I have a multivariate normal distribution with parameters mean = 0 and a variance-covariance matrix K which is n-by-n. I'd like to generate a vector of values (length n) that represent the expected values of this MVN. Any advice on how to do this?

I am currently trying to simulate values of a $N$-dimensional random variable $X$ that has a multivariate normal distribution with mean vector $\mu = (\mu_1,...,\mu_N)^T$ and covariance matrix $S$.  I am hoping to use a procedure similar to the inverse CDF method, meaning that I want to first generate a $N$-dimensional uniform random variable $U$ and then plug that into the inverse CDF of this distribution, so to generate value $X$.  I am having issues because the procedure is not well documented and there are slight differences between the  and a .  In my case, I am also choosing the parameters of the distribution randomly. In particular, I generate each of the means, $\mu_i$, from a uniform distribution $U(20,40)$. I then build the covariance matrix $S$ using the following procedure:   Create a lower triangular matrix $L$ where $L(i,i) = 1$ for $i=1..N$ and $L(i,j)  = U(-1,1)$ for  $i < j$ Let $S = LL^T$ where $L^T$ denotes the transpose of $L$.   This procedure allows me to ensure that $S$ is symmetric and positive definite. It also provides a lower triangular matrix $L$ so that $S = LL^T$, which I believe is required to generate values from the distribution.  Using the guidelines on Wikipedia, I should be able to generate values of $X$ using a $N$-dimensional uniform as follows:   $X = \mu + L * \Phi^{-1}(U)$   According to the MATLAB function however, this is typically done as:   $X = \mu + L^T * \Phi^{-1}(U)$   Where $\Phi^{-1}$ is the inverse CDF of a $N$-dimensional, separable, normal distribution, and the only difference between both methods is simply whether to use $L$ or $L^T$.  Is MATLAB or Wikipedia the way to go? Or are both wrong?


To reflect the way I draw math by hand, and because I find this more readable, I would like to have \left and \right (or a custom pair of commands) render parentheses‐like symbols with an increasing size, even if their actual content does not get taller.  As is, the code:  \left(\left(\left(\left(a\right)\right)\right)\right)   renders as:    I am seeking something roughly looking like:    Of course, just as \left and \right, it would have to work automatically, that is, I wouldn’t have to specify any size information manually. My guess is that \left and \right measure the height of what is between them and compute an appropriate size for the parentheses. So, it might do the trick to alter their behaviour so that they pretend their parentheses to be slightly taller than how they are actually rendered — say, by a 1.2 factor, or whatever.  How can I achieve that?

This question has bugged me for a while. I want to write a nested function, f(g(x)). If I naively enter it:  \begin{align}     f(g(x))=y \end{align}     The problem is that each and every parenthesis is the same size as all of the others. Shouldn't the outer parentheses be larger? But if I do this:  \begin{align}     f\left(g(x)\right)=y \end{align}     Now it looks even less like the functions are nested. What's the proper way to do this?


I would like to know how to reduce the size of this table, since it is larger than the text width on one page. Or should I fix the width of each column? If yes how?  \begin{document}  \begin{table}[!htbp]   \centering \caption{Comparison of the CCSHR estimators based on beta and logit-normal distributions} \begin{tabular}{c|ccc|ccc} \toprule    & \multicolumn{3}{c|}{pH 1.4} & \multicolumn{3}{c}{pH 2.2} \\ \midrule  & \multicolumn{1}{c}{\textit{N}$_{\text{max}}$ (nm)} & {\textit{C}$_{\text{D}}$\textsuperscript{'}} (µM)& \textit{D} & \textit{A}$_{\text{max}}$ (µm) & \textit{D}$_{\text{D}}$\textsuperscript{'} (µm) & \textit{A} \\ \\[-1em] {Molecule AB} & \multicolumn{1}{c}{2.0 ± 0.2} & {7.9 ± 0.6} & {4.7 ± 0.1} & {7.8 ± 0.3} & {26 ± 6} & {0.87 ± 0.09} \\ {Molecule C} & \multicolumn{1}{c}{9.2 ± 0.2} & {25.9 ± 1.4} & {2.07 ± 0.04} & {1.8 ± 0.3} & {70 ± 5} & {0.19 ± 0.06} \\ %\bottomrule \hline  \end{tabular} \label{tab:addlabel} \end{table}  tex tex tex text tex tex tex t ex text text  tex tex tex text tex tex tex t ex text text tex tex tex text tex tex tex t ex text text tex tex tex text tex tex tex t ex text text   \end{document}     I solve it while adding this line command:  \setlength{\tabcolsep}{.085cm}  However I have a discontinued vertical line before column Amax. Do you know how to fix it?

I have a table that I want to insert on a page, but at least one (perhaps both) of the following conditions are met:   The table is too wide to fit within the text block or page. That is, I'm exceeding some horizontal restriction. The table is too tall to fit within the text block or page. That is, I'm exceeding some vertical restriction.   What are my options to make this table fit? If it doesn't fit, regardless of my attempts, what other options exist?


i am trying to create a program which puts random numbers/letters in a textbox using javascript (in the browser console). I have tried my best to do it but i just couldn't do it.  my best attempt was:  var key = ((nums[Math.floor(Math.random() * nums.length)].toString()) + (Math.floor((Math.random() * 10)).toString()) + (Math.floor((Math.random() * 10)).toString())); var key2 = ((Math.floor((Math.random() * 10)).toString()) + (Math.floor((Math.random() * 10)).toString()) + (Math.floor((Math.random() * 10)).toString())); var key3 = ((Math.floor((Math.random() * 10)).toString()) + (Math.floor((Math.random() * 10)).toString()) + (Math.floor((Math.random() * 10)).toString()) + (Math.floor((Math.random() * 10)).toString()));   But unfortunately it  only generates numbers. Does anyone know how to randomize both? Would appreciate if anyone could help me .  Regards, 3hr3nw3rt

I'm trying to create globally-unique identifiers in JavaScript.  I'm not sure what routines are available on all browsers, how "random" and seeded the built-in random number generator is, etc. The GUID / UUID should be at least 32 characters and should stay in the ASCII range to avoid trouble when passing them around.


okay so i bought this laptop forever ago was just a shell. bought a hardrive battery and so fourth. then ran into the issue of what OS to use. well long story short a buddy of mine from work whom i no longer work with installed to my knowledge and understand is ubuntu mate 14.04. i would like to wipe the enitre old system off and replace it with brand new ubuntu 16.04 or 17.01 but i really am not the smartest when it comes to this whole terminal deal. so if maybe someone can give me some insight on how to go about this. all i want is to wipe everything off old and start OS brand new newest version and absolutely nothing on it at all other then the new OS. please Help, ty in advance. i have a 80gb hardrive.

How do I completely reinstall Ubuntu without affecting the Windows partition? The way I setup my laptop is like this:   Completely wiped everything using GParted from Ubuntu CD Partitioned the HDD to 3 partitions (one for Windows, one for Ubuntu, one for Storage) Installed Windows 7 Pro 64-bit Installed Ubuntu 10.04 LTS 64-bit   The reason why I want to reinstall is NOTHING works in Ubuntu. No internet at all both Ethernet, and Wireless and when I figured out how to fix the wireless, there is no way to download drivers for the display so everything is just ugly and big. To make things more complicated, upgrading to 10.10 via update manager just gives me an error.  The way I see it right now is I have to try to wipe 10.04 and just install 11.04 from scratch but I'm not sure how to do that? Does anyone know?


What is the indefinite integral of the following function: $$ \int{\mathrm{d}x \over \,\sqrt{\,\sin\left(x\right)\cos\left(7x\right)\,}\,} $$  And how can I compute this ?.

So it's given this indefinite integral $$\int \frac{1}{\sin ^{\frac{1}{2}}x \cos^{\frac{7}{2}}x}dx$$  Is there anyone could solve this integral? Thanks in advance.


Prove $\sum_{n=1}^\infty a_n \in \mathbb R \mathbb \leftrightarrow \sum_{n=1}^\infty\frac{a_n}{1+a_n}\in \mathbb R$ The hint says that for one direction argue that $b_n = \frac{a_n}{\frac{a_n}{1+a_n}}$ is bounded after some fixed cutoff point. I dont know where the $b_n$ is coming from or which test to use to prove this.

If $a_n \ge 0 $ for all n, prove that $\sum_{n=1}^\infty a_n$ converges if and only if $\sum_{n=1}^\infty {a_n\over 1+a_n}$ converges.   Here is my attempt!  => Suppose that $\epsilon \ge 0$ is given and $a_n$ converges, then  for all $N\le n \le m$$$\sum_{k=n+1}^m a_k \lt \epsilon.$$ let $b_n={a_n\over 1+a_n}$ and Notice that $b_n \lt a_n$ and   Then, applying the comparison test  $$|\sum_{k=n+1}^m b_k| \le \sum_{k=n+1}^m |b_k |\le\sum_{k=n+1}^m a_k\lt\epsilon$$Hence,${a_n\over 1+a_n}$ converges.  let me know if it is worng and I don't know how to start for the other direction. Any help is appreciated!


Recently a short fall broke not only my Nexus 4's cheap phone case, but the digitizer as well. The LCD and everything else is perfect, however the touch screen only works on the top quarter of the screen. I have no bluetooth mouse/keyboard and USB On-The-Go doesn't work for Nexus 4.  Unfortunately USB Debugging is disabled (I really regret turning it off). How can I unlock it or back up the data on my phone?

I just broke the screen of my (unrooted) Galaxy S.  How do I get back my SMS and contacts?   PS: I tried Kies but it won't detect my phone for some reason. (Kies works fine with another Galaxy I possess but not this one)


I want to scale the entire contents of a document to make them smaller. Changing the font size the usual way is not desired, as this changes how the text looks:     In other words, I want something similar to \scalebox{}{} or \resizebox{}{} — to change the size of the text without changing its font. I'm saying "size of the text" instead of "size of the font" or "font size" to clarify the difference from the readily available mechanism to change font size, which has the undesired side-effect of also changing the font itself ever so slightly.  What I can do, of course, is to just make the page bigger (i.e. use e.g. a3paper instead of a4paper, an approach taken ), but that seems like a dirty solution (if you'd print it out on A4 paper, however, it'd give pretty much exactly the desired output). I also don't want to change my \documentclass to KOMA-Script or such, as done .  I tried \relscale{} from  and \scalefont{} from the  package, but these just seem to change the font size the usual way (as opposed to scaling the text directly, i.e. linearly scaling/changing font size). \resizebox and \scalebox  (manual or automatic), and I think they're not really intended made for modifying an entire document.  Ideally, the answer would behave just like e.g. \small or \footnotesize, in the sense that it'd be a switch that would affect its entire scope and work with math-mode, multicols, tabular, etc.  I hope this is not a duplicate, I couldn't find any answer to my question here (though, as mentioned above, there are a few similar questions). MWE not really applicable, but I'm using \documentclass{article} and compiling with LuaLaTeX (ideally, though, the answer would work with other documentclasses and with pdfLaTeX as well).  Edit: Tried to improve the question by rephrasing or clarifying.

For some time I've seen LaTeX-produced documents that had slight differences in fonts. When you looked at them, they had the same Computer-Modern or Latin-Modern, however, they looked more stylized (more lightweight).  By chance, and looking at another question here, I came across this document:  in which I've seen clearly the difference, and has to do with optical size for a font at a given (output) point size. Here is a capture:    Look how the last line (even when they're all typeset at 12pt) looks with a more light font. I also noticed that in some Beamer documents using the sans-serif family (some had a more lightweight version of the font).  So the question is, without using XeTeX or LuaTeX (just plain LaTeX/pdfTeX), how can I get that lightweight (optical at 17pt) font for the size I want?  PD. I also noticed that there were some differences if one used tex->dvi->dvips->ps and pdflatex->pdf. In some .ps documents I've seen through the web, the fonts looked more lightweight by default. Maybe some TeX installations select those bigger optical sizes by default to obtain a more pleasing font rendering.


So the age of the universe can be estimated by doing 1 over Hubble's constant, but why is this?

How can the age of the universe be calculated as $1/H$, with $H$ the Hubble constant, when its expansion has been far from linear?    The $1/H$ comes from Hubble’s law, and implies that the universe expanded like a cone, as opposed to the above.  Also, wouldn’t the Hubble constant naturally change over time? Has the change since its discovery been negligible? I know it’s changed in terms of the recognised value due to improvements in the way we measure it—I mean the actual value.


I know how to shutdown a Mac from Terminal, but is there a way to actually bring up the shutdown dialog you get from Apple → Shut Down…?

I'm getting more interested in using Terminal as an alternative way to address solutions on my Mac. I have seen this question entitled .  I would therefore like to know:  How to shut down, restart and sleep my Mac using the Terminal command exclusively ?


Can I edit someone's post and attribute the image or other foreign / cited content, if post's author refuses to do so?  An . People say (in comments), that author should attribute the image, then that he must do this, then they even reverse-search the Internet for him to find the proper source, and he still refuses to edit the answer and add proper attribution.  I thought that, in this case, editing the answer and adding proper attribution is not only my privilege, but also my must. But, since many people found adding attribution needed and still refused to do the edit, that made me thinking, if I'm thinking correctly.  What should I do in case like this?

How should I act if I discover a user plagiarizing fellow users' posts? What if I find someone plagiarizing external resources without attribution?  See also:


Occasionally, I downvote a bad answer but the -1 is not subtracted immediately and may sometimes take a few hours. Why is that the case? Why is it not immediate like when gaining a reputation for an upvoted post/comment?

Recently, I read this  about how they have some of their infrastructure laid out. I was curious to know, does Stack Exchange use caching (both at the application layer and/or database layer) and if so, how?


Using ArcGis 10.0. What I am looking for is a way to get point features that are placed in a polygon to have the same "Address" value.  This is the same as the "Spatial Join" feature, however, I am only trying to extract one field not all the fields in the polygon layer.  Is there a way to "Spatial Join" from a polygon to a point feature while selecting what fields from the polygon you wish to keep?

I want to convert polygons into points using QGIS.   I know how it's done in ArcGIS Desktop.


Given a continuous random variable $X$, what are the units of the PDF and CDF of $X$?

On the , there is this line:      $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)    How can a value $>1$ be OK? I thought all probability values were expressed in the range $0 \leq p \leq 1$. Furthermore, given that it is possible to have such a value, how is that value obtained in the example shown on the page?


I'm making a game engine that can be used with multiple story modules. I want to keep the stories in a subdirectory and use a single PLAY.py file to allow the user to choose one of them.  So far, I have been able to use this simple code to get a list of all of the story modules:  import glob stories = glob.glob( ./stories/ds_*.py )   I then use a for loop and a format statement to list the options for the user. The problem is that I can't find out how to use the resulting strings to actually import anything. Maybe glob is not the best solution?

How can I load a Python module given its full path? Note that the file can be anywhere in the filesystem, as it is a configuration option.


Let $ p = 4n + 1$ cousin. Prove that p$ | n ^ n - 1$  The only thing I developed was:  $1 = n ^ n (mod p)$  $1 = n (mod p)$  $4 = 4n (mod p)$  Maybe it has to do with Fermat's cousins

Let $p=4k+1$ be a prime number.  I need to  prove that $p$ divides $k^k-1$.  Could anyone give me some hint?  Thank


Find the limit of $$b_{n+1}=\frac{1}{3}(2b_n+\frac{5}{b_n^2})$$ Using AM-MG inequity, Where $b_1>0$  I can show that the limit is $\sqrt[3]{5}$ by solving $$L=\frac{1}{3}(2L+\frac{5}{L^2})$$ Then I will need to show that it is monotonic increasing/decreasing, but how can AM-MG can be used here?

Let $ a_{n+1} = \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}), a_1 > 0 $. Show the sequence converge and find it's limit.    I did the following:  We see that $a_n$ is positive for every n obviously (considering $a_1 > 0$). Then:  $$ a_{n+1} - a_n = \frac{2a_n^{3} + 5}{3a_n^{2}} - a_n = \frac{5 - a_n^{3}}{3a_n^{2}}$$  We see that for each $a_n > ^3\sqrt{5}$ the sequence is decreasing. That means the proof collapses to prove  $a_n > ^3\sqrt{5}$ in order for $a_n$ to be decreasing. Suppose $ a_n > ^3\sqrt{5}$ then obviously $a_{n+1} = \frac{2a_n^{3} + 5}{3a_n^{2}} > \frac{2(\sqrt[3]{5})^{3} + 5}{3(\sqrt[3]{5})^{2}} = \sqrt[3]{5}$ so we deduced $a_{n+1} > ^\sqrt[3]{5} $.  (It's important to note $a_1$ might be less then $\sqrt[3]{5}$, hence the sequence will decrease from the second element.) So we observed $a_n$ is always positive and decreasig hence it's bounded below so it's bounded. As for it's limit:   $$\begin{align} L = \lim_{n \to \infty} a_{n+1} = \lim_{n \to \infty} \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}) = \frac{1}{3}(2L + \frac{5}{L^{2}}) =  \sqrt[3]{5}\end{align}$$  I'm not sure as of the correctness of the solution. I'm aware that it's not a contradiction because it only implies it's in the epsilon-environment of $\sqrt[3]{5}$, or rather in this case $(\sqrt[3]{5}, \sqrt[3]{5}+\epsilon)$.  Is it correct?  EDIT: If anyone encounter a question in the likes, to sum it up you obviously should show the sequence is montonic and bounded. In this case for example we can show it using AM-GM inequality to see the sequence is bounded by $\sqrt[3]{5}$ and then in the difference of two consequective elements we see the difference is negative due to every element being greater then the third root of 5. From here we know the sequence is bounded below and decreasing hence it's bounded. If we plug in the limit of the sequence to itself we will see it's the third root of five. And that's it.


I have an requirement to validate email and date fields from an Excel file using typescript Angular app.   And I am trying to validate using regular expression but the result returns always false for a correct email address.  Can anyone help me to validate the email and dates?  Below is the code I have written  Component:  import {  Component } from '@angular/core'; import * as FileSaver from 'file-saver'; import * as XLSX from 'xlsx'; import {UploadService} from '../services//upload.service';   import { FileUploader ,FileItem,ParsedResponseHeaders,FileLikeObject} from 'ng2-file-upload';  import { SpotCheck } from '../models/SpotCheckFields';    @Component ({       selector: 'my-app',       templateUrl:'./excelUpload.html',     providers:[UploadService] })    export class ExcelUploadComponent  {       public SpotChecklist: SpotCheck[];     public project_master:any[];      uploader:FileUploader;      constructor(private uploadservice: UploadService ){         this.SpotChecklist=[];         this.project_master=[];     }     ngOnInit(): void {         this.uploader = new FileUploader({             url: 'http://localhost:5000/upload'             // headers: [{name:'Accept', value:'application/json'}],             // autoUpload: true,         });         this.uploader.onErrorItem = (item, response, status, headers) => this.onErrorItem(item, response, status, headers);         this.uploader.onSuccessItem = (item, response, status, headers) => this.onSuccessItem(item, response, status, headers);          // retrieve projectmaster details         this.getProjectMaster("","SELECT PROJECT MASTER");     }      onSuccessItem(item: FileItem, response: string, status: number, headers: ParsedResponseHeaders): any {         //console.log("onSuccessItem " + status, response, item);           this.SpotChecklist = JSON.parse(response); //success server response          var data = this.validateRow(this.SpotChecklist);          console.log(data);       }      onErrorItem(item: FileItem, response: string, status: number, headers: ParsedResponseHeaders): any {         let error = JSON.parse(response); //error server response     }      validateRow(lst:any[]) : SpotCheck[]     {         var i:number;         for(i=0;i<lst.length ;i++)         {             var validation_message:string="";             var blnErrOccured:boolean=false;              if(!this.isEmail(lst[i].RESPONSIBLE_PERSON_EMAIL_ID))             {                 validation_message=validation_message+ "," +"RESPONSIBLE_PERSON_EMAIL_ID is invalid"                 blnErrOccured=true;             }              lst[i].VALIDATION_RESULT=validation_message;         }         return lst;     }      isDate(date:string) {         // return (new Date(date) !== "Invalid Date") && !isNaN(new Date(date));     }      isEmail(search:string):boolean     {         var  serchfind:boolean;          regexp = new RegExp('/^(([^<>()\[\]\\.,;:\s@"]+(\.[^<>()\[\]\\.,;:\s@"]+)*)|(".+"))@((\[[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}])|(([a-zA-Z\-0-9]+\.)+[a-zA-Z]{2,}))$/');          serchfind = regexp.test(search);          console.log(serchfind)         return serchfind     }      getProjectMaster(project_code:string,Flag:string):any     {           this.uploadservice.getProjectMaster(project_code,Flag).subscribe(             response=> {                 this.project_master= response[0];                 return response;             },             error=> {                 console.log("ERROR: ",error);                 console.log(error.json()); //gives the object object             },             () => {                 console.log("Completed");             }         );     } }

Is there a regular expression to validate an email address in JavaScript?


Let $a,b,c \in G$ and $G$ is a group, prove that the following items have the same order...  $a$ and $a^{-1}$ $ab$ and $ba$ $abc$ and $bca$  For the first, I see that I have to operate $a^{-1}$ n times to convert $\underbrace{a*\cdots *a}_n = e$ in $e$ but for the others I can't find the way...

How do I prove that if $a$, $b$ are elements of group, then $o(ab) = o(ba)$?   For some reason I end up doing the proof for abelian(ness?), i.e., I assume that the order of $ab$ is $2$ and do the steps that lead me to conclude that $ab=ba$, so the orders must be the same. Is that the right way to do it?


I'm from Brazil and I'm planning to fly to Panama and then take a bus from Panama City to Medellin, is it possible?  Direct flights are so expensive!

I'm planning a backpacking trip from Central America down to South America.  Does anyone have a recommended way of getting around the Darién Gap?  I read that you can fly, or you can take a boat but the information seems extremely limited.  How much does it cost?  Can I book alternative routes ahead of time?


Find the value of  $$\lim_{t\to 0}\left(\frac{1}{\ln(1 + t)}+\frac{1}{\ln(1-t)}\right).$$ I tried L'Hospital's Rule but can't get it to work. I can't seem to find the right algebra tricks to apply before attempting L'Hospitals' Rule.

Evaluate $\displaystyle \lim_{x \to 0} \left(\frac{1}{\ln(1+x)} +  \frac{1}{\ln(1-x)}\right)$   I am having trouble starting this one. I couldn't see any log laws that I'm familiar with to rearrange the formula. I also tried combining the fractions and using L'Hospital's, but it only seemed to make things worse.  What direction should I take with this?


30-day UK tourist visa rejected. Since i have booked the flights and hotels i am  planning to reapply. So can i reapply again and which are the additional documents required ?  Reason for rejection ( from Embassy note):     i have refused your application for visit because i am not satisfied that you meet the requirements of Appendix V: Immigration Rules for Visitor because      You have stated that you are a senior engineer for Company £ 625 per month after tax and you have evidenced this with Payslips and an employment letter.   You stated that the trip will personally cost you £ 4000 . As a evidence of your personal finances have provided the following bank details in your name.      Total bank balance £ 6500 ( Salary account and savings account combined).      How ever i note recent deposits have been credited to each of the bank accounts provided. Of particular note is a deposit of £3700 credited to account xxxxxx on 22/7/16. From the documents provided, the origin of these fund is unclear and deposit are inconsistent with the transnational history shown. I am not satisfied that the money is genuinely available to your exclusive use. Deposits in the account bear little relation to your stated income and i do not discount the possibility that an attempt has been made to provide an enhanced image of your financial circumstances for the purpose of this application.   i have therefore refused your application with paragraph v4.2 (a) and (c) and (e) of the immigration Rules.   The amount £3700 is credited from my father account it can be clearly seen from  the statement that i have submitted. He got the money from local saving scheme and i am paying monthly by cash for 4 years. I don't any proof to show the source of that money.   Please tell me which are the additional documents required for reapplying ?

The UK Visas and Immigration Directorate publishes  that provides helpful tips that can result in successful visa applications. Section 2 of this guidance opens is entitled "other documents you may want to provide" (emphasis mine).  Section 2: other documents you may want to provide – all visitors This section provides guidance on the types of documents that you may want to provide to help us consider your application against the Immigration Rules. Previous travel documents/passports, which show previous travel. Financial documents showing that you have sufficient funds available.  These must clearly show that you have access to the funds, such as:  bank statements building society book proof of earnings such as a letter from employer confirming employment details (start date of employment, salary, role, company contact details) where a third party (who is either in the UK or will be legally in the UK at the time of your visit) is providing financial support to you e.g. a business, a friend or a relative, documents to show that they have sufficient resources to support you in addition to themselves and any dependant family should be provided   The first item is "bank statements" and this ties in with the , which says...  evidence that you can support yourself during your trip, eg bank statements or payslips from the last 6 months  (Note 'eg' is a Latin abbreviation meaning "for example"; this appears to be optional rather than a fixed requirement.) Question: How should someone interpret this such that the chances of success are maximized? How many statements should I submit? What are they looking for and what do my bank statements tell about me?


I am very aware that the standard way of doing this in Ubuntu is Ctrl+⇬+C and Ctrl+⇬+V.  I come from an elementary OS background where they actually fixed this. So if eOS can fix this, so should I in vanilla Ubuntu.  How does one fix this? The Ctrl+⇬+C, for example, must be located somewhere in the settings?

Is it possible for me to make Ctrl+C perform a copy command if there is highlighted text in the terminal? Otherwise, it should retain its normal behavior.  (If there is a terminal that can do this other than gnome-terminal, that's probably fine too.)


let $k$ be an integer, and consider the set $S$ of functions from $\mathbb{N}$ to $\mathbb{N}$ where $g(x) =0$ for all $x>k$. I want to show $S$ is countable.   This is what I have so far, but I am not quite sure if I am going about it correctly, or what to do next.  So our functions will look like this   $A_1=\{(1,a_1),(2,a_2),(3,a_3),(4,a_4),....,(k,a_k), (k+1,0), (k+2,0)....\}$   It seems from here I should be able to show that there are only countable ways of doing this, but I am not quite sure how to say that. I think the best way would to come up with a bijection from the naturals to $S$ but for the life of me I can't come up with one.  I would love some help. Thanks in advance.

Prove that $\mathbb{N}^k$ is countable for every $k \in \mathbb{N}$.  I am told that we can go about this inductively.   Let $P(n)$ be the statement: “$\mathbb{N}^n$ is countable” $\forall n \in \mathbb{N}$.  Base Case: $\mathbb{N}^1 = \mathbb{N}$ is countable by definition, so $\checkmark$  Inductive Step: $\mathbb{N}^{k+1}$ $“=”$ $\mathbb{N}^k \times \mathbb{N}$  We know that $(A,B)$ countable $\implies$ $A \times B$ is countable. I am stuck on the part where I have to prove the rest, but I know that, for example, $(1,2,7) \in \mathbb{N}^3 \notin \mathbb{N}^2 \times \mathbb{N}$ but instead $((1,2),7) \in \mathbb{N}^2 \times \mathbb{N}$. So how would I go about proving the statement.


I am new so I am not allowed to vote.  I am not allowed to chat either.  Chances are all new questions especially from new programmers will get downvoted.  I slept over my question and planned on how to deliver them before I actually posted them so that I know I am actually lost and not lazy.  Nonetheless, I am still downvoted.  I saw some other new posters getting downvoted as well, and at first glance, newer programmers would assume that members here are unfriendly.  I know that is not true.  People with louder voices can be heard more.  Just like anything else, there are some unfriendly-"this guy is so noob he shouldn't be here" kind of people, and there are some really friendly user.  I'd like to thank and reward helpful and friendly members, what options do I have?

Most of the time, I don't need to ask questions to find the answers I am looking for. Because I just find all the answers on Stack Overflow. It is a huge resource of good tips, tricks and solutions. And by only looking around and searching (= ), my reputation stays at 1 of course.  But I also want to show my active participation by things like:   pointing out the answers that helped me out. somehow say "good answer, buddy, you saved my day today".   So no blablabla, just vote up the good stuff.  But I cannot. Frustrating.


I am traying to send special characters to a php server. I tried with angular and with jquery getting the same result:  myClient.js with JQuery:  data = "Ñoñón"; dataToSend={special_word: data}; $.ajax({       type : 'POST',   url  : 'myServer.php',   data : dataToSend,   success :  function(response){     console.log(response);  } });   myServer.php for JQuery client:  $special_word =mysqli_real_escape_string($mysqli, $_POST["special_word"])); saveWordInDB($special_word); echo $special_word;   myClient.js with angular:  data = "Ñoñón"; dataToSend={special_word: data}; $http.post('myServer.php', dataToSend) .then(    function(response){      // success callback      console.log(response.data);    },     function(response){      // failure callback      console.log(response);    } );   myServer.php for angular client  $postdata = file_get_contents("php://input"); $request = json_decode($postdata); $special_word = $request->special_word; saveWordInDB($special_word); echo $special_word;   In both cases, the word "Ñoñón" is not stored in the DB, but the word "Ã±oÃ±Ã³n" its stored instead. The same occurs with the word showed in the console. How can this be fixed?  Thanks in advance!

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


I'm writing about how companies in a particular industry are responding to the Covid-19 situation. I'm categorising their responses and labelling each category with a single word.  Two categories are similar yet different enough to remain distinct. I'm struggling to find single-word labels for them that are sufficiently differentiated. Currently I have:  "Giving" - companies are giving some of their products and services to regular and vulnerable customers for free to help them through the crisis (and of course to generate goodwill, customer loyalty, CSR points, etc.). For example, giving an extra 50% when a customer renews, making premium services freely available for a limited period, etc.  "Donating" - companies are donating money, facilities, employee time, as well as products and services, to governments and health organisations to help them tackle the crisis. For example, donating $X million to relevant charites, making now-empty buildings available for health worker training, giving products and services to organisations working on care, treatment, etc.  Both labels describe their respective activities well, but they overlap too much. Can I replace one with an alternative that reduces this overlap? The best I've come up with so far is to replace "giving" with "subsidising", but that seems a little flaccid in comparison. This is for a business audience and should be clear, impactful, easy to read, etc.  The following thread is close, but doesn't quite answer my question ("Bestowing" may be the best option in that thread, but again is too similar to "donating", and is also a little archaic for my purposes):

Are there any other words similar to these words:  Award, Bestow, Donate, Grant, Give, Provide, Tax  ...that give a meaning of:  I freely give to you a portion what I have acquired or earned, without hesitation or expectation of anything in return. You are owed this, without question. There is no emotion involved with this transaction. It just is what it is.  For example: as a member of the Thief's Guild, 20% of everything you acquire will be ______ to the Guild.  Bestowed and Granted are very close...  Any other ideas?


I have 2 PCs with Ubuntu 12.04 and I have had problems with syncronization of the files. When I modify a file or when I try to connect it my UbuntuOne don't make the synchronism and show me the message: (auth failed (AUTH_FAILED)). How do I do to fix it?  Thanks, Vinícius.

Recently I started getting a File sync error on all 3 of my PCs running Ubuntu One.  One is running Ubuntu, the other 2 are running Windows 8.  Looking at the list of clients on the web, none of them were there anymore.    I found this article:      On how to fix the issue for my Ubuntu PC and it worked perfectly.  Now I am looking for a similar fix for Windows but haven't found one yet.  I've tried un-installing Ubuntu One and re-installing it, but it must still be holding the keys somewhere because it never asked me to login again.    Does anyone know where I can clear these keys to get my files syncing on Windows again?


I know that Kirito didn't die at the end if episode 14 because of his will to fight overthrowing the system. But during the fight with Heathcliff, episode 14, when all players were paralyzed, how did asuna manage to move in front of the sword? Was it the same concept above, or was it because of somthing else?

In the last episode of Aincrad arc of Sword Art Online, how did Asuna survive even though her avatar disintegrated after being attacked by Kayaba? Also Kirito was stabbed by Kayaba as well. How did he survive?  Was it in the novel on how they really survived?


I'm sure cloud and cloud shadows have been, time and time again, a frustrating problem. Usually after masking the two, I composite multiple images (in a set time interval e.g. 2015-2016, months 6-8) and that solves the missing pixels caused by the masking.  Sometimes though it doesn't quite work.  Is there a way to interpolate lost data/lost pixels caused by cloud and cloud shadow masking in Google Earth Engine?

I have some code that is working properly to calculate the monthly NDVI averages for the previous two years from a date but I sometimes have missing data in some of the months and I would like to get an average based on the mean of the previous two months. I suppose I could also interpolate from the closest geographic data point but it seems like it would be better to interpolate across time than distance given that sometimes the clouds cover reasonably large areas.   But I'm certainly open to other opinions, I just want to fill these holes as accurately as possible. Is there an efficient way to do this.  and here is the code itself:  // pick a landsat tile footprint to use as my geometry var wrs2_descending = ee.FeatureCollection('ft:1_RZgjlcqixp-L9hyS6NYGqLaKOlnhSC35AB5M5Ll'); // use a manually defined point to pick the WRS2 tile var wrs2_filtered = wrs2_descending.filterBounds(roi); var layer1 = ui.Map.Layer(wrs2_filtered, {}, 'WRS2 filtered'); Map.layers().set(1, layer1);  var imageCollection = ee.ImageCollection('LANDSAT/LC08/C01/T1_SR').filterBounds(wrs2_filtered); var monthCount = ee.List.sequence(0, 11);  // Function to cloud mask from the pixel_qa band of Landsat 8 SR data. function maskL8sr(image) {   // Bits 3 and 5 are cloud shadow and cloud, respectively.   var cloudShadowBitMask = 1 << 3;   var cloudsBitMask = 1 << 5;    // Get the pixel QA band.   var qa = image.select('pixel_qa');    // Both flags should be set to zero, indicating clear conditions.   var mask = qa.bitwiseAnd(cloudShadowBitMask).eq(0)       .and(qa.bitwiseAnd(cloudsBitMask).eq(0));    // Return the masked image, scaled to reflectance, without the QA bands.   return image.updateMask(mask).divide(10000)       .select("B[0-9]*")       .copyProperties(image, ["system:time_start"]); }  // run through the image collection and generate monthly NDVI median images var composites = ee.ImageCollection.fromImages(monthCount.map(function(m) {   var startMonth = 1; // thinking that I should always start from Jan so the series are similar   var startYear = ee.Number(2017-1); // number is one year before the current one    var month = ee.Date.fromYMD(startYear, startMonth, 1).advance(m,'month').get('month');   var year = ee.Date.fromYMD(startYear, startMonth, 1).advance(m,'month').get('year')    // filter by year and then filter by month to get monthly mosaics   var filtered = imageCollection.filter(ee.Filter.calendarRange({     start: year.subtract(1), // we want an average of the last two years     end: year,     field: 'year'   })).filter(ee.Filter.calendarRange({     start: month,     field: 'month'   }));   // mask for clouds and then take the median   var composite = filtered.map(maskL8sr).median();   return composite.normalizedDifference(['B5', 'B4']).rename('NDVI')       .set('month', ee.Date.fromYMD(startYear, startMonth, 1).advance(m,'month')); })); print(composites);  Map.addLayer(composites, {min: 0, max: 1}, 'check');  // stack the ImageCollection into a multi-band raster for downloading var stackCollection = function(collection) {   // Create an initial image.   var first = ee.Image(collection.first()).select([]);    // Write a function that appends a band to an image.   var appendBands = function(image, previous) {     return ee.Image(previous).addBands(image);   };   return ee.Image(collection.iterate(appendBands, first)); }; var stacked = stackCollection(composites); print('stacked image', stacked);  // Display the first band of the stacked image. Map.addLayer(stacked.select(0).clip(wrs2_filtered), {min:0, max:1}, 'stacked');


When the Clonetroopers were working for the Jedi, they were dedicated, clever, and personable, whereas the Imperial Stormtroopers come off as bungling, uncoordinated drones with poor aim. Granted, as the original clones are presumably replaced by individual recruits over time, the people within the army will change. But is there any in-universe rationale given for the decline of the Grand Army's originally high standards?

In the Star Wars films we consistently witness just how poor soldiers stormtroopers are. They show very sub-par marksmanship, crappy house searching tactics, and are easily fooled and defeated by Ewoks and Rebels.   That being said, I remember reading a character guide that defined stormtroopers as the very best of the best (best marksman, above average intelligence, etc.). So, in the realm of the Expanded Universe, does the mold that the movies set continue to hold true or are they just the exceptions to the rule?


I was reading the proof of  before which Lemma 10 was proved, I was unable to understand the difference between Lemma 10 and Egoroff's theorem but after going through the answer to this question -       I find it little clear, but still I am unable to understand the proof of the lemma 10,     Any help guys!

Hi math stackexchangers,  I have a question about the difference between two math statements (for reference they can be found in Royden Fitzpatrick pages 64-65).     Egoroff's Theorem: Assume $E$ has finite measure. Let $\{f_n\}$ be a sequence of measurable functions on $E$ that converges pointwise on $E$ to the real-valued function $f$. Then for each $\varepsilon > 0$, there is a closed set $F$ contained in $E$ for which   $$\{f_n\} \to f\text{ uniformly on }F\text{ and }m(E \setminus F) < \varepsilon.$$      Lemma 10: Under the assumptions of Egoroff's Theorem, for each $\eta > 0$ and $\delta > 0$, there is a measurable subset $A$ of $E$ and an index $N$ for which   $$|f_n - f| < \eta\text{ on }A\text{ for all }n \geq N \text{ and }m(E \setminus A) < \delta.$$   My question is this. What is the difference between Egoroff's Theorem and Lemma 10? Am I misunderstanding uniform convergence? To me it looks like Lemma 10 provides uniform convergence. Is the difference that Egoroff's Theorem ensures that $F$ is closed but Lemma 10 doesn't ensure that $A$ is closed?  Thanks


now I begin learning regex, and I have set of string in format like "(9/13)", and I need get second number. I  try this regex: /\(.*?[^\d]*(\d+?)\)/g, in  it works normally.  But here:  var d = "(9/13)"; var v = /\(.*?[^\d]*(\d+?)\)/g; alert(d.match(v));   it returns "(9/13)" , what am I doing wrong?

I want to match a portion of a string using a  and then access that parenthesized substring:  var myString = "something format_abc"; // I want "abc"  var arr = /(?:^|\s)format_(.*?)(?:\s|$)/.exec(myString);  console.log(arr);     // Prints: [" format_abc", "abc"] .. so far so good. console.log(arr[1]);  // Prints: undefined  (???) console.log(arr[0]);  // Prints: format_undefined (!!!)   What am I doing wrong?    I've discovered that there was nothing wrong with the regular expression code above: the actual string which I was testing against was this:  "date format_%A"   Reporting that "%A" is undefined seems a very strange behaviour, but it is not directly related to this question, so I've opened a new one, .    The issue was that console.log takes its parameters like a printf statement, and since the string I was logging ("%A") had a special value, it was trying to find the value of the next parameter.


I am trying to install Windows font on Ubuntu 16.04. It says package has installed when I try to reinstall the same package but fonts are not found on LibreOffice. Also, while installing it gives some error.   $ sudo apt-get install ttf-mscorefonts-installer Reading package lists... Done Building dependency tree Reading state information... Done The following NEW packages will be installed:    ttf-mscorefonts-installer 0 upgraded, 1 newly installed, 0 to remove and 5 not upgraded. Need to get 0 B/29.5 kB of archives. After this operation, 134 kB of additional disk space will be used. Preconfiguring packages ... Selecting previously unselected package ttf-mscorefonts-installer (Reading database ... 208570 files and directories currently installed.) Preparing to unpack .../ttf-mscorefonts-installer_3.4+nmu1ubuntu2_all.deb ... mscorefonts-eula license has already been accepted Unpacking ttf-mscorefonts-installer (3.4+nmu1ubuntu2) ... Processing triggers for fontconfig (2.11.94-0ubuntu1.1) ... Processing triggers for update-notifier-common (3.168.2) ... ttf-mscorefonts-installer: processing... ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/andale32.exe Get:1 http://downloads.sourceforge.net/corefonts/andale32.exe [198 kB] Fetched 198 kB in 5s (35.9 kB/s)                                       W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/andale32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arial32.exe Get:1 http://downloads.sourceforge.net/corefonts/arial32.exe [554 kB] Fetched 554 kB in 4s (124 kB/s)                                        W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arial32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arialb32.exe Get:1 http://downloads.sourceforge.net/corefonts/arialb32.exe [969 B] Err:1 http://downloads.sourceforge.net/corefonts/arialb32.exe                Hash Sum mismatch Fetched 969 B in 2s (367 B/s)                        W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arialb32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) E: Failed to fetch http://downloads.sourceforge.net/mirrorproblem?failedmirror=excellmedia.dl.sourceforge.net Hash Sum mismatch E: Download Failed     I followed . There still some Warning (W) was visible but No Error (E). Warning is basically this:  W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/webdin32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied)   But after the steps mentioned in the link, I can see Window Font appear in LibreOffice font selection list.   Old Update Information Dialog Box still came. Not sure if it is coming due to old process or due to this one.   Do I need to take any more steps or everything is fine?

After fresh install 12.04 I && updating apt and system restart, I always get this annoying message after reboot :     Failure to download extra data files      The following packages requested additional data downloads after   package installation, but the data could not be downloaded or could   not be processed.      ttf-mscorefonts-installer      The download will be attempted again later, or you can try the   download again now. Running this command requires an active Internet   connection.   But if I run attempt now, it shows flashing terminal window and like nothing happen. It'll happen again when I restart system.  I found someone have  too, but he haven't replied yet.   I'm a newbie here, please help.


I was wondering if there is any known sum of reciprocals of distinct odd prime numbers such that $$\sum_{k=1}^{n}\frac{1}{p_k}=1$$ Could someone give an example of one, or tell if there is none known? Or maybe it is impossible to find one, then it would be great to know the proof. Thanks!

Inspired by        Can we solve the equation $$1=\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+\cdots +\frac{1}{a_n}$$ where $a_1,a_2,a_3,\cdots ,a_n$ are distinct prime powers (primes are allowed) ?   I tried a modified greedy-algorithm with different starting vectors and brute force with $6$ entris with limit $200$, but did not find a representation.


I have a Dell Inspiron 14 3000 Series. I just installed Ubuntu 18.04 dual booted with Windows 10.  The output of the speakers and headphones work just fine when booted to Windows 10, but when I boot into Ubuntu, the output of the speaker works while the headphones do not.  Pavucontrol shows sound from Rythmbox and that the headphone output is at 100%. I assume this means the headphones are being detected.  The headphones do work with other devices.  This question was asked more than one times before me on this site.

The headphones are detected, because when they are plugged in, they appear in the sound settings.  The problem is that they just don't output any sound.  Laptop speakers output sound just fine.  I'm running Ubuntu 16.04 x64  This is the output from running :    What steps can I take to try and debug this issue myself?  Edit 1  Thanks to @Rexford and this , I've worked out how to get detailed debugging output from pulseaudio, by temporarily modifying /etc/pulse/client.conf using the --log-level flag.  I'll report back after I play around with this new information and try to find the problem.  Edit 2  Woke up this morning planning on getting to the bottom of this issue, when I discovered that the sound from the headphones started working.  Last night I had tried many solutions (from various forums and webpages), but was not restarting my computer (was just doing pulseaudio -k && sudo alsa force-reload).  So I guess that the reboot was necessary to make one of the solutions kick in and actually work.  One of the biggest things I tried was uninstalling pulseaudio, installing gnome-audio as a replacement and going back to pulseaudio. So I recommend others try that if they are struggling. Just note that if you do that, you should follow the instructions  to get your volume/sound icon back (if it's missing after reboot - which it was for me).  I can't get to the root of this problem now, because it no longer exists for me.  Edit 3  The problem came back...  Debug logs from pulseaudio don't reveal anything useful (e.g. error messages).  According to , alsa is the next stop to check for the cause.


I cannot figure out how to prove that the sequence $x_n\:=\:\left(-1\right)^n\:+\:\frac{1}{n}$ does not converge. I tried a proof by contradiction but the sequence ends up being $\frac{1}{n}+1\:-\:\frac{1}{n}$ and I don't know where to go from there. I also tried showing that its subsequences don't converge but I did not know what to do with them $x_{2n} = (-1)^2n + \frac{1}{2n}$ $x_{2n-1} = (-1)^2n-1 + \frac{1}{2n}-1$

I am trying to find out if the following sequence $(a_n)_{n\geq 1}$ will either converge or diverge. $$ a_n = (-1)^n + \frac1n $$  If the limit converges, I need to find its limit.   I tried plugging in various numbers for n besides 1, but I am not entirely sure if it really does converge.


after my recent upgrades of miktex (may, 5) the tikz library calligraphy doesn't work anymore. for example, testing of :   \documentclass[tikz,border=10pt,multi]{standalone} \usetikzlibrary{decorations.pathreplacing,calligraphy} \begin{document} \begin{tikzpicture}   \draw[pen colour={red}, decorate, decoration={calligraphic brace, amplitude=6pt}, thick] (0,0) -- (0,3); \end{tikzpicture} \end{document}   which previously works, now gives error:  ! Undefined control sequence. <argument> \g__prg_map_int   l.707 ...igraphy pen copperplate}{\l__cal_tmpa_tl}  ?    forcing compilation gives correct result.  it seems that with this upgrade is introduced a bug. do anyone can help me with workaround?

Under MacTeX 2018 the following TeX file:  \documentclass{article}  \usepackage{tikz}  \usetikzlibrary{decorations.pathreplacing,calligraphy}  \begin{document}  \tikz\draw[decorate,decoration={calligraphic brace,amplitude=4mm},ultra thick] (0,0) -- (0,8);  \end{document}   gives the following warning  ************************************************* * LaTeX warning: "kernel/deprecated-variant" *  * Variant form 'VnV' deprecated for base form '\spath_get:nnN'. One should not * change an argument from type 'N' to type 'V': base form only accepts a * single token argument. *************************************************   and these errors:  /usr/local/texlive/2018/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex:707: Undefined control sequence. <argument> \g__prg_map_int   l.707 ...igraphy pen copperplate}{\l__cal_tmpa_tl}  /usr/local/texlive/2018/texmf-dist/tex/latex/spath3/tikzlibrarycalligraphy.code.tex:707: You can't use `\char"1' after \advance. \int_gincr:N ..._global:D \tex_advance:D #1\c_one    I reported the warning in , but the errors are new with TL2018 -- TL2017 does not give the errors.


How can I prevent the following text from exceeding the margins of my document?  \documentclass{article}  \begin{document}  We first left the DC loop open and inputted AC at frequencies of $\{50, 51, 67, 95, 102, 127, 147, 150\}$ Hz into the AC loop. Text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text.  \end{document}   Output:

In the inline math mode ($...$), if the formula is too long, LaTeX will try to break it on operators, e.g.  very long text followed by a very long equation like $a+b+c+d+e+f+g+h+i+j+k+l$ etc   may be rendered as  very long text followed by a very long equation like a+b+c+d+e+f+g+h+i+ j+k+l etc   However, the break won't happen if they are separated by commas, e.g.  very long text followed by a very long equation like $a,b,c,d,e,f,g,h,i,j,k,l$ etc   will overflow the page like  very long text followed by a very long equation like a,b,c,d,e,f,g,h,i,j,k,l etc   How to make LaTeX able to insert line breaks after a comma too?


In page 298 of Rosenthal's Probability of statistics, it says:  We are only interested in likelihood ratios $\frac{L(\theta_1 | s)}{L(\theta_2 | s)}$ for $\theta_1, \theta_2 \in \Omega$ when it comes to determining inferences for $\theta$ based on the likelihood function. This implies that any function that is a positive multiple of $L(\cdot |s)$ , i.e. $L^*(\cdot |s) = cL(\cdot |s)$ for some fixed $c>0$, can serve equally well as a likelihood function.  Question: I'm not sure why being interested in the ratios allows us to use any positive multiple of a likelihood function. For example: If I use $L(\theta_1 | s)$ and $L(\theta_2 | s)$, such that for given data $s_0$, I get $L(\theta_1 | s_0) = 0.1$ and $L(\theta_2 | s_0) = 0.3$, then the distribution associated with $\theta_2$ is more likely to have generated the data. But if instead of $L(\theta_1 | s)$ I use $cL(\theta_1 | s)$ where $c = 5$, and so $\frac{cL(\theta_1 | s_0)}{L(\theta_2 | s_0)} = \frac{5}{3}$, then the distribution associated with $\theta_1$ is more likely to have generated the data.

I'm reading  where the authors are leading from a discussion of maximum likelihood estimation to Bayes' Theorem, ostensibly as an introduction for beginners.  As a likelihood example, they start with a binomial distribution:  $$p(x|n,\theta) = \binom{n}{x}\theta^x(1-\theta)^{n-x}$$  and then log both sides  $$\ell(\theta|x, n) = x \ln (\theta) + (n-x)\ln (1-\theta)$$  with the rationale that:     "Because the likelihood is only defined up to a multiplicative constant of proportionality (or an additive constant for the log-likelihood), we can rescale ... by dropping the binomial coefficient and writing the log-likelihood in place of the likelihood"   The math makes sense, but I can't understand what is meant by "the likelihood is only defined up to a multiplicative constant of proportionality" and how this allows dropping the binomial coefficient and going from $p(x|n,\theta)$ to $\ell(\theta|x,n)$.  Similar terminology has come up in other questions ( and ), but it still not clear what, practically, likelihood being defined or bringing information up to a multiplicative constant means. Is it possible to explain this in layman's terms?


Your blood-related brother's wife? If she is older or younger than you?    I came up with a discussion some time ago. But, nobody or my friends seem to know. How should I address her?     Your blood-related sister's husband?   What if they are just or god brother or god sister?

Please refer the following questions asked elsewhere on this site:       I am a native Hindi speaker; Hindi has a plethora of terms referring to relationships. To take a trivial example, the term uncle may refer to father's elder brother, father's younger brother, mother's brothers, father's sister's husband, mother's sister's husband, all of which have specific addresses in Hindi.  I discussed the same with one of my teachers. She had the opinion that the development of language mirrors the cultural moorings of the society that uses the language. Now, since all of the above relationships have distinct status and reverence in the Hindi speaking society, that calls for different addresses. That may well not be the case in English speaking societies.  Is that correct? What other linguistic reasons may account for such a dearth of vocabulary in English in this area?


I'm trying to find out how QuickType.io works, however I cannot find a way to show my converted results.  I converted a JSON file to C# and got a satisfactory output:  public partial class Welcome {     [JsonProperty("relatiesoort")]     public string[] Relatiesoort { get; set; }      [JsonProperty("modifiedOn")]     public DateTimeOffset ModifiedOn { get; set; }      [JsonProperty("relatiecode")]     public long Relatiecode { get; set; }      [JsonProperty("naam")]     public string Naam { get; set; } }   I think the Welcome class can be used to do what I want:  public partial class Welcome {     public static Welcome[] FromJson(string json) => JsonConvert.DeserializeObject<Welcome[]>(json, APIconnectV2.JSON.Converter.Settings); }   This is the code I use to print the results:  var result = httpClient.GetAsync(new Uri("http://hidden.com')")).Result; var json = result.Content.ReadAsStringAsync().Result;  dynamic jObject = JArray.Parse(json); System.Diagnostics.Debug.WriteLine(Welcome.FromJson(json)[0]);   However, the output I receive is:  APIconnectV2.JSON.Welcome   Any number greater than 0 results in an out of bounds error. I'm not even sure if this is the correct way to print my output, however I cannot find a lot of documentation surrounding QuickType.

So for viewing a current object's state at runtime, I really like what the Visual Studio Immediate window gives me.  Just doing a simple  ? objectname   Will give me a nicely formatted 'dump' of the object.    Is there an easy way to do this in code, so I can do something similar when logging?


I have a problem where I'm supposed to expand an array, each time creating an array with identical results. Before you tell me to just use ArrayList or something else already in the Java API, I was specifically instructed to use my own code. I tried simply creating an array that is one slot larger than my current array, though that does not seem to work very well. Here is what I have that the current moment:  public static void expand(Object[] objArray) {     Object[] objArray2 = new Object[a.length + 1];     for (int i = 0; i < a.length; i++)         objArray[i] = objArray[i];     objArray = objArray2; }

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


I'm making a flat company sign for outside our building and the sizes are:  Left Sign: (Width) 8.0 Meters x 0.850M (Length)  Right Sign: (Width) 7.0 Meters x 0.850M (Length)  I have 2 questions.   What resolution would you suggest for a sign this big? I'm using Adobe Photoshop 7. The company that is printing the sign said "make it the biggest your computer can handle" i'm not sure what they mean by that. We run windows 7. I convert the meters into mm or cm but it says it's too high. what should I do?

(This question is meant to be a resource to direct others to given that this is a common question.)  Given the task of creating an image that will be printed at a certain size, what pixel dimensions and resolution should I be setting my file at?


I have a Windows 10 computer that was originally upgraded from a Windows 7.  About a year ago I got a Samsung External SSD drive and installed its accompanying software.  Whenever I attached the SSD harddrive, I would get a prompt asking for my password.  Everything worked fine.   However a month or 2 ago after the latest Windows 10 patch, I would get a prompt for password whenever I rebooted and logged in and not wait for me to attache the SSD harddrive.   I am trying to figure out how this is possible.  I can always rename the executable to prevent the popup, but I want to know how this executable is being initiated.  Knowing this would also ensure other programs are not being started without my knowledge.  I have checked my startup tag, searched registry settings and reviewed the Task scheduler, without success.  Is there any place else to check?  Also, I think when I installed the latest patch, I clicked on the option to auto login to complete the installation.  Thanks,  I figured out how this was happening.  Windows 10 "shut down" is different than the past.  Now when you "shut down", any program that is currently running automatically starts next time you reboot.  To prevent this from occurring you have to do a force shutdown.  One way is using this command:  Shutdown –s –f.

I'm trying to delay the startup of a specific program that loads at login. As per an answer in , I should be able to do it using Task Scheduler. The problem is, I can't find the program listed anywhere. Is there a particular pane I should be looking in? The program is Razer Synapse so I don't think it would be in the Microsoft or Western Digital folders.    If it's not in Task Scheduler, is there another way I can delay it at startup?  Out of curiosity how many ways are there for a program to be run at Startup in Windows?


I have CentOS-6.5 running in qemu-based virtual machine, with a single ethernet interface, which surprisingly is being renamed by udev from eth0 to eth1 for whoever knows reason (!)  So I want to to completely disable this behavior, i.e. passed "net.ifnames=0" to the kernel command line. It doesn't seem to work, the behaviour has not changed. Neither "biosdevname=0" as a kernel parameter didn't help.  % qemu-system-x86_64 -cpu host -boot c -hda my_image.qcow2 -snapshot -m 1024 --enable-kvm -name vm0 -nographic -display curses -pidfile /var/run/vm0.pid -mem-path /dev/hugepages -mem-prealloc -monitor unix:/var/run/vm0monitor,server,nowait -net none -netdev type=tap,id=net0,script=no,downscript=no,ifname=vhost1,vhost=on -device virtio-net-pci,netdev=net0,mac=00:00:00:00:00:01,csum=off,gso=off,guest_tso4=off,guest_tso6=off,guest_ecn=off   No warnings or errors, and I can login the VM afterwards. However it seems that udev has renamed single network interface form eth0 to eth1, here is a rule file automatically created at boot:  % cat /etc/udev/rules.d/70-persistent-net.rules # PCI device 0x1af4:0x1000 (virtio-pci) SUBSYSTEM=="net", ACTION=="add", DRIVERS=="?*", ATTR{address}=="00:00:00:00:00:0 1", ATTR{type}=="1", KERNEL=="eth*", NAME="eth1"   Why would virtio-pci driver choose eth1 for the single interface in the system?  However this does not happen if I run qemu without mac=.. option, ie. the MAC address is qemu predefined 52:54:xxx but I want to provide the macs via command line.

When I run ifconfig -a, I only get lo and enp0s10 interfaces, not the classical eth0  What does enp0s10 mean? Why is there no eth0?


 Credit Limit:  $@Model.CreditLimit.ToString().ToLocaleString()
  I am changing an Int to a String using ToString() Then I am trying to format the number I am getting using ToLocaleString(). The number looks like this: 80567. I am trying to format it to look like this: 80,567.   The error I get is "string does not contain a definition for "ToLocaleString"  Thoughts?  EDIT: Going to have this issue closed. Found where my error resided. Please refer to this link if you have any questions on the topic:

I want to add a comma in the thousands place for a number.     String.Format()?


I've just made a bootable usb on windows7, and now I want to replace my windows7 with Ubuntu. When I choose the option replace windows 7 with Ubuntu, I need to select a drive. Since I have only one drive in my desktop, I must use it. But on my windows the drive is partitioned into a C  and D drive (both 500GB). I put all my files on the D drive, so I can still use them in Ubuntu. My intention is to install Ubuntu on the c drive from windows, but when i click on advanced partitioning tool, I see that there are four partitions:  sda1(ntfs): 14.7 GB, sda2(ntfs): 104.9 MB, sda3(ntfs): 492.7 GB, sda4(ntfs): 492.7 GB   My problem is that I don't really know what the first two partitions are, and which one is the c:/ drive from windows. I guess it is the third, but I must be sure because otherwise all my data is lost. What exactly do I have to do to just install Ubuntu on one partition and keep another partition with my files (the d in windows)? Also I don't really know on what type of filesystem Ubuntu has to be installed on(fat, ntfs, ext,..). The desktop that I'm working on is a Acer Aspire AX3900. Thanks (and sorry for my bad English).

I would like to install Ubuntu alongside Windows 7 on a HP G62 Notebook. Although I have installed  Ubuntu in a dual-boot many times before, I found out that this model has already four partitions.    Partitions:   SYSTEM (NTFS, 199MB, used 66.59MB) Partition without any tag: NTFS (579GM, used 129GB)  RECOVERY (NTFS 16.74 GB, used 2.42GB)  HP_TOOLS (FAT32, 103.34 MB, used 13.23MB)   Since I am not an expert with partitions I would like to get advice on how to do this.  My first idea is this one:   Free some space from /dev/sda2 (I don't know if could also free some other space) delete the HP_Tools partition (I have already created a backup) create an extended partition with the free space in #1 containing three parititions: swap (1gb); / (EXT4, 30GB);  /home (EXT4, 120GB)   Another option is to use wubi instead.  What do you think? Is there any other way to achieve this?  PS: I really think this HP policy of using 4 partitions is not a coincidence  PS: I tried using gparted from the live CD and I got a warning message saying that if I freed some space from /dev/sda2 I could create serious issues in the system


So, after having spent the last 9 hours attempting to understand the basic tenets of stress tensors in fluids, I can honestly say that I think I know less now than when I began.  My questions are these: what precisely is a stress tensor in the context of fluid dynamics, and why is it the case that stress tensors are necessarily symmetric in this context?  One of the resources I found referred to the entries of the stress tensor matrix as being the representations of the directional stresses on an infinitesimal cube in a flow, supposing that this cube of fluid is static. This would explain the symmetry of the tensor (since the fluid cube is not rotating, the shear stresses would have to be equal in magnitude at the corners), but it would also indicate to me that the perpendicular forces (the diagonal elements of the tensor) must all be zero, since the particle is also not translating in the fluid. I know this is incorrect, but why?  Disclaimer: I have never actually taken a course in physics.  I'm in a graduate mathematics program, and this is my first time encountering any of these concepts.


Hi Stackoverflowers,  I wanted to know if anyones aware if the Stackoverflow team is working on a printable view for the Q&A's.  It'd even be cooler to have it output to PDF format for a very nice print job.  :)  It would be awesome to have a feature like that.

I would like to make a suggestion for a Stack Overflow/Exchange complete Q&A printer-outer.   It would print out the full question, its answers, and  its comments, which the normal web-browser print does not do.


Can anyone give me a hint in this problem? Please.  Let $X$ be a topological space. If $f,g$ are continuous function of $f,g \colon X\to S^n$  which $f(x)\neq -g(x)$ for all  $x \in X  $, show $f$ and $g$ are homotopics.

I'm new here. Can anyone give me a hint in this problem? Please.  Let $X$ be a topological space. If $f,g$ are continuous function of $f,g\colon X\to S^n$  which $f(x)\neq -g(x)$ for all $x$ in $X$, show $f$ and $g$ are homotopics. I try to show a homotopy using $$q(x) = \frac{f(x)+g(x)}{\|f(x)+g(x)\|}$$ it's well defined, but i'm stuck.


I am a researcher without a PhD.  Because most people in my field do have PhDs, I sometimes get emails addressed to "Dr. [MyName]."  How should I address this, if at all?  I don't want to complain because they are being polite, but also I don't want to lie by omission about my credentials.

I currently have a masters degree in an engineering field and I don't currently have any PhD degrees (I may study for a doctorate degree in future). It happens that when I go to conferences or scientific occasions, even in the emails I receive from people; they use a doctor prefix for my name; but I do not have a PhD degree.  What is a good etiquette to deal with such thing? Should I directly tell them that I do not have a doctorate degree? Or should I neglect such a mistake by them and don't do anything?  I think it is unethical not to correct such thing, because the person may still think that I have a PhD degree; and such wrong usage of title should be corrected some way. Once a person used doctor title for my name in an email and I just added a line in my reply to his email, stating that I have a masters degree.


I have run into a strange behavior with the style file of Neurips 2021 (a conference), . If I compile their sample TeX file on Overleaf, I get more content on the same number of pages, compared to when I compile it locally on my Machine, an Arch Linux system with TexLive 2020. Below are the screenshots: On my computer:  On Overleaf:  This matters since the conference has a 9-page limit and I get get more in 9 pages if I compile on Overleaf. Any idea why this happens and if there is a fix for it (i.e., to get a similar result as Overleaf locally)?

When working on a joint project, my collaborators and I encountered that we obtain significantly different PDF outputs with the same latex source. To be more specific, this already happens with the example .tex (and .sty) files for this year's NeurIPS 2021 conference: . When compiling the example .tex file on Overleaf, I obtain exactly the same pdf output as provided by the organizers, with a length of 5.5 pages (). When compiling the same file (with the same style file) on my local system, the result is half a page longer, filling the complete 6 pages. Here are some observations: Line breaks seem to happen at the same places. Instead all the vertical spaces seem to be a little bit larger in the file compiled on my own system. There is not a specific object that needs more space. Instead, it looks like every single line needs a bit more space. However, the font size itself is identical. Also the textwidth and textheight, as well as, the paper measures (letterpaper) seem to be the same. Even switching between MikTex and TexLive on my local system does not solve the problem. Since NeurIPS has strict page limits, it makes a crucial difference whether a file is half a page longer or not. Any help is highly appreciated! Thanks!


I am a nurse in a hospital in the nys retirement system. $1900.00 was contributed by my employer to my 414h plan. I am under 50 years old- can I contribute to my roth ira and if so how much?

My husband is a teacher in New Jersey; 61 years of age. He has a pension plan listed on w-2 in box 14 (other). It is coded as 414(h). He asked the tax advise person at the school if he could still contribute maximum yearly amount to an individual Ira and was told yes. An accountant we know told us this was incorrect. Can he deduct the amount placed in individual Ira?


Is it true, that we haven't any linear mappings (Let it be called $\phi$) between $\mathbb{R}^n \to \mathbb{R}^n$, where $n = 5$ and Ker $\ \phi$ = Im$\ \phi$ Where: Ker $\ \phi = \{v \  | \ \phi(v) = 0, v \in \mathbb{R}^n\}$ Im$\ \phi = \{\phi(v) \  | \ v \in \mathbb{R}^n\}$

I am trying to prove a series of propositions:  Given any homomorphism p from $\mathbb{R}$[X] to $\mathbb{R}$[X], show that it is equal to $\phi_g$ for a unique g in $\mathbb{R}$[X], with $\phi_g$(f) = f(g(X)). I've expanded the expression $p(f) = p(\sum_{i=0}^n a_iX^i) =\sum_{i=0}^n p(a_i)p(X)^i$ but I'm not sure how to show $p(f) = \sum_{i=0}^n p(a_i)p(X)^i = \sum_{i=0}^n a_ig(X)^i = \phi_g(f)$.  Show that if h,g $\in \mathbb{R}$[X] are such that h(g(X)) = X, then g(X) = aX+b for a $\in$ R$^x$ and b$\in \mathbb{R}$.


My 3.0 portable HD was corrupted, I've got personal data on it and I wanted to prevent any randoms from accessing it. I am not very tool-savvy, so I just broke the circuit board, and repeatably bashed it with a hammer on both sides. I wasn't able to access the platter but I did hear some broken shards on the inside traveling around when I would shake it, so I either broke the platter just by hitting with impact, or there was something else in there that broke. Thoughts?

I have 3 old 3.5" internal hard drives sitting gathering dust at the moment. 2 are SATA, and one IDE. I want to either start putting them to use, or dispose of them to clear up some space.  What is the best approach towards disposing of the drives in terms of thoroughly cleaning the contents before throwing away or selling? Are there any recommendations for good software to use to do this?   Are there any 100% successful methods which result in having a usable drive at the end?


Since  have already been earned by the time I'm writing this, and I think I found the perfect hat for my avatar already, why don't we start showing them off like ?  Post hats, hats, and more hats! Those that you're especially proud of, or that you simply look good in - all are welcome ;)

With Winter Bash 2017 nearing its end - another 3 days and all the hats go back in the box - why don't we take the opportunity to show off our hats and display our achievements? You can screenshot your hats and post an answer below, and show off your posh headgear!  Post hats, hats, and more hats! Those that you're especially proud of, or that you simply look good in - all are welcome ;)


import java.util.Scanner;  class Pal {     public static boolean Palindrome(StringBuffer str) {         StringBuffer str1 = str.reverse();         System.out.println(str1);         if (str == str1) {             return true;         } else {              return false;         }     }      public static void main(String args[]) {         System.out.println("Enter a string");          StringBuffer str = new StringBuffer();         Scanner input = new Scanner(System.in);         str.append(input.nextLine());          boolean result = Palindrome(str);         System.out.println(result);     } }   How sholud I improve my code such that values come out to be perfectly correct?

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


After I finished my taxed in last week of March, I received a Updated 1099 with only one modification where 199a is modified from zero to $50 or so. Refund is about to come in a week.  Initial values  Box 1a = 500 Box 1b = 200 (all other boxes empty)  similar question is at   Updated values Box 1a = 500 Box 1b = 200 Box 5 = $50    The effect of this update is about $5 more tax refund. And to get this refund I will spend more in postage.  So my question is , is it ok to leave the money with IRS or by law I am required to get it fixed.  This question was asked on April 08, 2019 before the  ( asked on April 18) @joetaxpayer , The marking says      This question has been asked before and already has an answer.   I agree that this question has answer at the referenced location, the part that I disagree is "asked before"

Long story short: I got a corrected 1099-DIV after filing my taxes. After going through the calculation, it appears that correcting the return would net me an extra $13 refund, i.e. I overpaid my Federal taxes by $13.  Apparently you can't efile an amended return, and frankly the hassle of printing new forms and mailing them isn't worth the $13 to me.  Is there any reason I shouldn't consider the extra $13 a gift to the government, ignore the corrected 1099-DIV, and not file an amended return?


I recently came across this 3x leveraged etf of the S&P 500 (NYSE:UPRO). I understand that it’s a risky investment, but I still see way more reason to buy it over any other thing that tracks the S&P 500. Since it’s 3x the S&P 500 (also 3x NYSE:IVV), then how about you throw a third of the money you normally would into it? The Pros of NYSE:UPRO: So,   profit potential is the same AND investing in A allows us to spend leftover money on other things (less money at risk)   The Cons: Expense ratio seems to be the only reason not to buy (0.93% for NYSE:UPRO vs. 0.03% for NYSE:IVV) ok, this is a big difference... but even still, let’s account for the expense ratios. Similar to what I said before, we’re going to invest one-third (since it’s 3x the volatility) that of NYSE:IVV, so we’ll just say $10 for NYSE:UPRO vs $30 for NYSE:IVV. Well, our expense at the end of the year for UPRO would be 0.0093(10)=$0.093 and our expense for IVV would be 0.0003(30)=$0.009, meaning our expense for UPRO is just over 10x that of IVV assuming we spend 1/3 of what we would on IVV. So,   our expenses will be a bit over 10x larger   Even knowing this, the S&P 500 is almost guaranteed to increase in value in the long run, so NYSE:UPRO should be too, but 3x more! All we have to do to account for the larger expense ratio is (yes, go against what I said before) spend a bit more than a third of what we would on IVV. Are there any other reasons that NYSE:IVV is a better investment? Yes, it’s less risky, but spending a bit over a third of what you would on IVV on UPRO allows you better profit potential, with slightly more risk. In the long run, I’d expect UPRO to be a far better investment that the S&P 500. Also, is there any other etfs that multiply the S&P 500 by more than 3, (yes I know there’s NYSE:SPXU which is -3x, but I’m talking even more volatile)?

I was reading this article about S&P 500 short ETFs:     and I was confused when it said: "investors should note that such products are suitable only for short-term traders as these are rebalanced on a daily basis". What is ETF rebalancing exactly? and why does it make these ETFs unsuitable for long-term short trading?


I know how to prove $0 \times a \cong 0$ in categories admitting exponentiation (and initial objects, of course). But does this hold for categories that don't have exponentiation?  I don't have enough examples in my mental categories library to give a counter-example, nor have I managed to prove that $0 \times a \cong 0$ based on just the notion of products.

In $Sets$, the initial object is $0 = \emptyset$. We have $C \times \emptyset = \emptyset$ for any set $C$. As there are no maps to the empty set, we don't get much of the universal property of the product.  I am now wondering what is special about arbitrary categories $\mathscr{C}$ with $C \times 0 \cong 0$ for all objects $C$ of $\mathscr{C}$, where $0$ is the initial object of $\mathscr{C}$.   From Sheaves in Geometry and Logic by MacLane (p.194), in any topos $\mathscr{C}$, any arrow $k:C \to 0$ is an isomorphism. The universal property of the product would then also not yield very much.   Are there any categories of higher interest?


I am window form guy and now have to deploy some web application. I am still consifering either choose mvc or webforms. I am not very familar wit html/css/ajax staff. SOmehow i heard mvc is a "new way to go" but i am a bit worry about time to learn all this stuff and just go with standard webforms to use my controls which are available inside toolbox also with devexpress controls. I am wonder if mvc doesnt have controls drag-drop available how to handle such things like grid to populate from database and other staff? How mvc developers handling with it without controls? Can you advice me a bit? I hear something that ajax could provide me with controls.

What are some of the advantages of using one over the other?


I saw the code below recently: std::error_code ec;  // --- some code  if (!!ec) { //error reaction }  For what purpose the !! is used? The only idea is to force bool operator, but for what? May it have sense for some implementations of boost error types?

I just came onto a project with a pretty huge code base.   I'm mostly dealing with C++ and a lot of the code they write uses double negation for their boolean logic.    if (!!variable && (!!api.lookup("some-string"))) {        do_some_stuff();  }                                      I know these guys are intelligent programmers, it's obvious they aren't doing this by accident.   I'm no seasoned C++ expert, my only guess at why they are doing this is that they want to make absolutely positive that the value being evaluated is the actual boolean representation. So they negate it, then negate that again to get it back to its actual boolean value.   Is this correct, or am I missing something?


$z=f(x,y)$ where $x=r\cos\theta $ and $y=r\sin\theta$. Find $ \frac{\partial z}{\partial x}$ and $ \frac{\partial^2 z}{\partial x^2}$   I'm having big troubles with using chain rule, in particularly the second derivative. Spent 2 hours on this already. What I have...  $ \frac{\partial z}{\partial x}=\frac{\partial r}{\partial x}\frac{\partial z}{\partial r}+\frac{\partial z}{\partial θ}\frac{\partial θ}{\partial x}$. So I'm guessing that $\frac{\partial z}{\partial r}$ and $\frac{\partial z}{\partial θ}$ are unkown? And I will need to use them to differentiate again. Any help is really welcome. This is simply only part of a bigger question.   Full Problem:

$z=f(x,y)$ where $x=rcosθ$ and $y=rsinθ$  Find $ \frac{\partial z}{\partial x}$ and $ \frac{\partial^2 z}{\partial x^2}$  I'm having big troubles with using chain rule, in particularly the second derivative. Spent 2 hours on this already. What I have...  $ \frac{\partial z}{\partial x}=\frac{\partial r}{\partial x}\frac{\partial z}{\partial r}+\frac{\partial z}{\partial θ}\frac{\partial θ}{\partial x}$. So I'm guessing that $\frac{\partial z}{\partial r}$ and $\frac{\partial z}{\partial θ}$ are unkown? And I will need to use them to differentiate again. Any help is really welcome. This is simply only part of a bigger question.   Full Question:


I have data that looks like   CUSTOMER,  CUSTOMER_ID, PRODUCT ABC INC    1            XYX ABC INC    1            ZZZ DEF CO     2            XYX DEF CO     2            ZZZ DEF CO     2            WWW GHI LLC    3            ZYX    I'd like to write a query that'd make the data look like this:   CUSTOMER, CUSTOMER_ID, PRODUCTS ABC INC   1            XYX, ZZZ DEF CO    2            XYX, ZZZ, WWW GHI LLC   3            ZYX    Using Oracle 10g if helps.  I saw something that would work using MYSQL, but I need a plain SQL or ORACLE equivalent.   I've also seen examples of stored procs that could be made, however, I cannot use a stored proc with the product i'm using.  Here's how'd it work in MySQL if I were using it  SELECT CUSTOMER,         CUSTOMER_ID,         GROUP_CONCAT( PRODUCT )  FROM MAGIC_TABLE  GROUP BY CUSTOMER, CUSTOMER_ID   Thank you.

I have a simple query:  select * from countries   with the following results:  country_name ------------ Albania Andorra Antigua .....   I would like to return the results in one row, so like this:  Albania, Andorra, Antigua, ...   Of course, I can write a PL/SQL function to do the job (I already did in Oracle 10g), but is there a nicer, preferably non-Oracle-specific solution (or may be a built-in function) for this task?  I would generally use it to avoid multiple rows in a sub-query, so if a person has more then one citizenship, I do not want her/him to be a duplicate in the list.  My question is based on the similar question on .  UPDATE: My function looks like this:  CREATE OR REPLACE FUNCTION APPEND_FIELD (sqlstr in varchar2, sep in varchar2 ) return varchar2 is ret varchar2(4000) := ''; TYPE cur_typ IS REF CURSOR; rec cur_typ; field varchar2(4000); begin      OPEN rec FOR sqlstr;      LOOP          FETCH rec INTO field;          EXIT WHEN rec%NOTFOUND;          ret := ret || field || sep;      END LOOP;      if length(ret) = 0 then           RETURN '';      else           RETURN substr(ret,1,length(ret)-length(sep));      end if; end;


What did James and Lily Potter do for a living? Did they have any job?

So, at the beginning of Harry Potter, Harry is found to have a large vault of gold at Gringotts. Where did all of that money come from? What did James (I assume it came from him, as Lily was muggle-born, and they were both young) do to get all of that cash?


I've recently read about the time dilation occurs at very high speeds. But I'm really wondering if it is just a mechanical slowdown of the clock only? What if we use clocks that does not use moving crystals or reflecting light to measure time? Can anyone please make it clear to me?

Is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then to B it APPEARS that A's clock moving slower, but A sees his own clock moving at normal speed.  Similarly, to A it APPEARS that B's clock is moving slower, but B sees his own clock moving at normal speed.  If the above is true, then both A seeing his own clock moving at normal speed and B seeing his own clock moving at normal speed means that in reality both clocks are moving at normal speed, and neither has slowed down, whereas the other person's clock APPEARING to move slowly is merely an illusion.   Now is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then A sees his own clock move slowly (compared to the speed of the clock when A was at rest with respect to B) and B sees his own clock move slowly, so that in reality both clocks are moving slowly, but they still remain synchronized (since both are slow by the same amount)  If the above statement is not true, then why do muons decay slowly when moving fast? [it could only be possible if the muon saw its own clock as moving slowly. If we saw the muon's clock moving slowly, but the muon saw its own clock moving at the normal rate, then the muon would decay at the normal rate, and not slowly]  Can anyone please explain where I went wrong?


I am running Lubuntu and it does not have LTS releases, so I want to know if my version is EOL or not and what versions are.   I know of the  on the wiki, but that only covers Ubuntu, not any of the distros of Ubuntu, such as Lubuntu, Xubuntu, Kubuntu, etc. I also know of the ubuntu-release-status command, and that is useful, but could be a bit confusing for new users and isn't easy to understand.  Are there any pages that has a list of all the distros and their life terms, or a page per-distro separate from the Ubuntu wiki page?

I want to know where I can find updated information about all the stable and in-development versions of Ubuntu, where I can find this information?     This question is meant to be a canonical question. It expects to answer the following questions:         Is X version stable yet?   Is X version in beta?   Is X version still supported?   What versions are still supported?   What are the versions in Beta/Alpha?   Until where X version will be supported?   Have X version ceased support?   When will be X version released?   Where I can download any release?   When will the next LTS version of Ubuntu be released?         The list is not exhaustive.


I have some templates that I need to change the font size on. Any suggestions as to the best free software to do this, and can you tell me how to change the font size? Thanks.

I have some e-books in PDF and Kindle, but the font is too small to read on it. I want to make fonts larger in PDF files so that the pictures and other stuff in it is unchanged (therefore I cannot use Calibre to convert it to another format).   Is there any editor for Ubuntu that can manage to change font size in PDF files?


If $f \leq M$ on $D$, we can use Cauchy's estimate to note that $f'(a) \leq M/r$ where $r$ is the radius of the largest circle around $a$ that is contained in $D$. Yet, we can make $r$ small by taking $a$ close to the boundary of $D$. So can $f'$ be unbounded on $D$?

Is there a bounded function $f$ that holomorphic on the open unit disc but $f'$ isn't bounded?  I think first $f$ shouldn't be analytic outside the unit disc then we can't use Cauchy's inequality, because  $$|f'(z)|\le\frac{\max|f|}{R}$$ When $z$ near the bound of unit disc $R$ should be small so $|f'(z)|$ can be large


I am copying a Map from another Map. After the copying is done, I am changing the values in the new Map. However the new changes done in the new Map are also reflecting in the original Map. Is there any way to prevent this from happening? Map<String,List<String>> map1 = new Map<String,List<String>>(); Map<String,List<String>> map2 = new Map<String,List<String>>();  map1.put('abc',new List<String> {'123'}); map1.put('xyz',new List<String> {'0987'});  map2 = map1; // Even tried putall method here  for(String str1  :map2.keyset() ){     map2.get(str1).add('extra value'); } system.debug('map2===>>'+ map2); //{abc=(123, extra value), xyz=(0987, extra value)} system.debug('map1===>>'+ map1); //{abc=(123, extra value), xyz=(0987, extra value)} -- extra value should not relect here

Context Around this Code: I am making a schedulable class run each Sunday to track a couple of metrics important to the team.   Question: I am looking to consolidate DML operations and a big part of this is understanding pass by reference vs pass by value.  I want to pass the salesOps user object to the method SDREfficiencyLastWeek. I made the return type void, because I figured that I will be passing this by reference and I can make all the updates in the method without having to anything.   Why I am confused:    I read the above article and am thrown off by the following statement:  "Non-primitive data type arguments, such as sObjects, are also passed into methods by value. "   If the object is indeed passed by reference, then the query for the salesOps user in my code should be sufficient enough to edit all fields on that object without actually having to state each field in the query.  global class SDREfficientMetricsSchedulable implements Schedulable  {     global void execute(SchedulableContext sc)      {         User salesOps = [SELECT ID FROM USER WHERE id = '0056A000002Z3p9QAC'];         List<String> queries = new List<String>();          String contactsWorked_lastWeek  = 'select count(id) results from contact where LastActivityDate = last_week';         queries.add(contactsWorked_lastWeek);          String demosSet_lastWeek            = 'select count(id) results from form__c where CreatedDate = last_week';         queries.add(demosSet_lastWeek);          String demosCompleted_lastWeek  = 'select count(id) results from opportunity where (stagename = \'Unqualified Demo Completed\'  OR stagename = \'Qualified Demo Completed\' )  and RecordTypeId = \'0126A000000yudDQAQ\' and CloseDate = last_week';         queries.add(demosCompleted_lastWeek);          String qualifiedDemos_lastWeek  = 'select count(id) results  from opportunity where RecordTypeId = \'0126A0000004Ao6QAE\' and isclosed = false and  SDR_Owner__c != null and CreatedDate = last_week';         queries.add(qualifiedDemos_lastWeek);          String closedWon_lastWeek       = 'select count(id) results  from opportunity where RecordTypeId = \'0126A0000004Ao6QAE\' and iswon = true and  SDR_Owner__c != null and CloseDate = last_week';         queries.add(qualifiedDemos_lastWeek);            SDREfficiencyLastWeek(queries, salesOps);          update salesOps;     }       public void SDREfficiencyLastWeek(List<String> queries, User salesOps )     {        }  }


I need to know how to do double face on objects created via curve mesh. I created this using curve path and used the "bevel object" on another curve. It created the slide that I needed. When I tried to import the 3D object as fbx for unity, the slide has face only on the surface but the moment you look from the bottom, it becomes transparent, obviously the face on the bottom is reversed. Please help.

I'm importing a mesh i made into unity before exporting I always rotate it by -90 degrees in the X axis, then set the orientation to Y forward and Z up so when the object is imported to unity the object's orientation will fit into unity's native orientation, However whenever I do this after being importing to Unity the mesh is inside out or transparent but When I don't do the rotation of -90 on the X axis the mesh loads correctly aside from the orientation of the mesh being incorrect and it doesn't match unity's native orientation, i really can't figure it out this is the first time I'm having this problem My setup usually works in the meshes i import to unity but this time i got this problem.


Show that $$\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}>1,\:\forall n\in\mathbb{N}$$ This is a 9th grade problem. I was trying to take the greatest numerator, which is the  last numerator of the last fraction. But there are only $2n+1$ terms. Right? After that I have no idea. Thx!

I have this inequality that I don't know how to prove. Possibly the inequality between means might be useful. For $n \in \mathbb{N}$:   $$\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1} \ge 1$$


I'm going to preface this by saying that I've seen many, many bug reports and threads with very similar issues, but no useful fixes. Using Ubuntu 18.04 and Xorg.  For some applications, clicking inside the window causes window focus to be "stuck" on that window until the application is closed. I can move the mouse freely, and scrolling works sometimes. I cannot move the "stuck" window or hit the x in the corner, but I can click within the window and alt tab to other applications. Alt tabbing to any other application will move that window to the top, but any clicks are registered on the "stuck" application. Sometimes, this brings the "stuck" application back to the front, sometimes not.

I recently switched to Linux. Everything went fine, but when I installed the gnome-shell, it started to ignore clicks outside the focused window. I cannot click on another window to focus it or click on any gnome UI elements. The super key also does nothing. I installed gnome-tweaks and I use a user theme, but that shouldn't be the problem because the problem remained even when I had a fresh install. Also, sometimes when I reboot it works normally. But after another reboot, it comes back.   PS- I found a very temporary fix: If I move the focused (or sometimes other windows) it will start recognizing my keystrokes. On Firefox I need to move the window by the bar with open tabs, as I cannot move it with the title bar.  I read  by someone who had a very similar issue, but the solution did not work for me. I think it has to do something with NVidia drivers, because if I change them then the frequency of this happening changes.  Sorry if something is weirdly written. English is not my native language.


I am currently working on a project and have hit a snag.  I'm taking in an unformatted string[] of football teams and I'm trying to filter the data and return it in a more orgainised format.   I'm fine with most of it (splitting the string to get the relevant values and sorting the format) except i have created a Team object which holds most of this data and as i loop through the original string i create a new team object each time i see a team name. Then i check to see if i've seen that object before and if i have i don't create a new object. After creating the Team or skipping that part i add the relevant info to the team object and continue.  My issue is the list i'm using to hold the final team info has many duplicates mean my check to see if the object exists or not doesn't work. The code is :   After splitting string,          List<Team> teams = new List<Team>();          for (int i = 1; i <= matches.Length - 1; i++)         {             string fullStr = matches[i];              string[] score = fullStr.Split(',');              string[] team1 = score[0].Split('!');             string team1Name = team1[0];              Team teams1 = new Team(team1Name);             if (teams.Contains(teams1) != true)             {                 teams.Add(teams1);             }              string team1Score = team1[1];             int team1ScoreInt = int.Parse(team1Score);              string[] team2 = scores[1].Split('!');             string team2Name = team2[1];               Team teams2 = new Team(team2Name);              if (!teams.Contains(teams2))             {                 teams.Add(teams2);             }   When i print the list i get the format i want but multiple Germanys etc. And only the score etc of that 1 game rather than them all adding to 1 Germany Team object.  Any ideas how i can stop the duplicates and maintain using only the 1 Team object every time i see that team name?   Thanks

Anyone have a quick method for de-duplicating a generic List in C#?


Specifically I need to know that whether a bounded linear transformation from the sequence space l_1 to Real numbers map the closed unit sphere to a closed set? I'm thinking of this problem for two days. I'll be thankful for any help

What is a bounded operator on a Hilbert space that does not attain its norm? An example in $L^2$ or $l^2$ would be preferred.  All of the simple examples I have looked at (the identity operator, the shift operator) attain their respective norms.