  qmake: could not exec '/usr/lib/x86_64-linux-gnu/qt4/bin/qmake': No such file or directory   I usr/lib/x86_64-linux-gnu,I have  qt4: bin  plugins  qt5: bin  libexec  mkspecs  plugins  qml  qtchooser: 4.conf  5.conf  qt4.conf  qt5.conf  qt-default: qtchooser   Why?

I have installed Qt5 from the Qt5 project site, to the following directory   /opt/Qt5    I would also like to mention that I had Qt4 installed previously, I have removed all instances of Qt4 through the software center.   Now that I issue designer from the command prompt, the system gives the following error:   designer: could not exec '/usr/lib/x86_64-linux-gnu/qt4/bin/designer': No such file or directory   What can be done to correct this problem?


My husband has a close family match of 1,517cM  across 61 segments and his niece shares 906 cM across 40 segments.   Is there a chance this is a half brother to my husband and half uncle to his niece?  Because of age we have ruled out the other possibilities. Because of high connection with his niece also is why we are considering a half brother situation.   What gets confusing is that this match shares a last name as my husband. Wondering if possible while father was serving in WWII he fathered a child he may or may not have known about and mother listed father on birth certificate giving him same last name.

Shared DNA: 1,655 cM across 46 segments.   Can someone that shows this as one of my matches on AncestryDNA be a half sibling?


I have a code block that I'm trying to convert from PHP to C++ and the compiler is getting hung up on my switch statements.  I have something along the lines of:  switch(//Some int) {     case 1:     default:         int32 x = 1;         doSomething(x);         break;     case 2:         doSomething(3);         break; }   And this is throwing errors:     error C2360: initialization of 'x' is skipped by 'case' label     I seem to be able to fix this by declaring and initializing the variables outside of the switch statement, but why is this? What's the problem with creating temporary variables in the scope of a switch statement?     Just for further clarification, I am only attempting to use x in that one call to doSomething(x). I don't attempt to use it outside of the switch statement's scope.

I've always wondered this - why can't you declare variables after a case label in a switch statement?  In C++ you can declare variables pretty much anywhere (and declaring them close to first use is obviously a good thing) but the following still won't work:  switch (val)   {   case VAL:     // This won't work   int newVal = 42;     break; case ANOTHER_VAL:     ...   break; }     The above gives me the following error (MSC):     initialization of 'newVal' is skipped by 'case' label   This seems to be a limitation in other languages too.  Why is this such a problem?


I am currently learning Python. in OOP what is the purpose of @classmethod decorator? What is the difference accessing class variables via @classmethod and accessing it through just normal method? Like I can do that same like this: class A():    _variable = A     def getVariable(self):       return self._variable     or class A():    _variable = A     @classmethod    def getVariable(cls):       return cls._variable     What is the difference between both methods? Why do I need to use when do I use the classmethod and when do I not have to? And what happens if I don't?

I'm teaching myself Python and my most recent lesson was that , and so I've just spent a while turning all my Class methods into functions.  I now realise that I don't need to use Class methods for what I would done with static methods in Java, but now I'm not sure when I would use them.  All the advice I can find about Python Class methods is along the lines of newbies like me should steer clear of them, and the standard documentation is at its most opaque when discussing them.  Does anyone have a good example of using a Class method in Python or at least can someone tell me when Class methods can be sensibly used?


Given that many jurisdictions (including my own) don't use postal codes, should the ZIP/postal codes be mandatory on web-forms?  Additional info: I'm a web developer building ecommerce sites, and while some of the target customers may be in the U.S., many are not. Given development deadlines, I don't have time to code a complex solution.  Is it reasonable to assume that users will know if they have to input a postal code or not?

What is the best and most usable format to capture address information from a universal user base? I was thinking to have the system detect the country by IP address and have that selected by default, and then state/province droplist would be populated accordingly. But the issue is some countries have states and provinces and some do not. Some have postal codes and some do not. Is there a universal standard to capture complete address info to ensure efficiency for most users?  FYI: I did research on here and while there are some questions that are close, none are about this exact same question (unless I missed something)


I used the upgrade manager to upgrade from 17.04 to 17.10. When I start the machine, I only get a black flickering screen now. I was using the nvidia binary drivers before the upgrade.     NOTE: This question (and answer) relate to a specific issue when upgrading from 17.04 to 17.10 while using Nvidia or AMD binary drivers. You might experience a completely different issue. For that please see the more general question .

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I have used a modified poisson regression to model a binary outcome because I want to obtain relative risks, rather than odds ratios. The predicted probabilities are of interest, but many are beyond the range [0, 1].  Is there an appropriate way to constrain these to occur in the range [0, 1]? If a solution exists, I am keen to apply it to standard glm models and models generated using glmnet in R.

All software programs I have tried report only odds ratios (ORs) for binary logistic regression predictors (as exponential of the betas).  I am interested to know how can I compute the relative risk (RR) from a binary logistic regression model?  My reason is that RRs (besides ORs) would make my variables more understandable. Also I see many journals (even many of the top ones) confuse these two, and I want to hopefully have a good report with scientific merit, and not repeating previous mistakes.  I found some methods over the net (which I have not tried yet).  and  for example.  However in a , I saw some experts had opposed reporting RRs for logistic regressions. For example:  "It is incorrect to use the relative risk as a measure of association in a logistic regression. The measure of association in a logistic regression is the odds ratio. The odds ratio is an approximation of the relative risk. The approximation becomes progressively better as the disease becomes progressively rarer. Regardless of whether the disease is rare or not, inferences drawn from a logistic regression are valid. Please do not report a logistic regression using relative risk. It is not correct to do so." --John Sorkin  Or  "I am curious why one would want risk ratios.  Unlike odds ratios, they are not interpretable without reference to the base risk.  For example a risk ratio of 2 cannot possibly apply to anyone with a starting risk exceeding 1/2." --Frank Harrell  So my questions are:   Is it a good way to estimate RR for binary logistic regression? Or do you agree with the above quotes, disagreeing with RR for logistic regressions? Could you please let me know why, if you agree or disagree? Do you know of any implemented algorithms (e.g., a macro or an R function) which can do it without needing to manually computing it?


I am looking for a word to describe a word or a sentence that is hard to pronounce, in a situation that even you know the pronunciation but just can't control your tongue. Tongue-twister is the closest that I have come up with so far, but I wonder if there is an adjective.   I want a word that can fit into the blanks:  The script was so _________ that I had to pause and repeat a lot.  This rap is insanely ________.(a word more specific than "hard"/"difficult")

Is there a single word which means "hard to pronounce" ? For example Dijkstra is "hard to pronounce".


I bought two flight tickets (two way) from my home country to Prague/Czech Republic as I was pretty sure I would get the visa when I applied for it. But I failed to have the Czech embassy set a time for the application process because of the high season, busy time and whatnot.  Now as I can't plan my trip as desired, I'd like to know whether there is a way to make use of the tickets. Is it possible to get the visa from another country in the Schengen area, then buy a flight ticket from Prague to that country? Or do the flights have to be connected?

Let's say I have Schengen visa issued by Dutch embassy as business visa for business in Holland. Can I fly to Frankfurt and spend some time in Germany and then come to Holland?   I know I can travel to all Schengen countries with this visa, but I am not sure whether I can enter from different country.


I am a totally new Ubuntu user.  I had Windows 7 and Ubuntu 14.04LTS side by side.I have 2 HDD- one 160 GB and 1TB.   I decided to delete ubuntu and change to ubuntu 12.04 as 14.04 does not have much softwares.. I opened Disk Management and deleted two partitions which were unnamed(so they belonged to Ubuntu).(Three of the local disks changed to dynamic) I forgot to proceed to the further steps which said to fix MBR(I got no idea what it is). I restarted the machine and I got this:  error:no such device .........  Entering rescue mode...  grub rescue>_ I tried to use Boot Repair and upgrade grub,but Boot Repair is giving an error and grub update says there is not enough space.   I don't know what to do.  Please help me .. Please !!

After an installation of Ubuntu 12.04, erasing an old partition with Ubuntu 10.10, I can't get grub to load. I can't access my Windows 7 partition either  I get the message:  > error: no such device: 58ABF29C...   grub rescue>   I suppose my master boot record got erased/corrupted. How can I check and fix this?


Suppose we have a triangle, call it triangle $XYZ$, and a point $W$ inside triangle $XYZ$. How would I prove that $XY + YZ > XW + WZ$? So the way I labeled everything, point $X$ is the bottom left corner, point $Y$ is the top point, and point $Z$ is the bottom right corner where the triangle is sitting flat.   I tried numerous variations of triangle inequality but could not get the result. I am wandering if I need to use something else to prove it.

This question looks really simple, but to my (and my co-workers) frustration we were not able to prove this in any way. I tried all triangle formulas known to me but I feel I'm missing the point, and proof will be or much simpler or much more complicated than what I tried.  So, the question:  Given a triangle ABC and point P inside that triangle, prove that for triangle APB the following inequality holds: |AB| + |BC| > |AP| + |PC|  (Actually it doesn't matter for me if it's > or >=).


I have a list of this type :  l = [{"id":"21", "region" :['2', '6', '4']}, {"id":"12", "region" :['1', '3', '8']}]   I want to sort the list on the "region" field, and that also at 2nd index. that is :  l = [{"id":"21", "region" :['2', **'6'**, '4']}, {"id":"12", "region" :['1', **'3'**, '8']}]   How do I do it ? I am aware of itemgetter. But couldn't do with that also.

I have a list of dictionaries and want each item to be sorted by a specific value. Take into consideration the list: [{'name':'Homer', 'age':39}, {'name':'Bart', 'age':10}]  When sorted by name, it should become: [{'name':'Bart', 'age':10}, {'name':'Homer', 'age':39}]


As I am new to understanding fractals, I appreciate their beauty when graphed in cartesian coordinates. My intuitive understanding of the definition of a 'fractal dimension' is the relation of the length of a fractal segment as a proportion of the subdivisions used in making it. In this way. the cartesian 2D coordinate system is calculated to have dimension 2. When we therefore create 2 axes, we can plot a set of points each of which has a real number value in each of these dimensions.  But I imagined a coordinate system not of 2 dimensions, but for example of the dimension of a Koch snowflake, 1.26186. But what does it mean for there to be 1.26186 coordinates for a point? Is this a concept that has been addressed in mathematics? Please do not be hasty to condemn this question as stupid- the concept of the square root of negative one seems equally absurd to me. Yet mathematicians invented a way to deal with that question. And the result was a tool that was miraculous-enabling Fourier transforms and a host of other useful tools-that still want to make my brain explode.  Certainly the concept of length in the fractal dimension has been addressed    So if there is length, then is there not a way to map the fractal coordinate system into the cartesian one so i can visualize it? or would the result be so mind boogling as to exceed comprehensibility- like those drawings of hypercubes in 3 space? We map all the aspects of a hypercube into different 3D cubes and either throw them into a 3D picture together (very messy) or we make a movie of transitioning from one cube to another through time.(very trippy)

Note: I'm not too experienced with branches of mathematics like topology, so a lot of the terminology I use is used pretty loosely.   I think we all understand the fact that a point in $n$-dimensional space is described with $n$ parameters. In 2d space, you have $(p_1, p_2)$ (where $p_k \in \mathbb{R}$), in 3d space you have $(p_1, p_2, p_3)$, so in an $n$-dimensional space you have $(p_1, p_2, ..., p_n)$. I know the way I'm stating this with the notation I use isn't as robust as it could be, but you get the idea.  Going into the world of fractal geometry, we find non-integer dimensional spaces. Applying what I said previously, how would you even express a point in such a space? What does it even mean to be that kind of space? Are you unable to express a "point" in such a space?


Hey guys i recently bought a razer laptop with rtx 2080 to improve my renders. But everytime i start rendering i get this error. CUDA error: out of mem aloc result line 855. Does anyone experience the same issue ?

Many of the people have asked almost the same question.  I'm trying to render a big mesh + fur/grass file with a few characters on the screen.  when I hit render, after a number of processing, copying data to gpu etc... i get following error.  Mem: 2960.07M, Peak:2960.07M | CUDA error: Out of memory in cuMemAlloc(&device_pointer, size).  I'm using Geforce GTX 690 which contains 4GB memory.   Can somebody tell me how can i get GPU rendering, while 2960M is far less then 4196M of memory.   I know somebody would suggest me to use CPU.. but i'm curios why not GPU?   I've already compressed texture, etc   Edited  I don't think any other application is using any of my 1GB remaining memory. everything is closed but blender is there, also the GPU utilities are showing 2000/2000 MB are free on one card and 1900/2000MB is free on 2nd card.    i'm using GTX 690. with two GPUs of 2GB each. If somebody thinks that one GPU should have memory matching to the cuda memory/or Peak memory then I'm doubtful. Because in preferences Blender does know that I have 2GPUs where I can select either first GPU or second GPU or even both.   When I render some of smaller objects/scenes both of my GPU renders simultaneously with two blocks.  I'm running following specs  Xeon E5-1660 0 24GB - 1600mhz GTX690


Neglecting any effect of spin,it is a well known fact,that orbital angular momentum of a system in ground state is zero.(For potential $V=V(r)$ .)  The angle-angular momentum uncertainty,gives $\Delta{L}\Delta{\phi}\ge\hbar/2$ , where $\Delta$L=$\sqrt{<L^2>-<L>^2}$.Now,<$L^2$>=$l(l+1)=0$(Since,$l=0$ for ground state).Therefore the uncertainty relation to be valid, expectation of Angular momentum <$L$>should be non-zero,and...non-real too!Why is this happening?

We know that for a position variable $x$ and momentum $p$, the uncertainties of the two quantities are bounded by  $$\Delta x \Delta p \gtrsim \hbar$$  Now, this is usually first explained with $x$ being a simple linearly measured position and $p$ being linear momentum.  But it should apply to any good coordinate and its conjugate momentum.  It should, for instance, apply to angle $\phi$ about the $z$ axis, and angular momentum $L_z$:  $$\Delta \phi \Delta L_z \gtrsim \hbar$$  The thing is, $\Delta \phi$ can never be greater than $2\pi$.  I mean, you have to have some value of $\phi$ and $\phi$ only runs from 0 to $2\pi$.  Therefore  $$\Delta L_z \gtrsim \hbar/\Delta \phi \geq \hbar/2\pi$$  But, uh-oh!  This means it is impossible for $\Delta L_z$ to be zero, and we should never be able to have angular momentum states with definite $L_z$ values.  Of course, it doesn't mean that.  But I have never figured out how this is not in contradiction with the Schroedinger eqn. calculations that give us states with definite values of $L_z$.  Can anyone help me out?  One answer I anticipate is that $\phi$ is sort of "abstract" in that if you chose your origin at some other point you will get completely different values of $\phi$ and $L_z$, and ipso facto, usual considerations don't apply.  I don't think this will work, though.  Consider a "quantum bead" sliding around on a rigid circular ring and you get the exact same problem with no ambiguity in $\phi$ or $L_z$.  (Well, there will be some limited ambiguity in $\phi$, but still, there won't be in $L_z$.)


I am finishing my first paper. I am unaware of how I should treat a certain situation, and have come  here for advice.  The paper is about 30 pages long. I have written 26 of those pages. On the pages I wrote, the other person helped with how thoughts are to be expressed, but all the theorems and proofs were done by me. The ideas of the paper are mine, and their execution.  How is the authorship to be divided in such an example? Should I be the first author or the corresponding author? Both? Should he be the second author, or the co-author?  I read this answer , saying in math and computer science all authors are considered to have contributed equally. How should the ranking be notated than?  EDIT:  Question in partially answered in the linking answer (duplicate), at the comments bellow.

One of the hot-button issues on this site is standards for coauthorship, especially variants of the question "Must I automatically include my thesis advisor as a coauthor on all my papers?"   Since these questions (sensibly) come up again and again, I thought it would be useful to have a collection of links to various ethical standards for coauthorship.  To the best of my knowledge, these standards will apply only to one particular academic field and/or to one geographic region.  For instance, most of my colleagues would point to .  It applies (explicitly) to mathematics and (implicitly, I think) to mathematics done in the US and by Americans.    I was thinking of a community-wiki question where each answer posts a link to ethical standards in some academic field(s) and geographic region(s).  To make the answers better, I would ask that respondents:   Quote in their answer the passages most relevant to coauthorship.   Please avoid "alphabet soup".  Above I wrote "American Mathematical Society" rather than "AMS": mathematicians will know what AMS means, but most other academics presumably won't.  Some other answers here refer to things like "BMJ": I certainly didn't know what that was.     (Ideally) Give commentary as to whether/how the standards in their answer differ from those posted in other answers.     The more comprehensive the list we can compile, the more authoritatively we can point future questioners to this list and tell them what is or is not an ethical practice.


I use   \usepackage[style=authoryear-ibid, maxnames=1, maxbibnames=6, minbibnames=6, backend=biber]{biblatex} \addbibresource{references.bib} \DeclareNameAlias{sortname}{last-first}   to format my references. This will display it as follows:    Now I would like the last reference (TRCRC (2015b)) to be displayed as such and not just a dash -- (2015b). I found similar questions but many people ask how to write a dash instead of the author, I would like to do the opposite.

I use biblatex with style=authoryear and when there are two references of the same author in the bibliography there is just a dash. How can I get the full name in the second entry too?


I see that the name of SE website names in  don't always match actual SE website names. Example:  while the actual SE website name is Cross Validated. Is that intended?

It appears that site meta data isn't updated in SEDE. As an example, Moderators.SE was  to  in December 2014. It is still listed in SEDE as Moderators.SE, as of July 2015.  To search for Community Building data, we need to search the "Moderators" community:    It is not listed as Community Building:


Suppose k is an integer such that $6k + 1$, $12k + 1$, $18k + 1$ are primes. Show that $n = (6k + 1)(12k + 1)(18k + 1)$ is a Carmichael number.  This is a question on a past exam that I find difficulty to answer. Can anyone help?

Let $t∈\Bbb N$ and let $x=6t+1, \:y=12t+1$ and $z=18t+1$. $x, y$ and $z$ are all primes and let $n=xyz$. Prove that  $a ^{n-1} \equiv 1 \pmod  n\;$ whenever $ a∈\Bbb Z$ and $\gcd(a,n) = 1$.  I have started using the Euler-Fermat Theorem since $\gcd(a,n)=1$. Giving $\phi (n)=(1296t^3) $ But unsure how to proceed?


I made a script to automate ffmpeg conversion from mkv > m4v > open the m4v in Subler.app to import the metadata manually, at which point I'll move the file into my iTunes library.  I use iTunes because I have two Apple TVs on the network and use a 2007 iMac to function as my media server. I locally ssh into this machine in order to execute this script.  This script fails if I enter a path with whitespace(s), or enter title for the movie that includes whitespace. How do I fix this script to accommodate whitespace? I know the syntax is sloppy, I’m very new to scripting, so any other pointers to make it run better would be appreciated :)  Here it is:      #! /bin/bash  #ffmp4  function convert {     ffmpeg -i $REPLY -strict -2 -c:v copy -c:a copy -c:s copy $PWD/out.m4v }  function rename {     echo "Please Provide the Title:"     read -e; mv $PWD/out.mp4 $PWD/$REPLY.m4v }  function subler {     open -a Subler.app $REPLY.m4v     }   cd ~/Public/ && while read -e; do     if [ ${REPLY: -4} == ".mkv" ];      then convert;         rename;         subler;         exit      else      echo "Error: This is not a valid response" && exit 1     fi done   —————————  EDIT:   Question may still be a possible duplicate, but I’ve tried to use the syntax  (both attempting “$REPLY” and “$(REPLY)”) in  and still failing to execute. The errors return either bad substitution for the […bracketed...] statement or my echo statement... Error:This is not a valid response…

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?


I would like to make a hanzi grid for practicing Chinese characters, like this one:   I am able to make the table with the arydshln package, like this:  \begin{tabular}{|c:c|c:c|c:c|c:c|}   \hline   & & & & & & & \\   \hdashline   & & & & & & & \\   \hline   & & & & & & & \\   \hdashline   & & & & & & & \\   \hline \end{tabular}   but how can I write the characters over the table?

I am writing some Chinese character and hope to draw simple pictures by tikz and use it as background of this chinese characters. In a short I'd like to get some results as this picture (ignore the lower right noise):    How could I do? Thanks in advance. As an example for least workable code:  \documentclass{article} \usepackage[CJKnumber]{xeCJK} \setmainfont{KaiTi}  \begin{document} \Huge 明月出天山 \end{document}


Recently  in last 15 days we have started loosing number one ranking in large number of keywords to our competitors. Probably it can be because of recent core web vitals release by google. Not sure.  Here are my findings  My site on those keywords is ahead by 20 to 30 points in overall page performance based on these  web vitals(FCP, SI, LCP, TTI, TBT, CLS) On three core web vitals i.e. LCP, CLS , FID   we are behind in LCP and CLS than our competitor , they are green we are orange, On FID both are green  Can it be right hypothesis that lost in ranking can be because of recent core web vital release where we are behind on LCP and CLS though we are much better on overall page score(based on all six web vitals) ?

There has been a significant drop (90%) in traffic from Google to one of my well-established sites (6+ years) in the last week. Searches show that the top 3 wide keywords all dropped 4 spots. Searches for other keywords do not show ANY results in the first 10 to 25 pages of results, while previously one 1st or 2nd page at most.  Since there are , the question really is:  What steps are necessary to figure out what caused such a drop?  There have been no major changes during this period or the last month on the site and certainly not in the homepage which has dropped in rank. Over all the years of running this site and plenty of others, I have never experienced this. There are is duplicate content on my site and I have rigorously used canonical links for the last few years to ensure it is not misinterpreted as such.