Probability of complete coupon set in $K$ boxes where a box has $N$ distinct coupons?

Say there is a contest to collect a full set of $M$ coupons.  Each box of product has $N$ distinct coupons of the $M$ possible coupons in it, selected uniformly without replacement from the $M$ possible coupons, the same $N$ in number for all boxes.  I'm interested in the probability that after opening $K$ boxes of product I have at least one complete set of the $M$ coupons.  My attempt has been to take the probability of a coupon not being in a box, use that to determine the probability of that coupon not being in any of the $K$ boxes, and then... I get flummoxed, and don't think this is the correct approach.  I searched the site for coupon collector problems, there are a couple that deal with similar situations (multiple in a box), but with the box having coupons selected with replacement, so duplication in a box is possible.  Right now I'm using a CAS to get probability of sums of hypergeometric samples having all bins covered to check my ideas, but that's utterly impractical for other than tiny cases.   Is this not as trivial as I think it is, or is there a direct way to calculate this?


I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers needed are total spin and total z-component.  But how do you add three 1/2-spins? It should yield 8 different eigenstates. Which quantum numbers do you need to characterise the 8 states?  It is not as easy as using C-G-coefficients and the usual quantum numbers as for the total momentum the doubly degenerate 1/2 state and quadruple degenerate 3/2 state can describe only 6 or the 8 states. You will need an additional quantum number for the degeneracy.  So how do you get the result?  (I actually tried out myself with a large 8x8 matrix. The total spin 1/2 is each doubly degenerate. For the additional quantum number I chose the cyclic permutation. Spin 1/2 states are neither symmetric nor antisymmetric. But what is the usual way to derive this?)  EDIT: For reference I'm adding my results for up to 4 spins from some time ago:   If you recall the basics of quantum mechanics with matrices it is actually a straightforward matrix diagonalization and requires no specialized knowledge. However, you still need to find an additional operator which breaks degeneracy. I chose the cyclic permutation, which seems to do the job. Please refer to the below answer, since I haven't checked all details.


Compiling skakdoc.tex, newcomer, new installation

I'm a newcomer to TeX trying to run skakdoc.tex from  .  I cannot get it to compile correctly using pdflatex.  It gives  ! undefined control sequence <recently read> \c@lor@to@ps   It seems to compile alright with xelatex, though no squares are highlighted. (Expecting highlighted squares based on the ps file in the link and the error)  My setup: proTeXt, Basic MikTeX installed. Also installed pstricks and other possible related packages. Using notepad++ to run pdflatex.


How to change the color of the text in a theorem in beamer?

Hello I'm writing a beamer presentation and I would like to change the colour of the text in the theorem block from one place and it will affect my whole presentation.  Is this possible?  My example:  \documentclass{beamer}   \usetheme{Madrid}   \usecolortheme[RGB={201,20,35}]{structure}   \setbeamercolor{background canvas}{bg=black}  \setbeamercolor{normal text}{fg=white}   \setbeamercolor{theorem text}{fg=black}    %\useoutertheme{shadow}  \useinnertheme{rounded}   \usepackage[utf8]{inputenc}  \usepackage{default}   \begin{document}   \begin{frame}{Primul Slide}   Bla bla bla    Bla bla bla   \begin{theorem}  This is a theorem it is very important!!  \end{theorem}   \end{frame}   \end{document}


What matters most : published papers or GPA? (for scholarship and future career)

I studied BSc chemistry and because I didn't like it, my BSc GPA is 2.46. Alongside with BSc duration, I studied mathematics at home as a self-learner. Since my BSc-GPA was too low, so I got admission to a very low ranking university in MSc-Maths. However, in my first year of MSc I got GPA 3.78 p. I am discouraged to apply for a PhD for a nice university because:  1- My current university's world ranking is >>4000 and I doubt that it would be a 'university' from the viewpoint of universities that I am trying to get my PhD admission.   2- I don't have BSc in math and very low BSc-GPA in completely different field.   My questions are:  1- Is it possible to get admission for PhD (with full scholarship) to a high-ranking universities in mathematics with such a conditions that I have?  2- If I have to study my PhD in the same university or a little better one, do my university reputation and and low GPA-in-BSc threat my future career after PhD (even if I show strong research ability and good recommendation letters)?  My target for PhD admission is countries: Canada (first priority), Europe and Australia. And I am not targeting USA.   Thank you for your helps. And, sorry for my terrible English.      Please feel free to edit the question to improve it.


The Google Maps in my OpenLayers plugin in QGIS 2.12 does not show anymore. The other maps do show, that is:   OSM Bing MapQuest Stamen Apple Maps   I tried in QGIS 2.8 and Google Maps does not show there either. This is the case in both my home and work computers, which are on different networks. Did the Google Maps go away?


Pros and Cons of a Decentralized Puppet Architecture

We have around 300 RHEL servers that are currently connecting to a Puppetmaster server.  However, we have noticed some performance bottlenecks and it is the point of failure in our system.  I am fairly new to puppet in general and I am considering creating a decentralized puppet architecture instead of having Puppet clients connect to the Puppetmaster server.  Aside from what I would suspect to happen such as performance gain and lack of signing and exchanging SSL certs for new machines, what are other pros and cons to setting up a decentralized architecture?


Our  has been frozen due to inactivity. I feel it is important it be revived, but after some searching on MSO it appears only moderators can unfreeze rooms. Can we reopen the room?


Problems with my new lens on my Nikkon D3000

I just added a new 70-300 Nikkor lens to my Nikkon D3000 camera. It will not auto focus or take a picture with the new lens. It seems to be installed properly and is communicating with my camera. It just does not allow me to take a picture. I can put the old 55mm lens on and it works fine. Help!


Using the rejection sampling with the method of inversion

I am hoping to write some rejection algorithm code in R to approximate a $\text{Gamma}(k,\lambda)$ distribution.  The problem is more for educational purposes than real-world implementation.  Given an $\text{Exponential}(\lambda)$ distribution with PDF:  $$f_{\lambda}(x) = \lambda\text{exp}(-\lambda x)$$  the CDF can be expressed as:  $$F_{\lambda}(x) = 1 - \text{exp}(-\lambda x)$$  where $x>0$ and $\lambda>0$.  And the inverse of the CDF can be expressed as:  $$F^{-1}(U) = -\text{log}(1-U)/\lambda$$  where $U$ is a random number generated such that: $U \sim \text{U}[0,1]$.  Assuming that:  $$X_{1}, X_{2}, \dots, X_{k} \stackrel{\text{ iid }}{ \sim }\text{Exponential}(\lambda)$$  and:  $$Y = X_{1} + X_{2} + \dots + X_{k}$$  then:  $$Y \sim \text{Gamma}(k, \lambda)$$  Now, the above approach for simulating a $\text{Gamma}(k,\lambda)$ from a sum of $k$  $\text{Exponential}(\lambda)$ random variables will, naturally, only work where $k \in {\bf N}$, but let's assume the objective is to simulate $\text{Gamma}(k,\lambda)$ where $k \notin {\bf N}$. It has been suggested to use an accept-reject approach with an envelope function being the $\text{Gamma}(\lfloor{k}\rfloor,\lambda-1)$ density, where $\lfloor{k}\rfloor$ is the function floor(k).  EDIT:  In the above example, it's clear that target distribution is given by:  $$f(x) = \frac{\lambda^{k}}{\Gamma(k)}x^{k-1}e^{-\lambda x}$$  But in order to solidify these concepts, could somebody provide the form of the simulating distribution ($h(x)$), the envelope function ($g(x) = M*h(x)$) and, of course, the optimal value of $M$?  Solidifying these ideas would really help me out.  Closely related     (one answer provides a clever R implementation).


How do I discover which application installed these programs?  /usr/lib/tracker/tracker-store, tracker-extract, tracker-miner-fs  It's eating up all my resources.  The CPU, one or two of them anyway,  is well over 100% usage, The memory is very loaded, system load is over 50%,  and disk read/write is very busy.    The man pages tell me it's a data miner set of programs for files on  my system only.  htop tells me I am the owner.  Yesterday I installed some programs, all from the software center, with one exception: Enthought Canopy, it's a Python IDE.  How do I discover which application installed these programs?


Today in physics we were looking at how the energy of a photon is the product of Planck's constant and the frequency of the photon, therefore the lower the frequency, the lower the energy of the photon.   The Cosmic Microwave Background, which I understand is a literal stretching of space over time, therefore increasing the wavelength of the radiation emitted  during the big bang, being electromagnetic waves (photons), which will of course decrease the frequency.   So, if over time an individual photon's frequency has decreased, so has its energy... Where has the excess energy gone?


Every time I try to upgrade from Ubuntu 13.04 to 13.10, it fails

How do I add space to my /boot directory? Every time I try to  upgrade I am told that I need 20MB more space (for a total of about 80MB), and I have already run commands to free up all unused kernels and headers. I have 60MB free, and am currently using 40MB. I am really stuck. Please help.


I'm running this query to fetch a post, if the member has access to it. Is it secure enough to just check if($row) ?  $sql = "SELECT f_title             FROM fields             INNER JOIN members                 ON m_group_id = f_group_id                 AND m_u_id = " . mysqli_real_escape_string($db_link, $_SESSION['u_id']) . "                 AND m_status > 0             WHERE f_id = " . mysqli_real_escape_string($db_link, $_POST['id']) . "             LIMIT 1"; $result = mysqli_query($db_link, $sql) or die(mysqli_error($db_link)); $row = mysqli_fetch_assoc($result); if($row) {     echo 'Permission granted!'; } else {     echo 'Permission NOT granted!'; }


I applied for a Georgian visa at the embassy and I was denied. I don't understand why it was denied, but I got my file from them saying this statement. I am from Nigeria and studying an MBA Program in Malaysia. I don't know if I should appeal or just forget about it.


How To Extend A WordPress Plugin Without Losing Your Changes

I want to extend the existing plugin. But i want when it update than it will not overwrite the change what i did.  SO please tell me the proper way to extend.  Thanks in Advance.


context: I am currently developing my first MVC application, I am following the examples in the book "Pro ASP.NET MVC Framework 2" by Steven Sanderson. I followed the first chapters and I have implemented a similar application to the "SportStore" full code  can be located at the following link   The application has two controllers  1 .- NavController designed to implement a user menu using a user control "Menu.ascx"  2 .- PostEntryController designed to list the post belonging to a particular menu option  The problem arises when running the application in debug mode NavController generated links do not work for some reason the PostEntryController is not instantiated.  When I examine the source code generated aspx file is shown as (PostEntry/Index.aspx)  <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">   <link href="/MarsWeb/Content/Site.css" rel="stylesheet" type="text/css" /> <link href="/MarsWeb/Content/jquery.treeview.css" rel="stylesheet" type="text/css" />         <title>Posts</title>

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    Can anyone help me?  This is Global.asax  routes.MapRoute("PostEntry", "PostEntry/{action}/{MenuItemId}/{page}", // Matches ~/MenuId             new { controller = "PostEntry", action = "Index", MenuItemId = (string)null },             new { page = @"\d+" }         );          routes.MapRoute("MenuItem", "PostEntry/{action}/{MenuItemId}", // Matches ~/MenuId             new { controller = "PostEntry", action = "Index", MenuItemId = (string)null, page = 1 }         );          routes.MapRoute(null, "", // Only matches the empty URL (i.e. ~/)              new { controller = "PostEntry", action = "Index", MenuItemId ="0", page = 1}         );   When I write the url in the address bar I can access the url


How do you define a class of constants in Java?

Suppose you need to define a class which all it does is hold constants.  public static final String SOME_CONST = "SOME_VALUE";   What is the preferred way of doing this?   Interface Abstract Class Final Class   Which one should I use and why?   Clarifications to some answers:  Enums - I'm not going to use enums, I am not enumerating anything, just collecting some constants which are not related to each other in any way.  Interface - I'm not going to set any class as one that implements the interface. Just want to use the interface to call constants like so: ISomeInterface.SOME_CONST.


How do we escape the cycle of bad college eating?

Mouseover text: And yet I never stop thinking, 'sure, these ingredients cost more than a restaurant meal, but think how many meals I'll get out of them! Especially since each one will have leftovers!'    Randall Munroe really hit the nail on the head with this comic and especially the mouseover text. There's this sort of cycle that I seem to follow when I try cooking, and I need to get my way out of it. It goes like this:   Decide I should cook something. Thumb through my recipe books, find one or two recipes I like. Write down the ingredients for the recipes in a list. Go to the grocery store, stumble around for a while and eventually find exactly those ingredients. Go back home; at some point in time soon after, cook each recipe. Whew, that was a lot of work! Spend the next week or two eating junk again, until I decide I should cook something. (repeat)   Very similar to the comic; sometimes I too let the leftovers go bad (usually not). And every time I rack up a huge bill at the supermarket and think to myself it's justified because of the leftovers or the amount of food. Not to mention, that's a lot of work for just a couple of meals, and a long list of ingredients.  I love cooking fresh meals but that's just so much overhead and so time consuming! So I always resort back to Easy Mac, Ramen, frozen dinners and frozen pizza. Yuck.  How can I escape this cycle and cut down on the overhead? How can I focus on more than 2 recipes at a time without buying giant lists of ingredients and spending tons of money? Is it really worth the trouble or should I just chock it up to being a college student and wonder about the years ahead of me where I'll have much more time to spend cooking one meal at a time?


Add an alert when answering a question that has at least a close vote as duplicate

I have one feature-request with the objective of having duplicate questions with no answers:   To (try to) avoid people answering duplicate questions, add an alert that says the question has a probable duplicate if it has a close vote as Exact duplicate, asking the answerer to go to the original and answer there.   What do you think? My objective is letting the duplicate question exist for search purposes, but the answers centralized in the root question.


How to extract a String from a TextView (AndroidStudio)?

My application retrieves data from the Firebase Database and displays it in a RecyclerView. The app already displays the title, the headline and the 3 labels just fine. Additionally it should check if a title is the String "Test". If it is it should display a certain image.  This is my Adapter    public class MyAdapter extends RecyclerView.Adapter<MyAdapter.MyViewHolder> {     Context context;    ArrayList<NewsCard> newsCards;      public  MyAdapter(Context c , ArrayList<NewsCard> n){        context = c;        newsCards = n;    }    @NonNull    @Override    public MyViewHolder onCreateViewHolder(@NonNull ViewGroup parent, int viewType) {        return new MyViewHolder(LayoutInflater.from(context).inflate(R.layout.row, parent, false));    }     @Override    public void onBindViewHolder(@NonNull MyViewHolder holder, int position) {        holder.title.setText(newsCards.get(position).getTitle());        holder.headline.setText(newsCards.get(position).getHeadline());        holder.label1.setText(newsCards.get(position).getLabel1());        holder.label2.setText(newsCards.get(position).getLabel2());        holder.lable3.setText(newsCards.get(position).getLabel3());     }      @Override    public int getItemCount() {         return newsCards.size();    }     class MyViewHolder extends RecyclerView.ViewHolder    {         TextView title, headline,label1,label2,lable3;        ImageView icon;           public MyViewHolder(@NonNull View itemView) {             super(itemView);             title = (TextView) itemView.findViewById(R.id.title);             headline = (TextView) itemView.findViewById(R.id.headline);            label1 = (TextView) itemView.findViewById(R.id.lable1);            label2 = (TextView) itemView.findViewById(R.id.lable2);            lable3 = (TextView) itemView.findViewById(R.id.lable3);            icon = (ImageView) itemView.findViewById(R.id.iconT);             String test = title.getText().toString();            if (test == "Test"){                icon.setImageResource(R.drawable.common_google_signin_btn_icon_dark_focused);             }         }    } }   As you can see I tried to extract the String from the TextView but somehow it isn't working even if there are titles with the value "Test".   @Override     public int getItemCount() {          return newsCards.size();     }      class MyViewHolder extends RecyclerView.ViewHolder     {          TextView title, headline,label1,label2,lable3;         ImageView icon;            public MyViewHolder(@NonNull View itemView) {              super(itemView);              title = (TextView) itemView.findViewById(R.id.title);              headline = (TextView) itemView.findViewById(R.id.headline);             label1 = (TextView) itemView.findViewById(R.id.lable1);             label2 = (TextView) itemView.findViewById(R.id.lable2);             lable3 = (TextView) itemView.findViewById(R.id.lable3);             icon = (ImageView) itemView.findViewById(R.id.iconT);              String test = title.getText().toString();             if (test == "Test"){                 icon.setImageResource(R.drawable.common_google_signin_btn_icon_dark_focused);              }          }     }   I have already checked if the problem is with the RecyclerView itself but I am confident that that's not the reason why it isn't working.


Pgfplots - ugly marks when using dotted or dashed line

Recently I spotted that applying the option dashed or dotted to a plot results in having ugly / distorted marks or marks with dots (when applying dotted) around them.   Here is a MWE:  \documentclass{minimal} \usepackage{tikz,pgfplots} \begin{document} % \begin{tikzpicture} \begin{axis} \addplot [mark=*,mark options={scale=2}] coordinates { (0,2) (1,2) }; \addplot [dashed,mark=*,mark options={scale=2}] coordinates { (0,1.5) (1,1.5) }; \addplot [dashed,mark=square*,mark options={scale=2}] coordinates { (0,1) (0.5,1.2) (1,1) }; \addplot [dotted,mark=*,mark options={scale=2}] coordinates { (0,0.5) (1,0.5) }; \addplot [dotted,mark=square*,mark options={scale=2}] coordinates { (0,0) (1,0) }; \addlegendentry{a} \addlegendentry{b} \addlegendentry{c} \addlegendentry{d} \addlegendentry{e} \end{axis} \end{tikzpicture} % \end{document}   Which will result in this:    Depending on the pdf-viewer this 'ugliness' can be seen with pretty low zooming level (the internal TeXworks viewer makes it especially worse).  Any discussion would be welcome! Greetings  PS: don't mind the third mark in the middle row - tried out something and forgot to undo the change :)      since I somehow screwed the sign up process up, this question I've asked is no longer my question, so I can't comment on it.. (maybe an admin could put it into my account? just for the sake of reputation, yeeey!)  Anyhow, about the 'duplicate' thing percusse wrote - yes, you're right that it leads to the same solution but I've searched stackexchange and google for this issue and couldn't find anything useful. So one should consider changing the title of the other question to something like "ugly/bad looking marks" (or add some keywords) since for finding that answer one has already to know what causes the problem, i.e. the marks not being solid. Since I had no clue where this problem comes from I used the above mentioned (key-)words :)  And thanks a lot y'all for answering it THAT quickly!


We have a directory that we cannot delete because...     Cannot remove item C:\myDir: The process cannot access the file 'C:\myDir\' because it is being used by another process.   Inside Resource Monitor > CPU > Associated Handles, a search for myDir shows that cmd.exe is using our directory.  Inside , running as administrator, our attempts to terminate cmd.exe are met with this:      Unable to terminate cmd.exe (PID 4656): An attempt was made to access an exiting process.    Beyond restarting the computer, how else can we kill this process and thereby delete or rename our directory?


Wireless connection issue on Ubuntu 20.04 LTS

Just done a fresh install of Ubuntu 20.04 LTS on a Lenovo Yoga 530.   I am having issues with my network, it's unrecognised.   *network UNCLAIMED    description: Network controller   product: RTL8821CE 802.11ac PCIe Wireless Network Adapter


Which of the following sentence sounds more professional

Can you help me in choosing a sentence that is most professional in technology   The lamp went out. The lamp died. The lamp was not working. The lamp was out of order. The lamp burned out.   Thank you for you help


Difference between vector spaces and fields

My doubt: What is the main difference between a field and a vector space?  In my mind, a field is simply a collection of eveything that follows a certain property. And it also comes with some built-in operations that you can perform on its elements. For example, the field $\mathbb{R}$ is a collection every number that follows the property of being real. It comes with two operations -  Addition Multiplication  and of course their inverses (Subtraction and Division). Thus, $\mathbb{R}$ is a field  But in my mind, vector spaces also have the exact same definition :- A collection of elements that has a few built-in operations. So $\mathbb{R}$ is a vector-space then   Which of the above is true? Is it a field or a vector space? Also, what is $\mathbb{C}$ then? I read somewhere that is a vector space over $\mathbb{R}$. I also read that it is a field. Which one is correct?


Why this error of the function of python?

I try to execute this source code for the multiplication but it doesn't work, it's shows error on te return , I want to know if it's possible why that happen, and how I can change my code so that it will work. thanks you  def multiples():       return [lambda x : i * x for i in range(4)]  print (m[2] for m in multiples())


What are your best practices to compile only a part of the document or presentation (or how do you prepare the big ones)?

I see that there a number of questions (, , , , ) on best practices, none of them answer the issue I am going to talk about.  We all need to prepare large documents (or slides) from time-to-time. And once you have reached a certain number of pages, you find that compiling the whole document takes a substantial time, which you need to do to check that the part you have written is error free, specially if it contains a number of images.   To circumvent the situation, I have used the following practices over years to keep compile time at minimum.   Divide the document in to many chapters: The chapters are put in separate files. Only the one I am working one is uncommented.  \documentclass{book}  \begin{document}  %\input {chapterone.tex} \input {chaptertwo.tex} %\input {chapterthree.tex} %\input {chapterfour.tex}  \end{document}    The above technique can also be used for \include.   Keep a preamble replica of the main file in a temporary file (build file): I use this technique when I am preparing a presentation with many slides, say a hundred. Prepare a main file, copy it to another build file. Delete everything between  \begin{document} and \end{document} in the build file. Prepare a slide (or a group of slides) in the build file. Cut and paste the contents between \begin{document} and \end{document} in the build file to relevant location in the main file only when satisfied with the output (image locations, overfull boxes etc.)     We can hear your inputs about the best practices you practice when a you are preparing a document or presentation from scratch.    Now, I have failed to find a good answer in the case when you have finished the whole document or presentation and now you need tweaking the small things, may be edit a text here, add an image there. What will be your best practice?  Perhaps, again keeping only one chapter uncommented will be usable here. But what about large presentations? May be adding a \end{document} just after the point-of-change will be beneficial, but only if you can put that before midpoint of the file.  Commenting a part of the file will also work, but that is error-prone, at least for me.


I have a working holiday visa from September 19th 2019 to March 22nd 2020 for Poland. I would like to stay here for 90 more days as a tourist. I traveled to Ukraine during Christmas 2019 for 1 week and then came back to Poland, and they gave me the stamps for entering the Schengen zone.  If I leave the Schengen zone again will I somehow keep my days as a tourist in Poland? I want to travel back to Ukraine before my visa expires.


How to prove that one of $2,3,6$ is a square modulo every prime $p$?  I am thinking in terms of quadratic reciprocity but not getting any clue.


The Higgs boson gives particles mass. And the graviton is the theoretical force-carrier of gravity. Gravity depends on mass. So if the Higgs Boson gives things mass, it therefore gives them gravity. Is the Higgs Boson the same thing as a Graviton? Or is there a difference? The only thing I know is that the Higgs Field is something very different from the Gravitational Field. Yet, I'm not satisfied with that fact. I want to know why the Higgs Boson is not the Graviton.


Why can't transverse waves travel through a liquid?

Can someone explain why a longitude wave can pass through the liquid, but a transverse wave can't. And can someone recommend some good animation of these processes.


Why space is being counted as newline in shell script?

I wrote the following script. I want to read a file and print as line by line but it considering space as new line. why is that?   #!/bin/bash for i in `cat data.txt` do echo $i done   Input: Saved in file name data.txt  B  FM_Server10_grp GPCBIOEMM10          Y          N               ONLINE   Output:   B FM_Server10_grp PCBIOEMM10 Y N ONLINE   Another question: How can I extract only number value like 10 from GPCBIOEMM10?


I am having a mighty difficult time interpreting the following results given to me based on a generalized linear model with a Poisson distribution:    Data: data represents the number of visitors to a store and whether their visits were necessary (they really needed something) while they were store members or not. Comparing stores 1 and 2.   Question 1: I am trying to interpret the meaning IRR here. What does IRR of 0.77 mean for Unnecessary category? Also, what does IRR of 1.12 mean (since it's above 1).   Question 2: so given all z-values are below 2, does it mean none of the results are statistically significant?


Conspiracy Theorist Hat counting procedure

The conspiracy theorist hat in Winter Bash is awarded on total number of flags or the flags done after the start of Winter Bash.?


A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond ?

A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond?   To me this seems like we can set up a fraction-like equation:  $$\frac{60 \ \text{seconds}}{1} = \frac{x \ \text{seconds}}{1/4}$$ then $x = 15$ seconds. But the answer is $58$ seconds which really makes no sense to me. Any suggestions are greatly appreciated.


Possible Duplicate:          How can I prove that a matrix is similar to its transpose?  My approach is: if $A$ is the matrix then $f$ is the associated application from $K^n\rightarrow K^n$. Define $g:K^n\rightarrow (K^n)^*$ by $g(e_i)=e_i^*$, and define $f^T$ to be the transpose application of $f$. I proved that $f^T=gfg^{-1}$. What I don't understand is, what is the matrix associated to $g$, so I can write $A^T=PAP^{-1}$.


"Add To favorites" does not works with appImages

I noticed that applications distributed as 'appimage' when run, they did not present the "add to favorites" in the command bar, when you right click on the icon. Why? Is there an alternative? Ubuntu 18.04.


If x and y are positive real numbers, show that $x^y+y^x≥1.$

If $x$ and $y$ are positive real numbers, show that $x^y + y^x ≥  1$.  I think it is trivial that the inequality holds when $x ≥ 1$ or $y ≥ 1$. I'm struggling to prove the inequality when $x < 1$ and $y < 1$.


Displaying build times in Visual Studio?

Our build server is taking too long to build one of our C++ projects. It uses Visual Studio 2008. Is there any way to get devenv.com to log the time taken to build each project in the solution, so that I know where to focus my efforts?  Improved hardware is not an option in this case.  I've tried setting the output verbosity (under Tools / Options / Projects and Solutions / Build and Run / MSBuild project build output verbosity). This doesn't seem to have any effect in the IDE.  When running MSBuild from the command line (and, for Visual Studio 2008, it needs to be MSBuild v3.5), it displays the total time elapsed at the end, but not in the IDE.  I really wanted a time-taken report for each project in the solution, so that I could figure out where the build process was taking its time.  Alternatively, since we actually use NAnt to drive the build process (we use Jetbrains TeamCity), is there a way to get NAnt to tell me the time taken for each step?


Reporting a bug about reCAPTCHA integration to blogs

Trying to comment on the InfoSec blog today (), I was redirected to a page stating "To use reCAPTCHA you must get an API key from " (in wp-comments-post.php).  I'm unsure whether this bug is specific to the blogs or to the InfoSec subsite or even the InfoSec blog.


I am trying to make an electric go-kart. I am new to the forum, so I may be missing some information but any help is greatly appreciated. After doing some math and discussing with friends I found the following with the given information. I have 4, 24V 14A motors, all connected to a read drive axle. I have 2 pairs of motors on each side of the drive axle. The motors have an 11 tooth sprocket that is chained to a 68 tooth sprocket that is connected to the drive axle. I currently have 2, 12V 7Amp 20 hour lead-acid batteries, which provide my 24V. Each pair of motors is connected in parallel to ensure they both get the 24V. However, the motors do not spin, even when there is no load (The wheels aren't contacting the ground). I believe that this may be because the motors do not have enough amps, only receiving 7 Amps of the 14 Amps from the batteries, because there are 2 motors in each pair. My main goal is to get the kart moving. I weigh about 130lbs, and the kart is likely around 30lbs. Would getting a battery/batteries with move amps (28A) allow the motors to run properly? Any advice is really appreciated. All the information I know Each motor is a DC motor that needs 14A and 24V The motor has a sprocket of 11 teeth The Watts of each motor is 250 The motors are rated to have an RPM of 2750 or around 45.83Hz The drive axle has a sprocket of 68 teeth. The 68 toothe sprocket is 5.5" The wheel diameter is 10" If my math is correct, given the ratio of the motors to drive shaft. Each motor produces 5.45Nm of torque, and after the sprockets, the torque is 33.69Nm. I don't know what impact the 4 motors would have on the torque, nor do I know what the torque is for each side. I really just want this kart to move. Would removing motors allow my vehicle to move? I think that my power supply does not provide enough amperage to my motors. Would having 1 or 2 motors be better in this situation?


Can MCPE and MC Java Edition play together

I've been seeing different articles. Granted some are years old. Is it possible when you are in the same internet connection to play together with mcpe and mc Java Edition and how? I was thinking mainly of using LAN


As you know, $x^2+x+41$ is composite when $x=41$ but, how can I claim that $41$ is the smallest positive integer satisfying condition ? Please explain why


Is the use of the word 'in' at the end of this sentence incorrect?

It is never too late to change the direction your life is headed in.


I am using the IRF540N. Its gate to source threshold voltage is 2v - 4V (VGS = VDS, ID = 250µA.)  Does "gate to source threshold" mean I need to apply voltage above 4V to the gate?  How is Id = 250uA related to the threshold voltage?  There is one more drain current in datasheet given a 33A.  In what situation do we need to use this?


In C++, I enjoyed having access to a 64 bit unsigned integer, via unsigned long long int, or via uint64_t. Now, in Java longs are 64 bits, I know. However, they are signed.  Is there an unsigned long (long) available as a Java primitive? How do I use it?


Anti Join based on multiple keys / columns (SQL)

The setting is simple, I wanted to retrieve all rows from table A that were not present in table B. Because a unique row can be identified using 4 columns, I needed to have a way to write the WHERE statement that it works correctly.   My solution is to concatenate the 4 columns and use that as "one" column/key to do the outer join:  select      *  from        table_A where       filter_condition = 0 and         (column1 || column2 || column3 || column4) not in (             select          A.column1 || A.column2 || A.column3 || A.column4             from            table_A A -- 1618727             inner join      table_B B             on              A.column1 = B.column1              and             A.column2 = B.column2              and             A.column3 = B.column3              and             A.column4 = B.column4             and             filter_condition = 0             )   My question is, is this a good way of doing this or am I doing something fundamentally wrong?   To be clear, the desired result is simply to get back only the rows of table_A that I "lose" due to the INNER JOIN with table_A and table_B.


Uniform continuity on $[a,b]$ and $ [b,c]$ $\implies$ uniform continuity on $[a,c]$.

Let $f:\mathbb R \to \mathbb R$. Prove that if $f$ is uniformly continuous on $[a,b]$ and $[b,c]$, then $f$ is uniformly continuous on $[a,c]$.  My attempt at a solution:  I've came up with a solution but I am having doubts if it is correct, so I would like to check that:  Let $\epsilon>0$, we know that there exist $\delta_1, \delta_2$ such that  if $x,y \in [a,b]  |x-y|<\delta_1 \implies |f(x)-f(y)|<\dfrac{\epsilon}{2}$   and if   $x,y \in [b,c], |x-y|<\delta_2 \implies |f(x)-f(y)|<\dfrac{\epsilon}{2}$  Let $\delta=\min\{2\delta_1,2\delta_2\}$, if $|x-y|=|x-b+b-y|\leq |x-b|+|b-y|<\delta \implies |f(x)-f(y)|\leq |f(x)-f(b)|+|f(b)-f(y)|\leq \dfrac{\epsilon}{2}+\dfrac{\epsilon}{2}=\epsilon$. This proves that $f$ is uniformly continuous.   I would appreciate if anyone could tell me if my proof is ok or if I've made any mistakes. (S.A. Understanding Analysis. pp 119 question 4.4.7)


This question has been always intrigued me. Why proof by Induction is admissible/acceptable ? We use this type of proof nearly every where and some times It's the easiest way of proof.


Why doesn't static friction point down the incline on a ball rolling down an incline?

In the figure above in which the sphere rolls without slipping down an incline, why is static friction directed upward? Static friction is meant to oppose impending motion so it should oppose the object's tendency to slide, and gravity would cause it to slide down in the absence of friction. Doesn't this mean that friction should point down since a downward force causes the sphere to move up?


Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional

Let $E$ be a Banach space and let $S$ and $T$ be closed subspaces, with dim$\space T<\infty$. Prove that $S+T$ is closed.  To prove that $S+T$ is closed I have to show that for any limit point $x$ of $S+T$, $x \in S+T$. So let $x$ be a limit point that subspace. Then, there is a sequence $\{x_n\}_{n \in \mathbb N} \subset S+T$ : $x_n \rightarrow x$. $x_n \in S+T \space \forall \space n \in \mathbb N$. This means that $x_n=s_n+t_n$ with $s_n \in S$ and $t_n \in T$ $\forall \space n \in \mathbb N$. Well, I couldn't go further than this. $\{s_n\}_{n \in \mathbb N}$ and $\{t_n\}_{n \in \mathbb N}$ are sequences in $S$ and $T$ respectively. I would like to prove that both of them converge to some points $s$ and $t$, for if this is the case, the hypothesis would assure $s \in S$ and $t \in T$. Then, I would have to prove that $x=lim x_n=lim s_n+t_n=lim s_n+limt_n=s+t$ and from all the previous steps I would conclude $x \in S+T$. $$$$Maybe I could start by proving that $\{t_n\}_{n \in \mathbb N}$ is convergent. But I don't see why this is true, I've tried to prove that $\{t_n\}_{n \in \mathbb N}$ is a Cauchy sequence (in a Banach space this would imply that the sequence converges) but I couldn't.


Ideal OP-AMP - why isn't output voltage zero?

Here is what I know about the Ideal Op-Amp.   The open loop voltage gain is infinite The output voltage is given by the following \$v_o = A(v_+ - v_-)\$ Only with a negative feedback loop is \$ v_+ = v_-\$   My query is with regards to the negative feedback loop as shown below:   My queries are as follows:   Clearly, \$v_o = A(v_+ - v_-)\$ should still apply and since \$ v_+ = v_-\$, shouldn't the output voltage \$ v_o = 0 \$ always? Since \$v_o = A(v_+ - v_-)\$ should still apply, is A still the open-loop voltage gain which for an ideal op-amp is infinity. Thus, would the output voltage always be infinity?


Find the Hamiltonian given $\dot p$ and $\dot q$

I have these equations:  $$\dot p=ap+bq,$$  $$\dot q=cp+dq,$$  and I have to find the conditions such as the equations are canonical. Then, I have to find the Hamiltonian $H$.   To answer to the first question, I have imposed that $$\frac{\partial}{\partial q}(\frac{\partial H}{\partial p})+\frac{\partial }{\partial p}(-\frac{\partial H}{\partial q})=0$$  $$\frac{\partial}{\partial q}(cp+dq)+\frac{\partial }{\partial p}(ap+bq)=0$$  $$\Rightarrow d+a=0.$$  And so I have that the canonical equations are in the form:   $$\dot p=ap+bq,$$ $$\dot q=cp-aq.$$  But how can I find the Hamiltonian? The result must be $H=-apq-\frac{1}{2}bq^2+\frac{1}{2}cp^2$. The general expression $H=\sum p_i \dot q_i-L$ doesn't help me.


What was the scene in King's Cross all about?

After being cursed by Voldemort for the second time, Harry spiritually goes to King's Cross and talks to Dumbledore. Is it like a coming back to life scene or is it caused by the dying Horcrux (or rather Voldemot's soul piece) inside him?


Can I combine my GTX 980Ti with another card like GTX 1660?

I have a GTX 980Ti and I'm looking for a lower end card to pair it with (like 1660 or 1070). Is this possible and what kind of AMD motherboard do you suggest for this?


Missing settings in GNOME control center installed in Ubuntu MATE

I installed GNOME Control Center following  to access Google Drive in Ubuntu MATE 16.04 LTS (MATE desktop environment 1.12.1)   The problem is GNOME Control Center is only showing language support, printers, firewall setup and backups... not online accounts or other settings.  This is what I get:  ~$ gnome-control-center gnome-online-accounts   ** (gnome-control-center:5744): WARNING **: Ignoring launcher landscape-client-settings (missing desktop file)  ** (gnome-control-center:5744): WARNING **: Invalid categories System;Settings; for panel software-properties-gtk.desktop  ** (gnome-control-center:5744): WARNING **: Ignoring launcher ubuntuone-installer (missing desktop file)  ** (gnome-control-center:5744): WARNING **: Could not find settings panel "gnome-online-accounts"   Any ideas?  Thanks!


I would like to recreate something like this    How would a header like that be achieved, would it be with the \maketitle command?  \documentclass{exam} \usepackage{graphicx}  %============================================================== \begin{document} %% %% \thispagestyle{empty} % \noindent \begin{minipage}[l]{0.1\textwidth}% \noindent \includegraphics[width=\textwidth]{logoUnimal.jpg} \end{minipage}% % \hfill \begin{minipage}[l]{0.9\textwidth}% \begin{center}  {\normalsize \bfseries PANITIA UJIAN AKHIR SEMESTER JURUSAN TEKNIK MESIN UNIMAL \par  \normalsize SEMESTER GANJIL 2015-2016\\[2pt]   \par}   \vspace{0.5cm}   \centering \begin{tabular}{lllllll} \textbf{Mata Kuliah}   & \textbf{:} & \textbf{Sitem Kendali}  &           & \textbf{Sifat}  & \textbf{:} & \textbf{Tutup Buku} \\ \textbf{Dosen Penguji} & \textbf{:} & \textbf{Fauzan, ST, MT} & \textbf{} & \textbf{Durasi} & \textbf{:} & \textbf{60 menit}   \end{tabular}   \end{center} \end{minipage}% \par  \end{document}


Add conditional stylesheet CSS for internet explorer only

The following methods can be used to add CSS for specific versions of IE:   Paste the code into html.tpl.php:  <!--[if lt IE 9]><link type="text/css" rel="stylesheet" src="/sites/all/themes/mytheme/less/ie.css"><![endif]--> Make use of the plugin  Use drupal_add_css() function   I have always used option #1 above, and adding yet another plugin for something so simple seemed crazy. BUT working with LESS and calling in statically means the file does not get processed by the LESS pre-processor, so the question:  How do you include a stylesheet using drupal_add_css() for specific versions of IE?


Why is spring force in a massless spring constant throughout the spring?  I had a similar question about tension is a massless string. This thread answered it for me.    Similarly, I want to prove that spring force in a massless spring is constant across throughout the spring. I thought it had to do with Newton's 2nd law too. If I consider a very small section of the spring, then forces at either ends of the spring should be equal in magnitude according to the 2nd law, because the section of the spring is massless. But what I don't understand is, a spring is coiled, unlike a string. So I am not sure if I can use the 2nd law here, because it's not a string. Is there another way I can prove this?


How to run program with Admin privs inside a batch/cmd file (no runas, no psexec allowed if password required)?

There's a program called MBRfix by Kåre Smith in Norway. It must be run with ADMIN privileges, and it requires multiple parameters... so, a user cannot simply right-click on it and choose "Run as administrator"! In order to use this program to help very inept users (like many old, first-time computer users with Windows 10, or 8 or 7), I need to create a batch/cmd file for them to simply click on and run; or at the most, right-click on and choose "Run as administrator". But if I do that with this batch file: @echo off echo. MBRFIX.EXE /drive 0 savembr Disk0MBR echo. echo. pause  It always comes back with: " 'MBRFIX.EXE' is not recognized as an internal or external command, operable program or batch file." (I've used both .bat and .cmd files, and in fact, it doesn't matter if you have any parameters/arguments at all, Win 10 simply will not run any program as ADMIN from inside a batch file like this!) I am working on coding my own program to open the Win UAC and ask user to run as ADMIN with built-in commands... But that will be very tedious compared to using Kåre's ready to go program. The reason neither "runas" nor "psexec" can be used is: They both require an ADMIN account with a login password... Well, my PC does not have one (on purpose) and neither do many other users who've had their PCs set up with good security (or, they were never set up as ADMIN). So, is this possible?  Or must we either school the inept user on how to open an ADMIN command prompt window (or PowerShell window) and use specific commands to navigate and parameters from a webpage or email in order to finally use mbrfix. Dan, TheStarman.


Prove that for any sequence $\{x_n\}$ of positive real numbers   $$\lim\text{sup}\sqrt[n]{x_n}\leq \lim\text{sup}\frac{x_{n+1}}{x_n}.$$   My attempt:  Let $A = \lim\text{sup}\frac{x_{n+1}}{x_n}$. Suppose $A<\infty$ and choose $\epsilon >0$, then $\exists$ an integer $N$ so that $N\le n \implies \frac{x_{n+1}}{x_n}\le \epsilon$. But I do not know how to proceed in finishing the proof?


I did a do_release_upgrade on my Ubuntu 16.04 (there were errors, in particular some were related to X11 or Xorg) and now I have this at boot:  Help ! EDIT I reinstalled grub from a live Ubuntu and now I have this at boot, still need help!  BOOT INFO is here  BOOT REPAIR report is here  lsb_release -a gives 18.04 Bionic . $ lspci -k | grep -A 2 -i "VGA" gives VGA compatible controller: Intel Corporation HD Graphics 5500 (rev 09) Subsystem: Lenovi HD Graphics 5500 kernel driver in use i915  then: sudo apt-add-repository ppa:ubuntu-x-swat/updates sudo apt-get update && sudo apt-get upgrade  EDIT 2 I have access to command line via tty1, I tried to reinstall xserver sudo apt-get install --reinstall xserver-xorg but it still boots on the black screen with [ OK ] lines as in the screeshot above. EDIT 3 I tried reinstalling GDM sudo apt purge gdm gdm3 sudo apt install gdm3 ubuntu-desktop sudo dpkg-reconfigure gdm3 #to choose GDM systemctl restart gdm  I also tried startx and I get: X.Org X Server 1.19.6 ... using system config directory "/usr/share/X11/xorg.conf.d" xf86EnableIOPorts: failed to set OIPL for I/O (Operation not permitted) xinit: connection to server lost waiting for X server to shut down. (II) server terminated sucessfully (0). Closing log file.


Method defined as testMethod do not support web service callouts, test skipped

I have been struggling with this error for a few days now. I get this error every time I try to run a test for a method that has an httpCallout. I followed the architecture from  , but to no avail. I thought it could be something I was messing up in my code, so I copied all three of the classes from the documentation, and I am still getting the error when I try to run the test. All of the classes are on Salesforce API 29. Has anyone run into this before?


Playing a remote movie on the remote computer

I have two computers (a desktop and a laptop) running linux connected to my local area network. I like to ssh from my laptop over to my desktop and run programs there, and sometimes listen to music on my desktop, which is connected to my stereo system. Lately, I've been wanting to play movies on the desktop and desktop screen, but cue them from my laptop across the room.   Unfortunately, I cannot play a movie in the current X session running on my Desktop on from my laptop. What is odd about this is that I can listen to the audio coming from the speakers that are hooked up to my desktop, by playing the audio files over ssh! This tells me that there must be a way to send the movie to that Xsession, from the ssh shell that I am connected to.  Does anyone have any ideas about this?


Setting bounties for an arbitrary amount of reputation

Why don't we have an option to propose a custom bounty like 23 or 12631 instead of the fixed 100, 200 or 500? Will this damage the ecosystem of Stack Exchange? Or do we have to wait for this? Edit: to clarify this is not about increasing but  about the freedom to choose what bounty you want to set for a specific question, which isn't discussed or answered in the suggested question.


Is it ok to start a sentence with the word "and"? Some of my students are challenging that using "and" at the beginning of a sentence is incorrect.


Animate winding a ribbon/rope/cable around a cylinder?

Actually, it's not so simple as the title suggests... :)  I might be asked to animate something like this -   Here's a still from that video:    It's the process of doing helical wrapping of carbon fiber a ribbon around a pressure vessel. And  you'll see a simpler activity of hoop wrapping, which I'd also need to animate.  I've got some basic experience with Blender (e.g. ), but I have no idea where to start with this kind of animation! At this point I haven't spoken to my client, so I don't know whether this will be requested; but I'd value input from Blenderheads here so that if I'm asked for it, I'll be able to respond with "sure!", or "can't be done", or "sure, but it'll cost ya!". :)  Pointers, anyone? Thanks!


This is currently a simple timer app with two activities, the first activity is the timer and the second will be used to set preferences that will be used later on.  I am not sure where the problem is in my code.  I've seen some solutions to similar errors but none of them are working. Keep in mind I am very new to coding (this is my first project) and I don't fully understand everything yet. Any help will be greatly appreciated, thanks!  Logcat error   Caused by: java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.Button.setOnClickListener(android.view.View$OnClickListener)' on a null object reference     at com.example.soswag49.showertimer.MainScreen.onCreate(MainScreen.java:29)     at android.app.Activity.performCreate(Activity.java:6251)     at android.app.Instrumentation.callActivityOnCreate(Instrumentation.java:1107)     at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2369)     at android.app.ActivityThread.handleLaunchActivity(ActivityThread.java:2476)      at android.app.ActivityThread.-wrap11(ActivityThread.java)      at android.app.ActivityThread$H.handleMessage(ActivityThread.java:1344)      at android.os.Handler.dispatchMessage(Handler.java:102)      at android.os.Looper.loop(Looper.java:148)      at android.app.ActivityThread.main(ActivityThread.java:5417)      at java.lang.reflect.Method.invoke(Native Method)      at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:726)      at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:616)  01-12 14:37:23.916 197-7464/? E/ACDB-LOADER: Error: ACDB AudProc vol returned = -19  01-12 14:37:29.535 7185-7496/? E/Finsky: [1619] com.google.android.finsky.ar.c.a(27): Unable to build selector: /storage/emulated/0/Download/marketenvs.csv: open failed: ENOENT (No such file or directory)   Main screen Java, not all of it but just the relevant stuff.  @Override     protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_main_screen);       setFlow.setOnClickListener(new View.OnClickListener() {         @Override         public void onClick(View v) {             moveToSetFlow();         }     });   *other code here   public void moveToSetFlow(){         Intent intent = new Intent(MainScreen.this, Flow.class);         startActivity(intent);     } }   Main screen XML, just the button used to switch activities    <Button         android:id="@+id/setFlow"         android:layout_width="175dp"         android:layout_height="wrap_content"         android:layout_marginTop="8dp"         android:layout_marginEnd="8dp"         android:backgroundTint="@android:color/holo_blue_dark"         android:text="@string/set_shower_flow"         android:textAlignment="center"         android:textStyle="bold"         app:layout_constraintEnd_toStartOf="@+id/historyText"         app:layout_constraintTop_toBottomOf="@+id/start" />


What are the differences between the following?

What are the differences between:   I did this for the first time in Tibet.  I did this in Tibet for the first time.    Which one should I use if I have done 'this' before, but it is my first time doing 'this' in Tibet? Which one should I use if I have never done 'this' before, and it is my very first time doing it and I am doing it in Tibet?


Which countries have significant magical populations?

While the Harry Potter books are primarily set in Great Britain, there are various references to wizards from other countries.  Which countries do we know to have significant magical populations?  Any level of canon is acceptable, but Rowling-canon is preferred.


How to show $e^{e^{e^{79}}}$ is not an integer

In , I needed to assume in my answer that $e^{e^{e^{79}}}$ is not an integer. Is there some standard result in number theory that applies to situations like this?   After several years, it appears this is an open problem. As a non-number theorist, I had assumed there would be known results that would answer the question. I was aware of the difficulty in proving various constants to be transcendental -- such as $e + \pi$, which is not known to be transcendental at present.   However, I was looking at a question that seems simpler, naively: whether a number is an integer, rather than whether it is transcendental.  It seems that what appeared to be possibly simpler is actually not, with current techniques.   The main motivation for asking about this particular number is that it is very large. It is certainly possible to find a pair of very large numbers, at least one of which is transcendental. But the current lack of knowledge about this particular number is even an integer shows just how much progress remains to be made, in my opinion.  Any answers that describe techniques that would suffice to solve the problem (perhaps with other, unproven assumptions) would be very welcome.


Show that $X_1X_2/\sqrt{X_1^2+X_2^2}$ is normally distributed. Where $X_1\sim N(0,\sigma_1^2),X_2\sim N(0,\sigma_2^2)$. Try to use jacobian transformation$$ U=X_1X_2/\sqrt{X_1^2+X_2^2}$$ $$V=X_1$$but I failed to solve the integration.   Edit, $X_1, X_2$ are independent.   Edit2, my effort so far  I use $ U=X_1X_2/\sqrt{X_1^2+X_2^2}$, $V=X_1$ to do the transformation and I solve for $X_1=V,X_2=\frac{UV}{\sqrt{V^2-U^2}}$.   Then I compute  $J=\begin{vmatrix} \frac{\partial X_1}{\partial U}&\frac{\partial X_1}{\partial V}\\ \frac{\partial X_2}{\partial U}&\frac{\partial X_2}{\partial V} \end{vmatrix}=\begin{vmatrix}0&1\\-\frac{V^3}{(V^2-U^2)^{\frac{3}{2}}}&\frac{\partial X_2}{\partial V}\\ \end{vmatrix}=\frac{V^3}{(V^2-U^2)^{\frac{3}{2}}}$  Substituting $|J$| and $U,V$ into $f_{X_1,X_2}(x_1,x_2)=f_{X_1}*f_{X_2}$ and integrate with variable $V$  $$f_U(u)=\int_{-\infty}^{+\infty}\frac{1}{2\pi\sigma_1\sigma_2}exp\left(-\frac{v^2}{2\sigma_1^2}-\frac{u^2v^2}{2\sigma_2^2(v^2-u^2)}\right)*|J|dv=\int_{-\infty}^{+\infty}\frac{1}{2\pi\sigma_1\sigma_2}exp\left(-\frac{v^2}{2\sigma_1^2}-\frac{u^2v^2}{2\sigma_2^2(v^2-u^2)}\right)\frac{v^3}{(v^2-u^2)^{\frac{3}{2}}}dv$$  It seems that the integration will get value $0$, since it's symmetric in $v$.  And, I apologize for not showing my effort when I ask a question. I know it's basic manner to do it but I was lazy.


How to interpret these acf and pacf plots

Following are acf and pacf plots of a monthly data series. The second plot is acf with ci.type='ma':    The persistence of high values in acf plot probably represent a long term positive trend. The question is if this represent seasonal variation?  I tried to see different sites on this topic but I am not sure if these plots show seasonality.           Edit: following is the graph for lag upto 60:     Following are plots of diff(my_series):     And upto lag 60:     Edit: This data is from:  Here the contributors did not consider acf and pacf plot of original or differenced series worth mentioning (so it must not be important). Only acf/pacf plots of residuals was referred to in a couple of places.


Finding Distance using multiple Lat Long points stored in SQLite table

I am new at SQLite (using n Android). my question is i have a table which has multiple latitude and longitude points, corresponding to the path traveled by a person. means first entry of longitude and latitude is when person started moving and last point shows where person stopped.  How can I get the values of lat long from the database and find the distance person traveled.  My table contains the following attributes-   numbering auto increment, by which i want to sort entries and calculate distance. Latitude Longitude Accuracy   Kindly help. Thanks in advance.


Finding a subgroup $H$ of $G$ where, for some $a \in G$, $aha^{-1} \in H$ but $a^{-1}ha \notin H$ (for all $h \in H$)

How can I prove the that the statements,  (i) $aha^{-1} \in H$ for each $h \in H$  (ii) $a^{-1}ha \in H$ for each $h \in H$  are not equivalent for any particular $a \in G$? I have been trying to come up with a counterexample but I have been unsuccessful. Evidently I would need to find an infinite group which satisfies this, since inductively,  $ \forall h \in H ( aha^{-1} \in H ) \implies \forall h \in H \; \forall n \in \mathbb{N}^+ (a^n h a^{-n} \in H)$  As was pointed out by user Robert Shore.


I've been trying to install .deb chrome file (google-chrome-stable_current_amd.64.deb). It is saved in my Downloads, so I tried this command   sudo apt-get install ~/Downloads/google-chrome-stable_current_amd.64.deb    After reading the package list it responds:  E: Unsupported file /home/stockton/Downloads/google-chrome-stable_current_amd.64.deb given on command line   I don't know why it says E: file, I though Linux drives and files are not named after letters like Windows drives, for example 'C:' but idk I can still be wrong. I did have Windows 10 before I booted Ubuntu.  Any help will be great.


$$\frac{1}{\Gamma(r)}\int_{\mu}^{\infty}t^{r-1}e^{-t}dt=\sum_{x=0}^{r-1}\frac{e^{-\mu}\mu^x}{x!}$$ What I have tried- $$\frac{1}{\Gamma(r)}\int_{\mu}^{\infty}t^{r-1}e^{-t}dt=e^{-\mu}\sum_{x=0}^{r-1}\frac{\mu^x}{x!}$$ $$\frac{1}{\Gamma(r)}\int_{\mu}^{\infty}t^{r-1}\sum_{n=0}^{\infty}\frac{(-1)^nt^n}{n!}dt=e^{-\mu}\sum_{x=0}^{r-1}\frac{\mu^x}{x!}$$ But I tried interchanging the sum and the integral and it didn't make sense anymore. Any ideas?


How to extract the last 2 characters of a variable with substring

I need to extract the last two characters of a phrase, but I don't know how as there isn't a minus 0.


Comment Inheritance for C# (actually any language)

Suppose I have this interface  public interface IFoo {     ///     /// Foo method     ///     void Foo();      ///     /// Bar method     ///     void Bar();      ///     /// Situation normal     ///     void Snafu(); }   And this class  public class Foo : IFoo {     public void Foo() { ... }     public void Bar() { ... }     public void Snafu() { ... } }   Is there a way, or is there a tool that can let me automatically put in the comments of each member in a base class or interface?  Because I hate re-writing the same comments for each derived sub-class!


I just realized that I am in a tricky situation right now.   I'm traveling with an Indonesian passport. I'm flying from New York to Christchurch, New Zealand in a couple of days, with a connection in Sydney, Australia. Upon scrutinizing my ticket recently, I realized that said connection is 11 hours long, with two different flights (Delta and Virgin) although it was bought on the same ticket, and that I am likely to have to collect my luggages in Sydney and recheck my luggages to Christchurch (which means that I have to pass Australian immigration).  There is no way I can get the Australian transit visa in time. Can anyone provide any helpful suggestions to solve this problem when I get to Sydney? Or share any similar past experience with the Australian border agents?  Thank you so very much.


I've just been accepted into Aeronautical engineering bachelors. Since I finished high school 2 years ago, I would like to refresh my memory on mathematics and physics. What would be some good books, that would have a wide summary of the subjects. possibly with some exercises.


Adding table notes over the length of the page

I have a very narrow table and having tables notes below that doesn't look good. I need to spread the notes over the width of the page. Im posting my current code herewith. Any help is much appreciated.  Chana      \begin{table}[]     \centering     \caption{Percentage (\%) ghdghgh}     \label{tab:si}%     \begin{threeparttable}     \begin{tabular}{|l|dd|}         \cmidrule{1-3}          \multicolumn{3}{c}{(1)} \\         \cmidrule{1-3}    \multicolumn{1}{r}{} & \multicolumn{1}{c}{Small} & \multicolumn{1}{c}{Big} \\         \midrule         \vspace{2mm}         L  & 0.1952 & 0.2310 \\          I & 0.6652 & 0.0807 \\         \midrule         IL   & 0.4699^{*} & -0.1503 \\          t-stat & (1.8508) & -(0.5168) \\         \midrule         \multicolumn{3}{c}{} \\         \cmidrule{1-3}          \multicolumn{3}{c}{(2)} \\         \cmidrule{1-3}         \multicolumn{1}{r}{} & \multicolumn{1}{c}{L}  & \multicolumn{1}{c}{I} \\                 \midrule         \vspace{2mm}         Small & 0.2433 &  0.5535  \\          Big   & 0.2428 &  0.1746 \\         \midrule         SMB   & 0.0005  &  0.3789^{**} \\         t-stat & (0.0029) &  (2.2308) \\         \bottomrule     \end{tabular}%     \begin{tablenotes}         \scriptsize          Note: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.         \end{tablenotes} \end{threeparttable} \end{table}%


Black spot on image while shooting with high aperture

I'm using 18-55 canon kit lens on Canon 700D body, the lens works fine with f/3.5 to f/14 , when increase that to f/16 , f/22 a black dot appears on the image, I have tried cleaning lens and body body. Please help.


How to remove all associated files and configuration settings of an app installed through 'force architecture' command

A few weeks ago I installed a 32 bit .deb file through the 'force architecture' command (on my 64bit notebook), however the procedure was unsuccessful and I used the apt-get purgecommand to uninstall the app. It seems there are some leftovers of the app I uninstalled which has now broken system update. Synaptic recommended a sudo apt-get install -fwhich I did in the terminal with this initial response:  Reading package lists... Done Building dependency tree        Reading state information... Done The following package was automatically installed and is no longer required:   libntfs10 Use 'apt-get autoremove' to remove them. The following packages will be REMOVED:   crossplatformui 0 upgraded, 0 newly installed, 1 to remove and 0 not upgraded. 1 not fully installed or removed. After this operation, 0 B of additional disk space will be used. Do you want to continue [Y/n]?   I chose 'Y' then got this response:  (Reading database ... 187616 files and directories currently installed.) Removing crossplatformui ... ztemtvcdromd: no process found dpkg: error processing crossplatformui (--remove):  subprocess installed post-removal script returned error exit status 1 Errors were encountered while processing:  crossplatformui E: Sub-process /usr/bin/dpkg returned an error code (1)   It seems the app I installed crossplatformuiis still on my system and has caused update manager to stop running with a partial upgrade warning. What do I do now?


Is the saying "It's not that big of a deal" incorrect? I would really like an answer to this as my children think it is correct.


How to implement the accent/diacritic insensitive search in Sqlite?

Is there a way to do an accent/diacritic insensitive search in sqlite?  Googling, I've found , but I sincerely don't know how to create my "collation function" in C#. I'm trying create the pt-br collation for Sqlite...


Rendering parts of an animation in different computers

Can I render the first half of an animation on my computer and the second half on my friends the make them video files and combine them?


Getting extent of composer map in PyQGIS?

In answering a labeling question:  I found myself wondering if there was a way to programmatically get the extent of a composer map so it could be displayed in labels and used in expressions.  So the question arose: Is there a way to find the extent of a specific map on a specific composer programmatically in a way that could be used in the expression engine? I've come up with a solution (I'm posting as an answer below) But I'd be happy if there was a more efficient solution. If you have a better one let me know.


Are pictures of this or that past dictator appropriate as avatar pictures?

I just came across a user who used this picture    of fascist dictator Mussolini for his avatar.  Is that legit, or well, not?


How do I create highlights on a screenshot?

In Chipaca's answer to  there's a screenshot with certain highlights. The highlights are the following:   A row of a GUI list is highlighted by the other parts of the screenshot being darker. A check mark is highlighted by being circled by what looks like a (orange) crayon.   How do I create both of these highlights on a screenshot? Is there an automated process?  The screenshot I'm referring to looks like this:


If point is nothing how come line which made up of set of points has length

As per wiki , In particular, the geometric points do not have any length, area, volume, or any other dimensional attribute.But when line is made up of set of points how come it has length? I am not too good in maths but this question was back in my mind since many days. Someone please clear things up. Thanks.


I want to put the caption of my figure in the center but I can't do that. when I put my figure in the center the caption is also in the center but when the caption is too long and there is a return to a newline it is not in the center


Could the machine from Contact be used again?

In the film Contact, Jodie Foster is searching for extraterrestrial life.  After a series of events where aliens give them a way to make a "spaceship."  She travels to a place where she sees an alien who looks like her father and returns, but she never traveled anywhere in space according to Earth, just time.  As such, no one believes that she really went to this place (despite the evidence that she recorded 18 hours of static in this time).  My question is, Could they have sent another person in the machine?  Maybe they mentioned this explicitly and I just missed it, but it seems bizarre that they just choose to not reuse this incredibly expensive alien device.


Undefined reference for member of Class I used as Static Member in another class

I have a C++ project with several classes each of them declared and defined in separated files. One by one, each file is compiled to .o file, however when I try to link them to get an executable, I get undefined reference error for one class member.  I'm adding a fake code that represent the situation to be more clear:  //filea.hpp #include "fileb.hpp" class A; typedef B<A> BA; class A { protected:    static BA *b; public:     static void setBA(){b = new BA();} };   /filea.cpp #include "filea.hpp" BA* A::b = nullptr; // will be initialized in main    //fileb.hpp #include <vector>  template <class A> class B {    std::vector<A*> v; public:    void some_stuff(A*); };   //fileb.cpp #include "fileb.hpp"  template <class A> void B<A>::some_stuff(A* a){     this->v.push_back(a);     }   //filec.hpp #include "filea.hpp"  class C: public A {   public:   void foo(); };    //filec.cpp #include "filec.hpp" void C::foo () {   this->b->some_stuff((A*) this);  }   // main.cpp #include "filec.hpp"  int main () {    A::setBA();    C c;    c.foo(); };   and my makefile is :  EXECUTABLE_NAME := execfile CFLAGS := -std=c++14 -g -pthread  CC := g++ DEPS := fileb.hpp   %.o: %.c %.h $(DEPS)     $(CC) -c -o $@ $< $(CFLAGS)  all: fileb.o filea.o filec.o     $(CC) fileb.o filea.o filec.o main.cpp -o $(EXECUTABLE_NAME) $(CFLAGS)    When I do make all, filea, fileb and filec compiled successfully. However, in linking and compiling to executable phase it gives   g++ fileb.o filea.o filec.o main.cpp -o he2ExecFile -std=c++14 -g -pthread filec.o: In function `C::foo()': filec.cpp:(.text+0x1e): undefined reference to `B<A>::some_stuff(A*)' collect2: error: ld returned 1 exit status Makefile:11: recipe for target 'all' failed make: *** [all] Error 1   While searching, found that not initializing static member causes similar error but it says undefined reference for A::b, which is completely different.  I looked same answer page, but didn't solve my problem.


A result on sequences: $x_n\to x$ implies $\frac{x_1+\dots+x_n}n\to x$ without using Stolz-Cesaro

If $x_n \to x$, how might we prove    $$\lim_{n \to \infty} \frac{\sum_{i=1}^{n} x_i}{n} = x$$  Of course, one has $\limsup x_n = \liminf x_n = x$, and thus, using the Stolz-Cesaro theorem:  $$\liminf x_n \le \liminf \frac{\sum_{i=1}^{n} x_i}{n} \le \limsup \frac{\sum_{i=1}^{n} x_i}{n} \le \limsup x_n$$ which shreds this easily. However, I'm wondering whether one could do this without the Stolz-Cesaro theorem.   Also, apparently the converse of this statement is not true. If we take $x_n = 0,\, n$ even, and $x_n =1,\, n$ odd, this suffices, correct? As the second expression tends to $1/2$, while the first has no limit?


Mechanically speaking, what makes an item more useful, a raw bonus or advantage?

I'm looking at D&D 5e to homebrew a specific item and I'm debating what would be better: advantage or raw bonus? The item is a coin that you toss before an ability check or an attack roll. If the coin lands heads, you gain a boon. If the coin lands on tails, you get a penalty. I was considering making the boon a raw bonus of +3 to the subsequent roll if it's a boon or -3 if it is a penalty. But it was brought to my attention that giving advantage/disadvantage could potentially be more balanced. So here's my question, what would be better mechanically for the player?


How to update/auto-update my private plugin?

I've made a private plugin for WordPress. How can I make this plugin update and/or even auto update?  Thanks a lot already!  EDIT:  got the update part done, the only thing i need to add is the Auto-Update/Background update option..  I've added a MUST-HAVE plugin with the following code:   add_filter( 'auto_update_plugin', '__return_true' );  but this isn't working.. How is that possible?


How to calculate the sine manually, without any rules, calculator or anything else?

I want to know how to calculate the value of sin, not using table values or calculator.  I found this $\frac{(e^{ix})^2-1}{2ie^{ix}}$, but how to deal with $i$ number, if it's $\sqrt{-1}$?


JAVA - How to generate Random number between 2 integers?

i'm trying to read in two integer numbers from the console and then display a random integer number generated between these two numbers.  this is my code.  import java.awt.*; import java.io.*; import java.util.*; import java.math.*;  public class Question8{      public static void main(String[] args)     {         int first, second;          Scanner myScanner = new Scanner(System.in);          System.out.println("Enter first integer: ");         int numOne;         numOne = myScanner.nextInt();         System.out.println("You have keyed in " + numOne);          System.out.println("Enter second integer: ");         int numTwo;         numTwo = myScanner.nextInt();         System.out.println("You have keyed in " + numTwo);          Random generator = new Random();         //int num = generator.nextInt(numOne) + numTwo;         System.out.println("Random number: " + numOne + generator.nextInt(numTwo - numOne));     } }   after i execute this program.. i do not get the random number that's between the 2 integers.  this is my output:  Enter first integer:  20 You have keyed in 20 Enter second integer:  30 You have keyed in 30 Random number: 204   hope you guys can help me in any way you can (:


How to find the sum of this infinite series.

How to find the sum of the following series ? Kindly guide me about the general term, then I can give a shot at summing it up.  $$1 - \frac{1}{4} + \frac{1}{6} -\frac{1}{9} +\frac{1}{11} - \frac{1}{14} + \cdots$$


Finding connected components of the graph

suppose that I have the following undirected graph   with the following adjacency matrix showing if there is an edge between the nodes: \begin{bmatrix}     0 & 1 & 0 & 0 & 0 \\     1 & 0 & 0 & 1 & 0\\     0 & 0 & 0 & 0 & 1\\     0 & 1 & 0 & 0 & 0\\     0 & 0 & 1 & 0 & 0 \end{bmatrix}  Now from the above matrix, I want to find the following matrix which shows if there is a path between each node:  \begin{bmatrix}     0 & 1 & 0 & 1 & 0 \\     1 & 0 & 0 & 1 & 0\\     0 & 0 & 0 & 0 & 1\\     1 & 1 & 0 & 0 & 0\\     0 & 0 & 1 & 0 & 0 \end{bmatrix}  We can find the second matrix by checking each node one by one (using transitivity rule)  My question is if there is an algorithm for finding the second matrix faster. The matrix I am working with is a huge matrix and I am looking for a good way to implement an algorithm to find the second matrix. In other words I am looking for connected components of the graph. I searched and found that one way is to use . For example, for the above example Laplacian matrix would be \begin{bmatrix}     1 & -1 & 0 & 0 & 0 \\     -1 & 2 & 0 & -1 & 0\\     0 & 0 & 1 & 0 & -1\\     0 & -1 & 0 & 1 & 0\\     0 & 0 & -1 & 0 & 1 \end{bmatrix}  Now using this matrix how can I find the connected components? Is there a fastest way to find the connected components?


Basically my code supposes to calculator the weight by using the height. The user has to choose between if he/she is male or female. After that, the if-else statement supposes to do the calculation. The problem is when the user types the choice between Male or Female. The code neglects the choice and goes to the else statement right away to tell that your choice is wrong.   import java.util.Scanner;  public class cals {  public static void main(String[] args) {      Scanner Scan = new Scanner(System.in);     System.out.println("\nAre you Male or Female: ");     String Choice = Scan.nextLine();     if (Choice == "Male") {         System.out.println("What is your hight in CMeters: ");         int Height = Scan.nextInt();          if (Height > 160) {             int Your_weight = (Height - 100) * 90 / 100;             System.out.println("Your_weight is: " + Your_weight);         }          else {             int Your_weight = (Height - 100);             System.out.println("Your_weight is: " + Your_weight);         }     }      else if (Choice == "Female") {          System.out.println("What is your hight in CMeters: ");         int Height = Scan.nextInt();          if (Height > 160) {             int Your_weight = (Height - 100) * 90 / 100;             System.out.println("Your_weight is: " + Your_weight);         }          else {             int Your_weight = (Height - 100);             System.out.println("Your_weight is: " + Your_weight);          }      }      else {         System.out.println("you Enter a worng choice");     }  }   }


Is there a rigorous definition of a line?

In the sources I can find, line is considered a primitive concept (a one without definition). There is something, however, in such an intuitive definition that doesn't sit well with me.  Were there any attempts to rigorously define line?  And if there weren't, why? What makes line a concept which shouldn't be defined rigorously?


Can't install any OS on laptop after deleting all partitions to switch to Windows 10

I was previously using Windows 8 but switched to Ubuntu. Since then I wanted to switch back to Windows 10 so I created a bootable usb and when I went to do the windows configuration I deleted all of the partitions and then my laptop shut off because the battery was dead.   Now when I turn on my laptop it says   error:no such partition entering rescue mode... grub rescue>   and I cannot boot off of the USB. Does anybody know how to fix this?


With respect to all the senior members,  I am a newbie & I make 50 backlinks for my site every day, (using forum, social bookmarking and Blog commenting) recently my experienced cousin said that Google doesn't value these type of link anymore like they once used to. They love backlinks which are valuable and natural & suggested me to build natural link via Guest Blogging and Broken link building methods, because instead of making those forum & other links(50), I should make 5 natural links a day which will help me rank better.  My question is, is it true? are natural links really powerful than the other ones?


I have the following code:  \documentclass{article} \usepackage{graphicx} \begin{document} Introduction  \begin{figure}[h!]   \includegraphics[width = 0.5\textwidth]{example-image-a}   \label{fig:a}   \caption{Image a} \end{figure}  \begin{figure}[h!]   \includegraphics[width = 0.5\textwidth]{example-image-b}   \label{fig:b}    \caption{Image b} \end{figure}  Comparison of Fig. \ref{fig:a} to Fig. \ref{fig:b}.  \end{document}   After running pdflatex on the document twice, the figure labels do not show up:    What is wrong?


Upvote / downvote bandwagon - and how to stop it

The issue isn't about downvotes themselves, it's the abuse done by them.  On my time on Stack Overflow I have often noticed the phenomena of dissatisfied people downvoting questions without any given reason (in my/other posters) opinion and that makes other site users not even go into the question thread seeing all the down-votes or going in the thread to also down-vote to help the apparent "cause" of the other users wanting to close the question down for whatever reason.  I think the downvoting system rather insults the question asker rather then helping him improve his question. Downvoting a question needs to have repercussions under abuse just like upvoting should have.  More often than not people that have a low post count and ask their first question aren't going to ask it in a way some more veteran users of the site expect it to be asked and therefor they feel like the community much prefers abusing his post instead of explaining to him what he did wrong and giving him a way to fix it.  Most people do not even bother to suggest edits leaving the beginner Stack Overflow experience to feel extremely "toxic" at first to people. The same people that don't understand the in and outs of it.  So whats the solution?  Making sure people that downvote don't abuse it by showing them if that is one of the first posts the question asker asked.  Making sure to people downvoting / upvoting in an abusive manner carries consequences and their vote practically looses its value because its never used in the right context.  Downvotes to people with low post counts should need to come with a short explanation or choice that is shown to the question asker to explain to him what he might have done wrong to receive that down-vote.  The voting system is highly problematic in my opinion and needs a serious rework.


Firing Community Managers: Stack Exchange is not interested in cooperating with the community, is it?

Less than a month ago, there was some settling of the . It's obvious that there was not a lot of approval from the community on the course of action chosen by SE, or .  Today, we are seeing a new wave of SE actions targeted on work with the community: firing / letting go / agreeing to separate (the actual term is unknown and can remain unknown forever) two very knowledgeable and very trusted community managers:  and :    about suddenly being in need of new job  indicating he is no longer with the company   and  – meta posts from the community   The following change in SE staff happened shortly after this event:    left his position as a Community Manager (but explicitly said that "I made this decision in December and it's not correlated with the recent CM team changes". Jon wants to apply for the moderator diamond back and continue participating). His  indicates that his decision to leave was connected to the incident with firing Monica.   The following moderators resigned shortly after this event:   resigned:  resigned:  (explicitly stating that firing CMs was the final straw) resigned:  (explicitly stating that firing CMs was the final straw) resigned:  (explicitly stating that firing CMs and the lack of resolution with Monica were the final straws) resigned and deleting accounts:  resigned:  resigned:  and  (irreconcilable view on the role of the community and SE policies) resigned:  resigned:  (Shog and Robert were the last nail and final straw) resigned:  resigned:  (explicitly stating that firing CMs and the  were the final straws) resigned:  resigned:  resigned:  (explicitly connecting the resignation with firing CMs and the preceding  events) resigned:  (explicitly connecting the resignation with firing CMs and the preceding events) resigned:  (explicitly connecting the resignation with firing CMs and the preceding events)   The following moderators suspended their activity shortly after this event:   suspended activity:  and  (explicitly links the suspension with firing CMs and preceding sad events, has since )   Timeline:  2020-01-13: Firing (for the lack of better term) of community managers Shog9 and Robert Cartaino. Shorty   2020-01-15: George Stocker starts a  to thank Shog9 for cultivating Stack Overflow  2020-01-16: Official policy on   . Rendered inactive on 2020-02-10.  2020-02-10:  on handling  posts. While the previously introduced 24-hour policy (see item above) is rendered inactive, the new policy covers a much wider range of cases when and why the post can be un or deemed unable to be   2020-02-20: Teresa Dietrich, the new Head of Product and Community, has posted a  (and response, of sorts) to the community.  At the bare minimum, as a result:    does not have any active moderators (Shog9 and Robert were moderating it)  does not have any active moderators (Robert was moderating it)  does not have any active moderators (one mod last seen Oct 2019)  has only one active moderator left  has only one active moderator left  has only one active moderator left  has only one moderator left  has only one moderator left     I wonder:   if there is any plan on the SE's side to actually be involved in the building of the community who is now responsible for community building and interaction of community/moderators with developers and upper management if the remaining CM team will be re-staffed since it is already heavily understaffed in my opinion if there is an intent from the company to at least thank the CMs that served Stack Exchange many-many years, even if it is a dry lawyer-written "thank you"   I am devastated. Both as an SE user and as an SE moderator.


Calculating limit of $\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert$

I want to show that for each $n \in \mathbb N$ it holds that $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = 2n \frac{n^n}{n!}.$$ But I have absolutely no idea how to do that. I tried to split the series like this:  $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = \sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) + \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n)$$ Now I want to show that $\sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) = \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n) = n \frac{n^n}{n!}$ holds. But I got no idea how to achieve that. I tried to use induction but things became pretty messy and I don't think it will work like that. On the other hand I got the idea that it might have to do with $\exp$ or binomial coefficients but I don't see where I can facilitate that. I would appreciate some hints :)


Theoretically if I were able to build some sort of device that let me sit 1 foot away from the surface of the Sun (or any star for that matter) without being vaporized, would a star produce any sort of audible sound at that distance?   From my understanding, sound waves need a medium to propagate through (air, water, etc).   Does this mean that all stars are completely silent (in the audible spectrum of frequencies at least) as they fuse  hydrogen into helium?   I know stars emit radio, xray, infrared, ultraviolet electromagnetic waves, but how about audible (20 Hz to 20Khz) frequencies?   For some reason it seems like this process would produce some sort of sound.


I'm desperately looking for a way to enable TUN/TAP on a VPS in order to use an OpenVPN client. The VPS is based on Parallels Virtuozzo. I've been reading a ton of tutorials and forum topics, and here is the output I'm getting with the commands I often see :  lsmod | grep tun (no output)  modprobe tun FATAL: Module tun not found.    When I try to run the client, here is what I get at some point :  ERROR: Cannot open TUN/TAP dev /dev/net/tun: Operation not permitted (errno=1)   The server is running CentOS 6.7. Let me know if there is anything other piece of information I need to provide.  UPDATE : I found out that only the host should be able to help me by enabling TUN/TAP on the container. However, they don't "offer this feature" for some reason. I found a similar case here :  Do you have any suggestions?  Thanks


Running sudo <command> failed with:  sudo: unable to change to root gid


How to make array.push() a string multiplied by i

I have been looking for a while for this answer and most results bring up people NOT wanting to push more than once, and its hard to find a straight forward solution / alternative.   I have been tasked with a exercise to output a tower in an array. It increments based on its floor size. For example.  [   '  *  ',    ' *** ',    '*****' ]   I am still leaning the ropes of Javascript and I am intrigued to learn, here is what I have come up with:  function towerBuilder(floors) {   let arr = [];   let space = " ";   let tower = "*"      for (i = 0; i < floors; i++) {     arr.push(space, tower * i, space);   }     console.log(arr) }  towerBuilder(3);   console.log shows (Array [ 0, NaN, 0, 0, NaN, 0, 0, NaN, 0 ]) - I guess multiplying a string is a bad idea.   I could probably create multiple for loops and have each push in its own loop, but that would look really messy.  Is there a way to push spaces and *'s multiplied by the for loop?   Thanks


is a one-by-one-matrix just a number (scalar)?

I was wondering. Clearly, we cannot multiply a (1x1)-matrix with a (4x3)-matrix; However, we can multiply a scalar with a matrix. This suggests a difference.  On the other hand, I was, for example, in an econometrics lecture today, where we had for a (Tx1)-vector $\underline{û}=\left( \begin{array}{c} û_1\\ \vdots\\ û_T\end{array}\right)$:     $S_{ûû}:= \sum_{i=1}^T û_i^2$ shall be minimized. We see see that   $S_{ûû}=\underline{û}^T\underline{û}$.   Well, formally, shouldn't it be $(S_{ûû})=\underline{û}^T\underline{û}$ or $S_{ûû}=\det(\underline{û}^T\underline{û})$, to ensure that we stay in the space of matrices and not suddenly go to the space of scalars? So here, the professor (physicist) not only treats $\underline{û}^T\underline{û}$ like a scalar, but also calls it a scalar. Is this formally legit or a wrong simplification (though it does not seem to have any impact, and surely makes life easier)?


How to center div with two inline buttons in it (css)?

I'm currently designing a webpage using Bootstrap and I have two  buttons laid inline with each other inside of the

  Here's the HTML code:

Jason's Summer Vacation

There doesn't seem to be a description here!

             Copy Link             Create Drop

   And here's the CSS of the div wrapping the buttons and the buttons themselves:  .hub-btns {     display: inline-block;     margin: auto; }  .hub-btns .copy-link {     border-bottom-color: #EBEBEB; }  .hub-btns .create-drop:hover {     background-color: #03a9f4; }  .hub-btns .create-drop:focus {     background-color: #03a9f4;     border-bottom-color: #0398db; }  .hub-btns a {     margin: 0 10px; }   I'm still not great with CSS so I'm probably missing something obvious here. But, I simply want to take the div that is wrapping the two buttons and center that div within the jumbotron div.  Any help is greatly appreciated!


We can express a square number as the repeated addition of that number in this manner:  $1^2 = 1$  $2^2 = 2 + 2$  $3^2 = 3 + 3 + 3$  Generalising this, we get:  $x^2 = x + x + x...$ $x$ $times$  If we differentiate with respect to $x$ on both sides, we get:  $2x = 1 + 1 + 1...$ $x$ $times$  $2x = x$  $2 = 1$  This is obviously wrong. What's the mistake in my proof?


I'm unable to run sudo apt-get update successfully for the past few days now.  When running sudo apt-get update from terminal, it shows error as,  W: Failed to fetch http://in.archive.ubuntu.com/ubuntu/dists/wily/InRelease  Unable to find expected entry 'main/binary-i386cddcd/Packages' in Release file (Wrong sources.list entry or malformed file)  W: Failed to fetch http://in.archive.ubuntu.com/ubuntu/dists/wily-updates/InRelease  Unable to find expected entry 'main/binary-i386cddcd/Packages' in Release file (Wrong sources.list entry or malformed file)  W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/wily-security/InRelease  Unable to find expected entry 'main/binary-i386cddcd/Packages' in Release file (Wrong sources.list entry or malformed file)  W: Failed to fetch http://archive.canonical.com/ubuntu/dists/wily/InRelease  Unable to find expected entry 'partner/binary-i386cddcd/Packages' in Release file (Wrong sources.list entry or malformed file)  W: Failed to fetch http://archive.canonical.com/dists/wily/InRelease  Unable to find expected entry 'partner/binary-i386cddcd/Packages' in Release file (Wrong sources.list entry or malformed file)  E: Some index files failed to download. They have been ignored, or old ones used instead.   And when using the Software Updater GUI to update, showing message as,  Failed to download repository information Check your Internet connection     Seems like some entry/configuration got corrupted. I tried changing the channels in the      Software & Updates   by enabling/disabling the restricted,multiverse options in Ubuntu Software tab as well as Canonical Partners option in Other Software tab.    Is there any way to reset/cleanup this repository sources list?   I could've done a re-install of Ubuntu but I'm lazy to reinstall and reconfigure all my softwares and stuff. Thanks in advance.


Two pictures next to a big one, to fit in textwidth

I want two pictures next to another big one and every picture has a different size (like the example below).    I want that all pictures keep their aspect ratio and the pictures to the right should have the same height. Also all 3 pictures should be as wide as the \textwidth.  I've tried subfigure and \resizebox, but I could not set the right heights dependent on the height of the left picture. Manually trying to fit all the sizes is way too tedious, is there an easy way to do that?  Edit:  Here are more informations for my problem. My current code looks like this. I've just adjustet the sizes of the pictures until they fit (trial end error). A very tedious process.   The pictures have individual caption with (a), (b) and (c) and the whole picture has another caption.  It would be nice to manage the size of the right pictures so that they are not bigger than the left one and that alle 3 pictures don't exceed the linewitdh.  \begin{figure}[H] \centering \begin{subfigure}[p]{.45\textwidth}     \includegraphics[height=\textheight]{MMC.eps}     \caption{MMC Schaltbild, \cite{Eremia.2016}} \label{fig:ch2_MMC \end{subfigure} \qquad \begin{subfigure}[p]{.45\textwidth}     \centering     \includegraphics[height=0.39\textheight]{Halfbridge.eps}     \caption{Halfbridge, \cite{Shah.17.07.201621.07.2016}} \label{fig:ch2_Halfbridge}      \vspace{2ex}      \includegraphics[height=0.39\textheight]{Fullbridge.eps}     \caption{Fullbridge, \cite{Shah.17.07.201621.07.2016}} \label{fig:ch2_Fullfbridge} \end{subfigure} \caption{MMC and Submodule}\end{figure}


my phone may have virus but my antivirus scans clean that phon is protected

A pop up window appeared on my phone ,about some wifi booster simuntaneously an other window got on and told that my phone was infected by an virus ,but my antivirus was active and then i scaned my phone but it was clean . Please explain did my phone really have a virus in it?


Unbiased weighted variance was already addressed  and  but there still seems to be a surprising amount of confusion.  There appears to be a consensus toward the formula presented in the first link as well as in the .  This also looks like the formula used by R, Mathematica, and GSL (but not MATLAB).  However, the Wikipedia article also contains the following line which looks like a great sanity check for a weighted variance implementation:     For example, if values {2,2,4,5,5,5} are drawn from the same   distribution, then we can treat this set as an unweighted sample, or   we can treat it as the weighted sample {2,4,5} with corresponding   weights {2,1,3}, and we should get the same results.   My calculations give the value of 2.1667 for variance of the original values and 2.9545 for the weighted variance.  Should I really expect them to be the same?  Why or why not?


I am using an HP pavilion G6 notebook and it has AMD graphic which is not supported by Ubuntu 16.04. I want to downgrade my PC, unless there is any other solution to fix this graphic problem.


Sum of two independent normal distributed random variables

If $X_i$, $i =1,2$ are independent and have normal distribution with mean $0$ and variance $\sigma_i ^2$. Show that $X_1 + X_2$ has a normal distribution with mean $0$ and variance $\sigma_1^2 + \sigma_2^2$.  Any idea is appreciated.


Equivalent definition of normal subgroups

A subgroup $N<G$ is called normal if $gN=Ng  ,\forall g \in G$. My book then says this is equivalent to $gN\subset Ng ,\forall g \in G$.  How do I see this? One way is obvious, but how do I show that if $gN\subset Ng ,\forall g \in G$, then $gN=Ng, \forall g\in G$?  I have tried to say, let $g \in G, n \in N$. Then $gn= n' g$ for some $n' \in N$ From there I have to somehow show $ng= g n''$ for some $n'' \in N$. Could someone help? Thanks.


Given sets $A,B$, there exists injection $f:A\to B$ or injection $g:B\to A$

The claim in the title is pretty obvious when choice is assumed (Apply Zorn's lemma to the subset of the powerset of $A$ of subsets of $A$ which allow injections to $B$. Consider a maximal element and construct an injection backwards if the maximal element isn't $A$)  Is it possible to show this without choice? If not, what is the weakest form of choice we need to assume?


using a dummy to indicate zero values of a overdispersed continuous predictor variable

I have a predictor variable that has many zeros.  The predictor variable is simply a count of the occurrences of some behavior.  The zeros are qualitatively meaningful.  I'd like to use a log transformation of the variable but am unsure what to do with the zeros - again - because they are qualitatively meaningful.  I'd rather not simply add 1 to the variable before logging it.   I've seen others allude to some example from Hosmer and Lemeshow where they use a dummy variable to indicate if a person smokes or not and a continuous variable accounting for the number of cigarettes smoked.  I'm not sure exactly how this coding would work. Does the dummy need to be coded as 1 to indicate zero values of the other continuous variable or should 1 indicate positive values?  I'd also like to log transform the continuous variable because I've got serious over dispersion.  I'm guessing I'd log transform the positive values and just keep the zeros as zeros but some of those zeros are going to be 'true' zeros and others are going to be zeros only because they were '1' on the original scale.    I looked through the applied logistic regression text and I'm not seeing the example that others have alluded to.    Thanks for your input.


Php artisan migrate unable to access mysql database

This is similar to  but my situation is a little different.  I have laravel, composer, and valet running on Ubuntu 18.04. I'm trying to run php artisan migrate and it throws errors related to being unable to connect to the mysql database.   Illuminate\Database\QueryException  : SQLSTATE[HY000] [1698] Access denied for user 'root'@'localhost' (SQL: select * from information_schema.tables where table_schema = blog and table_name = migrations)  at /home/david/Sites/blog/vendor/laravel/framework/src/Illuminate/Database/Connection.php:664   660|         // If an exception occurs when attempting to run a query, we'll format the error   661|         // message to include the bindings with SQL, which will make this exception a   662|         // lot more helpful to the developer instead of just the database's errors.   663|         catch (Exception $e) { > 664|             throw new QueryException(   665|                 $query, $this->prepareBindings($bindings), $e   666|             );   667|         }   668|   Exception trace:  1   PDOException::("SQLSTATE[HY000] [1698] Access denied for user 'root'@'localhost'")     /home/david/Sites/blog/vendor/laravel/framework/src/Illuminate/Database/Connectors/Connector.php:68  2   PDO::__construct("mysql:host=127.0.0.1;port=3306;dbname=blog", "root", "", [])     /home/david/Sites/blog/vendor/laravel/framework/src/Illuminate/Database/Connectors/Connector.php:68   it seems pretty clear to me that the .env file doesn't contain the right information... but it does. here's my .env for mysql database:  DB_CONNECTION=mysql DB_HOST=127.0.0.1 DB_PORT=3306 DB_DATABASE=blog DB_USERNAME=root DB_PASSWORD=   Database I'm trying to enter is called blog, and the user name is root and the password is blank. That's how I access mysql on my machine... sudo mysql -uroot -p and it logs me right in.  Any idea what might be going wrong?


Do you add new HP or change ability score first when leveling up (eg, to 4th, 8th)?

When leveling up to 4th level, I add 2 ability points to CON, e.g., going from 14 (+2) to 16 (+3). For my new max HP, do I use my new CON modifier, or the old one?