The zeros are $\{2 \pi i n ,n\in \mathbb{Z}\}$. They are all simple. The function is of order 1. Hence, the factorization should be   $$ e^z - 1 = e^{p(z)} z \prod_{n=1}^\infty (1 + z^2/4n^2\pi^2) . $$  The problem left is to determine the polynomial $p(z)$, which is at most first order.   But how to proceed?

Assuming the formulas $$\sin(z)=\frac{e^{iz}-e^{-iz}}{2i}\quad\text{and}\quad\frac{\sin(\pi z)}{\pi z}=\prod_{n=1}^\infty\left(1-\frac{z^2}{n^2}\right),$$ I want to find the Hadamard product of $e^z-1$. I think I've done the work correctly, but I end up having an extra factor of $2\pi i$ at the end (this is from Stein and Shakarchi's book and they list the answer for this particular problem). So, my work is \begin{align} e^z-1&=e^{z/2}\left(e^{z/2}-e^{-z/2}\right)\\ \\ &=e^{z/2}\left(e^{i(-iz/2)}-e^{-i(-iz/2)}\right)\\ \\ &=2ie^{z/2}\left(\frac{e^{i(-iz/2)}-e^{-i(-iz/2)}}{2i}\right)\\ \\ &=2ie^{z/2}\sin(-iz/2)\\ \\ &=2\pi i ze^{z/2}\frac{\sin(-iz/2)}{\pi z}\\ \\ &=2\pi i ze^{z/2}\frac{\sin\left(\pi(\frac{-iz}{2\pi})\right)}{\pi z}\tag{*}\\ \\ &=2\pi i ze^{z/2}\prod_{n=1}^\infty\left(1-\frac{\left(\frac{-iz}{2\pi}\right)^2}{n^2}\right)\\ \\ &=2\pi i ze^{z/2}\prod_{n=1}^\infty\left(1+\frac{z^2}{4n^2\pi^2}\right). \end{align}  The answer according to the book is $$e^z-1=e^{z/2}z\prod_{n=1}^\infty\left(1+\frac{z^2}{4n^2\pi^2}\right).$$Have I made a simple mistake in calculation, or are the two somehow compatible with each other?  Update: Thomas Andrews has pointed out a mistake in my infinite product formula. I've corrected that mistake.  $(*)$ The error occurs from this line to the next. Instead of multiplying and dividing by $z$, I should have multiplied and divided by $\frac{-iz}{2\pi}$. That would cause the appropriate cancellation.


I'm trying to check for the existence of a site in my siteList. I'm getting this data from the command line and I'm trying to make sure the user inputs a site that is in the list, if they don't, they get a usagePrompt()  This is the site list  var siteList = [     { site: 'github', password: null },     { site: 'stackoverflow', password: null } ]   This is the if statement it's going in  if (!process.argv[2] || !process.argv[3] || /* PROBLEM */)) {     usagePrompt() }   And this is my /* PROBLEM */ check that I'm going to replace the comment with.  console.log(typeof(siteList.find(site => site.site == process.argv[2]) != 'undefined'))   I want to .find() the site, and if it exists it should therefore not be undefined - but this just returns boolean, which exists and is true in the if statement regardless of whether the site is in the list.

What is the most concise and efficient way to find out if a JavaScript array contains a value? This is the only way I know to do it: function contains(a, obj) {     for (var i = 0; i < a.length; i++) {         if (a[i] === obj) {             return true;         }     }     return false; }  Is there a better and more concise way to accomplish this?


At the end of The Hobbit: The Battle of the Five Armies Legolas was sent to find Aragorn. But in The Lord of the Rings: The Fellowship of the Ring, Bilbo is already 111 years old. So Aragorn must be very young in the first place.  How old is Aragorn at the time of the Hobbit movies?

On the last Hobbit movie, after the Battle of the Five Armies, Legolas tells Thranduil that he won't be coming home. The latter tells him to go to find the infamous son of Arathorn, that goes by the name of Strider.  But, the Battle of the Five Armies was fought on T.A. 2941 and Aragorn was only born on T.A. 2931.  Aragorn did not leave Rivendell until 20 years old.   How could Aragorn be such an infamous rogue in the age of only ten and still in Rivendell??  Sources: ,  and .


I was reading Stong's Cobordism Theory, the following lemma to be precise. In the proof, he gives a total order on the set of non-dyadic partitions with the given partial order After some research, I came to know that we can always give a total order to any set courtesy . But could not find anything about the existence of a Total order, Compatible with a given Partial order. As I am not really an expert on Discrete Mathematics. Any hints, suggestions will be really helpful. regards

How do I show that every partial order can be extended to a linear ordering?      I think that I manage to prove that claim for finite set, how can I prove it for infinite set?  Thank you.


I have developed my first website and ready to publish to the internet. I'm confused with how the COPYRIGHT under the footer works? Do I just ...   Show COPYRIGHT WEBSITE NAME at the footer? Not showing anything? Register my copyright before showing?    I have read so many posts discussing about the copyright, I'm still confuse. As different source seems to give different answer  (Example, you need to register copyright with $35, you don't need copyright, etc..)  By far,  seems to be accepted by most. Can I confirm this is true?     You automatically have the copyright to any work you create.   Meaning that, I can simply just add my COPYRIGHT WEBSITE NAME in my website without any registration?

My website has been in development for a long time and cost a lot of money.  How do I go about securing an enforceable copyright on my website design and what is the proper way to post a copyright notice on the site so others know the work is copyrighted?


i was using Windows 10. I had 3 partitions before.Then one of my friend tried to do dual boot in my system with ubuntu14.During this process instead of dual booting he Accidentally deleted my windows 10 and all my data from my Hard Disk.(It was so important and sentimental data that was deleted)Now the machine is running with Ubuntu OS.i have tried recovering with terminal with this command.   sudo apt-get install testdisk(installed testdisk) sudo photorec(run photorec)   Then asked for select partition   Disk/dev/sda-500GB/465 GiB(RO)-THOSHIBA MQ01ABF050               Start   End          size in sector                 0     976773167     97673168(whole disk)   And start The recovery But the recovering files look like this  f000920.dll,f000120.txt,f000511.exe,f000024.java etc(more than around 500 of them in a folder) In folder named Recup_dir.1,Recup_dir.2,Recup_dir.3 etc(not completed yet still running) so its impossible to organize like it were before (and my Java projects and some of my own Java codes are arranged in a folder before Now it is shattered across the folders with unrecognizable names.So there is no way i can read all the files(From 970,000000) and find which is which in this lifetime. So is there any other way i can use to get all my data by folder by folder or at least with same file name.I'm ready for any other alternatives please help Thanks in advance.

What steps can I take to try to recover lost or inaccessible data from any storage device?  Answers:   This applies to any computer storage device, e.g. internal/external hard drives, USB sticks, flash memory. The most important thing is to STOP using it, any type of I/O can ruin your chances of a recovery.     We have separate questions covering common problems with USB flash drives in greater detail:


Is there any way to clear the terminal's previous output? If so, how? Here is a code example to work off of.  print "Hello..." #Code that clears previous terminal output print "All cleared!"   I know that there is an iOS module for the mobile app pythonista that can do this, but I am wondering how to do it on Linux.

Like most Python developers, I typically keep a console window open with the Python interpreter running to test commands, dir() stuff, help() stuff, etc.  Like any console, after a while the visible backlog of past commands and prints gets to be cluttered, and sometimes confusing when re-running the same command several times.  I'm wondering if, and how, to clear the Python interpreter console.  I've heard about doing a system call and either calling cls on Windows or clear on Linux, but I was hoping there was something I could command the interpreter itself to do.  Note: I'm running on Windows, so Ctrl+L doesn't work.


I mean there are tons of religious communities on Stack Exchange like Biblical Hermeneutics, Buddhism, Hinduism, Islam etc. Why not a community for atheism, where every religion and its practices can be questioned in purely logical terms?

I have an idea or subject that should have a Q&A, and want to propose a new site. How can I do this?  Related:


I am trying to declare a RecyclerView in an activity in my project. When I switch to this activity, the project crashes. I am getting a NullPointerException when I try to instantiate my RecyclerView, see error below:  E/AndroidRuntime: FATAL EXCEPTION: main     Process: com.example.marykate.marykatefordefyp, PID: 13490     java.lang.RuntimeException: Unable to start activity ComponentInfo{com.example.marykate.marykatefordefyp/com.example.marykate.marykatefordefyp.ViewFavourites}: java.lang.NullPointerException         at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2264)         at android.app.ActivityThread.handleLaunchActivity(ActivityThread.java:2313)         at android.app.ActivityThread.access$1100(ActivityThread.java:141)         at android.app.ActivityThread$H.handleMessage(ActivityThread.java:1238)         at android.os.Handler.dispatchMessage(Handler.java:102)         at android.os.Looper.loop(Looper.java:136)         at android.app.ActivityThread.main(ActivityThread.java:5336)         at java.lang.reflect.Method.invokeNative(Native Method)         at java.lang.reflect.Method.invoke(Method.java:515)         at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:865)         at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:681)         at dalvik.system.NativeStart.main(Native Method)      Caused by: java.lang.NullPointerException         at com.example.marykate.marykatefordefyp.ViewFavourites.onCreate(ViewFavourites.java:54)         at android.app.Activity.performCreate(Activity.java:5302)         at android.app.Instrumentation.callActivityOnCreate(Instrumentation.java:1090)         at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2228   I have looked at similar questions on this site but none have the answer I am looking for. I am not referencing the wrong xml file and I am calling the correct RecyclerView. See my code below:   RecyclerView eventsListview; List<Favourite> favourites = new ArrayList<>();     FaveAdapter adapter = new FaveAdapter(this, R.layout.eventlist_layout, favourites);  @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_view_favourites);          eventsListview.findViewById(R.id.eventsListview1); //the line causing an error   Does anyone know what might be causing this?

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


From mathematics we know that the cosine of a 90 degree angle is 0 but Python says it's a bit more than that.  import math math.cos(math.radians(90)) 6.123233995736766e-17   What's the matter between Python and the number "0"?

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


Please tell me the best option among these options displayed in the screenshot.

I have NVIDIA Geforece 7025 / nForce 630a integrated gfx card on my UBUNTU 12.04.And I have 4 options in Additional drivers:    NVIDIA accelerated graphics driver (version 173)   NVIDIA accelerated graphics driver (post-release updates)(version current updates)  NVIDIA accelerated graphics driver (version current)[Recommended]  NVIDIA accelerated graphics driver (post-release updates)(version 173 updates)   I am currently using the First option.  My Problem is there I can't update the version 173 to the latest version of drivers using xswat PPA. Whenever I do it and reboot but the NVIDIA xserver sttings always shows me the same version.  Which option would allow me to update my drivers to the current version?


Here is my example (from an SAT question):     No one is sorrier than I that you missed the awards ceremony   I don't know understand why it is "I". Shouldn't it be "me" since "I" is the subject here? Thanks

Consider the sentence "I can run faster than 15 miles per hour." Its meaning is clear and to my eyes obviously grammatically correct. Now let me present some variations that have given me trouble for a long time.  I am faster than 15 miles per hour. – To me this is clearly incorrect. Directly comparing me to a speed doesn't seem right. We need to compare my speed to a speed, or me to another person.  I can run faster than him. – Compared to the base sentence, there is a distinct shift in meaning of the comparison. While before I named a speed faster than which I can run, now I am naming a person. It doesn't seem quite right. I realize the parts of speech can change, but my initial objection is that "him" is not a speed.  I can run faster than he. – This seems most correct to me, but still somehow feels objectionable. Is this in fact the correct way to say it? And if so, is it proper as is or need I say "... faster than he can" or even "... faster than he can run?"  I am faster than him. – With "am" instead of "can run" it now seems slightly more correct. But is it?  I am faster than he. – I'm in doubt here. It doesn't seem wrong to me to say, "I am faster than he is" or even "I am faster than he is fast." (Though I suppose that is a given since I could hardly properly compare to some other category as in "I am faster than he is smart.")  My speed is faster than his. – Hmm. This seems more proper as "my speed is greater than his."   So which of these constructions is correct and which is incorrect? Is there a general rule that I can follow? UPDATE The scholarly article  may be of great interest to some readers!  Once we accept that the elided constituent and its antecedent can differ in form, it becomes reasonable to ask how large this difference can be. The answer in Rooth (1992), Fiengo and May (1994), Chung et al. (1995) and subsequent work is that the wiggle room is actually quite small: the elided constituent and its antecedent are allowed to differ only in the realization of inﬂectional morphology. Other than that, both constituents have to be syntactically and lexically isomorphic.


I am trying to do a fancy resume and I want to include in it a pie skill chart (see image below). Any Idea on How Can I create this image in Latex.  Thank you for your help, Cheers

I want to create a pie chart in LaTeX. Do you know a package which manages that? I tried datatool which uses tikz as backend but seems to be unusable due to mysterious floating point errors.


Hello after the update and upgrade on my Ubuntu, the firefox is not loading specific websites like stackoverflow, askubuntu and such sites. It loads other sites like lichess.org and also able to play youtube videos. But on these sites the error is server not found. The same error that comes when you are not connected to the internet. Now that's that I also have another problem which I don't know if related to this. When I do apt-get upgrade then it says http.kali.org not found. And on upgrade it says not secure to download. It seems like the dns is messed up from the errors that it can't connect to any such websites. I don't have any proxy or any VPN or anything of that sort. Please help me. Sorry for just this plain html but I have to write this via my phone as my Ubuntu says nope.

I tried installing Kali Linux tools.  I started installing some tools and there were several things I had to "agree" to and one message said add users... something in terminal, and when I came back I saw terminal reporting removing a bunch of core programs that I needed. I canceled the process but I don't know if I should reinstall Ubuntu or not.  How can I repair my system?


A and B two sets. |A|=k,|B|=n. prove: the number of partial function from A to B is (n+1)^k. proof: x-object not in B. B*=BUx.  The total function (not partial) between A and B* is (n+1)^k. Now I need to find a bijection between the set of all partial function from A to B and the set of all function between A and B*.  someone can show me please explicit bijection that would do the work  thanks.

$A$ and $B$ two sets. $|A|=k, |B|=n.$ I need to prove in a combinatoric way that the number of partial function from $A$ to $B$ is $(n+1)^k.$ I thing the number is $Σ(n^i),$ for $i=0$ to $k.$ but I have no idea how to show equality, and how to prove it in a combinatoric way.  If someone can show me the way or guide me that will be great!  thanks for helpers.


Let S be a finite set of vectors $S\subseteq V$ with a vector space V over a field F. I have two alternate definitions of span(S): $span(S)=\bigcap_{S\subseteq M\subseteq V} M $ and $span(S) = \left \{ \sum_{i=1}^{k}\lambda _{i}v_{i}: k\epsilon \mathbb{N}, v_{i}\epsilon S, \lambda _{i}\epsilon F \right \}$. Why are these two definitions equivalent?

In Linear Algebra by Friedberg, Insel and Spence, the definition of span (pg-$30$) is given as:     Let $S$ be a nonempty subset of a vector space $V$. The span of $S$,   denoted by span$(S)$, is the set containing of all linear   combinations of vectors in $S$. For convenience, we define   span$(\emptyset)=\{0\}$.   In Linear Algebra by Hoffman and Kunze, the definition of span (pg-$36$) is given as:     Let $S$ be a set of vectors in a vector space $V$. The subspace   spanned by $S$ is defined to be intersection $W$ of all subspaces of   $V$ which contain $S$. When $S$ is finite set of vectors, $S = \{\alpha_1, \alpha_2, ..., \alpha_n  \}$, we shall simply call $W$ the   subspace spanned by the vectors $\alpha_1, \alpha_2, ..., \alpha_n$.   I am not able to understand the second definition completely. How do I relate "set of all linear combinations" and "intersection $W$ of all subspaces"? Please help.  Thanks.


We want to verify if the means of the 3 samples are equal. When we test the homogeneity through Bartlett test we get that the hypothesis is rejected. Can we apply ANOVA test? (we applied ANOVA test and we get that the hypothesis is rejected).How can we interpret this?

I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.  One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a  ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.   I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.  Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?  P.S.: my raw data are below:   A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36  0.363 0.371 0.398 0.407 0.409 0.432     0.494 0.719 B: 0.11  0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19  1.233 1.505 1.897 C: 0.106 0.114 0.143 0.435 0.448 0.51  0.576 0.588 0.608 0.64  0.658 0.788 0.958


Why are there so many user names like user123456?   Is that really their name, or just the name that I'm allowed to see?  I don't believe that so many people chose such a uniform name because they wanted to have a generic name.  Previously I assumed that these were users who deleted their profiles or perhaps died or were imported from another site, but there are certainly a lot of examples of users with great activity and recent activity.    So, where do they come from?

It's been more than a month since I have started using . It has these users with user names in the format of "user-random number". I have observed them in some of the stack activities, most of the time asking questions.   Does the moderators create them for their own purpose. If yes what purpose do they serve?   I mean a user is free to have any user name. But it's just a hunch that such users are actually moderators. I may be wrong; just need some clarification.


I have written the LINQ query as following but just wondering if i can make it more generic and get rid of the hard coded values.  switch (sortOrder) {     case "DESC":         if(sortBy == "A")             query = query.OrderByDescending(x => x.Field1);         if(sortBy == "B")             query = query.OrderByDescending(x => x.Field2);         if (sortBy == "C")             query = query.OrderByDescending(x => x.Field3);         break;     default:         if(sortBy == "A")             query = query.OrderBy(x => x.Field1);         if(sortBy == "B")             query = query.OrderBy(x => x.Field2);         if (sortBy == "C")             query = query.OrderBy(x => x.Field3);         break; }   The link mentioned as duplicate is not the answer i am looking for. In that question user asked by sorting 1st of ASC and then Desc.  In my case i have to either sort ASC or DESC.

I found an example in the  for Dynamic LINQ that allows you to use a sql-like string (e.g. OrderBy("Name, Age DESC")) for ordering. Unfortunately, the method included only works on IQueryable<T>. Is there any way to get this functionality on IEnumerable<T>?


When in a list, adding a picture that is indented covers up the background on the right where links normally go. See picture below:    (source: )  As you can see, with multiple indents, the image is mixing with the links on the right, making some hard to read. I think it would be better if images were forced to be to the far left, instead of indenting them with the rest of the text.

A   B   C   D   E   F             I don't even know. It just seemed weird.  Yes, I understand I could just avoid doing something like that. But the problem already exists with a single level.   Consider having 2 images in a post. Both exceed the maximum width of a post. One is nested in a list. Key to this issue is that my original images were much larger. They were automatically resized.  Image    List      I think it looks weird.


Yo Hi! I'm currently trying to fix my code. I'm making a basic math to calculate the appropriate time spent in front of my computer When I ran my code, it says: File "BasicProblemSolving.py", line 21, in <module> Result = Calculations(answer2)  File "BasicProblemSolving.py", line 19, in Calculations x = x * average_minus TypeError: can't multiply sequence by non-int of type 'float'  This is the code: # This explains how to do basic maths to calculate daily problems `# Let's go! import math bad_time_usage = 8 #In hours  time_usage = 365 - (round(365/7*2 + 30)) * 8 #In hours  current_minus = 6.5  average_minus = 0.011  answer1 = input("Hi, enter your name! ")  print("\nOwh hi {}!".format(answer1))  answer2 = input("Try to enter the daily usage of how many hours do you spend  everyday ")  def Calculations(x):   x = x * average_minus  Result = Calculations(answer2)  answer = input(f"So, you would get... {Result} minus.")  Your help would be a great help to me Thanks!

I am typing to get a sale amount (by input) to be multiplied by a defined sales tax (0.08) and then have it print the total amount (sales tax times sale amount).  I run into this error. Anyone know what could be wrong or have any suggestions?   salesAmount = raw_input (["Insert sale amount here \n"]) ['Insert sale amount here \n']20.99 >>> salesTax = 0.08 >>> totalAmount = salesAmount * salesTax  Traceback (most recent call last):   File "<pyshell#57>", line 1, in <module>     totalAmount = salesAmount * salesTax TypeError: can't multiply sequence by non-int of type 'float'


X ∪ (Y ∩ Z) = (X ∪ Y) ∩ Z  If it were true I'd know how to prove that it is, but if it's not how do I go about finding a counter example?

Title says it all.  Prove the statement is false with a counter-example:  For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T  Explain thoroughly if possible. I'm new to this


Is the word and equivalent to the && operator?  if (inner > 10 and !id) {     std::cout << "idle" << std::endl; }   This code was originally translated from Python.  I was sure that the 'if' line would result in a compilation error. But it does pass.  Visual studio (2015) marks it as an error, but it does compile with g++ (and also on this site ) and seems to run as expected.   Is this correct syntax or did I miss something?

I've just read this  from Reddit.  They mention and and or being "Alternative Tokens" to && and ||  I was really unaware of these until now. Of course, everybody knows about the , but and and or? Since when? Is this a recent addition to the standard?  I've just checked it with Visual C++ 2008 and it doesn't seem to recognize these as anything other than a syntax error. What's going on?


My cousin and I want to play Minecraft together but I don't want to join a multiplayer server or use mods. How can we do this?

Is it possible to get people to join your singleplayer world if they are connected to your LAN?


I am trying to run multiple Node.js web servers locally on my machine.  Because the code I'm writing needs to reference a domain name I'd like to keep a convention of dev.myHost.com and point that to the non-port-80 service running from Node (technically I'm running one on Harp.js and one on Sails.js).   So dev.hostOne.com should point to localhost:123 and dev.hostTwo.com should point to localhost:456   Is this possible? If so, how.

This is a  about DNS/Hostnames resolution to IPs/Ports   Example 1  I'm running a web server on port 80 and another on port 87. I would like to use DNS so that www.example.com goes to port 87. How can I accomplish this using DNS only?  Example 2  I'm running a service on my server on a non-standard port. How can I get clients to connect to this non-standard port automatically? Can I use DNS? Is there some application specific support where DNS could indicate the IP and Port?   Example 3  Do some application protocols specifically support hostname awareness, and allow special actions to be taken based on this information? Are there other questions on Server Fault that cover some of these?  Commandeering: This question was originally asking about running IIS and Apache on the same server, but the same concepts can be applied to any server software receiving connections from clients. The Answers below describe the technical problems and solutions of using DNS and application protocol support to assign a port number for a client to connect.


I have to find the types of roots (i.e real or complex) of the equation $$ 11^x + 13^x+ 17^x -19^x = 0 \dots (1) $$  If $$ f(x) = 11^x + 13^x+ 17^x -19^x = 0 $$ , then obviously $ f'(x)= 0 $ has a 0 solution, and indeed every derivative of $f(x)$ has a  0 solution.   In this context a question arises in my mind : if all the conditions of Rolle's Theorem are satisfied for a function $g(x) $ in $[a,b]$, and in addition if $g'(c)=0$ ,then is it necessary that $c$ lies between $a$ and $b$ ?    If it's true, then we can conclude that $f(x)=0 $ has more than 2 real roots right?  Any insight ? Thank you.

The Equation $11^x + 13^x + 17^x =19^x  $  Has    No Real Roots Only One Real Roots Exactly Two Real Roots  More than Two Real Roots    What I have done is   The function $f(x)=11^x + 13^x + 17^x -19^x  $ is strictly increasing and being always positive it have no roots


Vectors are basically described by two quantities and have some magnitude and direction.  Why did the people who invented vectors invent it?What is the use of bundling numbers into groups of two?Why do vectors exist?

It is natural to understand the need for scalars (numbers), but why did we invent vectors? Who invented it and for what?  EDIT: As George Lowther pointed out, the problem is too broad; I added the following questions as concrete supplements.   It's easy for humans to understand the law of addition of scalar numbers, but why does the vector addition follow the parallelogram rule, and not some other law? (link to physics: How do we know that the addition of forces follows the parallelogram law?) The length of a 2-dimensional vector is the hypotenuse of the triangle constructed from the two components of the vector and the length of 3-dimensional vector also follows this way. But what about 4-dimensional vectors? Why do we define dot products of vectors like it is now? Is it because of its physical essence or its equivalence to the law of cosines?


I am using the beamer class and consider the following frame:  \documentclass{beamer} \begin{document} \begin{frame} \begin{itemize} \item blabla \end{itemize} \end{frame} \end{document}   It appears that the text "blabla" is vertically centered on the slide. I would like to avoid this so that this text "blabla" appears on the first line of the slide.  A global change on all slides is suitable for me.   Thanks

When I create beamer frame, the content is centred in the slide. How do I make the content move to the top of the slide by default?


I was wondering if there is any possible way to define a limit for this form?  I tried using L’hopital rule and tried evaluating the limit:  $$\lim _{x\to 0} x^{x^{x^{x^{x^{x\cdots}}}}}$$  $$\lim _{x\to 0} x^{x^{x^{x^{x^{x\cdots}}}}} = \lim _{x\to 0} y$$  $$\lim_{x\to 0} x^y = \lim_{x\to 0} y$$  $$\lim _{x\to 0} \ln y = \lim _{x\to 0} \frac{\ln x}{\frac{1}{y}}$$  $lim _{x\to 0}$ $\ln y$ =  $lim _{x\to 0} $$\frac{\frac{1}{x}}{-\frac{1}{y^{2}}\frac{dy}{dx}}$  $lim _{x\to 0}$ $\ln y$ =  $lim _{x\to 0}$ $-\frac{y^{2}}{x}\frac{dx}{dy}$  $lim _{x\to 0}$  $x^{x^{y}}$ = $lim _{x\to 0}$  $y$  $lim _{x\to 0}$  $\ln y$ = $lim _{x\to 0}$  $\ln\left(\frac{\ln y}{\ln x}\right)$  following the same steps yield the result: $lim _{x\to 0}$  $\ln\left(\frac{\ln y}{\ln x}\right)$ = $lim _{x\to 0}$ $-\frac{y^{2}}{x}\frac{dx}{dy}$ substituting the previous result leads to the equation   $lim _{x\to 0}$ $\ln y$ = $lim _{x\to 0}$  $\ln\left(\frac{\ln y}{\ln x}\right)$   $lim _{x\to 0}$ $x^{x^{x^{x^{x^{x...}}}}}$ =  $lim _{x\to 0}$ $\log_{x}\left(x^{x^{x^{x^{x...}}}}\right)\$$  substituting $x^{x^{x^{x^{x^{x...}}}}}$ as 0 or 1 does not satisfy the equation (as manually checking the limit with a calculator yields a result of a number that approaches 0 or 1).  However if I let $lim _{x\to 0}$ $x^{x^{x^{y}}}$= $lim _{x\to 0}$ $y$ then I will get the result such that  $lim _{x\to 0}$ $\ln\left(\frac{\ln\left(\frac{\ln y}{\ln x}\right)}{\ln x}\right)$ = $-\frac{y^{2}}{x}\frac{dx}{dy}$ = $lim _{x\to 0}$ $\ln y$  therefore another equation is made such that $lim _{x\to 0}$  $\log_{x}\left(\log_{x}\left(x^{x^{x^{x^{x...}}}}\right)\ \right)$= $lim _{x\to 0}$ $\ x^{x^{x^{x^{x...}}}}$ However, substituting the value of $\ x^{x^{x^{x^{x...}}}}$ as 0 or 1 satisfies the above equation.  So how does this work?

I got this problem from my teacher as a optional challenge. I am open about this being a given problem, however it is not homework. The problem is stated as follows. Assume we have an infinite tetration as follows $$x^{x^{x^{.^{.^.}}}} \, = \, a$$ With a given $a$ find $x$. The next part of the problem was to discuss the convergence radius of a. If a is too big or too small the tetration does not converge. Below is my humble stab at the problem.  My friend said you would have to treat the tetration as a infinite series, and therefore could not perform algebraic manipulations on it before it is know whether it converges or diverges. However my attempt is to first do some algebraic steps, then discuss the convergence radius. I) Initial discussion At the start it is obvious that the tetration converges when $a=1$ (just set $x=1$) Now after some computer hardwork it seems that the tetration fails to converge when a is roughly larger than 3. II) Algebraic manipulation $$ x^{x^{x^{.^{.^.}}}} \, = \, a$$ This is the same as $$ x^a \, = \, a$$ $$ \log_a(x^a) \, = \, \log_a(a)$$ $$ \log_a(x) \, = \, \frac{1}{a}$$ $$ x \, = \, a^{\frac{1}{a}}$$ Now, if we let $a=2$ then $x = \sqrt{2}$. After some more computational work, this seems to be correct, which makes me believe this formula is correct. III) Discsussion about convergence By looking at the derivative of $ \displaystyle \large a^{\frac{1}{a}} $ we see that the maxima occurs when $a=e$, which also seems to correspond to the inital computational work. Now I think, that the minima of $\displaystyle \large a^{1/a}$ is zero by looking at its graph, studying its derivative and the endpoints. So that my "guess" or work shows that it converges when $$ a \in [0 \, , \,  1/e] $$ VI) My questions Can my algebraic manipulations be justified? They seem rather sketchy taking the a`th logarithm and so on . (Although they seem to "magically" give out the right answer) By looking at Wikipedia it seems that the tetration converge when $$ a \in \left[ 1/e \, , \, e \right] $$ This is almost what I have, why is my lower bound wrong? How can  I find the correct lower bound?


I need to add a dynamic number of Join operations to a LINQ expression. The number is the size of the DemHeaderIDs array. The Joins include a Where clause with a parameter taken from the DemoHeaderIDs array. Using DemoHeaderIDs[0] in the first set works fine.  But when trying to use a DemoHeaderID[i] in a loop I get the error message below.  When I use a hard coded integer instead of DemoHeadersID[i], the code runs fine and the result is correct.  My Code:  private void DoSomething(int[] DemoHeaderIDs, OVContext _context) {   //first set of joins     var q = from oh in _context.OrgHierarchy             join odd in _context.OrgDemoData on oh.Identifier equals odd.Identifier             join dh in _context.DemoHeader.Where(h => h.DemoHeaderId == DemoHeaderIDs[0]) on odd.Demoheaderid equals dh.DemoHeaderId             select new             {                 Name = odd.Demovalue,                 Parent = "All",                 Identifier = oh.Identifier             };      for (int i = 1; i < DemoHeaderIDs.Count(); i += 1)     {   //dynamic joins         q = from qObj in q             join odd in _context.OrgDemoData on qObj.Identifier equals odd.Identifier             join dh in _context.DemoHeader.Where(h => h.DemoHeaderId == DemoHeaderIDs[i]) on odd.Demoheaderid equals dh.DemoHeaderId             select new             {                 Name = odd.Demovalue,                 Parent = qObj.Name,                 Identifier = qObj.Identifier             };     }      var ql = q.ToList();   The Error Message:     System.IndexOutOfRangeException: Index was outside the bounds of the   array.    at lambda_method(Closure )    at   Microsoft.EntityFrameworkCore.Query.ExpressionVisitors.Internal.ParameterExtractingExpressionVisitor.Evaluate(Expression   expression, String& parameterName)   Adding EnableSensitiveDataLogging() to the DbContext configuration did not add information to the message.  I'm using EntityFramework.Core 2.2.

I met an interesting issue about C#. I have code like below.  List<Func<int>> actions = new List<Func<int>>();  int variable = 0; while (variable < 5) {     actions.Add(() => variable * 2);     ++ variable; }  foreach (var act in actions) {     Console.WriteLine(act.Invoke()); }   I expect it to output 0, 2, 4, 6, 8. However, it actually outputs five 10s.  It seems that it is due to all actions referring to one captured variable. As a result, when they get invoked, they all have same output.  Is there a way to work round this limit to have each action instance have its own captured variable?


Is there a way to know which badges can be obtained more than once?

Formerly List of all badges with full descriptions.  What are badge name's requirements? Why didn't I get badge name ? Which badges can I earn multiple times?    Jump to:                    Note: Some badges are awarded based on score. The term score means the total number of upvotes minus the total number of downvotes.  Any badge with a *** next to it is one of 20 badges that count towards the  displayed on a moderator candidate in an election. The candidate score is a total of 40 points: the first 20 are awarded based on the user's rep divided by 1000 and rounded down; the second 20 represents the total number of unique badges earned of the 20 that count. Note that if the same badge is earned multiple times, it will only count once towards the candidate score.  Any badge with a "(retired)" next to it is no longer awarded, but is retained by users who previously earned them. See  for more info on what it means for a badge to be retired.       Visit the  of the  on any site to see a complete list of badges that you can filter by earned, unearned, or type.


I started recently to work on a spare part to print with a 3d-printer and I repeated my workflow that was successful in prior versions of blender and then i noticed changes in the with the bools. I can not find apply for the boolean operation since i upgraded to 2.9 (from 2.83) The first picture is the bool operations for blender 2.9,  The second picture is the same file in blender 2.83.

Why I can't apply mirror modifier? Here's screen


On at least CentOS systems and previous versions of Fedora, I could run the following command and get a list of files with the corresponding grep matches:  $ find -name "version.php" -type f | xargs grep "^\$wp_version" site.com/wp-includes/version.php:$wp_version = '4.7.3';  Apparently though on at least Fedora 22 and newer, running that same command no longer includes the path and filenames:  find -name "version.php" -type f | xargs grep "^\$wp_version" $wp_version = '4.7.3';  I know I can include -l to show just the path, but is there a way to include the path without dropping the match? I don't see anything in the man file.

When using find, how do I return the file name and the line number when searching for a string? I manage to return the file name in one command and the line numbers with another one, but I can't seem to combine them.  File names: find . -type f -exec grep -l 'string to search' {} \;  Line numbers: find . -type f -exec grep -n 'string to search' {} \;


I have seen some videos on how to make Ubuntu into a beautiful and efficient i3 system with all unnecessary apps removed. But rather than having to configuring such a system multiple times, I would prefer to make a flavour of Ubuntu myself. How difficult would it be to do that?

I would like to customize Ubuntu live CD by installing some additional packages. I have followed   but it doesn't seems to work. Can anyone provide clear instructions?   Note: I do not prefer Remastersys, manual way will be appreciated.  Customization  Packages that I want to install:   Thunderbird    Samba    SSH       Changes that I need:   Remove Games menu from the Application menu Firefox shortcut on Desktop Radiance as the default Theme Different default Ubuntu Wallpaper   Configuration file changes   I want the panel to be placed at the bottom I want to paste my Samba configuration file instead of default Samba configuration I have few Firefox shortcuts and folders I would like to show that in Desktop Also it will be nice if you say me how to change the icon sets   Recent Updates   I have customized Ubuntu 10.10 with Firefox shortcuts and few folders on desktops. Everything went smooth. But the installer gets crashes after choosing the timezone. How do i fix this issue? Also setting wallpaper affects the login screen. The wallpaper which i set is displayed on the login screen also. I just want the default one for the login screen.


I have a PostgreSQL/PostGIS spatial relational database for my university project with objects, their coordinates and attributes (1:n, n:m relations). I would like to map my spatial objects online and run queries, however, I am not ready yet to set up a web server and write server side scripts.   Are there any web mapping platforms that will allow me for now to visualize the data from the exported database? I suppose in this case I have to merge all of the related tables with attributes into one file.

I am very new to web-mapping, so this question may be a little misguided.  I want to have a very simple web interface using OpenLayers (or even Google Maps if that will be easier) which can display a number of point and polygon tables that are currently in PostGIS.  I want this to be as simple (and as low maintainence) as possible:   I don't want to have to create tiles (unless there is a very good reason), or have a massive, complex layer of middleware.   Performance doesn't need to be phenomenal, as this is for internal use and thus doesn't need to scale beyond a couple of concurrent users. Styling of the vector layers is of minimal importance. Open source tools are much preferred as I have almost no budget for this.   What is the recommended approach for this?


$E$ is a finite-dimensional vector space over a field K and $E^∗$ its dual.  $$\boxed{x\in E, x=0\iff \forall \phi\in E^*,\langle\phi,x\rangle=0}$$  The proof for ($\implies$) seems to be obvious since $x=0\implies\langle\phi,x\rangle=\phi(x)=0$  But for ($\Longleftarrow$)that is a little more difficult, below the proof:  $\bigg [\forall \phi\in E^∗,\langle \phi,x\rangle=0\implies x=0\bigg ]\iff \bigg[x\in E, x\neq0\implies \exists \phi \in E^*, \; \langle\phi,x\rangle\neq 0\bigg]$  Let $x\neq 0$ and $\mathcal{B}=\big\{e_1,e_2,...e_n\big\} \text{a basis of $E$} \implies x=\lambda_1e_1+\lambda_2e_2+...+\lambda_ie_i+...+\lambda_ne_n\quad i\in[\![0,n]\!]$ so there exists a basis of $E$ such that $\mathcal{B}'=\big\{x,u_2,u_3,..u_n\big\}$  Let $f$ such that:  $\begin{array}lf:&E&\to K\\&\lambda_iu_i&\to \lambda_i\end{array}\qquad\implies f\in E^* \text{ and } f(x)=1$  If the proof is correct, I understand the logical path, but I don't really understand it?  I know there is a similar question but it doesn't help me:

Let $X$ be an infinite-dimensional vector space, and let $x_0$ be an element of $X$ such that $f(x_0)=0$ for every linear functional $f$ defined on $X$. Then can we prove that $x_0$ is the zero vector in $X$? Or, is it possible to find a non-zero $x_0$ whose image under every linear functional is zero?   In the case of $X$ being finite-dimensional, we can prove that if $f(x_0)=0$ for every linear functional $f$ on $X$, then $x_0$ must be the zero vector. What is the situation in the infinite-dimensional case?


if you run this in python     print 'Äppleß','Äppleß'.decode('latin-1').encode('utf-8')   thats a mojibake (garbled text due to incorrect encoding/decoding) but python does not raise an error.  I want it to throw an error in the case of a mojibake.  I have heard of things like this that can help:   any other ideas or experience on shortcuts?

I received some text that is encoded, but I don't know what charset was used. Is there a way to determine the encoding of a text file using Python?  deals with C#.


Let's say hypothetically that a gun fires a bullet which has a mass of 1 gram and a $V_\mathrm{initial}$ of 10 m/s, which becomes lodged in a wooden block that has a mass of 9 grams and is initially at rest. The impact causes the block (with the lodged bullet) to travel at a velocity $V_\mathrm{final}$. What is $V_\mathrm{final}$?  I'm confused. I don't know whether I should use momentum or kinetic energy to figure out the $V_\mathrm{final}$. I plugged in the numbers to both equations, and the resulting values of $V_\mathrm{final}$ didn't agree.

I am confused as to when each should be used to solve problems.I am not looking for the answer to this question, but I will include it here so you have all the information about what I am asking about.      A 15.0 kg block is attached to a very light horizontal spring of force   constant 400.0 N/m and is resting on a frictionless horizontal table.   (See (Figure 1) .) Suddenly it is struck by a 3.00 kg stone traveling   horizontally at 8.00 m/s to the right, whereupon the stone rebounds at   2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.   I see that the idea suggested  is to use conservation of momentum to solve this problem. But I wanted to solve using conservation of energy in the following way:   $K.E =\frac{mv^2}{2}$  $Spring-P.E=\frac{kx^2}{2}$  $KE_i = KE_f + PE_f$  $KE_i - KE_f = PE_f$  Solving the equations, you get  $x = 0.670m$  The correct answer given is 0.387m.


I'm working with many shp file point format with geometry attributes like this:    But I need convert it into such format in textfile like below:    Are there any ways to arrange my shapefiles format into coordinates separated by comma orderly using PyQGIS or another python script.  Since I'm still learning with Python, I try to learning by doing.

Using ogr2ogr and python, I'm running into a wall with trying to create a CSV with WKTs for a shapefile that contains multipart polygons. Currently this is this code I'm using (found it on internet):   #Purpose: To export a shapefile to WKT  from osgeo import ogr import sys, os  input = ogr.Open(sys.argv[1])   layer_in = input.GetLayer() layer_in.ResetReading() feature_in = layer_in.GetNextFeature()  outfile = open(sys.argv[1] + ".wkt", "w")  while feature_in is not None:      geom = feature_in.GetGeometryRef()     geom_name = geom.GetGeometryName()      outfile.write(str(geom)+ '\n')      feature_in = layer_in.GetNextFeature()   So, do I need to use a different geometry container or do I need to evaluation each feature and if it's a multipart use a different set of geometry classes? I've looked around in the gdal/ogr documentation but I'm having a hard time reconciling it.


In the Deathly Hallows Harry and Voldemort are fighting in the forest. Voldemort defeats and kills Harry, why didn't Voldemort become the true owner of the Elder Wand and therefore win their final battle?

There's a lot of emphasis on Harry becoming the master of the Elder Wand after he defeats Draco. But what constitutes a “defeat”?  It seems that Harry wins a wrestling match with Draco, so now he’s the master of the Elder Wand.  But lots of other stuff happens to Harry: Nagini almost kills him, and he escapes just in time, but his wand breaks. The Snatchers chase him through the forest. He and his friends practically surrender (and Hermione even tries to disguise Harry). Voldemort almost kills Harry in the Forbidden Forest (or actually does, depending on how you look at it).  Why are none of these considered to be “defeats”?


I'm creating a messaging system with PHP and MySQL but am having problems when certain characters are entered. Particularly the Pound sign (£).  The form where users write their message is POSTed to a PHP script with the following functions:  $message = htmlspecialchars($message, ENT_QUOTES); $message = utf8_encode($message);   Then $message is INSERTed into a Database where it is stored in a Text Column.  However, when inputing a Pound sign no data appears in the database at all on my live server, but on my localhost (using MAMP) Â£ appears in the database.  Anybody know whats going on? And is there a way to encode £ as &pound;, I feel like that might solve my issue.

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


If I get a schengen visa issued from greece embassy, and it was the first visa on my passport, can I enter germany without any problem as a first entry?

In case, if I get a multiple-entry Schengen visa in one of the embassies in Ukraine, Kyiv - should my first trip be to the country which issued the visa?  Any there any requirements of this sort? Does this condition vary depending on embassy which issued the visa?  What are the possible consequences on not visiting that country first? Does it somehow depend on country where the embassy is (i.e. non-Schengen and not EU members)?


I'm making a batch script that will automatically compile some projects for me and I want to know how (if possible) to program said script to first locate a specified file (i.e. .txt, .ini, .cpp, .py,  ect), then find a specific line of text and finally re-write said line to something that I specify. An example would be as follows:  find file >  locate line #x >  re-write as %TEXT%  save(?) >   I added a question to save because I don't know if such a function needs to be made or if the script can simply re-write the line upon execution.  Another thing I would like to experiment with is instead of seeking a specific line, would bt to seek a specific string to be re-written. This example would go (theoretically) as such:  find file >  locate string "Sample text" >  re-write as "New sample text" >   The goal of this would mainly be to compensate for scripts where a certain string will not always be on the same line or that will vary in location.  Currently I can write a simple text document with this script:  (   echo %SampleText% ) > %DOCUMENT%.txt   Any help would be greatly appreciated, I've done a lot with batch scripts but never anything like this.

I tried searching previous questions but none worked, or I couldn't adapt them to my needs.  I want to write a script that asks for:   folder criteria old string new string   And replace every file in the specified folder and subfolders (and force user to type one) with specific criteria (for example, it must be a ".cue" file), and:   If the file is read-only, disable it. Search for specified old string in the file content and replace it with new string , and save changes in same file. If the file was read-only, enable it again.   I have this code so far, but I don't know what to do in the do part:  @echo off   setLocal enableDELAYedexpansion  :START set "var2=" set /P var2="type folder "  if "%var2%"=="" goto ERROR  set /p old="old string ? " set /p new="new string ? " set /p files="what criteria ? " echo modifying files...  for /r "%var2%" %%v in (%%files) do (  ???  ) pause  goto START  :ERROR echo type something!! goto START


I had a 5.6 MySQL Server instance that was hosted on a computer that suffered a very bad lightning related power outage.  For whatever reason, MySQL 5.6 Server does not want to start/stay running now.  However I still have access to all the files, Program Files\MySQL Server 5.6\Data and ProgramData\MySQL\Data,etc. Could I hypothetically start a new instance of MySQL Server 5.6 on another computer and be able to bring over the entire database by copying the data files to the right place?  I just need to get it up and running again with the same database that was hosted on it before, I don't need to integrate it with a different database or anything, and I would like all the settings from the old system to be present in the new system.  It's InnoDB as well.

I have a mysql installed inside a windows virtual machine. The hard drive was crashed and the system is not able to restore all again. But I can have access to entire c: ROOT. So I went to  c:/ProgramData/Mysql/Mysql Server 5.5/data/myDatabaseName    There I can see different files like: .frm, .opt, .trg and .trn. In a regular way, I could run a mysqldump to backup and restore all database from command line, but the system is not able to be restored. So I had to copy all these files and past inside inside the same  directory inside same database in another physical instance.   The issue is some tables are not been recognized by this new instance. So I think copy and past is not enough to restore the database.   What am I missing?    Note: Database has innoDb and Myisam tables.


This is occurring on my Avanti Discovery 8, which is a hybrid bike with an in-hub 8 speed.  Problem is I seem to be applying so much torque it's pulling the rear wheel forward in the frame, loosening the chain. I've tightened the rear nuts as hard as I can - to the point where the nuts got a little damaged (hex edges started to 'flatten' inside the spanner) - but the wheel keeps moving forward as soon as I go up a hill and apply pressure. You can even see the scrape marks where the nut and washer has been digging into the frame and being pulled forward.  Is there any solution to stop this?

I have a  and I'm finding the rear wheel slips forward when riding (horizontal dropouts), causing the chain to loosen and thus a sub-optimal riding experience. It's not enough to be critical, just annoying.  I have the bolts extremely tight on the frame with the chain taut, but it still slips a little when riding. I'm wondering if there are any tricks out there to solve this problem, or if I'm doing something wrong?


I  don't know what is the example of cochain $ f$ from $A^*$ to $B^*$ such as the map $f^i$  from $A^i$ to$ B^i $ is bijective.

I am looking for a injective cochain map $\psi: C^*\rightarrow D^*$ such that the map $\Psi^i$ from $C^i$ to $D^i$ is injective, but the map $\psi^*$ from  $H^i(C^*)$ to $H^i(D^*)$ is not injective for any $i\geq0$.


I'm new to ES6 and Node.js  I would like to understand how callback functions work in a synchronous environment and asynchronous environment.   I tried to run the following in Node:   function func1() {      console.log('hello');  }  func1(function(){      console.log('world'); });    From my understanding of asynchronous callbacks, func1 should execute first, and when func1 finishes execution it calls back the function inside its argument list.   So in this case:   console.log('world')    should execute in second place, but i'm only getting as an output:hello.  Am i missing something? Can someone explain to me with clear examples how callbacks work? Is it the same in a synchronous environment?

I understand passing in a function to another function as a callback and having it execute, but I'm not understanding the best implementation to do that. I'm looking for a very basic example, like this:  var myCallBackExample = {     myFirstFunction : function( param1, param2, callback ) {         // Do something with param1 and param2.         if ( arguments.length == 3 ) {             // Execute callback function.             // What is the "best" way to do this?         }     },     mySecondFunction : function() {         myFirstFunction( false, true, function() {             // When this anonymous function is called, execute it.         });     } };   In myFirstFunction, if I do return new callback(), then it works and executes the anonymous function, but that doesn't seem like the correct approach to me.


I have a problem with the placement of conjunctions in a sentence. (Especially when I am writing an academic article.)  In many articles, writers place the conjunctions in the middle of sentence.   For exp.; It cannot, however, be inferred from the fact that.. or  However, it cannot be inferred from the fact that...  When should I place them in the beginning of sentence/in the middle of sentence?   I am confused about it.  It is also applicable for therefore, furthermore, otherwise etc.

Basically, what's the difference between this:     However, it didn't mean that I didn't have the potential to become a   rock star.   and this?     It didn't mean, however, that I didn't have the potential to become a   rock star.   Or does it mean exactly the same thing?


Below is a snippet of code from a class in a simple program I'm writing that plays a simple game of Blackjack. I don't understand why the hit method isn't executing whenever, upon execution of the program, I enter "hit". It goes to the else part of the statement every time regardless of what I enter. I even added a System.out.println statement to make sure that the strings matched. I feel like I must be making a very basic mistake but I just can't seem to figure it out.      System.out.println("Would you like to hit or stand?");     Scanner input = new Scanner(System.in);     String playerDecision = input.nextLine();     //System.out.println(playerDecision);      if(playerDecision == "hit") {         hit();     }     else { System.out.println("ERROR");      }  }  public void hit(){     player.makeHand(deck.draw());     System.out.println("You have the following  cards: ");     player.getHand();     System.out.println("Your hand total is ");     System.out.println(player.findHandTotal());   }

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


I have the following HTML code which allows me to remove a product when the button Remove is clicked.

         <form method="POST" class='form-product-ajax' action='{% url "shopping-cart-remove" %}' data-endpoint='{% url "shopping-cart-remove" %}'>             {% csrf_token %} {% for item in cart.items %}
                 {{ item.quantity}} x {{ item.product.name }} {{ item.subtotal }}                     <input type="hidden" name='id' value='{{ item.product.id }}'>                     <button class='remove-btn'>remove</button>                 	                 {% endfor %}
         </form>

         {{ cart.total }}

   I want to get this working using Jquery/Ajax and currently stuck on the following point. I can dynamically create a Remove button and I assign a class of 'remove-btn' to it but I still can't remove a product. How do I code the Jquery so that clicking on the dynamically generated button executes the action specified on the HTML form action?                   $.each(data.products, function(index, value) {                      console.log(value)                      console.log(data.count)                      var removeSpan = thisForm.find(".remove-btn")                      cartBody.append("
" + value.quantity + " x" + "	"+ value.name + "	" + "£" + value.price + "	" + "<button type='submit' class='remove-btn'>Remove</button>
")

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.


Here $n_i$ are integral numbers, and not all of them are zero.  It is natural to conjecture that similar statement holds for even more prime numbers. Namely,   $$ n_1 \sqrt{2} +n_2 \sqrt{3} + n_3 \sqrt{5} + n_4 \sqrt{7} + n_5 \sqrt{11} +n_6 \sqrt{13} $$ is never zero too.  I am asking because this is used in some numerical algorithm in physics

I need to find a way of proving that the square roots of a finite set    of different primes are linearly independent over the field of    rationals.    I've tried to solve the problem using elementary algebra  and also using the theory of field extensions, without success. To  prove linear independence of two primes is easy but then my problems  arise. I would be very thankful for an answer to this question.


I'm beginning to program in C# 2.0, so I have never used lambda expressions, but, why so much fuss about it? Are them just syntactic sugar around anonymous delegates, or is there something more which I can't see?

I have quickly read over the  documentation.  This kind of example has helped me to understand better, though:   delegate int del(int i); del myDelegate = x => x * x; int j = myDelegate(5); //j = 25   Still, I don't understand why it's such an innovation. It's just a method that dies when the "method variable" ends, right? Why should I use this instead of a real method?


When the installation is almost completed through wubi I get following error:  Also the log file is   I am using Win7 pro 64bit  Edit: corrected the link for log file

I've been trying to install 12.04 for a while now, I'm running on Windows 7 and I already made the partition (it's dynamic). I've tried booting from a disc and also the Windows installer. I haven't tried used any repair-boot programs or anything. Every time I tried to load from either, I get an error:  command=C:\windows\sysnative\bcdedit.exe /set {03f9077f-661f-11e1-845a-d08b36406c3d} device partition=U;  retval=1  stderr=An error has occured setting the element data. The request isn't supported  stdout=   Then after that, it makes a log file with information that I don't understand.  If it is simply due to the fact of it being a dynamic partition, someone please help. If it is more extensive, anyone with details on possible solutions or definite ones please express them.


I am working with a script which automatically enrolls macOS devices (installs software, sets up system preferences etc.) using Jamf. While the script is running, I want a real-time log to appear on the desktop for the administrator to check progress etc. Using the SE search I could only find logging to files after script was finished. Q: how do I add real-time logging to a text-file on the desktop into my bash script?

In a bash script, how can I redirect all standard outputs to a log file and tee the output on the screen using exec ?  log_file="$HOME/logs/install.txt-`date +'%Y-%m-%d_%H-%M-%S'`" [ -f "$log_file" ] || touch "$log_file" exec 1>> $log_file 2>&1   This code redirect all the log to the log file but not to the screen .


It is required to find limit using L'Hopital rule $$\lim_{x\to\infty}\frac{x+\sin x}{x-\sin x}$$ first I tried using L'Hopital rule right away, which gives us $$\lim_{x\to\infty}\frac{1+\cos x}{1-\cos x}$$ playing with this a bit I managed to get it to the form of $$\lim_{x\to\infty}\frac{1}{1-\cos x}$$ I don't know how to move further. Did I do something wrong in previous steps or am I on the right path?

Consider the Limit  $\frac{x+\sin x}{x-\sin x}$  as $x  \rightarrow \infty$. Clearly this limit exists and is equal to $1$. Also notice that the function is of the form  $\frac{\infty}{\infty}$ and thus, L'Hopitals rule can be applied here. But on applying L'Hopitals rule, I am getting  Limit  $\frac{1+\cos x}{1-\cos x}$ as $x  \rightarrow \infty$, which is obviously non-converging. Where did I go wrong?


How can I change the default applications from the command line (specifically from a script) in Ubuntu 18.04?   The link below describes setting the default applications from the GUI, and also by editing ~/.local/share/applications/mimeapps.list. However, it appears mimeapps.list has been moved or is no longer present in Ubuntu 18.04.    See, e.g.,

How do I set the default program that I use?  I have tried to open System Info → Default Program → change my program, but it won't work,  Any idea? Or should I use Terminal?   I want to replace the default movie player with VLC media player, because the current movie player is useless to me.


I would like to label data entries with multiple fields (that is easy, using the expression editor) in QGIS 2.18. But I fail to alter the styling of the labels, so that say the colour of the label from one data field (e.g., in the first line) was different to the second label value (second line). An older answer had the standard solution (duplicating the layer, ) I am wondering whether QGIS 2.18 or even the up and coming 3.0 will have a solution.

I would like to place the elevation-number of a point in a different front size and centred under its name:    Is that possible?  (That is my actual labeling: label || '\n' || elevation)


Input = 'RaamKuumabbbb' Output = b   b appeared four times in the string A='RaamKuumabbbb'

I would like to find out the number of occurrences of each of the alphabets in a word. Eg  input  aabbbddd    output  a@2 b@3 c@0 d@3   How can I perform this using shell script?


Why we should say North and South City instead of South and North City??

I think the term "back and forth" gets thrown around a lot without much thought.  From Dictionary.com:         [fawrth, fohrth]      adverb    1.  onward or outward in place or space; forward: to come forth; go forth.   Wouldn't the term be more meaningful if "forth" was used first since you have to have a starting place before you can go "back"?  Examples:        I've been going back and forth from Houston to New York.   I've been going forth and back from Houston to New York.      Which is more correct?


I have to read in a string from std::cin in my program.  The lines from cin are in the format of two numbers followed by a colon, another two numbers followed by a colon, and then a straight line. Then, the same string would be repeated. An example:  00:33:11|22:55:22  and then I would want two ints a and b to be: a = 3311 b = 225522  I'm trying to find the best way to extract the numbers from the first numbers before the straight line and store that into an int, and do the same for the second set of numbers.   I'm a little unfamiliar with c++, but I have thought about making a for loop, storing characters into a char array, and then using atoi on that array. However, I feel that this method is not the most elegant of approaches. Any suggestions to this problem?   thanks

What's the C++ way of parsing a string (given as char *) into an int? Robust and clear error handling is a plus (instead of ).


I would like to reinstall the driver of my wifi card. In order to find out the name of my driver, I have used:  sudo lshw -C network  and the output for the wifi card is  *-network DISABLED        description: Wireless interface        product: RTL8723BE PCIe Wireless Network Adapter        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:04:00.0        logical name: wlan0        version: 00        serial: 4c:bb:58:dc:ad:10        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless        configuration: broadcast=yes driver=rtl8723be driverversion=4.2.0-30-generic firmware=N/A latency=0 link=no multicast=yes wireless=IEEE 802.11bgn        resources: irq:19 ioport:1000(size=256) memory:90400000-90403fff   Therefore, I think the device name is RTL8723BE PCIe Wireless Network Adapter.  Can anybody guide me how to reinstall its driver again?

I have installed Ubuntu 15.04 on my laptop with RTL8723BE Wi-fi card. But it is always disconnecting from network. I have tried echo "options rtl8723be fwlps=N ips=N" | sudo tee /etc/modprobe.d/rtl8723be.conf but that didn't helped. What can I do to prevent the wifi from disconnecting? If I upgrade to kernel 4.X, will it help?  ~$ lspci -knn | grep Net -A2  09:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723]     Subsystem: Hewlett-Packard Company Device [103c:2231]     Kernel driver in use: rtl8723be   ~$ rfkill list 0: hci0: Bluetooth     Soft blocked: yes     Hard blocked: no 1: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no   ~$ ifconfig && iwconfig && route -n && ping -c 1 google.com eth0      Link encap:Ethernet  HWaddr 38:63:bb:cd:4a:7e             UP BROADCAST MULTICAST  MTU:1500  Metric:1           RX packets:3 errors:0 dropped:0 overruns:0 frame:0           TX packets:53 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:752 (752.0 B)  TX bytes:8445 (8.4 KB)  lo        Link encap:Local Loopback             inet addr:127.0.0.1  Mask:255.0.0.0           inet6 addr: ::1/128 Scope:Host           UP LOOPBACK RUNNING  MTU:65536  Metric:1           RX packets:3870 errors:0 dropped:0 overruns:0 frame:0           TX packets:3870 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:0            RX bytes:314613 (314.6 KB)  TX bytes:314613 (314.6 KB)  wlan0     Link encap:Ethernet  HWaddr c0:38:96:6d:c4:83             inet addr:192.168.1.205  Bcast:192.168.1.255  Mask:255.255.255.0           inet6 addr: fe80::c238:96ff:fe6d:c483/64 Scope:Link           UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1           RX packets:15240 errors:0 dropped:0 overruns:0 frame:0           TX packets:14627 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:14410285 (14.4 MB)  TX bytes:2192744 (2.1 MB)  eth0      no wireless extensions.  wlan0     IEEE 802.11bgn  ESSID:"DIR-615"             Mode:Managed  Frequency:2.437 GHz  Access Point: 00:90:4C:08:00:0D              Bit Rate=150 Mb/s   Tx-Power=20 dBm              Retry short limit:7   RTS thr=2347 B   Fragment thr:off           Power Management:off           Link Quality=70/70  Signal level=-22 dBm             Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0           Tx excessive retries:0  Invalid misc:186   Missed beacon:0  lo        no wireless extensions.  Kernel IP routing table Destination     Gateway         Genmask         Flags Metric Ref    Use Iface 0.0.0.0         192.168.1.1     0.0.0.0         UG    400    0        0 wlan0 169.254.0.0     0.0.0.0         255.255.0.0     U     1000   0        0 wlan0 192.168.1.0     0.0.0.0         255.255.255.0   U     0      0        0 wlan0 PING google.com.Dlink (172.26.136.19) 56(84) bytes of data. 64 bytes from 19.136.26.172.in-addr.arpa (172.26.136.19): icmp_seq=1 ttl=249 time=102 ms  --- google.com.Dlink ping statistics --- 1 packets transmitted, 1 received, 0% packet loss, time 0ms rtt min/avg/max/mdev = 102.547/102.547/102.547/0.000 ms


Why do I get different values when I do System.out.println(s[0] == "java"); and System.out.println(args[0] == "java");  public class StringDemo {     static void print(String[] s) {         System.out.println(s[0] == "java");     }      public static void main(String[] args)     {         // java is passed as command line argument         System.out.println(args[0] == "java");         String s[] = new String[3];         s[0] = "java";         print(s);     } }

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


How are Penrose diagrams derived?    (source: )

I've never seen a precise definition of a Penrose diagram for a $(1+1)d$ Lorentzian metric, merely the statements that it's conformally equivalent to the true metric and that null trajectories are oriented at 45 degrees.  These requirements do not uniquely specify the quantitative form of the diagram, so I wasn't clear whether general Penrose diagrams are merely qualitative depictions of the causal structure, or actually quantitatively precise.  I asked a GR postdoc, who told me that there is a unique and general algorithm for drawing a quantitatively precise Penrose diagram for a completely general $(1+1)d$ Lorentzian manifold (subject only to some weak smoothness requirements).  But I haven't encountered any textbooks on general relativity that actually do so.  Carroll only explains how to draw the Penrose diagrams for the Minkowski, Einstein static universe, and certain FRW metrics.  Misner, Thorne, and Wheeler only explain the Penrose diagrams of the Minkowski and Schwarzchild metrics, and neither Wald nor Thorne and Blandford have any systematic discussions of Penrose diagrams at all that I could find.  What is the general (quantitatively precise) algorithm for mapping an arbitrary $(1+1)d$ metric to a unique Penrose diagram?


How to pronounce # in a proper way?  Currently, I know it's used to pronounce "pound" in US English, "hash" in British English, "sharp" for C#--a programming language, and number sign to list items. Not sure if I'm right or not.   Also, I lives in non-English speaking country and many pronounce "hashtag" for this symbol, though I'm suspicious about this.   I'd be glad if you can list more examples about this.  -  Update: To be clear: The question is about the pronunciation, not how it came from.

I used to say "sharp sign" to refer to the # sign.   Today a friend told me that the correct term is number sign or hash sign or even just hash.  What is the difference between these options and what's the correct usage of the names for this sign?


Where do I ask general architecture and framework questions?  I want to build a content management system in .NET/C# that will work to a site similar to reddit and social media. I have a lot of specific questions while I'm, getting started that aren't actual programming questions. Where would I ask these?

There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.


The tab is overlapping in the activity page.  Actually, I earned a new badge and when I go to grab it. I found this glitch. The activity tabs are overlapped on congratulation badge area.

When I visit  I see this:     The "Congratulations! You've earned (badge)" section has dropped down completely beneath the tabs under it. The "You've earned a new privilege!" section has a gap at the bottom:     Shog9 says in comments how to reproduce this:     Gotta have earned a badge, not dismissed the notification, and be looking at your own profile.


In the spoken English I used to hear to people who ask "Isn't it?" while it is apparently supposed to be "Is it not?". What is the explanation for that? Is it a mistake or there's an explanation for it?

I'm aware that both it's not and it isn't are contractions of the same phrase, it is not.  Till today, I was convinced that choosing them depends on desired emphasis. This way, choosing it's not allows one to make an emphatic stress on not:     It's NOT my fault!   ...and other than that it's just a matter of style, not grammar.  Recently, I was watching :     M: An argument isn't just contradiction.   A: It can be.   M: No it can't. An argument is a connected series of statements intended to establish a proposition.   A: No it isn't.   M: Yes it is! It's not just contradiction.   A: Look, if I argue with you, I must take up a contrary position.   M: Yes, but that's not just saying 'No it isn't.'   A: Yes it is!   M: No it isn't!     I was surprised they have never used it's not during the whole sketch. This confused me a lot as it opposed my prior understanding: two people contradicting each other would rather use it's not. More than that, at 01:42 they have used you did NOT and then you DIDN'T, which must indicate that the latter is more pathetic than the former.  So, how to choose a proper contraction between "it's not" versus "it isn't"? Which one is more emphatic, and how come a contracted variant looks more pathetic than the expanded one?


This is the code of which i am not able to understand the flow of and also how the value of i persist even after the for loop ends.     var printNumTwo;  for (let i = 0; i < 5; i++) {   if (i === 2) {     console.log("now");          printNumTwo = function() {       console.log("inside");       return i;     };          console.log(i);   }   console.log(i); }  console.log(printNumTwo());     The output of the program is  0 1 now 2 2 3 4 inside 2

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


Is it good English to say "They have just left", when talking about a single person (perhaps someone you don't know the gender of)?  (I am a native English speaker, I'm looking for the view held by lexicographers).

Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end.


While I was cleaning the code for my project, I stumbled upon a method within the class like following (simplified)  public static class HelperClass {    public static void DoStuff(this DifferentClassName obj) }   After performing a quick search, aside from definition, the search result gave me the following:  varname.DoStuff();   Obviously, I thought that it didn't have anything to do with the method in the class, so I commented out the class method so see if it would cause any errors. To my surprise, the line from search result was redded-out.   The snippet of the search result line is as following:  var varname = new DifferentClassName() {     //stuff inside }  varname.DoStuff(); //<==what about parameter??   I initially thought that it was because a new instance of class created, but shouldn't it still be a parameter inside the line in question? Can anyone please explain why these methods are tied to each other, while the parameter inside the method call was omitted?

What are extension methods in .NET?    EDIT: I have posted a follow up question at


Consider the configuration pictured below: a cart with a u-shaped pipe on it, with a fan on one end blowing air into the pipe.  The fan rotates and makes wind towards the left. The wind will be curved in the bent part of the pipe and will come out with changed direction. The pipe is attached to the cart. There are factors to know the answer. The factors are like air pressure, force that fan pushes the air, force that wind pushes the pipe, momentum change of air and cart. Considering this, will this cart move or not, if move, which direction?

How it this possible? Even if the gif is fake, the Mythbusters did it and with a large sail it really moves forward. What is the explanation?


I upgraded today from Sierra to Mojave and now my share menu seems to be broken.  Previously I could share content directly to sites like Facebook and Twitter. For instance I could right-click on a photo and choose to share it to Twitter, Facebook and so on like so:    Now if I click on a photo and choose to share, I don’t get Twitter or Facebook as options anymore:    How can I enable these options?

Why is Facebook missing from the list of ways to share a page in Safari?  That option used to exist before the latest update.  When I'm directed to the extensions box Facebook is not there.


I am trying to deserialize a JSON response.  public class CLiveExMarketPriceHistory{ public String lwin11;   //11227502005 public String lcurrency;    //GBP public String priceFrom;    //2013-07-12 public cls_prices[] prices; public class cls_prices {     public String ldate;    //2013-07-12     public Decimal marketPrice; //880 } public static CLiveExMarketPriceHistory parse(String json){     return (CLiveExMarketPriceHistory) System.JSON.deserialize(json, CLiveExMarketPriceHistory.class); }   The JSON response is   {"lwin11":"11227502005","currency":"GBP","priceFrom":"2013-07-12","prices":[{"date":"2013-07-12","marketPrice":880.0},{"date":"2013-07-13","marketPrice":880.0},{"date":"2013-07-14","marketPrice":880.0},{"date":"2013-07-15","marketPrice":880.0},{"date":"2013-07-16","marketPrice":880.0},{"date":"2014-01-28","marketPrice":950.0}]}   The issue I am facing is that the JSON has attributes like date and currency which i am not able to use in my class as they are salesforce datatypes. I tried changing the class variables as lcurrency and ldate. But after deserialisation the values for these changed class variables are null as they don't match with the JSON response.   Any thoughts on how i can get values for the date and currency from JSON?

Is there any way to deserialize JSON into an object using JSON.deserialize if some of the property names in the JSON are reserved words in apex? I want to do something like this:  string jsonString = '{"currency" : "ABC"}'; public class JSONResult {     public string currency; } JSONResult res = (JSONResult) JSON.deserialize(jsonString, JSONResult.class); system.debug(res);   but of course I get an error that the identifier name is reserved.


This is not a duplicate of  because that is a support question asking if one can use moderator attention flags to indicate that questions should be closed. This is a feature request asking for the ability to use recommend closure flags (which feed questions into close review, and don't go to moderators) when one is out of close votes.  Currently, flagging for closure  for users with the . From what I can see, this is basically for users' convenience - if I think the question should be closed, there's hardly ever a reason not to cast a vote if I can.  I cannot see however why I cannot still use a flag to nominate the question for close review - since this won't include casting a vote - same as if I didn't have the privilege.  This goes for all close reasons, including .  If a vote creates a review item, why not consume both a flag and a vote? This will mitigate the cumulative effect referred to in  and is quite logical: flags are used to create review items while votes to vote on them.  It's also very strange that users with <3,000 reputation can add dozens, if not up to 100, questions to the close vote queue (provided their flagging history is excellent, and this number can increase quickly since a single close vote results in the flag being marked helpful), but when a user earns 3,000 rep, they're all of a sudden limited to adding only 24 questions to the queue.  Related discussions:    (considered flagging for moderator attention instead which is obviously a no-go)

I'm out of close votes again today. But I still have 100 flags. How do the mods feel about me flagging questions for closure, even though I would be able to VtC myself, if I weren't already out of votes?  Related: How do the mods feel about me flagging a question for closure (a super obvious code-dump, for example), even if I have CVs remaining, in an attempt to preserve my close votes for less clear cut close decisions?


I numbered an equation in an equation environment in the introduction of a paper alluding to a formula that I prove later in the paper. However when I actually state the theorem and restate the formula in the equation (before proving it) the numbering differs than what I had when I first mentioned it. How can I change the number of the equation that appears later in the paper so that it matches what I have earlier?   EDIT: So it seems I may have been to vague. In the paper I am writing, I work out a few specific examples in regards to what I am writing about and then end the introduction with a conjecture that reads to the effect \begin{equation} (formula for what we believe will be the answer in the general case) \label{awesome equation} \end{equation}. Then I discuss a few other things (lemmas and such) before proving that (\ref{awesome equation}) is true.   Once everything is in place, then I state the theorem for the general case: \begin{thm} For blah blah blah in the general case we have: \begin{equation} (same equation as we had before) \label{still want everything to be the same} \end{equation} \end{thm}.   When I compile, the numbering of these two equations is different, but they are the exact same and so I would like there numbers to be the same. How can I accomplish this?

Let's say I have written an equation in my paper and numbered it:  y = a + bx    (1)   Then, later in the paper, I want to remind the reader by showing the same equation with the same equation number.  Sure, I can repeat the equation, but LaTeX gives it a new equationn number:  y = a + bx     (2)   How do I force LaTeX to use the original equation numbers?


As per the title, comments which are truncated in the feed end abruptly*:    There should be an indication that there's actually more text in the comment; the main site uses an ellipsis for this purpose.  *They also can get truncated mid-word, which the main site is guilty of too, but bonus points if we can have a smarter truncation so you don't have the comment ending on the first letter of the next word

It seems that some featured questions also show their last line as cut, while others do not.  See image:        I assume there is a set number of line used, so shouldn't each featured question section have a fixed height so that it always fit in?


I want to center verticaly a paragraph in a div. For that, I tried to add an image front my text and I add the css "vertical-align:middle" on it.  The first line of my text is verticaly aligned : it's good, but the second line is under my div.  How can I solve my problem ?  Thks    div {     height:200px;     width:200px;     text-align:center;     background:cyan;     position:absolute; }  span {     height:inherit;     width:inherit;     position:absolute;     left:0;     background: yellow;     text-align:center  }  img {     height:100%;     vertical-align:middle;     width:3px;} }

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


Attempting to reproduce this picture from an old book (sorry for the resolution)    I used tikz's patterns library to generate the grid, which provides an honorable result.    However, with the default grid patterns, it doesn't seem to be possible to have a grid parallel to the borders of the path, as in this case obtained using a foreach-based grid.    While this solution works fine, it requires potential fine tuning.  So, is there a way to define grid patterns for 4 sided paths with parallel borders (of course, this could make no sense for some other shapes) where the grid is parallel to the borders  Here is the code used to generate the pictures  \documentclass[tikz,border=3.14mm]{standalone} \usetikzlibrary{calc,patterns.meta}  \begin{document}     \begin{tikzpicture}[]      \draw[pattern={Hatch[distance=5pt]}] (0,0) -- (1,0) to[out=120,in=-95] (1,4) -- (0,4) to[out=-95,in=120] (0,0);     \begin{scope}[xshift=3cm]         \coordinate (sw) at (0,0);         \coordinate (se) at (1,0);         \coordinate (nw) at (0,4);         \coordinate (ne) at (1,4);         \pgfmathsetmacro{\gridstep}{5}         \path[clip,preaction={draw=black}] (sw) -- (se) to[out=120,in=-95] (ne) -- (nw) to[out=-95,in=120] (sw);         \draw          foreach \xpos in {1,...,10}{($(sw)+(\xpos*\gridstep pt,0)$) to[out=120,in=-95] ($(nw)+(\xpos*\gridstep pt,0)$)}         foreach \ypos in {1,...,30}{($(-5,0)+(0,\ypos*\gridstep pt)$) -- ($(10,0)+(0,\ypos*\gridstep pt)$)}         ;     \end{scope}     \end{tikzpicture}  \end{document}

Hi I want to recreate the following picture but with a grid:   To something like this:   However, I'm finding the use of   \pgfsetcurvilinearbeziercurve{}   and even attempts with   \pgftransformnonlinear{}   very difficult to work with.  Here is some attempts (This one is with \pgftransformnonlinear{}.. you can see the normal grid that i want transformed on the bottom. I was trying to play around with some type of gaussian transformation, but it was not working (two commented lines above the current transformation):  \documentclass[tikz]{standalone} \usepgfmodule{nonlineartransformations} \makeatletter %def\mytransformation{\pgfmathparse{3/(sqrt(2*pi))*exp(-((0.01*(\pgf@x-6))^2)/(2^2))}\pgf@y=\pgfmathresult\pgf@x} %\def\mytransformation{\pgfmathparse{(1/10000)*1/(sqrt(2*pi))*exp(-((\pgf@x)^2)/(2^2))}\pgf@y=\pgfmathresult} \def\mytransformation{\pgfmathparse{\pgf@y*2/100}\pgf@x=\pgfmathresult\pgf@x} \makeatother \makeatother \makeatother \begin{document} \begin{tikzpicture} \begin{scope}%Inside the scope transformation is active \pgftransformnonlinear{\mytransformation} \draw (-6,0) grid [step=1] (6,4); \end{scope} \end{tikzpicture} \begin{tikzpicture} \draw (-6,0) grid [step=1] (6,4); \end{tikzpicture}  \end{document}    This is an attempt with \pgfsetcurvilinearbeziercurve{}:  \documentclass[landscape,svgnames]{article} \usepackage[a3paper]{geometry} \usepackage{tikz} \usetikzlibrary{fadings,shapes.arrows,shadows,arrows,positioning,shapes} \usepgflibrary{curvilinear} \usepgfmodule{nonlineartransformations} \usepackage{tikz} \usetikzlibrary{shapes.arrows} \usepgflibrary{curvilinear} \usepgfmodule{nonlineartransformations} \makeatother   \begin{document} \begin{tikzpicture} \pgfsetcurvilinearbeziercurve     {\pgfpointxy{14}{10}}{\pgfpointxy{10}{10}}     {\pgfpointxy{-4}{-10}}{\pgfpointxy{2}{2}}   \pgftransformnonlinear{\pgfgetlastxy\x\y%     \pgfpointcurvilinearbezierorthogonal{\y}{\x}}%     %\pic (a) {grid};     \draw [thin] (0,0) grid ++(16, 4);   \end{tikzpicture} \end{document}


is it possible / / how do i make an object give off "godrays" so that, for instance you can see it through slits in a wall?   I'm trying to make this, (an icosphere with a sphere inside, the inner sphere gives off a blue glow) into a sort of "disco ball" is the best i can describe it. but i'm fairly new to anything blender and have no clue how to achieve this.   I read somewhere that the only object that could give off volumetric light is a spot lamp, but the thread was like 3 years old.  Edit: thanks for the help, what you said to do worked, just can't have a material output and lamp at the same time apparently :D but that's fine it looks good now!

I'm trying to do a volumetric light on Cycles, and I've followed tutorials, but nothing has worked yet. How can I make a proper volumetric light in Blender, like the following one?    But to leave the light in the middle, like, almost a star, is this possible? I'm at the point to use an image plane besides the light which would be better... I need to use it moving the camera.  I'm actually trying to do this because I want to simulate the brightness of the Sun.  I tried the effect, but it still gave me an error:


Essentially I require:  if( [1,2].contains(2) ) {...}   I am surprised that I can't find a simple solution to this.  Is it possible to add a contains method to JavaScript's List type?   offers:  _.contains([1,2], 2);   However, _ is JQuery, and it is still rather clumsy.

What is the most concise and efficient way to find out if a JavaScript array contains a value? This is the only way I know to do it: function contains(a, obj) {     for (var i = 0; i < a.length; i++) {         if (a[i] === obj) {             return true;         }     }     return false; }  Is there a better and more concise way to accomplish this?


I have Schengen Visa which have been issued by Italy. I would like to know that if I can travel to Paris after Paris Attacks? It is appreciated if someone give me any information about this case. because I've heard that french government suspend schengen visas policy. I have bought flight tickets from Milan to Paris for next week and I do not know that if i can take that flight.

Can someone with a non-European nationality and a French 'carte de séjour' freely enter and travel (particularly by air) from France after the unfortunate events?  I have been checking the news, some of them said Schengen visas are banned but none say anything about carte de séjour holders. If I knew earlier I wouldn't have booked but it is too late now and I am worried I might be able to go out but not come in again. I am a student so it will be a real inconvenience if such thing happens.


In my Ubuntu 16.04 , 64 bit OS, I tried the following   * * * * * export DISPLAY=:0.0 && notify-send Hey "How are you"   And  * * * * * export DISPLAY=:0.0 && /usr/bin/notify-send Hey "How are you"   But, unfortunately, it is not working.  I found in other threads that the above command works.   How to run it on my machine?  The command notify-send Hey "How are you" works on the terminal.  Also the command * * * * * echo "trying to notify at $(date)" >> /home/user/Desktop/test.txt works fine from crontab file  The output of $ echo $DISPLAY is :0  also  $ who -u cosmicraga   tty7         2016-11-07 06:45 06:12        2524 (:0) cosmicraga   pts/1        2016-11-07 12:54   .          6333 (:0) cosmicraga   pts/17       2016-11-07 12:50 00:02        6333 (:0)

I made a script that should notify me when there's a new chapter of manga that I'm reading. I used the command notify-send to do this. The program works when I am trying to run it in terminal. The notification is showing. However, when I placed this in my crontab, the notification doesn't show. I'm pretty sure that the program is running since I made it to create a file for me. The file was created, but the notification didn't show.  Here's my script  #!/bin/bash    #One Piece Manga reminder     #I created a file named .newop that contains the latest chapter.     let new=$(cat ~/.newop)     wget --read-timeout=30 -t20 -O .opreminder.txt http://www.mangareader.net/103/one-piece.html  if (( $(cat .opreminder.txt | grep "One Piece $new" | wc -l) >=1 ))     then         (( new+=1 ))         echo $new         echo $new > ~/.newop         notify-send "A new chapter of One Piece was released."     else         notify-send "No new chapter for One Piece."         notify-send "The latest chapter is still $new."     fi         exit   And here's what I wrote in my crontab  0,15,30,45 12-23 * * 3   /home/jchester/bin/opreminder.sh


I can't hear any sounds on my newly installed Ubuntu 19.04, all I get from the menu "sounds" is a Dummy output. What should I do?

The soundcard I want to use is detected and works (it only recently switched to dummy output and didn't allow me to go back). HDMI is no longer listed under Audio and Video - KDE Control Module; everything under audio module is set to dummy output and its the only 'soundcard' on the list now. I can view my previous sound cards in alsamixer, but changing the settings from there does nothing. How can I get my real soundcards to work again? I have already tried the following answers without success:  EDIT: name@name-desktop:~$ lspci -vvv | grep -A8 Audio 00:01.1 Audio device: Advanced Micro Devices, Inc. [AMD/ATI] Kaveri HDMI/DP Audio Controller         Subsystem: ASRock Incorporation Kaveri HDMI/DP Audio Controller         Control: I/O+ Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx+         Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=fast >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-         Latency: 0, Cache Line Size: 64 bytes         Interrupt: pin B routed to IRQ 43         Region 0: Memory at ff764000 (64-bit, non-prefetchable) [size=16K]         Capabilities: <access denied>         Kernel driver in use: snd_hda_intel         Kernel modules: snd_hda_intel -- 00:14.2 Audio device: Advanced Micro Devices, Inc. [AMD] FCH Azalia Controller (rev 01)         Subsystem: ASRock Incorporation FCH Azalia Controller         Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx-         Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=slow >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-         Latency: 32, Cache Line Size: 64 bytes         Interrupt: pin A routed to IRQ 16         Region 0: Memory at ff760000 (64-bit, non-prefetchable) [size=16K]         Capabilities: <access denied>         Kernel driver in use: snd_hda_intel  Could this image possibly help?:  There is another soundcard but I'm unsure of what its for because it never outputs sound, but it does have a lot of settings: that sound card is labelled as "HD-Audio Generic".   So I went into Software & Updates under the Additional drivers tab and I see this:  It was on Do not use the device so I changed it and applied the settings but unfortunately the soundcard isn't back even after reboot.


I'm usually inside GNU Screen or tmux, and that doesn't give me great scrolling functionality. Is there an alternative to tail -f that allows me to quickly scroll up?  A tool that is like most is to less and more.   is related but far from specific. I'm really looking for something that lets me scroll.

I am seeing a delay of several seconds with the tail command. I found the cause for it has something to do with nfs services. I am using Arch linux and yet to find out how to disable all these services.   I have searched and had some indication that other tools will not be affected such as cat so what can give equivalent results to tail -f?


I know that in case of String class, you must normally use .equals() where comparing two strings, like:  String s1 = "123"; String s2 = "123"; String s3 = "1234"; s1.equals(s2); // true s1.equals(s3); // false   but, i've tried today this code:  s1 == s2; // true, but different references so had to return false s1 == s3; // false   so, is something changed in java? does now string use standard comparable implementation when using == ?

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