"Beans is our only option" or "Beans are our only option"— which is correct?

This sentence is in the context of dinner.     Beans is/are our only option   I'm confused as to whether "is" or "are" is necessary in this construct.


Check differentiability of multivariable functions

I am trying to determine if the following functions are (totally)   differentiable at $(x,y)=(0,0)$.      $$f(x,y)=\sqrt{\vert xy \vert}$$      $$g(x,y)=e^{{{\vert x \vert}^3}y}$$   However I am not particularly sure where to start. The concept of the total derivative being the Jacobian matrix makes sense but I don't really understand how to work with functions that may not have a Jacobian matrix. Any help would be greatly appreciated!


Unable to load Windows and unable to mount Windows partitions (probably corrupted )

It is a kind of messed up situation. I installed Ubuntu 13.10 on Windows 8 which didn't display Ubuntu. I then tried Boot-Repair by opening Try Ubuntu without installing. Here is the URL:   At this instant I was unable to load Windows. Then I changed the BIOS setting from UEFI to Legacy which on restarting displayed the message No operating system found.  I installed Ubuntu 13.10 again.  Here are my problems:     I am unable to load Windows. (It is asking for recovery media which I don't have right now.)   In Ubuntu I am unable to mount any Windows partitions.    Error message:  Error mounting /dev/sda8 at /media/dew/Songs, Videos & Movies: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda8" "/media/dew/Songs, Videos & Movies"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda8': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option.   I guess that Windows was hibernated or didn't shutdown properly. I can't open Windows again to ensure that it is properly shutdown (as mentioned earlier I don't have recovery media). I am happy to use Ubuntu for a while until I get my recovery media, but meanwhile is there any way to mount my Windows partitions?


I'm new to Latex and can't seem to find an answer to what is a pretty basic question: How can I reference a particular page in an article?  Is there a way of doing this within the \cite{} command or do I have to modify the reference in the .bib file?


Error throwing on checking whether app got notification access or not?

I have an app in which i have to check whether my app got notification acccess or not for this i am using below mention code but this is throwing error on testing on device above api level 23. Pls help me to resolve this issue.  code:-   ContentResolver cr = getContentResolver();         String setting = "enabled_notification_listeners";         String permissionString = Settings.Secure.getString(cr, setting);         if (permissionString.contains("com.ermo.batt")) {             intent = new Intent(mContext, CNotificationHomeActivity.class);             startActivity(intent);         } else {             intent = new Intent(mContext, CNotificationManagerWalkThrough.class);             startActivity(intent);         }   error:-  java.lang.NullPointerException: Attempt to invoke virtual method 'boolean java.lang.String.contains(java.lang.CharSequence)' on a null object reference


Howto install latest Oracle Java JDK (32-Bit) to Linux Xubuntu 14.04 (64-Bit) easiest way

I have managed to install the latest Openjdk version of Java JDK via :i386    suffix so far.   But my JavaFX app depends on the Oracle JDK to run properly I have only successfully installed the 64-Bit of Oracle Java JDK via ppa:webupd8Team/java But how can I install the 32-Bit Version of Oracle JDK?    I thank you for taking your time to read this message and trying to help me in finding a solution. Very much appreciated!


How to prevent losing transparency when pasting an image

I noticed that when I paste a transparent image like this  in GIMP, it loses it's trasparency and is given a black background. Is there any way to disable that behaviour or at least prevent it?


Disable white background of pasted text in PowerPoint

When I paste text from another source with "Keep source formatting option" into PowerPoint 2010 I receive a white background, that I don't want.    How can I make this text background transparent, so there would be just red text on purple?


I want to fill a line with asterisks just like as with \cdots or \ldots that can be used in tables, \leaders solution doesn't work well.  I'm working in a fixed columns width table, where at the end of the data it is fill with asterisk to denote the end of data.  this what i get inserting asterisks manually and using a command base on \leaders:      As is shown in the picture the \leaders way do not fill well the column


Alright so I've seen some postings about loop cuts and done some research. I am very new to blender and modeling overall. I am trying to loop cut this concrete barrier. Now I'm following a tutorial and kind of did my own thing in some areas. I cleaned it up following some instructions in another answer here on stack exchange.  I can't for the life of me figure out why I can loop cut around the whole bottom:   ...but not the whole middle:   I see this marked as answered by another question. That question refers to ngons and inside faces. Now once again I'm totally new to this. I looked on the inside. I don't believe I have inside faces or any ngons by the terms I've read online in my research.  Here is a wireframe picture and the inside view:     Maybe I'm missing something the answers on other posts are saying. If so and you know what it is I'd be very appreciative of what it is.


I have a bunch of pendrives with live Linux ISOs loaded onto them and I would like to check one if it is persistent. Rebooting is not an option right now (system rescue).  Is there a simple command or utility to check if the current pendrive Linux installation is persistent on the pendrive?


Question regarding unexpected hanging paradox

The following is the unexpected hanging paradox:  A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.  Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.  He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.  The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.  Observations  In my opinion the above reasoning is a case of a "proof by assumption" with extra steps. Here's why:    prisoner assumes hanging didn't occur on Monday, ..., Thursday to conclude that it can't happen on Friday he works backwards from Thursday to Monday using the same argument as for Friday   The second step is redundant since we already established in step 1, that hanging did  not occur on Mon, ..., Thu.  In this way, the "paradox" is reduced to a single implication: (no hanging Mon, ..., Thu) -> (no hanging on Fri). It's easy to agree with and not a paradox.  Is my thinking correct here?


How to make a Stopwatch without rewrite line for each display

I want to display a stopwatch but i don't want to clean my console for each dislay ,              Stopwatch chrono = new Stopwatch();             chrono.Start();              bool isMyComputerOn = true;             while (isMyComputerOn)             {                 Console.WriteLine("Time :  "+chrono.Elapsed);             }   Any idea ?


How can I commit only specific files in Git?

If there are 1000 files in my local repository, and I want to commit and push only 700 files, is there a possibility?


In simple (univariate) OLS $y = \beta_0 + \beta_1 x$, the estimate of the slope coefficient is asymptotically equal to the ratio of covariances, i.e.  $$ \hat{\beta_1} \rightarrow \frac{Cov[X,Y]}{Cov[X,X]} $$  so if we know what the covariance matrix for the joint distribution of $[X,Y]$ is we can derive OLS coefficients without needing any data.   Can we do the same for the multivariate case? For example, if we know the covariance matrix of the data-generating process for $[Y,X_1,X_2]$, what would be the asymptotic expression for OLS coefficients in $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2$?  Add 1 If the data was centered (or the means where zero) then the data matrix $\textbf{X}^T\textbf{X}$ (without column of 1s) would asymptotically be equal to the co-variance matrix of $[X_1,X_2]$. But the estimate includes the column of 1s and work with non-centered data, so it's not clear to me what this becomes in this case.  Add 2 If do apply the OLS formula for zero-mean RVs without adding the column of 1s to the data matrix, then for 2 explanatory variables we get $$ \textbf{X}^T \textbf{X} =       \begin{bmatrix}     x_{1,1} & x_{1,2} \\     x_{2,1} & x_{2,2} \\     \vdots & \vdots \\     x_{n,1} & x_{n,2}\\     \end{bmatrix}^T     \begin{bmatrix}     x_{1,1} & x_{1,2} \\     x_{2,1} & x_{2,2} \\     \vdots & \vdots \\     x_{n,1} & x_{n,2}\\     \end{bmatrix} =     \begin{bmatrix}    \sum_{i=1}^{n} x_{i,1}^2 & \sum_{i=1}^{n} x_{i,1}x_{i,2} \\    \sum_{i=1}^{n} x_{i,1}x_{i,2} & \sum_{i=1}^{n} x_{i,2}^2 \\        \end{bmatrix} $$ and its inverse is  $$ (\textbf{X}^T \textbf{X})^{-1} = \frac{1}{\sum_{i=1}^{n} x_{i,1}^2 \sum_{i=1}^{n} x_{i,2}^2 - (\sum_{i=1}^{n} x_{i,1}x_{i,2})^2}    \begin{bmatrix}    \sum_{i=1}^{n} x_{i,2}^2 & -\sum_{i=1}^{n} x_{i,1}x_{i,2} \\    -\sum_{i=1}^{n} x_{i,1}x_{i,2} & \sum_{i=1}^{n} x_{i,1}^2 \\    \end{bmatrix} $$ The other term is given by $$ \textbf{X}^T \textbf{y} =       \begin{bmatrix}     x_{1,1} & x_{1,2} \\     x_{2,1} & x_{2,2} \\     \vdots & \vdots \\     x_{n,1} & x_{n,2}\\     \end{bmatrix}^T \begin{bmatrix}     y_{1} \\     y_{2} \\     \vdots \\     y_{n} \\     \end{bmatrix} =     \begin{bmatrix}    \sum_{i=1}^{n} x_{i,1}y_{i} \\    \sum_{i=1}^{n} x_{i,2}y_{i}  \\        \end{bmatrix} $$ Putting it together gives $$ \begin{bmatrix}     \hat{\beta}_{1} \\     \hat{\beta}_{2} \\     \end{bmatrix} = (\textbf{X}^T \textbf{X})^{-1} \textbf{X}^T \textbf{y} =  \frac{1}{\sum_{i=1}^{n} x_{i,1}^2 \sum_{i=1}^{n} x_{i,2}^2 - (\sum_{i=1}^{n} x_{i,1}x_{i,2})^2}   \begin{bmatrix}    \sum_{i=1}^{n} x_{i,2}^2 \sum_{i=1}^{n} x_{i,1}y_{i} -\sum_{i=1}^{n} x_{i,1}x_{i,2} \sum_{i=1}^{n} x_{i,2}y_{i} \\    \sum_{i=1}^{n} x_{i,1}^2 \sum_{i=1}^{n} x_{i,2}y_{i} -\sum_{i=1}^{n} x_{i,1}x_{i,2} \sum_{i=1}^{n} x_{i,1}y_{i} \\    \end{bmatrix} $$ which seems to agree with the result in the OP of the question pointed to by whuber. Asymptotically, this looks like $$ \begin{bmatrix}     \hat{\beta}_{1} \\     \hat{\beta}_{2} \\     \end{bmatrix} \rightarrow (Cov(\textbf{X},\textbf{X}))^{-1} Cov(\textbf{X},Y) $$ where $\textbf{X}$ now indicates a multivariate RV, not the data matirx of observations. Since covariances do not depend on means, I believe that this result also holds for non-zero mean RVs.


Emails from my domain treated as spam by Gmail and Outlook

I know that this question asked multiple times before but I have a little bit different situation.  In Brief:  I have reverse DNS, PTR records, SPF records, DKIM 1024-bit key, IP not blacklisted, message content not spam characteristics.  Emails delivered to inbox on Yahoo and AOL. but, they go to spam / junk on Gmail and Outlook.    In details:  Reverse DNS checked:  host 12.34.56.789   Note: This IP isn't the real IP of the server.  Output:  789.56.34.12.in-addr.arpa domain name pointer mydomain.com.   SPF records:  "v=spf1 +a +mx +ip4:12.34.56.789 -all"   SPF Checked by :    DKIM Checked by :    IP blacklist test checked by : Passed All  Yahoo and AOL works fine, but Gmail and Outlook mark emails as spam.  I contacted the gmail team couple of times but they didn't respond for over 10 days.  I'm sending plain text, no html codes.  No bulk emails, no newsletter.  Does anyone have a solution for this issue? Am I missing something? Appreciate any suggestions.    Further Details (Email Header):  Delivered-To: myemail@gmail.com Received: by 10.202.86.147 with SMTP id k141dre728845oib;         Tue, 4 Nov 2014 23:26:11 -0800 (PST) X-Received: by 10.170.225.135 with SMTP id r129mr14547913ykf.104.1412359371276;         Tue, 04 Nov 2014 23:26:11 -0800 (PST) Return-Path: <sales@mydomain.com> Received: from hostname.mydomain.com (mydomain.com. [12.34.56.789])         by mx.google.com with ESMTPS id v44si1322694yhv.201.2014.11.04.23.26.10         for <myemail@gmail.com>         (version=TLSv1.2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128);         Tue, 04 Nov 2014 23:26:10 -0800 (PST) Received-SPF: pass (google.com: domain of sales@mydomain.com designates 12.34.56.789 as permitted sender) client-ip=12.34.56.789; Authentication-Results: mx.google.com;        spf=pass (google.com: domain of sales@mydomain.com designates 12.34.56.789 as permitted sender) smtp.mail=sales@mydomain.com;        dkim=pass header.i=@mydomain.com DKIM-Signature: v=1; a=rsa-sha256; q=dns/txt; c=relaxed/relaxed; d=mydomain.com; s=default;     h=Content-Transfer-Encoding:Content-Type:MIME-Version:Message-ID:Subject:From:To:Date; bh=lr4CWwmBPE2kmCn+bQZxuDI83bEg03tG585GFUO9nbM=;     b=gsXWNQFoHVg/98V1pfGYpqCmzeKE6BK/93Zy/vT61ySaEdeLrTl9TW6Ca8C/nh+1C19vRfQbv716c+Q2gDEfAXw5/S8mEPjoBAlF96bXfLUuIpnY2OLLELAobd+VkpYaeOpAVnVMUDoie5M+m+lp98btL31BXWOKfPCCJ8UHZ5Q=; Received: from localhost ([::1]:36366 helo=www.mydomain.com)     by hostname.mydomain.com with esmtpsa (TLSv1:DHE-RSA-AES256-SHA:256)     (Exim 4.82)     (envelope-from <sales@mydomain.com>)     id 1Xluyo-00032t-Az     for myemail@gmail.com; Wed, 05 Nov 2014 02:26:10 -0500 Date: Wed, 5 Nov 2014 02:26:10 -0500 X-Priority: 3 MIME-Version: 1.0 Content-Type: multipart/alternative;     boundary="b1_73e9fc0155fddc64feb30693a746sd5c" Content-Transfer-Encoding: 8bit X-AntiAbuse: This header was added to track abuse, please include it with any abuse report X-AntiAbuse: Primary Hostname - hostname.mydomain.com X-AntiAbuse: Original Domain - gmail.com X-AntiAbuse: Originator/Caller UID/GID - [47 12] / [47 12] X-AntiAbuse: Sender Address Domain - mydomain.com X-Get-Message-Sender-Via: hostname.mydomain.com: authenticated_id: sales@mydomain.com  --b1_73e9fc0155fddc64feb30693a746sd5c Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit


How to grep standard error stream (stderr)?

I am using ffmpeg to get the meta info of an audio clip. But I am unable to grep it.      $ ffmpeg -i 01-Daemon.mp3  |grep -i Duration     FFmpeg version SVN-r15261, Copyright (c) 2000-2008 Fabrice Bellard, et al.       configuration: --prefix=/usr --bindir=/usr/bin        --datadir=/usr/share/ffmpeg --incdir=/usr/include/ffmpeg --libdir=/usr/lib       --mandir=/usr/share/man --arch=i386 --extra-cflags=-O2        ...   I checked, this ffmpeg output is directed to stderr.  $ ffmpeg -i 01-Daemon.mp3 2> /dev/null   So I think that grep is unable to read error stream to catch matching lines. How can we enable grep to read error stream?  Using  link, I redirected standard error stream to standard output stream, then grep worked.  $ ffmpeg -i 01-Daemon.mp3 2>&1 | grep -i Duration   Duration: 01:15:12.33, start: 0.000000, bitrate: 64 kb/s   But what if we do not want to redirect stderr to stdout?


Is there a way to simulate the C++ 'friend' concept in Java?

I would like to be able to write a Java class in one package which can access non-public methods of a class in another package without having to make it a subclass of the other class. Is this possible?


I have a 13" Macbook Pro 2010. Should I download the 32-bit version or the 64-bit version of Ubuntu?


I am an Indian Resident working for a US Company as an employee. The work location is Bangalore, India. The salary is credited by US company after Deduction of tax as per US laws then credited to the Bank  account in India. I am in India for more than 180 days and I guess I would be treated as Resident Indian [and not "Non-Resident Indian"] How should I claim credit of tax paid in US when accounting periods for US are calander year Jan to Dec and in India are April first year to March Next year. Where should I disclose the taxes already deducted by US company and paid to IRS when I am filing Returns in India. I believe dual tax avoidance should allow me a tax credit?


Balancing opacities between fill and draw

Probably my Title is not so informative. My problem is that I try to "draw" hyperedges on some vertices with the following code:  \usepackage{tikz}  \tikzstyle{vertex} = [fill, shape=circle, opacity=1, node distance=80pt] \tikzstyle{hyperedge} = [fill, opacity=1, cap=round, join=round, line width=60pt] \tikzstyle{elabel} = [fill, shape=circle, node distance=30pt]  \pgfdeclarelayer{background} \pgfsetlayers{background,main}  \begin{document}  \begin{tikzpicture} \node[vertex,label=above left:$v_1$] (v1) {}; \node[vertex,right of=v1,label=above right:$v_2$] (v2) {}; \node[vertex,below of=v1,label=below left:$v_3$] (v3) {}; \node[vertex,right of=v3,label=below right:$v_4$] (v4) {};  \begin{pgfonlayer}{background}  \draw[hyperedge, color=yellow] (v1.center)--(v2.center)--(v3.center)--cycle; \draw[hyperedge, color=pink, line width=45pt] (v2.center)--(v3.center)--(v4.center)--cycle;  \end{pgfonlayer}  \node[elabel,color=yellow,label=right:$C_1$]  (e1) at (-3,0) {}; \node[elabel,below of=e1,color=pink,label=right:$C_2$]  (e2) {}; \end{tikzpicture}  \end{document}   This produces the following:    It is not bad, but the intersection is not so visible. If I set opacity of the hyperedges to 0.5:  \tikzstyle{hyperedge} = [fill, opacity=0.5, cap=round, join=round, line width=60pt]   I get:    The intersection is more visible here, but since the "fill" and the "lines" of the cycles also intersect, the affected  parts become more opaque(?). Is there a workaround for this situation? Maybe to draw the lines only on one side of the cycle avoiding intersection with the fill, but is it possible?


A little bit ago, I was stupid and deleted my Windows (7) registry key for auto starting Steam on login. I foolishly had deleted it, not disabled. Now I'd like it to auto start on login, but I have no way of setting it up to do so.  Any thoughts? Should I attempt to reinstall Steam or what?


While working on some field extensions I came across this "proof" that $i = 1$, but I am not sure what is wrong with it:   We know $ i = \sqrt{-1} = (-1)^{1/2}$. Now we have the following equation: $$\begin{align} i \sqrt[4]{-2} =(-1)^{1/2}(-2)^{1/4} &= (-1)^{1/2}(-1)^{1/4}(2)^{1/4}  \\ &= (-1)^{3/4}(2)^{1/4}\\  &= (-1)^{1/4}(2)^{1/4} \\ &= \sqrt[4]{-2} \end{align}$$  Dividing both sides by $\sqrt[4]{-2}$  would yield $i = 1$.


When travelling a (US) Greyhound service including a transfer, is it possible to skip the first leg of the journey? For flight tickets  that this is generally not allowed. But does Greyhound consider it as two distinct bookings or is it one indivisible whole?


Cause of "curtain" when looking through camera

I used the OpenStreet Maps plugin to import automatically landscape. When I look at it in Layout mode, I see nothing that jumps out at me. But, when looking through the camera, a "curtain" that stays at the same distance from the lens stays there as I move through the scene. I can guess this is an easy cutoff or other setting that I am overlooking as a noob.  enough.


What can I do to stop hot sauce from separating?

I make homemade cayenne pepper sauce every year. I do add some liquid pectin to slightly thicken it so it will stick to food rather than roll off. After a month or so on the shelf it seems to separate a bit. What can I add to this so that it won't or is there a method I can do to stop this. We are slowly working our way into marketing this product down the line and this won't work for that reason. We are using a water bath canning method, vinegar based, no sugar added.


Let $X,Y$ be independent exponential RV's with respective pdf's $f(x) = \lambda e^{-\lambda x}$ and $f(y) = \mu e^{-\mu y}$. We want to find the pdf of $Z=X-Y$.   I originally tried the convolution method (but with wrong limits). $$ P[X-Y \le z]= \int_0^{\infty} \Bigg( \int_0^{z+y} \lambda e^{-\lambda x} dx \Bigg) \mu e^{-\mu y} dy$$  which is wrong.   I was told that I'm supposed to split the inner integral into two, depending on $X-Y$ being positive or negative. I don't understand why.  I'm thinking that since we've got $X \in (0,\infty)$ and $Y \in (0, \infty)$ we should have $Z \in (-\infty, \infty)$.  Any hints?  I just thought of another way: the moment generating function. But there's a catch, we only know that product of MGF's is an MGF of a SUM (not difference). I'm wondering if a ratio of MGF's might be an MGF of a difference?


What tools exist to remove metadata from photos?

Whenever I share my photographs, I also share lots of information that I do not want to pass on:   specific camera model that the photo was taken with exposure time focal ratio ...   How can I remove all those metadata for sharing?  I'm particularly looking for solutions for Max OS X.


How to change encrypted volume password on command line?

Disk util shows the encrypted disk I am using for time machine with the following info:  But the Menu entry "file -> Change Password" is greyed out. Tried to turn to the command line, I found this , and the first part works nicely: > diskutil cs list CoreStorage logical volume groups (1 found) | +-- Logical Volume Group DDE89BDF-9537-45FF-A786-697E828EB040     =========================================================     Name:         egmac2.bak     Status:       Online     Size:         2000021315584 B (2.0 TB)     Free Space:   9392128 B (9.4 MB)     |     +-< Physical Volume DFEAFE30-FF0B-417B-B845-7C0A283FB4D4     |   ----------------------------------------------------     |   Index:    0     |   Disk:     disk2s2     |   Status:   Online     |   Size:     2000021315584 B (2.0 TB)     |     +-> Logical Volume Family 0A741FD9-F957-4188-B1D9-233145A76ABF         ----------------------------------------------------------         Encryption Type:         AES-XTS         Encryption Status:       Unlocked         Conversion Status:       Complete         High Level Queries:      Fully Secure         |                        Passphrase Required         |                        Accepts New Users         |                        Has Visible Users         |                        Has Volume Key         |         +-> Logical Volume 253049D8-C1A5-41B1-A9C5-788AA41E0157             ---------------------------------------------------             Disk:                  disk3             Status:                Online             Size (Total):          1999659597824 B (2.0 TB)             Revertible:            No             LV Name:               egmac2.bak             Volume Name:           egmac2.bak             Content Hint:          Apple_HFS  But then: > diskutil cs passwd 253049D8-C1A5-41B1-A9C5-788AA41E0157 -oldpassphrase whatever -newpassphrase whattheheck diskutil: did not recognize coreStorage verb "passwd"; type "diskutil coreStorage" for a list


I use pushd to work with multiple directories in bash and zsh. I've aliased dirs to dirs -v so that I get an ordered list when I want to see what's on the directory stack:  chb$ dirs 0  /Volumes/banister/grosste_daever_gh/2013-03-27/reader 1  /tmp/20130618202713/Library/Internet Plug-Ins 2  ~/code/foo/view/static/css 3  ~/Downloads   Is there a way (either in bash or zsh) that I can refer to one of the directories listed on the command line using an alias for its position on the stack? For example, instead of typing:  chb$ cp ~/code/foo/view/static/css/baz.css ~/code/bar/view/static/css/   I'd type:  chb$ cp <2>baz.css ~/code/bar/view/static/css/   ...or something like that, maybe using a dollar sign and a variable name instead of <n>.


How can I crop a raster layer to a hemisphere?

I have a raster layer that I want to crop to a hemisphere centered on 30°N, 100°W, to use in an orthographic projection map. What is the best way to do this?  There doesn't seem to be an easy way to generate a hemisphere polygon to mask it by (which I'd think would be the obvious solution).  (Note that, unlike the question this is marked a duplicate of, this is asking about raster layers; the solutions presented in that question are for vector layers and do not work here.)


Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$

This an interesting problem my friend has been working on for a while now (I just saw it an hour ago, but could not come up with anything substantial besides some PMI attempts).  Here's the full problem:  Let $x_{1}, x_{2}, x_{3}, \cdots x_{y}$ be all the primes that are less than a given $n>1,n \in \mathbb{N}$.   Prove that $$x_{1}x_{2}x_{3}\cdots x_{y} < 4^n$$  Any ideas very much appreciated!


Gradient of $x^T B^T B x - x^T B^T b - b^T Bx$

I want to compute the gradient $\nabla_x f(x)$ of $f(x) = x^T B^T B x - x^T B^T b - b^T Bx$ with respect to the vector $x$. So far I have tried below. But when I try to add them together, I couldn't see they come together.  Edits  Now I think I got it. They does come together as the following answers. Since $C=B^TB$, $C$ is symmetric. Then $c_{ij} = c_{ji}$, so  $$\frac{\partial D}{\partial x} = 2\Big[\sum_{i=1}^n c_{1i} x_i \ \ \sum_{i=1}^n c_{2i} x_i \ \ \cdots \ \ \sum_{i=1}^n c_{ni} x_i\Big] =2 C x.$$  Hence $$\frac{\partial x^TBb}{\partial x} = \Big[ \sum_{i=1}^n b_{i1} b_i \ \ \sum_{i=1}^n b_{i2} b_i \ \ \ \ \cdots \ \ \sum_{i=1}^n b_{in} b_i \ \ \Big] = B^T b.$$  So $\frac{d}{dx} (x^T B^T B x - 2x^T B^T b) = 2B^T B - 2B^Tb$.  Thank you!    Let $C = B^T B$. \begin{align*} x^T C x =&  \begin{pmatrix} x_1 & x_2 & \cdots & x_n\end{pmatrix} \begin{pmatrix}  c_{11} & c_{12} & \cdots & c_{1m}\\  c_{21} & c_{22} & \cdots & c_{2m}\\ \vdots & \vdots& \ddots & \vdots \\  c_{n1} & c_{n2} & \cdots & c_{nm}\\  \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ \vdots \\x_n\end{pmatrix}\\ =&  \begin{pmatrix} x_1 & x_2 & \cdots & x_n\end{pmatrix} \begin{pmatrix}  c_{11} x_1 + c_{12} x_2 + \cdots c_{1n} x_n\\ c_{21} x_1 + c_{22} x_2 + \cdots c_{2n} x_n\\ \vdots\\ c_{n1} x_1 + a_{n2} x_2 + \cdots a_{nn} x_n\\ \end{pmatrix}\\ =& x_1(c_{11} x_1 + c_{12} x_2 + \cdots c_{1n} x_n)+x_2(c_{21} x_1 + c_{22} x_2 + \cdots c_{2n} x_n) + \cdots + x_n(c_{n1} x_1 + a_{n2} x_2 + \cdots a_{nn} x_n) \end{align*} Since the derivative of the scalar $D = x^T C x$ by a vector $x$ is $$\frac{\partial D}{\partial x} = \bigg(\frac{\partial D}{\partial x_1} \frac{\partial D}{\partial x_2} \cdots  \frac{\partial D}{\partial x_n}\bigg),$$ I have: \begin{align*} \frac{\partial D}{\partial x_1}  &= c_{11} x_1 + c_{12} x_2 + \cdots c_{1n} x_n  + c_{11} x_1 + c_{21} x_2 + \cdots + c_{n1} x_n = \sum_{i=1}^n (c_{1i} + c_{i1})x_i \end{align*} Hence $$\frac{\partial D}{\partial x} = \Big[\sum_{i=1}^n (c_{1i} + c_{i1})x_i \ \ \sum_{i=1}^n (c_{2i}+c_{i2})x_i \ \ \cdots \ \ \sum_{i=1}^n (c_{ni}+c_{in})x_i\Big].$$ \begin{align*} x^T B b =&  \begin{pmatrix} x_1 & x_2 & \cdots & x_n\end{pmatrix} \begin{pmatrix}  b_{11} b_1 + b_{12} b_2 + \cdots b_{1n} b_n\\ b_{21} b_1 + b_{22} b_2 + \cdots b_{2n} b_n\\ \vdots\\ b_{n1} b_1 + b_{n2} b_2 + \cdots b_{nn} b_n\\ \end{pmatrix}\\ =&  x_1(b_{11} b_1 + b_{12} b_2 + \cdots b_{1n} b_n)+ x_2(b_{21} b_1 + b_{22} b_2 + \cdots b_{2n} b_n)+\cdots+ x_n(b_{n1} b_1 + b_{n2} b_2 + \cdots b_{nn} b_n) \end{align*} Hence $$\frac{\partial x^TBb}{\partial x} = \Big[ \sum_{i=1}^n b_{1i} b_i \ \ \sum_{i=1}^n b_{2i} b_i \ \ \ \ \cdots \ \ \sum_{i=1}^n b_{ni} b_i \ \ \Big].$$


I am trying to runa  query in a .js button to pull out an ID of a contact that is associated with a record so I can auto send an  document.  However I can not get this working, my googling skills have been made defective by this!  Basically I have a button that runs a URL and sends a document to EchoSign to be sent out, but it needs to be sent to the most recent contact that was sent an EchoSign document.  Example below:  var contactCheck = sforce.connection.query("SELECT echosign_dev1__Recipient__c FROM echosign_dev1__SIGN_Agreement__c WHERE echosign_dev1__Account__c = '{!Account.Id}' AND echosign_dev1__Status__c = 'Signed'");   I'm still very new to .js so I am not 100% sure if I am doing things correctly, but I have seen the following 2 ways of pulling out just the ID and neither work:  var contactId = templateId.records[0].Id; var contactId = contactCheck.records[i].get("Id"));   Can anyone help? This is stressing me out... I am going to turn prematurely grey at the age of 22


Why didn’t I get an election notification in iOS app?

I’ve just missed the Aviation.SE voting because I only normally use the iOS app and the notification didn’t come through to the app, yet it’s there when viewing through the website.  Is this a bug? If not can we make it a feature request?  iOS app notifications - missing election notification      Website notifications - has election notification       App Version: 1.6.6.2 Device: iPhone 5s (Global) OS Version: Version 11.0.2 (Build 15A421)


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I'm using MiKTeX 2.9 and have recently installed the Minion Pro fonts for use with pdftex. I followed the instructions available on  to install them.  Everything works as expected, but in place of the Greek letter epsilon I get a box with a cross (see below), and the following warning:    I found the issue was reported , but I still can't fix it. xelatex works fine, but I'd like to to stick to pdftex so I can use microtype.  \documentclass{article}  \usepackage[T1]{fontenc} \usepackage{MinionPro}  \begin{document}  Text here. $\epsilon$  \end{document}       UPDATE: a set of instructions for the installation of the up-to-date FontPro scripts with MiKTeX can be found .


Can I have multiple valid ESTAs in different passports?

I'm a citizen of country X and have a valid United States ESTA in my X passport.  Recently, I became of citizen of Y and now have a Y passport as well, which I would like to use for future travel to the US.  Both countries qualify for the Visa Waiver Program.  Can I have ESTAs in both passports at the same time?  The official CBP site seems contradictory, first :     If you obtain a new passport or change your name, gender or country of   citizenship, you will be required to apply for a new travel   authorization. This is also required if one of your answers to any of   the VWP eligibility questions changes. The associated fee of $14 will   be charged for each new application.   And then :     If you have dual citizenship and have registered with ESTA, you should   use your VWP-eligible passport to board the plane when you leave your   country of departure and when you arrive in the U.S. If both your   countries of citizenship are VWP-eligible, then we strongly recommend   you choose which one you want to claim for purposes of travel to the   U.S., and use that country's passport each time you travel. One person   with two different ESTA authorizations creates confusion that will   only delay your travel.   Cancelling the old ESTA would seem a valid way to fulfill both requirements, but there doesn't appear to be any way to do this?


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(a) Given the column vector $a$ as an $n\times 1$ matrix. Write out its singular value decomposition, showing the matrices $U, \sum$, and $V$ explicitly.  (b) Given the row vector $a^T$ as an $1\times n$ matrix. Write out its singular value decomposition, showing the matrices $U, \sum$, and $V$ explicitly.  I currently get stucked on this question, since I couldn't find the eigenvalues of the $n\times n$ matrix $aa^T$ in part (a), and $a^Ta$ in part (b) to find the columns of $U$ and $V$, respectively. Can someone please help me on this problem?


Does anyone have experience with using very large heaps, 12 GB or higher in Java?   Does the GC make the program unusable? What GC params do you use? Which JVM, Sun or BEA would be better suited for this? Which platform, Linux or Windows, performs better under such conditions? In the case of Windows is there any performance difference to be had between 64 bit Vista and XP under such high memory loads?


How to uninstall a Windows program from Wine?

I have installed several Windows programs using Wine. The problem is that I wont to uninstall some of them because I don't need them. And I wont to that without affecting the Windows apps that I wont to keep. But I can't see any way to uninstall them! Even if I explore drive C trough Wine I can't find any unistall.exe file for them although I can find the install.exe   Please, help me in this, even if it may sound childish. I think I can't find the solution because I am still influenced by some kind of "Windows mentality" wich makes me blind to such an easy solution.   Thanks!


Remember window sizes and placement when unplugging and replugging second monitor

Here’s something that sucks:   Plug in external monitor to laptop (Mac OS X Leopard in my case). Arrange your windows to have the IDE on one screen and browser on another. (Etc etc.  Resize, rearrange, fuss, fuss, fuss.) Unplug monitor to run to a meeting, or whatever. Goto 1.   I’d like to replace step 2 with “computer remembers exactly how I had it and just puts it back that way”.  (I personally only need a solution for Mac but collecting solutions for other systems here might be useful to others.  I’m sure it’s a common problem.)


Null Pointer Exception Error in arrayList add declare

when I'm trying to use sentMessages method in testClass, I got a NullpointerException error in the line receiverUser.privateMessageList.add(privateMessage); even I initialized the "privateMessageList" list. How can I deal with this problem?   public class User {      private String userName;     private String password;     private String firstName;     private String lastName;     private String userType;     int topicCount = 0;     final int maxTopicNumber = 5;      ArrayList<PrivateMessage> privateMessageList;      public User(String userName, String password, String firstName, String lastName, String user_type) {         this.userName = userName;         this.password = password;         this.firstName = firstName;         this.lastName = lastName;         this.userType = "USER";      }     //private message section     public PrivateMessage sentMessage(String newMessage, User receiverUser) {         privateMessageList = new ArrayList<>();         PrivateMessage privateMessage = new PrivateMessage(this.userName, newMessage);         receiverUser.privateMessageList.add(privateMessage);         System.out.println("Message sent successfully!");         return privateMessage;     }      public void ListMessages(User receiverUser) {         System.out.println("Inbox of " + receiverUser);         for (int i = 0; i < receiverUser.privateMessageList.size(); i++) {             System.out.println(receiverUser.privateMessageList.get(i));             System.out.println("Sent by: " + this.userName);         }     }


C#: How to create an attribute on a method triggering an event when it is invoked?

Is there a way in C# or .NET in general to create an attribute on a method which triggers an event when the method is invoked? Ideally, I would be able to run custom actions before and after the invocation of the method.  I mean something like this:  [TriggersMyCustomAction()] public void DoSomeStuff() { }   I am totally clueless how to do it or if it possible at all, but  might do a similar thing in the background. I am not sure though.  EDIT: I forgot to mention that due to the circumstances of my specific case, performance is not really an issue.


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There is weird candidate information block on the :    Whole block is grayed, no information, no up/down-vote button, score is missaligned etc ... What's going on here? If that candidate is removed from election, can we show more obvious information in that block? Or even do not show that candidate at all.


If I copy the title of this question below it appears as  Why can't I put the phrase System.Data.Entity.DbSet in my question?


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I would like to use the command line to put text in the GUI clipboard so that it can, for example, be pasted into a graphical web browser's text input field. I am using Kubuntu 20.04. I tried as an example uptime | xclip, and when I press the middle mouse button, the uptime output is pasted. However, when I press Ctrl-Shift-V on the command line, or Ctrl-V in a GUI application, the uptime text is not pasted; instead, the previously copied text is pasted. I read that there is a distinction between the selection and the clipboard. I presume xclip is copying into the selection. How can I copy into the clipboard?


I am reading ID tags for music files in my program. I am using Taglib sharp for this.  But what I have troubles with is when I'm reading the album-art tag.  I get the album art image just fine. But it's in System.Drawing instead of WPF's System.Windows.Media.Imaging.BitmapImage. And from what I've seen; the "Image" control inside of WPF can't use system.drawing images as a source?  What I've been doing is to save a local image every time I select a new song, and loading Imagebox.Source with a bitmapimage URI of that local image. And I'm actually smart enough to understand that it isn't such a smart solution of the problem.  But how would I set the image without saving it to a file and then opening it again?  Like if there's a similar feature to winforms picturebox.image in WPF?  I hope you all understand what I'm trying to tell you guys.  Thanks in advance.


Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.

Firstly, this is a homework problem so please do not just give an answer away. Hints and suggestions are really all I'm looking for.  I must prove the following using mathematical induction:     For all $n\in\mathbb{Z^+}$, $1+2+2^2+2^3+\cdots+2^n=2^{n+1}-1$.   This is what I have in my proof so far:     Proof: Let $p\left(n\right)$ be $\sum_{j=0}^n 2^j=1+2+2^2+\cdots+2^n=2^{n+1}-1$. Then $P\left(0\right)$ is    \begin{align} \sum\limits_{j=0}^0 2^j=1=2^1-1.\tag{1} \end{align} Hence    $P\left(0\right)$ is true. Next, for some $k\in\mathbb{Z^+}$, assume    $P\left(k\right)$ is true. Then \begin{align}  \sum\limits_{j=0}^{k+1}2^j&=\left(\sum\limits_{j=0}^k  2^j\right)+2^{k+1}\tag{2}\\ &=2^{k+1}-1+2^{k+1}\tag{3} \\ &=2\cdot 2^{k+1}-1\tag{4}\\ &=2^{k+2}-1\tag{5}\\ &=2^{\left(k+1\right)+1}-1.\tag{6} \end{align}   Therefore, $P\left(n\right)$ holds for all $n$.$\;\;\;\;\blacksquare$   Is everything right? My professor went over the methodology in class quite fast (and I had a bit too much coffee that night) and I want to make sure I have it down for tomorrow night's exam.


Executable statements in the header part of a Python class

I am trying to create a class with various data which are read in from several files. The usual way is probably to define a constructor (__init__) and read data inside this routine, e.g.,  from SomeOtherMod import reader   # some data reader  class Myclass:      def __init__( self ):         self.N = reader.readN()         self.data = reader.readdata()         self.foo = self.data.foo()         self.bar = self.data.bar()         ...    # more data to read and associated properties follow      def othefunc( self ):         ...    # use self.N, self.data, ...   But it also seems that I can write the same thing in a header part of the class without using __init__, e.g.,  class Myclass:      N = reader.readN()     data = reader.readdata()     foo = data.foo()     bar = data.bar()     ...      def otherfunc( self ):         ...   which looks more terse than the first code. So I am wondering whether this second code is a valid way for defining various fields of a Python class? Is it considered bad practice to do so, or is there any difference between the first and second approaches? I would appreciate any suggestions because I'm still new to Python. Thanks much!


My PC won't start after installing the latest version of Ubuntu. I press the button to start the PC and then I see the BIOS start, but after that I get a black screen and nothing is happening. I can't even reinstall Windows 7 or choose between Windows 7 and Ubuntu.   Please help. I don't want to pay for fixing this. I don't remember the hardware, and since I can't access Windows 7, I can't tell you. The only thing that I know is that it is an HP Compaq 500bmt.


What is the population of the Star Wars Galaxy?

I have been searching around the web for approximate numbers of sentients in the Galaxy. I found the following pages: ,  but the problem is that they do not even give estimates of the number of sentient individuals in the Galaxy.  I am unaware of any canon where the numbers are estimated except in the trillions. I am looking for a more exact number (e.g. 900 trillion). I'm especially curious because of the mention of hundreds of trillions of dead sentients in the Yuuzhan Vong war and similar discreet statements.  How many sentients are there in the Star Wars Universe?


I have Gigabyte GSmart Tuku T2 and it runs 4.0.4 version of android. I don't have update software option in my settings. Is there any way to update my android version to jelly bean?


I was surprised when I heard zero is plural, and even 1.00001 is plural.  Then, what about following numbers ?  (1) 1.00  which means the value measured  between 0.995-1.004, having possibility that it was exactly 1.  (2) 0.99999.....  which is mathematically equal to 1. Also, are others that are mathemattically equal to 1 than this, treated completely same as 1?  (3) -1  Is this singular? Or negative numbers are generally plural?  (4) i = square root of -1  I know it's weird to count things with imaginary numbers, nonetheless, if you were to count, which form, plural or singular, would you be to use?  That's it.


X a locally compact Haussdorf space, each singleton of which is the intersection of countably many open sets. Show that X is first countable.

Let $X$ be a locally compact Haussdorf space, each singleton of which is the intersection of countably many open sets.   Show that X is first countable.


Windows 7 taskbar preview popup - How to keep it open?

In Windows 7, I would like to keep the thumbnail preview of an application in the taskbar open even when the mouse is not hovering over the icon in the taskbar. Is this possible and if so, how? Like Windows Media Player had a popup from the taskbar, but for other applications.


$f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$

I am studying for a qualifier exam in complex analysis and right now I'm solving questions from old exams. I am trying to prove the following:     Prove that if $f$ and $g$ are entire functions such that $f(z)^2 + g(z)^2 = 1$ for all $z \in \mathbb{C}$, then there exists an entire function $h$ such that $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$.     My Attempt  The approach that occurred to me is the following. Since $f(z)^2 + g(z)^2 = 1$ then we have $(f(z) + ig(z))(f(z) - ig(z)) =  1$. Then each factor is nonvanishing everywhere in $\mathbb{C}$ and thus by the "holomorphic logarithm theorem" we know that since $\mathbb{C}$ is simply connected, there exists a holomorphic function $H:\mathbb{C} \to \mathbb{C}$ such that  $$e^{H(z)} = f(z) + ig(z)$$  and then we can write $\exp(H(z)) = \exp\left(i\dfrac{H(z)}{i} \right) = \exp(ih(z))$,    where  $h(z) := \dfrac{H(z)}{i}$.  Thus so far we have an entire function $h(z)$ that satisfies  $$e^{ih(z)} = f(z) + ig(z)$$  On the other hand, we also know that $e^{iz} = \cos{z} + i \sin{z}$ for any $z \in \mathbb{C}$, thus we see that   $$e^{ih(z)} = \cos{(h(z))} + i \sin{(h(z))} = f(z) + ig(z)$$  Thus at this point I would like to conclude somehow that we must have $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$, but I can't see how and if this is possible.    My questions   Is the approach I have outlined a correct way to proceed, and if so how can I finish my argument? If my argument does not work, how can this be proved?   Thanks for any help.


I use a dedicated server with 2gb ram, 6ghz (Dual Xeon) cpu and 500gb Bandwith (actually I need %30 of this bandwith) and 120 gb storage capacity (and I need only 50-60 gb capacity) I have a Java application, my app visited by approximately 2000 users everyday (these user don't upload or download file, only database operations). I want to migrate to aws but I am a little confused. Amazon has many plans and I can't choose which plan is proper for me? I just want to have a stable server solution.


So I'm having some countries in a mysql tables, the problem is that when I list the countries it list them with some funny charcters, I've also had a look into the database an they are the same in the database too.  Here you have an image, on how the results look, I've tried mb_convert_encoding(string,"UTF-8") but that doesn't do anything, do you know how can I fix these?


gcd$(x,y) = 1$ how can i prove that there exist $m, n \in \mathbb{Z}: mx+ny = 1$ I'm studying abstract algebra - cyclic group part, and wondering how $<d>$ is same group with $<r,s>$.


I acctualy work on C project compiling with gcc. I can do error checking thought file, but I want to know how to do it inline. gcc -o test.exe test.c;./test.exe  I want to exec test.exe only if no errors in compilling. Like if [gcc -o test.exe test.c no error] => ./test.exe


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How to explain the differences between ridge, lasso, and elastic net to a smart layman? Such as including the pros and cons of each method and when they should be used.


What is one command to specify a file and what text is in it in that order without repetition?

I'm looking for the perfect way to make a file. I want to specify the file name first I want to specify the text content for that file. I want to do it in one console line. I don't want to have to retype the file name. Ideal


codingbat xyxThere always returning false

public boolean xyzThere(String str) {   for (int i=0; i < str.length()-3; i++){     if (str.substring(i+1, i+4) == "xyz" && str.charAt(i) != '.'){       return true;     }   }   return false; }   The above function always returns false, cannot work out why. I'm going through the codingbat.com Java exercises, here is the brief:     Return true if the given string contains an appearance of "xyz" where the xyz is not directly preceeded by a period (.). So "xxyz" counts but "x.xyz" does not.   Can anyone help?


python see the full definition from the name of the function

I recently asked a question with title "python find the type of a function" and got very helpful answers. Here is a related question.  Suppose I import *.py files written by me, and these imports result in f being one of the functions defined by me. Now I write to my python interpreter x = f. Later, I want to see the full definition of f, preferably with comments still in place, knowing only x. Is this possible? Does python remember which file the definition was imported from, which is, of course, not enough to give the full definition of f, unless one can find the actual relevant definition?


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For a plugin I'm creating it generates custom JavaScript that should be executed in the footer of the page. Being that it's custom JavaScript, I can't simply put it in a file and register & enqueue the file. How should I go about Registering and Enqueuing custom JavaScript? Note: It would be for a Shortcode. The JavaScript would look something like this, $("#CustomID").aFunction(withCustomData); Again, I need it to be executed in the footer of the page, I can't simply return it in the shortcode. Edit 1 The JavaScript is "truly" unique. It takes in parameters from the shortcode itself and may change depending on the time. Again, this is something that is constantly changing and something that should not be put in a file each time it needs to be loaded.


equality operators for object properties and values

Hey guys so i came across some unexpected behavior in js... and i have no idea why this happens... can someone explain to me? Thank  you  campaign = {   "ppmv_ref": "1324232571",   "type": "value off",   "title": "20% off the weed item",   "percentage": "20",   "product": "weed",   "productId": "46482649",   "quantity": "50",   "startDate": "10/22/2018",   "expirationDate": "10/23/2018",   "couponFlag": "true",   "active": "true" } condition = campaign.active === true;  console.log(campaign.active)// logs true console.log(condition); // logs false


How to pass dictionary items as function arguments in python?

My code  1st file:  data = {'school':'DAV', 'standard': '7', 'name': 'abc', 'city': 'delhi'} my_function(*data)   2nd file:  my_function(*data):     schoolname  = school     cityname = city     standard = standard     studentname = name   in the above code, only keys of "data" dictionary were get passed to my_function(), but i want key-value pairs to pass. How to correct this ?  I want the my_function() to get modified like this   my_function(school='DAV', standard='7', name='abc', city='delhi')   and this is my requirement, give answers according to this   EDIT: dictionary key class is changed to standard


I have a question for Ubuntu Touch un-support phone device. I have got Device Phone, but i have checked for Ubuntu Running Movie via Youtube. so, i want to know for unsupport android device setup.  and My phone device hardware satisfy the system(Entry level Ubuntu smartphone) requirements.  It is check through   so,, First, Can i installation ubuntu touch ? Second, if you do not installation, Installed on all Android devices, do you have any support plan?  Thanks Ubuntu,


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People say things like, "I'm so OCD," but it's incorrect. What's a better way of saying that?


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This is so called a hyperbolic set  $$\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$$  We proceed to prove that it is convex by showing that a convex combination of points (a line segment) will lie in the set  Suppose $x = (x_1, x_2)$, $y = (y_1, y_2)$ and $x \geq y$ in the elementwise sense  Then set: $z = \theta(x_1,x_2) + (1-\theta)(y_1, y_2)$  $z = (y_1,y_2) + \theta(x_1 - y_1, x_2 - y_2)$  Clearly, any $z_1,z_2 \in z$ lies in the hyperbolic set (i.e. $z_1z_2 \geq 1$)  How do we proceed to prove the case when $x \not \geq y$ in the elementwise sense?


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Consider this code example:  function Person(config) {     this.name = config.name;     this.age = config.age; }  Person.prototype.getAge = function() {     return this.age; };  var tilo = new Person({name:"Tilo", age:23 }); console.log(tilo.getAge());   Rather than defining getName() as an appendage to the constructor's prototype property, it seems to me it could be defined within the constructor to achieve the same thing? Is there any useful difference? In other words, does doing it one way or the other have any particular implementation advantage?


Evaluate the remainder of $2^{100}$ upon division by $7$.

Not sure how to find the remainder. Any help would be much appreciated. Thanks  Checked out the solution for $\frac{2^{2014}}{7}$ but, I wasn't 100% sure of the actual working for finding the remainder of such equations.    Therefore requested help for a different value so that i could perhaps know how the whole process worked for a different value.


Leaving the Schengen E.U. with resident permit about to expire

I am trying to get a single answer to the question.  If I leave the eu on a resident permit from Poland that expires while I am out of the E.U. can I return to the E.U. at anytime following the expiration as a visitor on short term visit up to 90 days?   Thanks in advance


I saw , and voted to close it as the dupe that it is.  However, one thing that the author wrote caught my eye:     Believe me, I've been participating in lots of tech forums and this is the first time I'm being banned.   So, I wrote up an explanation of how SO isn't a tech forum.  I hurried, because I knew the post was going to get closed.   It did, of course. But this?:      Uhh... 44 > 32. I answered a question 12 seconds after it was closed.  If this isn't a bug, nothing is.


Can you make an unwilling creature willing? In other words, what defines “willing”?

Going through the spells, I see the phrase "Willing creature" used to determine who you can cast some spells on. I don't ever see a proper definition of what a willing creature is, but I would assume that it would go something like if you asked them "Can I perform this spell on you" they would answer yes. Is there a more formal definition of what makes a target willing in 5e?  What are the ways I could make an otherwise unwilling creature willing? Suggestion spells, for instance, should probably work but what other options do I have?


Atoms In Space - More Specifically Helium

I've read several articles regarding the limited supply of helium gas on our planet and one that many scientists/engineers require for their research. I suppose if the government were to issue any mandates limiting the commercial sale of helium it would be bursting balloons leaving behind pouty children in its wake. Now, I know the proceeding observation is probably oversimplified but the article didn't mention the 'life of helium' after earth.   As far as I understand it, untethered helium will float into space leaving us in want once it is all gone. So then, imagining a helium atom floating beyond our atmosphere, where will it ultimately arrive? Does the earths magnetic field prevent the helium atom from escaping too far from our planet? Or, do the solar winds sweep those loose atoms into deeper space?  I know the space vacuum is not perfect and full of different elements and I would imagine the distance between these atoms is great. Will the helium atom eventually bond with other atoms -- given a strong enough electromagnetic attraction -- and form new elements??


I have a layer in GeoServer and its projection is EPSG:27700. When I query the layer in my app I get and error.  Explanation:  The GeoServer preview displays it correctly. So I copy the JavaScript from the OpenLayers preview page of the layer and use it in my map, and then I compare the browser console for network requests. My map sends an SRS parameter of EPSG:3857 in its requests, whereas the GeoServer preview sends an SRS parameter of EPSG:27700 in it's requests. When I copy the request and past it into the browser I get a WMS file with this seemingly unrelated error message:  Error rendering coverage on the fast path java.lang.IllegalArgumentException: The reference geometry must be either Polygon, MultiPolygon, or a polygonal PreparedGeometry The reference geometry must be either Polygon, MultiPolygon, or a polygonal PreparedGeometry   If I manually modify the SRS value in the URL and paste it into the browser again... I get a valid png file.  I assume the SRS it is sending is identifying what the projection of the map object and I cannot change it? Can anyone help me to understand what is going on please?  === marked as duplicate, although the question linked doesn't help me much === By "copy the request" I meant that Using the browser console I copied the URL my map was firing to GeoServer to request tiles.  The only difference between what my map's URL and the URL from the GeoServer's OpenLayers preview is that the SRS parameter is different.  The GeoServer preview request gets a valid png, the request from my map results in the error mentioned. I guess specifically I want to understand how that results in the error as I cannot understand how referencing a geometry even comes into this scenario.


Holomorphic functions on a complex compact manifold are only constants

Is there a simple proof that every holomorphic function $M\to\mathbb{C}$ on a compact complex manifold $M$ is constant?


Will downvoting affect an user who does not have enough reputation

Suppose if a user asks a question with a reputation of 1 and his question is downvoted(more than his reputation. say for eg here downvote is 2) for some reasons but he is not having enough reputation to get it reduced. In that case when Reputation for downvote will get reduced? is there any time limit to get it decreased?


'Petrovski's home/residence' or 'Petrovski home/residence'

What's correct? Petrovski's home/residence or Petrovski home/residence. Note that Petrovski is the family name (last name), not the first name.   I know that for first name is always 's, but what about family name?


Is there a way to destroy my enemy's planet without taking it over?

Often my people become unhappy about the unwieldy size of my empire. Is there any way to just destroy the population on an opposing planet, rather than taking control of it?


Deleting a specific edge without affecting the face

The white edge is the one I am trying to remove, but when I try doing so via delete > edges, It deletes the whole yellow face with it. How can I keep the yellow highlighted face and delete the white edge only? Thanks always community


"Our house floor" or "our house's floor"?

What's the correct form? Example:     Our house floor was sparkling clean.      Our house's floor was sparkling clean.   I always get confused about this. And when I search on Google I always get the two versions.


Proof that if the set $F_p={0, 1, ..., p-1}$ is a field defined with addition and multiplication mod p, then $p$ must be a prime

I'm studying about the field of Galois (Finite Fields) and I'm going through a proof that tries to show that if a finite set $F_p$ is a field, then $p$ must be a prime. *note: I cannot link the materials since they're in foreign language    I don't understand the last reasoning of the proof, so I will write all of it out.    Let's assume $p$ is not a prime i.e. $p = qs$. Since we assumed that $F_p$ is a field, than each element different from $0$ has a multiplicative inverse, i.e. $ql=1(mod p)$. From here, we can deduce that $p$ is divisor of $ql-1$. From here, we can deduce that $q$ also has to be divisor of $ql-1$.   I understand everything until the following point: "The last statement is possible only if $q=1$." This means that $p$ must be a prime.  Why is it that if $q|ql-1$, then $q=1$?


OGR Shapefile to CSV: Using Python to get WKT for multipart Polys

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


Issue sony vaio : greater than (>) and less than (<) french keyboard

Originally my keyboard is QWERTY , and greater than (>) and less than (<) symbols work well, but when I switch my language from english to french ( AZERTY) . I don't know where is the location of those keys. I will be thankful for your help. Regards!


Cannot delete two files in Windows 7 -- "You need permission to perform this action."

I did something stupid. I reinstalled Windows on my computer but decided to leave the old installation on the drive instead of reformatting. Now I'm trying to delete the old Windows folder and for the most part have been successful, but cannot for the life of me delete two files:   E:\Windows\System32\Macromed\Flash\Flash64_11_1_102.ocx E:\Windows\SysWOW64\Macromed\Flash\Flash11e.ocx   When I try to delete the files I get the error     You need permission to perform this action      You require permission from Nathan-PC\Nathan to make changes to this file   I tried changing the permissions as explained in this guide: , but I still cannot delete the file.  I initially got this error for many/all of the files in the old Windows folder, but I read this: , and downloaded and ran the "take ownership" script. After running that command on the directory I was able to delete all but the two files above.  I have tried everything in normal mode and safe mode.  This is driving me nuts! Can anyone help me delete these two files?   Windows shall not defeat me!


Can someone explain why we take Second Countability and Hausdorffness conditions in Manifold definition?

The definition of Differential Manifold or Smooth Manifold include $\text{Second countability}$ and $\text{Hausdorffness condition}$.  My question is why we include Second countability and Hausdorffness in the defintition of Differentiable manifold?  I got something from a online article that Second countability is used to exclude large space .  But I could not mean it.  Can someone explain why we take Second Countability and Hausdorffness condition ?


"Compared with" vs "Compared to"—which is used when?

Is only one of them correct? Are they used in different situations? Or are they interchangeable?


why do we use 'non-increasing' instead of decreasing?

In english based math language it seems that non-increasing $\Longleftrightarrow$ less or equal  (non-strict decreasing) decreasing     $\Longleftrightarrow$ strict less    (    strict decreasing) Is that correct ? If so, how does it make sense ? precision I should note that even very good math teacher are making mistakes about this. Actually I asked this question after watching Boyd's video on convex optimization where even him is confused about this.... So I imagine many many people are, and there must be classes and tests about this absurd and buggy concept, which yields absolutely nothing interesting. So I just wonder if I really am missing something, or if, yes, some people decided to create an abstraction that is leaky (not not increasing $\neq$ increasing ?) verbose (4 words, with special negation logic, instead of using the word 'strict'  and keeping the usual well defined predicate logic rules) absurdity of the concept This notation is absurd for the following reason :  when dealing with element instead of functions we dont apply the same logic : we dont phrase $x < y$ as  "$x$ is less than $y$" nor  "$x\leq y$" as "$x$ is not-more than $y$". (If we did though, at least it would not be so harmful as not not-more would mean more)  you have to define functions using a not notation, $f$ is non-increasing function $\Longrightarrow$ if $x$ is not-less than $y$, say 0.3 feet and 2.5 inches, then $f(x)$ is not-more than $f(y)$   This also violates a very basic tenet in programming style 101, which is here for a reason : never define or use something with a negation, it is confusing.  To apply composition rules between functions, you better be buckled up with all the not. must be a fluff of cases  More profoundly, this violates a fundamental principle of logic which is that given some ambiguity, you should assume the most general case apply. It is way worse than measuring things with non integral units. This is violating logical rules, and leaving a very basic concept obfuscated.


Maximal number of monomials of multivariate polynomial

If we consider a multivariate polynomial of $n$ variables with degree $N$, how do we show that the maximal number of monomials is $$\binom{N+n}{n} = \frac{(N+n)!}{n!\, N!}\quad ?$$  The hint our teacher gave was that the number of monomials is the number of independent coefficients. So how many independent coefficients does a multivariate polynomial have (at most)?  Thank you.


Windows 10 preventing me from loading Ubuntu (from *.ISO file)

Windows 10 is preventing me from loading Ubuntu 20.04 (from an iso-file) parallel to it (Windows). Am I doing something wrong or has Windows found a way of preventing one from doing this? Thank you for your time and expertise.


How do I choose what shows up in PuTTY title bar from Linux?

In the PuTTY configuration there's an option in Terminal → Features called Disable remote-controlled window title changing. Without that enabled, the title bar of PuTTY will change every time I press return in the console.  I was thinking it'd be a more clean solution to set the title bar text from Linux than to specify one for every PuTTY client I have laying around. So where can I modify what Linux sets as the window title?     $ uname -a Linux drevo 2.6.32-5-amd64 #1 SMP Mon Jan 16 16:22:28 UTC 2012 x86_64 GNU/Linux  $ cat /etc/debian_version 6.0.4


Galley proofs for journal article - can I make statistical changes?

I have had a paper accepted to a good journal (Animal Ecology) and have just received the proofs for checking. However my supervisor has suddenly decided that we need to redo some of the statistics(!) and present the statistics in a different way. I know that you can't make lots of changes, but this won't be too many words, just some statistics. Is is possible at this stage or is it too late?


How to take population size into account when running a Poisson regression?

My data takes the following form: Outcome variable = no of suicides (count data) Explanatory variables = Age (grouped into young, middle and old), Gender, Country, Year I am running a Poisson regression. I have been told that I need to take the population size of each country into account, in order to be able to compare no of suicides in different countries. I have now included population in my dataset, and in my regression. What do I do? - How do I interpret the coefficient of Population, or should I ignore this? - Do I need to do anything else? Thank you in advance!


Reversed effective force in D'Alembert's Principle

In D'Alembert's Principle,what is reversed effective forces and how to determine it's direction?


I'm setting up a buildserver (java) with mercurial, maven, jenkins. After installing and configuring jenkins i'm unable to push to my repository   waiting for lock on repository /home/javabuild/main-java-repository held by 'ubuntu:3949'   the computer 'ubuntu' is my testserver in a virtual machine, i'm trying to document everything before using it on my main server (i'm completely new to this).   As I issue the commands over time the value of the ports change. I'm thinking that it has something to do with the jenkins build test not releasing the lock?  Anyone? How can i fix this?  EDIT: This question has been asked before but the answer of deleting the wlock or lock file in the .hg/store or .hg/data folder doesn't work since there is no such file in those folder in my case.


#include<stdio.h>  void main() {     int a = 4;     switch (a)     {         case 4:             int res = 1;             printf("%d",res);         break;      } }  When I compiled this code with gcc I got error root@ubuntu:/home/ubuntu# gcc test.c -o t test.c: In function ‘main’: test.c:9:4: error: a label can only be part of a statement and a declaration is not a statement     int res = 1;  But when I add ; like case 4:; I can compile my code. What is the problem and why ; fix that?


Intuitively why time period of shm do not depend on displacement from mean position, ie. amplitude

Why simple harmonic motion time period equation is independent from displacement from mean position?


Probability of success on third and fourth trials?

I have a pretty basic probability question, but I'm just having difficulties remembering what distribution this is.  A coin is tossed until a head appears two times in a row. Given that we are using a fair coin, what is the probability that we toss the coin exactly 4 times such that the two consecutive heads are the 3rd and 4th trials?  I know that this would be fairly easy to solve by brute force and listing out the different probabilities, but I'm a little confused as to how to use a "shortcut" such as identifying this as a binomial distribution. I also don't know how to account for the probability that we are using 4 tosses.  Any help is appreciated. Thanks!


Deleting a post makes the rep count go crazy

If you delete a question that was modifying your reputation count (+/-), close the site page and come back, you will have a nice surprise. Your rep count will show you all the reputation points you made today.     That was the point of my test post btw. Reproduced again:


What is the word/expression when you take pleasure in doing something that convention says you are not supposed to do?

What is another way of saying when you take pleasure in doing something that convention says you are not supposed to do ? (ie the word or expression that I am looking for is very similar to saying for example, I take "subversive pleasure" in talking loudly in the library. I am not thinking of "perverse pleasure", though that is an equally good synonym, its just not the one that I can't think of.)


My user validation in my login is working fine, the only problem is that it doesn't stores the PHP SESSION. I've debugged it to see if any session were stored, but they werent. Because when i send the user to the destination page.  The destination page checks with if (!isset($_SESSION['username'])) { etc.. } if the user is logged in or not. Otherwise it sends the user back to the login page. So that is what is going wrong, it sends the user back to the login page.. and ofcourse to confirm the debug says NULL on all.  PHP5:  <?php require ('../lib/config.php'); ?> <?php ob_start();  if (isset($_POST["username"]) && !empty($_POST["username"]) && isset($_POST["password"]) && !empty($_POST["password"])) { $tbl_name='users'; $user_name='Username'; $pass_name='Password'; $salt='';  mysql_connect("$cchost", "$ccuser", "$ccpass")or die("cannot connect");  mysql_select_db("$ccname")or die("cannot select DB");   $myusername=$_POST['username'];  $mypassword=$_POST['password']; $username=str_replace(' ','_', $myusername); $password=hash('whirlpool', $salt . $mypassword);  $username = stripslashes($username); $password = stripslashes($password); $username = mysql_real_escape_string($username); $password = mysql_real_escape_string($password); $sql="SELECT * FROM $tbl_name WHERE $user_name='$username' and $pass_name='$password'"; $result=mysql_query($sql); $row=mysql_fetch_array($result); $donator=$row['donator']; $player=$row['player']; $count=mysql_num_rows($result); if ($donator == '1') { $_SESSION['donator'] = $donator; } if ($player == '1') { $_SESSION['player'] = $player; } if($count==1){ $_SESSION['username'] = $username; header("Location: index_ucp.php"); } else { header("Location: login_ucp.php?err=1"); } } else { header("Location: login_ucp.php?err=9"); } ob_end_flush(); ?>


I have a button that i make. but what i want is that to make the button center alligin. i use alignment center. but it is not working. what i have to do is that to make the button allignement in center in whole page.   .button {   text-decoration:none;   text-align:center;   display: flex;   background: #333333;   color: white;   justify-content: space-between;   align-items: center;   pointer-events:none;   max-width:660px;   border-bottom:solid gray 1px     font-family: DIN pro;     font-weight: bold; } .button .fa {   padding:1em;   pointer-events:auto;   width:1.5em; } .button::before {   content: '';   padding: 1em }  CONTACT


Find the limit of the sequence $ \frac{x^n}{n^k}$ as $n \to \infty$ for all values of$ x > $0 and $k = 1, 2,\cdots$

I have tried using the ratio lemma to tackle this question and also the fact $(n+1)^k \geq 1 + nk$ and I haven't reached an answer. How should I go about solving this problem?


Consider $f(x) = 2x$ and $g(x)=4x$. Is there any homeomorphism $h:\mathbb{R}\rightarrow \mathbb{R}$ such that $h\circ f=g\circ h$? Well it means $h(2x)=4h(x)$ but I don't know what to do from here?


Microsoft just released the final Windows 8 versions for MSDN members, before its consumer release in october.  Anyway, I am a MSDN member. Today I went to see my downloads page and I found a list of the new versions to be downloaded.   Windows 8 Windows 8 N Windows 8 Pro Windows 8 Pro N Windows 8 Enterprise Windows 8 Enterprise N   I know the difference between the  versions "Windows 8", "Windows 8 Pro" and "Windows 8 Enterprise", which you easily find at wikipedia.  But, I really need to know the difference between these versions and the "N" versions before download one of them.


An unknown limit with nth root: $\lim\limits_{n\to\infty}n(x^{1/n}-1)$

How can I find such a limit: $$\lim_{n\to\infty}n(x^{1/n}-1)$$ I tried using a kind of binomial formulas. But nothing helped so far.  Thank you!


Why is Area 51 showing the Stack Overflow logo on Site Stats?

We see site stats on the home page of beta sites. Below the site stats, we have two more options to show the stats in detail.   Area 51      Previously, the Area 51 showed a Area 51 logo beside its name. But now, the Stack Overflow logo is being shown. I didn't notice this before. Is this showing up since the ?  Is this intentional or a bug?


I'm currently undertaking a part time BEng in Digital Embedded Systems Design and Development whilst working as a Control Systems Engineer. When I graduate I plan on doing an MEng in Space Systems Engineering.  After this, I want to move on to some sort of doctoral study. I have yet to decide whether or not I want to do an EngD or a PhD.  Whilst I understand that, on-paper at least, they are equally placed I'm wondering if the EngD option will be seen as less of an achievement due to the taught component and lesser research amount.  Is there any truth to this?    Note on duplication: This question is mainly surrounding the perception, both industrially and academically, of these two degrees.


I can't install any packages without it failing - I get an error about config.dat being locked - how can I fix this?

I had a power failure on my laptop, so I ended up crashing in the middle of a package installation. How do I fix this error?  jrg@atlantis:~$ sudo apt-get upgrade --fix-missing Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 1 not fully installed or removed. After this operation, 0 B of additional disk space will be used. Do you want to continue [Y/n]? Y debconf: DbDriver "config": /var/cache/debconf/config.dat is locked by another process: Resource temporarily unavailable Setting up man-db (2.6.3-1) ... debconf: DbDriver "config": /var/cache/debconf/config.dat is locked by another process: Resource temporarily unavailable dpkg: error processing man-db (--configure):  subprocess installed post-installation script returned error exit status 1 Errors were encountered while processing:  man-db E: Sub-process /usr/bin/dpkg returned an error code (1) jrg@atlantis:~$


\dots alignment in math environment and amsmath

In some cases, with amsmath, it seems that the dots are not well aligned. For instance, when in parenthesis, it is normally aligned, but when followed by a colon, it is in the middle of the line.  MWE:      \documentclass{article}     \usepackage{amsmath}      \begin{document}     $(\dots) = \dots:$     \end{document}   Which gives the following result:


Clarification on getting paid from a company which filed for Bankruptcy?

I work as an employee for a contracting firm which supplies IT labor resources for their (or) to another contracting firm's clients.   As there is a 45 day holding period for the contract firm which i'm employed to get paid, that delays my paycheck.  Meaning of 45 days holding period is, I worked for first 45 days without getting paid. I received first 15 day paycheck after completing 45 days. Next paycheck will be on the 30th day which will be following 15 days of pay. So, there is always a 45 day pay behind.  My concern or clarification is " What if my employer filed bankruptcy? " - If that's the case, will i ever get paid for those delayed 45 days of my pay.


How to prevent registraton e-mail from being treated as SPAM?

I have a website which sends e-mails to users on 2 occasions:   when they register then receive "hello there" e-mail when they ask for a new password they receive a new password   Both e-mails are generated from a template, so all "register" e-mails look very similar. Also all "password reset" e-mails look alike.  And now I see they go directly to SPAM folders when sent to gmail accounts.  When I display such a message from Gmail's SPAM folder I am notified they were treated as SPAM because Gmail already got lots of similar messages (and I know there were less than 30 of them sent).  So what can I do to be sure Gmail is NOT considering my e-mails as SPAM?  The "hello there" e-mail is not that necessary but the "password reset" ones are VERY important and there is no way to make them look different.  I use PhpMailer with SMTP.  I checked my e-mails with  and it says they are not blacklisted, have SPF and basically look fine. Nothing mentioned here:  works for me and it's a thread that is 7 years old. And 7 years in computer science is really long. Therefore I think this is NOT a duplicate.


Fundamental group of two tori with a circle ($S^1✕${$x_0$}) identified

Compute the fundamental group of the space obtained from two tori $S^1✕S^1$ by identifying a circle $S^1✕${$x_0$} in one torus with the corresponding circle $S^1✕${$x_0$} in the other.  Using van Kampen's theorem, I can fairly quickly show that if $T_1$ is one torus and $T_2$ is the other, then the group has to be isomorphic to $((π_1(T_1) ∗ π_1(T_2)))/N ≅ (\mathbb{Z} ✕ \mathbb{Z})∗ (\mathbb{Z} ✕ \mathbb{Z})/N$, where N is generated by elements of the form $i_{12}(w)i_{21}(w)^{-1}$, w is in $\pi_1(S^1✕${$x_0$}$) ≅ \mathbb{Z}$ and $i_{12}$, $i_{21}$ are the maps from $\pi_1(S^1✕${$x_0$}$)$ to $π_1(T_1)$, $π_1(T_2)$ respectively determined by inclusion. My problem is, as it seems to always be with van Kampen-related problems, figuring out what the elements of N look like. My attempt to do this in a pure-algebra way, as far as I can tell, failed me: I tried examining the case where w represents a loop that goes n (some integer) times around the circle, but then it seems like $i_{12}(w)$ "$=$" $(n, 0)$ in $T_1$ and $i_{21}(w)$ "$=$" $(n, 0)$ in $T_2$, which says to me that $i_{12}(w)i_{21}(w)^{-1} $"$=$"$ (n, 0) + (-n, 0) = 0$. The notation here isn't right, since $(n, 0)$ in $T_1$ is not the same as $(n, 0)$ in $T_2$ and their addition (composition?) shouldn't be written quite that way, hence my quotes around the equals signs, but certainly no loop in $S^1✕${$x_0$} is going to magically include anything but the 0 loop in either torus's second component, right? But this doesn't seem right to me, since if a, b are the generators of the circles in $T_1$ and d, e are the generators of the circles in $T_2$, and c is the constant path then the identification of the circle should make, say, $a = d$, so for example $(a, b)*(d, e)$ $ = (a^2,b)*(c, e)$ $ = (c, b)*(d^2,e)$. This doesn't match with what I just worked out N might be, but I also can't figure out what N should look like to make this equivalence make sense. My attempt to understand this geometrically has gone even worse. What I know for sure is that the resulting figure isn't the "2-torus", 2 tori glued together at a disc. What I don't know for sure is whether this identification should actually create the hypertorus $S^1✕S^1✕S^1$ or something completely different.


C#: Round decimals for var made of Random

I got this (C#) :  Random RNG = new Random(); decimal divab50 = RNG.Next(50,100); decimal divbl50 = RNG.Next(6,50); decimal decreturn = divab50 / divbl50; Console.WriteLine(decreturn);   How can I round the decreturn var to two decimals? I've tried Math.Round and String.Format they don't seem to work for vars generated in RNG. I think. I'm new at c# just started


How do I take a backup of my Master Boot Record (MBR) and Partition Table (PT)?

I'd like to know how to:       of all the MBRs and all the PTs of all my disks to a file so I can easily back them up using rsync or a comparable program.


Soft wrap (white-space: pre-wrap) instead of horizontal scroll bars in code blocks

I know , but wouldn't they be better without the horizontal scroll bars?   Sort of related to . (The consensus seemed to be that people were lazy or didn't notice. But there are still some legitimate reasons to have lines over 80 chars or so.)


Regex replacement with lowercase monthnames for biblatex/biber to eliminate the warning “month not integer…”

I had already asked a nearly identical question   I am using biblatex with biber from TL2018 for my PhD thesis. Due to various reasons, I am forced to use Mendeley for citation managements and cannot switch to another tool now. Mendeley is capable of generating a bib file - but it is compatible with only the classic natbib/bibtex combo (although it correctly escapes special characters).  I understand that with biblatex/biber combo, the month field is not a string, but rather must be an integer.  So, as expected and discussed , I get the warning      WARN - month field 'jan' in entry 'Guo2012' is not an integer - this will probably not sort properly.   (this time for jan  wherein unlike my original question, the month does not begin with captial J).  For tackling the original question, I used the regex given in that question in my preamble (given below)   \DeclareSourcemap{     \maps[datatype=bibtex]{         \map[overwrite]{             \step[fieldsource=month, match=\regexp{\Ajan\Z}, replace=1]             \step[fieldsource=month, match=\regexp{\Afeb\Z}, replace=2]             \step[fieldsource=month, match=\regexp{\Amar\Z}, replace=3]             \step[fieldsource=month, match=\regexp{\Aapr\Z}, replace=4]             \step[fieldsource=month, match=\regexp{\Amay\Z}, replace=5]             \step[fieldsource=month, match=\regexp{\Ajun\Z}, replace=6]             \step[fieldsource=month, match=\regexp{\Ajul\Z}, replace=7]             \step[fieldsource=month, match=\regexp{\Aaug\Z}, replace=8]             \step[fieldsource=month, match=\regexp{\Asep\Z}, replace=9]             \step[fieldsource=month, match=\regexp{\Aoct\Z}, replace=10]             \step[fieldsource=month, match=\regexp{\Anov\Z}, replace=11]             \step[fieldsource=month, match=\regexp{\Adec\Z}, replace=12]         }     } }   How can this be modified suitably to handle this lowercase situation?


I see a lot of post about inserting into MySQL database. The vast amount of them seem to forget that its user input we are dealing with. What would be the best was to insert data in to the table. Would mysqli_real_escape_string be okay? Or would using prepared statements be a better option, maybe both?


Add conditions in code depending on python version

I am currently writing some code on python 3.3. Unfortunately some of the plugins I rely on are not yet compatible with Python3 and I need to switch back to Python2.7.  In order to avoid refactoring all the code, I would like to do something like  if(os.python.version<3.0): from _future_ import print, super   What is the proper way of doing this


I have some functions that use curl to pull information off a couple of sites and insert them into my database. I was just wondering what is the best way to go about executing this task every 24 hours?  I am running off windows now, but will probably switch to linux once I am live (if that makes a difference). I am working inside symfomy framework now.  I hear cronjobs can do this this...but looking at the site it seems to work remotely and I would rather just keep things in house...Can i just "run a service" on my computer? whatever that means ;) (have heard it used)  thanks for any help, Andrew


Convergence of Sets? (Topology on a Powerset of a Set?)

Given a sequence of sets, is there some well-defined notion of a limit of a set?   In other words, given some universe set $U$, I am wondering if there is a topology on $2^U$ (the powerset of $U$) such that the usual intersection and the union limits converge in that topology.  As an explicit example, let $U=\mathbb{N}$,  $S_n = \{x\in \mathbb{N} | n< x \le 2n \}$,   $T_n = \{n\}$.  The limit of both sequences above should be the empty set by the following argument:  \begin{align} S_n &\subset (n,\infty) \\\\ \lim_{n\to\infty} S_n &\subset \lim_{n\to\infty} (n,\infty) = \cap_{n\in\mathbb{N}} (n,\infty) = \emptyset  \end{align}  (I'm not sure how to justify passing a set inclusion to the limit.)


Does a magnetic field do work on an intrinsic magnetic dipole?

When you release a magnetic dipole in a nonuniform magnetic field, it will accelerate.  I understand that for current loops (and other such macroscopic objects) the magnetic moment comes from moving charges, and since magnetic fields do no work on charges ($F$?perpendicular to $v$) it follows that the work done on the dipole (that caused its gain in kinetic energy)  must have come from somewhere other than the magnetic forces (like electric forces in the material).  However, what about a pure magnetic moment? I‘m thinking of a particle with intrinsic spin. Of course, such a thing should be treated with quantum mechanics, but shouldn't classical electrodynamics be able to accommodate a pure magnetic dipole? If so, when I release the pure dipole in a nonuniform B-field and it speeds up, what force did the work? Is it correct to say that magnetic fields DO do work, but only on pure dipoles (not on charges)? Or should we stick with "magnetic forces never do work", and the work in this case is done by some other force (what?)?  Thanks to anyone who can alleviate my confusion!


how to transfer installed programs to other pc

My ubuntu laptop is customised with all the programs and themes of my choise,can i transfer these software to another computer running ubuntu and install them there via usb drive.


Can you call a variadic function from a variadic function?

I have written a function which sums columns together (if there is a built in for this, that would also be good to know) and another which calls that function and replaces the sum with a different value if it is zero or null. When trying to call the second function I get the following error:   ERROR:  function enc_sum_columns(numeric[]) does not exist LINE 1: SELECT            enc_sum_columns(summed_values::numeric[]) HINT:  No function matches the given name and argument types. You might need to add explicit type casts....   The sum columns function is as follows:  create or replace function enc_sum_columns(VARIADIC cols_to_sum numeric[], OUT total numeric) RETURNS numeric AS $BODY$ BEGIN  SELECT INTO total SUM(cols_to_sum[i])    FROM generate_subscripts(cols_to_sum, 1) g(i); END;   $BODY$   LANGUAGE plpgsql    And the function that calls it:  CREATE OR REPLACE FUNCTION public.enc_sum_with_choice_for_zero(     IN replacer numeric,     VARIADIC summed_values numeric[],     OUT total numeric)   RETURNS numeric AS $BODY$  BEGIN    SELECT INTO total enc_sum_columns(summed_values::numeric[]);    IF total=0 OR total IS NULL THEN    total = replacer;    END IF;  END; $BODY$   LANGUAGE plpgsql VOLATILE   And an example of calling the function :  SELECT cov_s_fib, cov_s_cop, enc_sum_with_choice_for_zero(500::numeric, cov_s_fib::numeric, cov_s_cop::numeric) from test_dynamo_with_geom1   Here is some expected output from the query above:  |---------------------|------------------|------------------| |     cov_s_fib       |     cov_s_cop    |      total       | |---------------------|------------------|------------------| |          1          |         3        |          4       | |---------------------|------------------|------------------| |          0          |         0        |          500     | |---------------------|------------------|------------------| |                     |                  |          500     | |---------------------|------------------|------------------| |          0          |                  |          500     | |---------------------|------------------|------------------| |                     |        1         |          1       | |---------------------|------------------|------------------|   Can I not pass a variadic varaible to another function like that? Did I just mess up something syntactically? Originally, I had the code in enc_sum_columns inside of enc_sum_with_choice_for_zero and it worked fine.


Simple but hard 2 by 2 system in $x$ and $y$

Is there a systematic way of solving this system, analytically?  $$\begin{cases} x \  + \ y^2=11\\ x^2+y\ \ =\ 7\\ \end{cases} $$  I mean, other than brute-force.


In my Class I declared an Array  myUsers = new Array();   Where I want to Add Usernames, unique. So i thought I would check if the ArrayLenght is 0, if yes, add a User. Which works fine. I if a Username wants to be added, which exists in the Array, it should be deleted. But this way, If I add one User the console says ["User1"] If I try to add another one (another one User2) the console says ["User1", empty] Can't get behind that...  isChecked(e) {      var usersArray = this.myUsers;      console.log(usersArray.length);    if(this.myUsers.length == 0) {       console.log("is 0");       this.myUsers.push(e);     } else {       console.log("is not 0");       for (var i= 0; i < this.myUsers.length; i++) {         if (this.myUsers[i] == e) {            console.log("is in array");            delete this.myUsers[i];           } else {             this.myUsers.push(e);           }      }   }   }


How can I prove that the determinant of the matrix is $0$ only when $a=b=c=d=0$? I tried with the Laplace Method of Expansion but I cannot solve the final equation.   \begin{bmatrix}         a & b & c & \ d \\         b & -a & d & \ -c \\         c & -d & -a & \ b \\         d & c & -b & \ -a \\         \end{bmatrix}  Thanks in advance!


What are the key points for a beginning genealogist to consider?

I'm an absolute starter to genealogy and I've always found it very interesting so last week I decided to build my family tree.  What are the key things I should consider when getting started?


I would like to have a vector graphic with the font I'm using for my captions in my PDF file.  I normally create my graphics in DIA and save them as .eps files. In my .tex file I use following  \usepackage{ifpdf} \usepackage{graphicx, epstopdf} \ifpdf   \DeclareGraphicsExtensions{.pdf,.jpg,.png} \else   \DeclareGraphicsExtensions{.eps} \fi   and  \includegraphics[width=\linewidth]{my_image.eps}   to include images (and auto generate PDF files).  I'm using Windows 7 (64-bit), miktex 2.9 and pdflatex


Is there a numerical solution to a mixture model of two normal distributions?

I'm building a mixture model with the two normal distributions $\mathcal{N}(\mu_1,\sigma_{1}^{2})$ and $\mathcal{N}(\mu_2,\sigma_{2}^{2})$.  So, the density function is $$ f(x) = p_1 N(x; \mu_1, \sigma_1^2) + p_2 N(x; \mu_2, \sigma_2^2), $$ where $p_1+p_2=1$, and $$ N(x;\mu,\sigma) = \frac{1}{\sqrt{2\pi \sigma^2}}\exp\left\{-\frac{(x-\mu)^2}{2\sigma^2}\right\}. $$.  Suppose I have all the sampling data, is there some numerical solution or formula that could derive $p_1$, $\mu_1$, $\sigma_1$ and $p_2$, $\mu_2$, $\sigma_2$?


If $A$ and $a$ are the radii of a triangle's circum- and in-circles, and $b$ the distance between the circles' centers, prove $A^2-b^2=2 A a$

Given a triangle, denote by $A$ the radius of the circumscribed circle and denote by $a$ the radius of the inscribed circle. The distance between the centers of those circles is $b$. Prove that $A^2 - b^2 = 2Aa$.   I found this in a prelim paper. I really dont know where to start. (Sadly, I can only use tangent properties, arc properties and trignometry)


How can I decide network speed of my dedicated server?

I have a dedicated server managed by WHM which has 100 websites. Bandwidth is 1 Gbps.  I found another company which offers better CPU and RAM and HDD same price but bandwidth is 0.5 Gbps.   I am not good at calculating bandwidth that needed. What should I do?


If you're writing a library, or an app, where do the unit test files go?    It's nice to separate the test files from the main app code, but it's awkward to put them into a "tests" subdirectory inside of the app root directory, because it makes it harder to import the modules that you'll be testing.    Is there a best practice here?


If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex

Let $\,\,f :\mathbb R \to \mathbb R$ be a continuous function such that $$ f\Big(\dfrac{x+y}2\Big) \le \dfrac{1}{2}\big(\,f(x)+f(y)\big) ,\,\, \text{for all}\,\, x,y \in \mathbb R, $$ then  how do we prove that $f$ is convex that is $$ f\big(tx+(1-t)y\big)\le tf(x)+(1-t)f(y) , \forall x,y \in \mathbb R , t\in (0,1)? $$ I can prove it for dyadic rational's $t=\dfrac k {2^n}$ and then argue by continuity ; but I would like a more direct proof . Thanks in Advance


How does Stack Overflow manage notifications and templates?

Each Stack Exchange site has the same kind of style. How are these styles maintained in a uniform fashion? Is there some sort of base template that each site shares and overrides as necessary?  And similarly, how does each site implement the notification system? Is each site responsible for implementing it, or is there an underlying framework that is utilized?  I'm gearing up to implement a system that has base functionality shared across multiple sites, so I'm very interested to hear how it's been done before.


I received an email saying documents are /were

I received an email saying that the documents are/were being processed.   Which is correct? Are or were?


BibTeX natbib with super does not allow using occasional \citet

I am using natbib with superscript numbered citations as follows:  \usepackage[super,comma,sort&compress]{natbib}    It works great when I have the case This is a reference~\cite{author1999}. My reference appears as a superscript.   However, I occasionally want write something like: As shown by \citet{author1999} where I want the citation written out and not as a superscript. natbib in super mode inserts a superscript when using \citet.  Is there a way to have natbib use \citet in regular mode despite being in super mode? Can one change the mode temporarily to not have super and then switch it back on again?


How to revoke permissions from applications?

I don't understand, why some programs are requesting some permissions, especially concerning my privacy.   So I want not to grant them or revoke after granting.  I don't care if application will crash. I expect, that polite application will never access my private data without first asking explicitly. Since I won't permit this, then polite application will never crash. And mutual, if application will crash, then it is not polite and should be uninstalled.  How to revoke permissions on Android?


Tan π/(2n + 1) Tan 2π/(2n + 1) Tan 3π /(2n + 1) .... Tan nπ /(2n + 1) = √(2n + 1  Dividing by √ (2n + 1)  (Tanπ/(2n + 1) Tan2π/(2n + 1) Tan 3π /(2n + 1) .... Tan nπ/(2n + 1))/(√(2n + 1)) = 1  To be equal to 1, the top term must be 1 or equal to (√ (2n + 1)  Putting  1 = tg (pi / 4) = tg45th (Tanπ/(2n + 1) Tan2π/(2n + 1) Tan 3π / (2n + 1) .... Tannπ/(2n + 1)) = opposite collared (√(2n + 1) = adjacent collet  Note that in a rectangular triangle if it is an angle is 45º, the other is also, characterizing the triangle as isosceles, both sides are equal, so (Tan π/(2n + 1) Tan2π/(2n + 1) Tan 3π/(2n + 1) .... Tan nπ/(2n + 1)) = (√ (2n + 1)  Can anyone show me anything better than this? (other than complex) or Who can prove using De Moivre's formula?