If a sequence converges in a metric space, it is Cauchy, and in $\mathbb{R}^k$ every Cauchy sequence converges.   Therefore, in $\mathbb{R}^k$ a sequence converges iff it is Cauchy.  Let $\{s_n\}$ be a sequence in $\mathbb{R}$ where each $s_n=\sum_{k=1}^na_k$. Therefore, by the above, every series converges iff  $$\left | \sum_{k=m}^n a_k\right| <\epsilon$$ For a given $\epsilon >0$ and an integer $N$ such that $N\le m\le n$. If $n=m$ then the statement reduces to:  A series converges if and only if $$|a_n| < \epsilon $$ For a given $\epsilon >0$ and an integer $N$ such that $N\le n$.  This clearly cannot be (e.g Harmonic series). When does the equivalence become an implication.


Android: crash at trying to paste nothing

Basically I have a button on my activity that pastes text from the clipboard. My problem is that after testing it, the app crashes if there is nothing to paste from the clipboard (as in, nothing was copied to the clipboard). The paste function works if there is something in the clipboard, so I would like to know how to handle it. I tried handling this kind of crash but it doesn't work for me.  public void PasteText(View v) {     TextView mainText = (TextView) findViewById(R.id.editext);     ClipboardManager clipboard = (ClipboardManager) getSystemService(CLIPBOARD_SERVICE);      ClipData cData = clipboard.getPrimaryClip();     ClipData.Item item;     String text = "";     if(cData.getItemCount() > 0)     {         item = cData.getItemAt(0);         text = (String) item.getText();         mainText.append(text);         return;     }     else     {         item = null;         mainText.append(text);         return;     } }   Logcat:  01-01 15:07:56.860: E/AndroidRuntime(10567): java.lang.IllegalStateException: Could not execute method of the activity  01-01 15:07:56.860: E/AndroidRuntime(10567):    at android.view.View$1.onClick(View.java:4025)  01-01 15:07:56.860: E/AndroidRuntime(10567): Caused by: java.lang.NullPointerException: Attempt to invoke virtual method 'int android.content.ClipData.getItemCount()' on a null object reference  01-01 15:07:56.860: E/AndroidRuntime(10567):    at com.karimo.tester.MainForm.PasteText(MainForm.java:109)  01-01 15:07:56.860: E/AndroidRuntime(10567):    ... 13 more


I am flying Delhi-Lisbon and have a transit in Heathrow. My jet flight from Delhi arrives at terminal 4 at 5:40 PM and I have a TAP Portugal flight from Terminal 2 at 7:55 PM. This is single e ticket with both flight segments listed on the same ticket, so I am assuming my baggage will be checked through to Lisbon.  Do I need a Visa transiting at Heathrow and also is this enough time to make the connection? I am an Indian citizen with a valid US visa, so technically I am expecting as per UK website. But I am not sure given the fact that I need to take a train/bus to change terminals.


"W: Possible missing firmware for module i915_bpo" when updating initramfs

When I run a kernel or NVIDIA driver update on my 16.04, this triggers an initramfs rebuild which outputs the warning below:  Processing triggers for initramfs-tools (0.122ubuntu8.1) ... update-initramfs: Generating /boot/initrd.img-4.4.0-34-generic W: Possible missing firmware /lib/firmware/i915/skl_guc_ver6.bin for module i915_bpo   I have a notebook with two graphics chips, an NVIDIA GeForce 940M and the Intel i5-6200U's integrated graphics.  The device in use is my NVIDIA card:  $ inxi -G Graphics:  Card-1: Intel Sky Lake Integrated Graphics            Card-2: NVIDIA GM108M [GeForce 940M]            Display Server: X.Org 1.18.3 driver: nvidia Resolution: 1920x1080@60.03hz            GLX Renderer: GeForce 940M/PCIe/SSE2 GLX Version: 4.5.0 NVIDIA 367.35   Here's the output of lshw -c video, corresponding to my Intel graphics chip which should use that driver:      *-display                   description: VGA compatible controller          product: Sky Lake Integrated Graphics          vendor: Intel Corporation          physical id: 2          bus info: pci@0000:00:02.0          version: 07          width: 64 bits          clock: 33MHz          capabilities: pciexpress msi pm vga_controller bus_master cap_list rom          configuration: driver=i915_bpo latency=0          resources: irq:125 memory:a2000000-a2ffffff memory:b0000000-bfffffff ioport:5000(size=64)   The file in the warning does not exist, only those:  $ ll /lib/firmware/i915/ total 336 drwxr-xr-x  2 root root   4096 Aug 11 13:24 ./ drwxr-xr-x 74 root root  32768 Aug 11 13:24 ../ -rw-r--r--  1 root root   5872 Jul 21 17:03 bxt_dmc_ver1_04.bin -rw-r--r--  1 root root   5872 Jul 21 17:03 bxt_dmc_ver1_05.bin -rw-r--r--  1 root root   8380 Jul 21 17:03 bxt_dmc_ver1_06.bin -rw-r--r--  1 root root   8380 Jul 21 17:05 bxt_dmc_ver1_07.bin lrwxrwxrwx  1 root root     19 Jul 21 17:05 bxt_dmc_ver1.bin -> bxt_dmc_ver1_07.bin -rw-r--r--  1 root root   8824 Jul 21 17:03 skl_dmc_ver1_23.bin -rw-r--r--  1 root root   8928 Jul 12 21:33 skl_dmc_ver1_26.bin lrwxrwxrwx  1 root root     19 Jul 12 21:33 skl_dmc_ver1.bin -> skl_dmc_ver1_26.bin -rw-r--r--  1 root root 109636 Jul 21 17:03 skl_guc_ver1_1059.bin lrwxrwxrwx  1 root root     21 Jul 21 17:03 skl_guc_ver1.bin -> skl_guc_ver1_1059.bin -rw-r--r--  1 root root 128320 Jul 21 17:03 skl_guc_ver4_3.bin lrwxrwxrwx  1 root root     18 Jul 21 17:03 skl_guc_ver4.bin -> skl_guc_ver4_3.bin   The latest driver package seems to be installed though:  $ apt-cache policy xserver-xorg-video-intel xserver-xorg-video-intel:   Installed: 2:2.99.917+git20160325-1ubuntu1   Candidate: 2:2.99.917+git20160325-1ubuntu1   Version table:  *** 2:2.99.917+git20160325-1ubuntu1 500         500 http://ftp.uni-stuttgart.de/ubuntu xenial/main amd64 Packages         100 /var/lib/dpkg/status   What does this warning mean exactly and how can I fix it?


How to find the limit without L'Hospital?

$$\lim_{x\rightarrow 1} \frac{x^m-1}{x^n-1}$$   I found this in a book (recommended by the professor) without solutions or hints.  My problem is that I can't find definitions about this kind of problems and I have no idea how to start, any kind of help would be great. So far I've been dealing with "$\lim_{x\rightarrow ∞}$" only. Also without L'Hospital, because we haven't had this in lecture.


How can I uninstall Ubuntu when dual-booted?

I've been deciding on whether to install Ubuntu and keep it as dual-boot, or to only use Windows, and I need to know how to uninstall Ubuntu and keep Windows alone, with all my Windows data left on the system.


Recursively rename files and directories

I'm using this command to rename files:  for fname in *; do     mv "$fname" $(echo "$fname" | sha1sum | cut -f1 -d' ') done   But it only renames in the current directory. Let's say I have many directories, and each directory contains some other directories, and last directory tree contains files. I want to rename them with random characters.  I think find . -type f should work, and have tried it, but still did not get any working command.


How do I Validate the File Type of a File Upload?

I am using <input type="file" id="fileUpload" runat="server"> to upload a file in an ASP.NET application. I would like to limit the file type of the upload (example: limit to .xls or .xlsx file extensions).   Both JavaScript or server-side validation are OK (as long as the server side validation would take place before the files are being uploaded - there could be some very large files uploaded, so any validation needs to take place before the actual files are uploaded).


A function is discontinuous at all rational points and continuous at all irrational points

Define $f(x)$ for $x\in[0,1]$ by $f(\frac pq)=\frac1q$ if $p$ and $q$ are relatively prime, and $f(x)=0$ if $x$ is irrational.  How can we see that $f$ is discontinuous at all rational points and continuous at all irrational points?  Furthermore, if $g(\frac pq)=q$ for $(p,q)=1$ and zero otherwise, how can we see that $g$ is not bounded on any subinterval of $[0,1]$?


Change abstract title in IEEEtran when used with other language

When I use the -class with a german -package loaded, the title of the abstract automatically gets translated to Zusammenfassung. However I'd like it to be Kurzfassung.  The solution one can find all over the web, is just to use:  \def\abstractname{Kurzfassung}   Why is that approach not working in my case?  I use lualatex, here is my minimal example:  \documentclass{IEEEtran}  \usepackage[T1]{fontenc} \usepackage[utf8]{luainputenc} \usepackage[ngerman]{babel}  \def\abstractname{Kurzfassung} \def\IEEEkeywordsname{Stichwörter}  \usepackage{blindtext}  \begin{document}  \begin{abstract} \blindtext \end{abstract}  \begin{IEEEkeywords}      myKeyword \end{IEEEkeywords}  \section{Einleitung} \blindtext  \end{document}     But the appearance of the abstract remains unchanged in the german default Zusammenfassung:


Have you noticed the different responses when catching Pokémon?  Most of the time there is a ring that shoots out. Sometimes however there are fiery wisps that go up from the Pokémon.   Any idea what this means?


Multiple API requests from CSV file as parameters

Let's say that my domain is api.test.com, path is /v1/products and I have to do 1000 API requests with different products as parameters. Examples:   GET api.com/v1/products/product1  GET api.com/v1/products/product2 GET api.com/v1/products/product3 GET api.com/v1/products/product4   How to do this in Postman or Jmeter and read products as parameters from CSV file?


I have implemented custom search and displaying 10000 records on page using pagination. Pagination is done by using StandardSetController only. I also have implemented sorting of data. Can anybody suggest any solution to reduce view state?


where can i found salesforce latest dumps for dev 401 exam

I would like to know the study plan  of Certification (401). can you help me the sites to download the dumps.


My fiancee and I are shopping for a house, and very fortunate to have the assets to allow us to make a healthy downpayment.  We both like the idea of a lower monthly mortgage payment, specifically the career flexibility that comes with it.  We are looking at houses in the $1.2-1.4MM range, and can put down ~$800K, which delivers a very affordable monthly. After doing so, we'd have ~1.4MM in equities together outside of the house, though about $550K would be locked in retirement accounts.  Question is - are we misguided to make such a large downpayment, even though it buys us some job choices and peace of mind?


Virtual Programmable Keys software for Mac?

I've got a PC and a Macbook Pro. I use a piece of software where I frequently need to press TAB, SPACE, TAB, SPACE. So instead of hitting 4 buttons, I have a gaming keyboard which I can program to press one button and it presses those keys for me.  So now I'm on my Mac, I'm using the software but of course, I haven't got my USB gamer keyboard with me.  Is there any 'virtual' software that can do this? It would be a huge help. I've googled it but with no luck.


In multiple regression, why are interactions modelled as products, and not something else, of the predictors?

Consider multiple linear regression. This question might be deceptively simple, but I'm trying to intuitively understand why, say if I have predictors X1 and X2, then interactions between these predictors can be adequately captured by X1 * X2.  I know interaction terms are modelled as products, just because that's what I was taught in school, and that's what everyone says to do.  I'm guessing there is maybe some geometric argument.  But why is a product (of say two numeric features, and not the extra complexity of multiplying by one being a dummy variable while other is numeric etc) going to adequately capture interactions?  Why are not "interactions" best captured by another f(X1, X2) by default instead of specifically X1 * X2?  I can see the idea that X1 * X2 may capture situations where the signs of X1 and X2 are the same or not, but then why would not, say, by default interactions be modelled by say f(X1, X2) = sign(X1) * sign(X2) instead of f(X1, X2) = X1X2?  I realise I can add any other f(X1, X2) to a regression or any predictive model, but finding the exact shape of interactions by hand coding is time consuming. How do I know X1X2 is a good first guess?


GUI application to rotate single PDF pages and save in 14.04?

In OSX, this is easy but not so in Ubuntu.  flpsed is not the answer here, since it does not include rotate capability.  How can you rotate single pages of PDF and save the result?


I'm trying to use the svg package for inserting svg images in my latex file, as suggested in other questions. But now I ran into a problem:  For example I have a image figure1.svg, if I write  \includesvg{figure1}   it will give an error says  ERROR: LaTeX Error: File `figure1.pdf_tex' not found.   But if I write  \includesvg{figure1.svg}   it will give another error says  ERROR: LaTeX Error: Unknown graphics extension: .svg.   How can I fix this problem? I'll prefer not having to convert all my svg files to pdf_tex files with some external program.    Update  My LaTeX environment is latest the TeXLive 2013 on Windows 7. A MWE code would be  \documentclass{article} \usepackage{svg}  \begin{document}  \begin{figure}[htbp]   \centering   \includesvg{figure1.svg}   \caption{svg image} \end{figure}  \end{document}


Zooming in QGIS stops at particular scale

I seem to have a problem with the zooming levels in QGIS 2.6 Brighton. When I go to zoom in to a vector or raster layer, e.g. for digitizing purposes, the scale seems to be fixed at 1:2,256, I can't zoom in any further than this scale. My previous version of QGIS, 2.2.0 did not have this problem.  Is there a fix for this?


Required Bash Code for Hide Password during Typing

How can I write Bash Code for Hiding Password Or convert into '*' user input will be in string so no spaces, and change or hide password String.


Is this a question on probability? Or not a question at all?

If you choose an answer to this question at random, what is the chance you will be correct?  A) $25\%$  B) $50\%$  C) $60\%$  D) $25\%$


I just came across this question:      This tree (be) _____ planted by the settlers who (found) _____ our city over four hundred years ago.    I think "over four hundred years ago" is an unspecified time. My answer was that the two gaps require present perfect. So I was a little surprised with the answer that both of them require simple past. Why is this the case?


If $\lim_{n\rightarrow\infty} f(n+1) - f(n) = L$, prove that $\lim_{n\rightarrow\infty} f(n)/n = L$

Here's the problem in full. I've stared at it for hours and can't get anywhere, so a hint would be nice.  Suppose that $f:\mathbb N\rightarrow\mathbb R$. If $$\lim_{n\rightarrow\infty}f(n+1)-f(n) = L$$ prove that $\lim_{n\rightarrow\infty}f(n)/n$ exists and equals $L$.  This problem is marked with the word "Cauchy", so I'm guessing Cauchy sequences or something related to them will be necessary, but I can't figure out what.  Edit: It appears as if the Stolz-Cesaro Theorem makes this quite easy. Unfortunately though, we have not discussed this, so I won't be able to use this.


Why doesn't incoherent light cancel itself out?

What is the precise mathematical description of an incoherent single-frequency signal for any type of wave? The reason I'm asking is because of the following apparent paradox in which incoherent light cannot exist. Consider sunlight, for example, which has passed through a polarizing filter and frequency filter, so that only waves with wave numbers very close to $k_0$ are allowed to pass through. Since sunlight is totally incoherent, it seems reasonable to model the signal as a sum of sine waves $E_\alpha(x,t)=A_\alpha\sin(k_0x-\omega_0t+\phi_\alpha),$ where $E$ is the electric field in the direction of the polarizing filter, $\omega_0=ck_0$, $A_\alpha$ is a random amplitude, and $\phi_\alpha$ is a random phase shift. If the light were coherent, then the $\phi_\alpha$'s would all be identical; so it seems reasonable that for "maximal incoherence" the $\phi$'s and $A_\alpha$'s would be different and uniformly distributed. But then for every component with phase shift $\phi$ and amplitude $A$, there exists a wave $A_\alpha\sin(k_0x-\omega t-\phi-\pi)$, which cancels the original. Hence all components cancel and there is no wave (spectrometer detects nothing). So what's the flaw here? I'm guessing the model of incoherent light is where the problem lies, but maybe it's in the reasoning. I'm also curious whether or not the answer necessarily relies on quantum mechanics. EDIT: Since there are some votes to close based on the proposed duplicate, I'll just say that both questions get at the same idea, but I think mine (which could also have focused on polarization) is more specific, since I'm asking for a precise model and whether quantum physics is a necessary part of the explanation. From what I can tell, the answers to the linked question do not address these points.


Help a nervous flyer plan routes that minimise flight changes and time spent in the air

I'm new here!  I'm just looking for some advice and some guidance.  So, I feel like it's just better if I cut to the chase.  I'm from Scotland and this year I was accepted to study abroad in the USA for a semester.  It's something I've always wanted to do and the school is perfect for my degree, so I feel really fortunate to be given the opportunity.  I can't wait to get started!  However...I don't fly very well.  I've been to Ireland, Belgium, Bulgaria, Portugal, The Netherlands, Cyprus (North and South), Turkey, USA (x3), Thailand and the UAE and it feels as I'm getting older, I am becoming a bit more anxious on flights.  I have a fear of heights, which I think contributes to it.  So, I have been looking for flights and I can find some really good prices from Scotland to North Carolina for around £360 (albeit with a monsterous stopover), however, it requires me to take a 10 hour flight from Glasgow to Toronto (on WestJet), then wait for 16 hours, then take another flight to New York, then wait again, then finally another flight to North Carolina.  Ideally, I don't want to be on any flight for 10 hours and ideally, I don't want to have to take 3 flights.  When I start looking for other ways to get there - different routes, less flights, less time on flights - and the price is creeping higher and higher.  I was just wondering if anyone knows of any good websites that have features that cater to my criteria? Any people/companies I could phone anything at all, that might improve my chances of getting a better price for a better flight.  I'm in no way asking anyone to do the leg work for me, however, if you want to, I'd pay a small fee haha.  Any advice or guidance would be really appreciated.


Multiple Instances of /dev/loop0: TYPE="squashfs"

I am having real troubles sorting this out!    Why is the blkid output flooded with so many instances of /dev/loopx: TYPE="squashfs"?  No significant information is available on the internet!  Any help would be really appreciated.  Abbas.


I frequently find myself needing more than the standard anchors TikZ nodes provide, i.e. north, north east, east and so forth. I usually use coordinate calculations for this, as in the example below, but it's a bit tedious for such a seemingly simple task.  Do you have a better idea for accessing points on the sides of nodes? Ideally, what I'd like are anchors like north north east for the standard shapes.  \documentclass{article} \usepackage{tikz} \usetikzlibrary{positioning,calc}  \begin{document} \begin{tikzpicture} \tikzstyle{every node}=[draw,fill=yellow,minimum width=2cm,thin] \tikzstyle{every path}=[-latex,ultra thick] \node (A) {A}; \node (B) [below=2mm of A] {B}; \node (C) [below=2mm of B] {C}; \node (D) [right=of B,fill=green] {D};  % Is there an easier way to get the lines from A and C to off-centre points on the left side of D? \draw (A.east) -- ($(D.south west)!0.75!(D.north west)$); \draw (B.east) -- (D.west); \draw (C.east) -- ($(D.south west)!0.25!(D.north west)$); \end{tikzpicture} \end{document}


Using rigify, Automatic weights parenting fails

I'm doing a basic human rig for practice. All of my bones are set up and the rig generates just fine, however, when I try to parent to the rig with auto weights, a majority of my mesh disappears (See pictures)   Any ideas on what's happening?


rename a list of files according to a text file

I have a list of files in a folder, which I will like to rename according to a textfile. For example:  These are the 5 files in the folder.  101_T1.nii 107_T1.nii  109_T1.nii 118_T1.nii 120_T1.nii   I will like to have them rename using a text file containing a list of new filenames in the same order, without the extension .nii:  n01 n02 n03 n04 n05   How may I go about doing so?


(Windows 10) offline nt password registry editor fails

I forgot my password on a Windows 10 machine. So I tried the offline nt password registry editor to clear it. But whenever I start the cd, it cannot find the partion:    Does someone know how to fix this?


jubil@junel:~$ sudo apt-get update  E: Type 'by' is not known on line 4 in source list /etc/apt/sources.list E: Type 'nano' is not known on line 1 in source list /etc/apt/sources.list.d/some-ppa.list E: The list of sources could not be read.      jubil@junel:~$ cat -n /etc/apt/sources.list    1. # deb cdrom:[Ubuntu 14.04.5 LTS _Trusty Tahr_ - Release amd64   2  # (20160803)]/ trusty main restricted  3  deb-src http://archive.ubuntu.com/ubuntu trusty main restricted #Added   4  by software-properties  5    6  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade   7  # to newer versions of the distribution.  8  deb http://ph.archive.ubuntu.com/ubuntu/ trusty main restricted deb-src   9  http://ph.archive.ubuntu.com/ubuntu/ trusty main restricted universe  10  multiverse #Added by software-properties 11   12  ## Major bug fix updates produced after the final release of the  13  ## distribution. 14  deb http://ph.archive.ubuntu.com/ubuntu/ trusty-updates main restricted  15  deb-src http://ph.archive.ubuntu.com/ubuntu/ trusty-updates main  16  restricted universe multiverse #Added by software-properties 17   18  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the  19  ## Ubuntu team. Also, please note that software in universe WILL NOT  20  ## receive any review or updates from the Ubuntu security team. 21  deb http://ph.archive.ubuntu.com/ubuntu/ trusty universe deb  22  http://ph.archive.ubuntu.com/ubuntu/ trusty-updates universe 23   24  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the  25  ## Ubuntu team, and may not be under a free licence. Please satisfy  26  ## yourself as to your rights to use the software. Also, please note  27  ## that software in multiverse WILL NOT receive any review or updates  28  ## from the Ubuntu security team. 29   30  deb http://ph.archive.ubuntu.com/ubuntu/ trusty multiverse deb  31  http://ph.archive.ubuntu.com/ubuntu/ trusty-updates multiverse 32   33   34  ## N.B. software from this repository may not have been tested as  35  ## extensively as that contained in the main release, although it  36  ## includes newer versions of some applications which may provide useful  37  ## features. Also, please note that software in backports WILL NOT  38  ## receive any review or updates from the Ubuntu security team. 39  deb http://ph.archive.ubuntu.com/ubuntu/ trusty-backports main  40  restricted universe multiverse deb-src  41  http://ph.archive.ubuntu.com/ubuntu/ trusty-backports main restricted  42  universe multiverse #Added by software-properties 43   44  deb http://security.ubuntu.com/ubuntu trusty-security main restricted  45  deb-src http://security.ubuntu.com/ubuntu trusty-security main  46  restricted universe multiverse #Added by software-properties deb  47  http://security.ubuntu.com/ubuntu trusty-security universe deb  48  http://security.ubuntu.com/ubuntu trusty-security multiverse 49   50  ## Uncomment the following two lines to add software from Canonical's  51  ## 'partner' repository. This software is not part of Ubuntu, but is  52  ## offered by Canonical and the respective vendors as a service to  53  ## Ubuntu users. 54  deb http://archive.canonical.com/ubuntu trusty partner deb-src  55  http://archive.canonical.com/ubuntu trusty partner 56   57  ## This software is not part of Ubuntu, but is offered by third-party  58  ## developers who want to ship their latest software. 59  deb http://extras.ubuntu.com/ubuntu trusty main deb-src  60  http://extras.ubuntu.com/ubuntu trusty main 61   62   63        jubil@junel:~$ cat -n /etc/apt/sources.list.d/some-ppa.list    1.  2        jubil@junel:~$    jubil@junel:~$ sudo rm /etc/apt/sources.list.d/some-ppa.list [sudo] password for jubil:  jubil@junel:~$ sudo apt-get update E: Type 'by' is not known on line 4 in source list /etc/apt/sources.list E: The list of sources could not be read. jubil@junel:~$


Why was the zero-gravity effect not transferred to the third level in Inception?

In Inception, near the end there are three dream levels. In Level 1, when the van enters freefall, there is zero gravity in level 2.   This means that the members of level 2 experience no gravitational force. At one point in the movie you are shown these members floating in midair.  Why doesn't this carry over to level 3? Our sensory organs (or any sensory organ you devise, for that matter), cannot distinguish between freefall and zero gravity. Shouldn't the zero-G in level 2 cause zero-G in level 3?


Why are the two following result different? The result of the following multiplication should be an integer anyway.  uint16_t test = 500.00 * 128.51; std::cout << test << std::endl; ----> 64254   but  float test = 500.00 * 128.51; std::cout << test << std::endl; ----> 64255


Does exist a continuous real valued function on the rational number but discontinuous on the irracional numbers?

There is a famous example of a function continuous on irrational numbers but discontinuous on the rational numbers. My question  is the converse of this example.  Thanks!


Triangle tangent to 3 Parabolas, finding the common area

Triangle $ABC$, $AB=4$, $BC=15$, $AC=13$. Two sides are tangents to the respective Parabolas. We have to find the area shaded. My approach-  I tried finding the area of the quadratures(Archimedes) formed but it doesn't help as- I have to find the area between the 2 intersecting Parabolas also which I can't find.


I just built the lake view manor and it is fully furnished. I have 2 children's beds and chests. My husband gave me the option to move to the new location, but my kids don't have that option. Is there something else I need?


I have a problem with the danish letters ÆØÅ

I have this problem with the Danish letters ÆØÅ. I use the following script to arrange posts alphabetically when loading the page.  if($stmt=$mysqli->prepare("select `titel` from `ann` order by `titel` asc "))      {     $stmt->execute();     $stmt->bind_result($titel);     while($stmt->fetch())         {         $letter=substr($titel,0,1);         $res[$letter][] = array('titel' => $titel);         }          foreach($res as $key=>$val)         {         ?>         <div class="<?php $letter;?>">
         <?php         echo "
$key
";         foreach($val as $reqvals)             {             echo $reqvals['titel'];              }         }     $stmt->close();     }     Unfortunately, the script is unable to handle the 3 Danish letters, which are in the end of the alphabet. They are placed first - before "A" hen loading the page.   � Åben dialog......  A Altid klar Astrids hemmelighed  B Bravo Klaus  D Den hemmelige klumme   How can I fix this?


Minimum value of $ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $

If $x>0$, $y>0$, $z>0$ and $x+y+z=6$ then find the minimum value of    $$ f(x,y,z)=\left(x+\frac{1}{y}\right)^2+\left(y+\frac{1}{z}\right)^2+\left(z+\frac{1}{x}\right)^2. $$   Thanks in advance.


Prove that there exist uncountable family of subsets of $\mathbb{N}$ which is linearly (totally) ordered by relation of inclusion.

Prove that there exist uncountable family of subsets of $\mathbb{N}$ which is linearly (totally) ordered by realtion of inclusion.  I do not know how to prove it. Actually I cannot concieve that such family of set can be uncountable. I would be thankful for help


How to cover this code?     Test class Code        @isTest static void getPageNumberListTest(){     Controller controller = new Controller();       controller.TotalPages=10;     controller.getPageNumberList();  }   Conroller Class  public Integer TotalPages { get {        if (setList.getResultSize() <= 10)         this.TotalPages = 1;     if (Math.Mod ( setList.getResultSize(), setList.getPageSize() ) == 0)         this.TotalPages = ( setList.getResultSize() / setList.getPageSize() );     if (Math.Mod ( setList.getResultSize(), setList.getPageSize() ) != 0)      this.TotalPages = ( setList.getResultSize() / setList.getPageSize() )+1;     return TotalPages; } set;    }  public Integer TotalRecords {     get {          this.TotalRecords = setList.getResultSize();         return TotalRecords;     }     set; } public ApexPages.StandardSetController setList { get {     if (setList == null) {          setList = new ApexPages.StandardSetController(Database.getQueryLocator(         [SELECT  Name, Email, Contact_Level__c, AccountID, OwnerID, CreatedByID, CreatedDate FROM Contact]));     }     if (this.PageSize == null) PageSize = 10;      setList.setPageSize(PageSize);        return setList; } set;   }


How to define a function with optional key-value arguments

I have setup a function called quickfigure which has the purpose of inserting a centered image with a one-line command:  \newcommand{\quickfigure}[2] {     \begin{figure}[H]         \centering         \includegraphics[width=0.6\linewidth]{#1}         \caption{#2}     \end{figure} }   This function is used as follows;  \quickfigure{img/testImage.png}{Test image}   I would like this function to accept optional arguments to define width and height of the image, as well as a label. The syntax is desired to be something like;  \quickfigure[width=0.6, label=img:test]{img/testImage.png}{Test image}   How would I go about setting this up? I need a push in the right direction. Thanks!  Edit: Thanks everyone for the ideas, this is my solution;  \includepackage{keyval} \includepackage{ifthen}  \newlength{\qf@width} \define@key{quickfigure}{width}{\setlength\qf@width{#1}} \define@key{quickfigure}{label}{\def\qf@label{#1}}  \newcommand{\quickfigure}[3][] {     \setkeys{quickfigure}{width=0.6\linewidth,label=\@empty}     \setkeys{quickfigure}{#1}     \begin{figure}[H]         \centering         \includegraphics[width=\qf@width]{#2}         \caption{#3}         \ifthenelse{\equal{\qf@label}{}}{}{\label{\qf@label}}     \end{figure} }


pgfplot same size font in figures and same size figures

Hi I've created figures with standalone and pgfplot package. The figures output size are different to one another but more importantly the font size are different. I would like all figures to be of same output size and font size. Should this be controlled in the individual figure files or the main.tex file? My text file of data can be found here   First figure file ...      \documentclass{standalone}     \usepackage{tikz}     \usepackage{pgfplots}     \pgfplotsset{compat=newest}     \begin{document}     \providecommand{\plotdataDir}{plotdata}     \begin{tikzpicture}     \begin{loglogaxis}[xlabel={$Aspect\:Ratio$},     ylabel={$\mu_c$},ymajorgrids,xmax=1e7,     ytick={0.1,1,10,100,1e3,1e4,1e5,1e6},ymax=1e7,ytick pos=left,xtick pos=left]     % G14     \addplot[blue,thick] table[x=AspectR,y=G14] {\plotdataDir/effectivemu.txt}         node[fill=white,pos=0.85,font=\tiny]{$1,250,000$};     % G15     \addplot[blue,thick] table[x=AspectR,y=G15] {\plotdataDir/effectivemu.txt}         node[fill=white,pos=0.52,font=\tiny]{$\mu_r=\infty$};     \end{loglogaxis}     \end{tikzpicture}     \end{document}     Second figure file ...      \documentclass{standalone}     \usepackage{tikz}     \usepackage{pgfplots}     \pgfplotsset{compat=newest}     \begin{document}     \providecommand{\plotdataDir}{plotdata}     \begin{tikzpicture}     \pgfplotsset{set layers}     \begin{semilogxaxis}[scale only axis,     xlabel={$turns \times I \left(n \cdot A\right)$},     ylabel={$B_z \left(T\right)$},xmin=1,ymin=0,xmax=100000,     xtick pos=left,     ytick pos=left,xmajorgrids,legend entries={$Supermendur         \:2V$,$Metallic\:Glass$},legend pos=north west]     \addplot[blue,ultra thick] table[x=nxI,y=Bfield1] {\plotdataDir/ellipbmoment.txt}         node[fill=white, fill opacity=0.7, text opacity=1,anchor=south east,font=\tiny]        {$\mu_r=80,000$};     \end{semilogxaxis}     \end{tikzpicture}     \end{document}     And the main document ...      \documentclass{article}     \usepackage{standalone}     \usepackage{tikz}     \usepackage{pgfplots}     \pgfplotsset{compat=newest}      \begin{document}      \providecommand{\plotdataDir}{tikdir/plotdata}     \begin{figure}[here]     \centering     \includestandalone{tikdir/effectivemu}     \caption{test}     \end{figure}      \providecommand{\plotdataDir}{tikdir/fig1}     \begin{figure}[here]     \centering     \includestandalone{tikdir/fig2}     \caption{test}     \end{figure}      \end{document}   If the main document.tex file is run as above fig1 and fig2 are different sizes. I am aware I can control the width and height of image by using \includestandalone[width=\textwidth] but doesn't solve the font size differences between the plots. You can see I adjusted the font size for nodes as \tiny but \tiny is different for both plot. Should this be adjusted globally if so how?  Ideally the preferred structure I would like is of fig2. It seems fig1 has smaller width than fig2 thereby stretching the font size.


How do I solve limits such as these? The $...$ always make it seem hard to me. From what I can understand from them, they both are $0/0$ limits, and I should be looking to write the numerator in such a way that the denominator should simplify it somehow. For the first I tried writing each element from the numerator as $(a-1)$ where $a = 1, x, x^2 ... x^n$ so that I can simplify the denominator eventually, but I didn't get much out of that. I'm guessing these two are solved in similar ways, hence why I posted them both. Any clues/hints I can get would be appreciated.  $$\lim \:_{x\to \:1}\frac{1+x+x^2+...\:+x^n-\left(n+1\right)}{x-1}$$ $$\lim _{x\to 1}\frac{x+x^2+...\:x^n-n}{x+x^2+...\:+x^m-m}$$  $n,\:m\:\in \mathbb{R}$


Safari autofill multiple e-mail adresses

My personal vCard has multiple email addresses. When I use the autofill feature from Safari I always get the wrong email address filled into the web form. How can I get Safari autofill to use the right email address?


How do I avoid selection box shrinkage when working with transparent layers?

TLDR: When I use the marquee tool to select a box around layer and then move it with the move tool, the selection box shrinks to surround the populated region of the layer. Is there a way to keep the selection box's dimensions, instead of it shrinking on move?  Here's my situation: I have a uniform spritesheet made up of 30+ layers. I need to adjust different sprites in the sheet to different areas, but because the movement isn't uniform I need to do it sprite-by-sprite, layer-by-layer. I would save hours if I could just select a region and move the objects inside the region layer-by-layer, but because moving a selection with transparency shrinks the selection region to the populated areas, I have to reselect every time I switch layers. Any way to avoid the selection box shrinkage?


Installing programs. Understanding Ubuntu. Command Prompt hard time

I'm new to the whole Linux Ubuntu. I have to be honest...I have a hard time trying to install programs from outside the Software Center. Any tutorials recommendations on how to understand the command prompt and how to install from outside Ubuntu Software Center will be great. And by how to understand I mean the symbols, what they mean, what they execute, what to write for executions etc. I like the fact that I'm stepping away from the mainstream softwares and I would like to keep self educating in Linux.


Check if array exist inside an nested array JavaScript

let arr1 = [['item 1', 'item 2'],['item 3', 'item 4']] let arr2 = ['item 1', 'item 2']  I need to check whether arr2 exist in arr1


Formative and Summative Usability Testing

I bumped into  and it suggests the use of (a)  and (b)  Usability Testing.  To be honest, is the first time that I bumped into this kind of terminology, and I while reading about it, it's not quite clear to me how can I use these tools to assess usability.  Can anyone give me an example of each?


how could I disable the Windows hotkeys? I need the button to work for a virtual machine, but the windows hotkeys are overriding my vm input and locking my actual computer and such.


Where can I find El Capitan's default and beachball/busy cursors?

I saw from  how I can get most of the cursors, but the busy and default cursors aren't there. Why is that?


How to send key bind occupied/interpreted by tmux to program running in tmux?

Let's say I'm running ranger inside tmux session, but I want to send a keyboard shortcut to ranger (e.g. Ctrl+H) which is already used in tmux.  Is there a passthrough mode to send key binding to underlying program similar to vim's Ctrl+O in "insert mode"?  I know you can set a key bind to send a key bind, but that's not practical to map all other program key bind.


What causes highly compacted matter to collapse into a black hole?

"The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole".  Why does this happen? I mean, why something finite (like the core of a very masive star) should lead to an infinitly small point (singularity). For me it's like spacetime has a "wekness" and it breaks if a region contains to much mass/energy.  I imagined that the matter will just be very very compacted, but not infinitly compacted and the spacetime bent accordingly.  Neutron stars are also very compacted and they bend a lot the space time.   I don't understand why if we continue to compress the matter even more (and I don't say "compress it to an infinitly small point"), suddenly the black hole is created. Why is this happening?


Can I temporarily borrow from my IRA accounts?

I have several IRA mutual fund accounts in Vanguard Funds.  To pay taxes on time, I want to borrow some from the IRA's, but then pay it back within 60 days.  Does the IRS allow this?


Does the Epsilon-Delta Definition of a Limit Work with Closed Intervals?

I was thinking about the epsilon-delta definition of a limit and began to wonder if it would work with closed intervals instead of open intervals. That is, for some function $f$, would the folowing definition work? $$\forall \epsilon>0\,\exists\delta>0\,(0<\lvert x-c\rvert≤\delta \, \implies \lvert f(x)-L\rvert≤\epsilon) $$ I've been trying to think of a counterexample, but can't seem to find one.  edit: If it does work, why choose open intervals rather than closed?


Just wondering if there a way to temporarily disable PulseAudio as I am trying to run a specific Wine game (Left 4 Dead 2) and it makes the game crash occasionally.  If I kill the process it automatically comes back up. Any suggestions?


Equations, tables, figures, sections: reference with chapter number but label without

Using the book class equations, tables, figures and sections have the chapter number as first number of the label (e.g. the first equation of chapter 2 is equation 2.1).  I want to remove the chapter number from the label but I want to keep it when I refer to it (the best would be keeping it if and only if the reference is outside the chapter where the label is)


Let $S$ and $W$ be subsets of a vector space $V$. Show that if $S$ is a subset of $W$, then $\mathrm{span}(S)$ is a subspace of $\mathrm{span}(W)$.  Ok I'm finally understanding what each of these things mean.. but I'm running out of ideas on how to actually show it without using arbitrary vector space examples like Rn. Since sets and subspaces are kind of new its hard to figure out how to write correct proofs with them.   I can see how if $V = \mathbb{R}^3$ and $S = \{(1,1,1)\}$ and $W = \{(1,1,1), (1,1,2)\}$ then $\mathrm{span}(S) = R1(line), span(W) = R2(plane)$ and that R1 is a subspace of R2... im just having trouble showing this officially when all vector spaces and sets are completely in general....  I could get as far as writing out $S=(u_1,u_2,\dots,u_n)$, $u_i \in V$ and same with $W$, but I can't really figure out what else to do in this sort of proof.


As the daily maximum reputation limit is 200 what will happen if I receive a vote after the daily maximum limit?  Is it added in the next day or those votes remain unaffected.?  Can somebody explain?


How to remove temp installation packages

Not very well versed with Ubuntu. I got this message when I tried to get some updates:   The upgrade needs a total of 31.9 M free space on disk '/boot'.  Please free at least an additional 27.6 M of disk space on '/boot'.  Empty your trash and remove temporary packages of former installations using 'sudo apt-get clean'.   When I'm trying to run 'sudo apt-get clean', it says command not found. How do I remove temp packages?


Cooking pasta: why does adding a lid lead to overflow?

When cooking pasta, some organic foam usually forms on the surface of the boiling water and the situation can be kept under control by adjusting the heat (and/or adding some oil). Covering the pot with a lid, even loosely so, usually leads to the foam overflowing within a short time (removing the lid fixes the problem). Everybody knows that - the question is why?  It seems to me that the only variable that changes noticeably when adding the lid is the vapor pressure but I don't see how that should affect the foaming process.


I have a code piece that I'm analysing but I don't understand this lines:   double level = 0;  ...  if (!(level == level) && !(level < level) && !(level > level))     exit(0);   I think it is about double comparison subject. Any idea what it is?


MAC why the other part of my hard disk is completely full?

For my MAC laptop, I only have 250GB and out of this 250GB MAC is taking up 129GB in the other section. I looked everywhere to the best of my knowledge. Please note my home directories is only 45GB. Can you somehow please help me?


Concatenation script is not working as expected

I have the following script that is concatenating files in a directory in a particular fashion. I did some testing on a toy example and it is not doing what I thought it was doing. First, to describe the directory structure, there are three types of files(bulk, reference, and single-cell), each with a "left" and "right" polarity. I want to merge all files of the same type and polarity. That is, files labeled with "bulk_left_*" are all merged into a final file "left_bulk" and the same for the reference files. The single cells are unique in that there are a specified number of single cells and each must be merged by index. That is, if all files with the prefix single_cell_left0_* are merged together but should NOT be merged with "single_cell_left1_*" type files. In the end I should have 4 + 2*(number of singlecells) files in the directory. Here is the current script I use to do the merging. I tested it on a directory with some made up files and I saw that it merged every single cell file into the specified outputs instead of only selecting them one index at a time. I think this has something to do with way I write the variable into the bash directory, and it is treating it as an integer instead of a string variable, but I am not sure. WORKING_DIR=/media/drive0/USER/data cat $WORKING_DIR/bulk_reads_left_*.fasta > $WORKING_DIR/left_all_bulk.fasta cat $WORKING_DIR/bulk_reads_right_*.fasta > $WORKING_DIR/right_all_bulk.fasta rm $WORKING_DIR/bulk*.fasta cat $WORKING_DIR/reference_fast_number_left*.fasta > $WORKING_DIR/left_reference.fasta cat $WORKING_DIR/reference_fast_number_right*.fasta > $WORKING_DIR/right_reference.fasta rm $WORKING_DIR/reference*.fasta NCELLS=5 for i in `seq 0 $(($NCELLS-1))`  do                                                                                do     cat $WORKING_DIR/single_cell_number_left$i_*.fasta > $WORKING_DIR/left_single_cell_$i.fasta     cat $WORKING_DIR/single_cell_number_right$i_*.fasta > $WORKING_DIR/right_single_cell_$i.fasta done rm $WORKING_DIR/single*.fasta ~


I am trying to solve Exercise 8, Chapter 2 of Rudin's Real and Complex Analysis, but I am not sure of what I have done and I am not able to answer to the final part of the question. The requirement is as follows  Construct a Borel set $E \in \Bbb R^1$ such that $$0<m(E\cap I) < m(I)$$ for every nonempty segment $I$. Is it possibile to have $m(E)< \infty$?  My try on the construction: Let $E_0 =\emptyset$, and let $r_1, r_2, \dots$ be an enumeration of the rationals. For $i\geq 1$, do the following.  If there exists a nonempty segment $I_i=(a_i,b_i)$, with $a_i < r_i < b_i$, such that $m(E_{i-1} \cap I_i) = 0$, then let $m_i = \min\left(b_i-r_i,r_i-a_i\right)$ and $$E_i=E_{i-1} \cup \left(r_i-\frac{m_i}2,r_i+\frac{m_i}2\right).$$ Otherwise, if there is a nonempty segment $I_i=(a_i,b_i)$ with $a_i<r_i<b_i$ such that $m(E_{i-1}\cap I_i) = m(I_i)$, let \begin{eqnarray*} E_i &=& E_{i-1} - \left[r_i-\frac{m_i}2,r_i+\frac{m_i}2\right]=\\ &=& E_{i-1} \cap \left[r_i-\frac{m_i}2,r_i+\frac{m_i}2\right]^c,\end{eqnarray*} with $m_i$ defined as above.  $E = E_1 \cup E_2\cup E_3\dots$ is a Borel set, since it is obtained with a countable number of unions, intersections, and complements of open sets. Since any nonempty segment $I$ contains rationals, both $m(E \cap I)=0$ and $m(E\cap I) = m(I)$ would contradict the construction.  Question 1: Is my construction correct? Question 2: I would like to show that $m(E) < \infty$ cannot hold, in general. I would appreciate a hint on how to do that, if possible.


JS Jquery, global variable in parameter won't get changed after giving him new value in function

I am trying to use my global variable "count" as parameter in function (EXAMPLE 2) but when I add it as parameter, then this variable won't get changed and still equals to 0, even I gave him new value: oldCount = newCount;. What I want to achieve is adding variable count to function parameter and give him new value in function. WORKING EXAMPLE(1): let count = 0; updatePlayerCount(10); const $players = $('#bans');  function updatePlayerCount(newCount) {     $({          counter: count     }).animate({          counter: newCount     }, {         duration: 1000,         easing: 'swing',          step: function() {             $players.text(Math.ceil(this.counter));         },         complete: function() {             count = newCount;         }     }); }  NOT WORKING EXAMPLE(2): - which I want to fix let count = 0; updatePlayerCount(count, 10); const $players = $('#bans');  function updatePlayerCount(oldCount, newCount) {     $({          counter: oldCount     }).animate({          counter: newCount     }, {         duration: 1000,         easing: 'swing',          step: function() {             $players.text(Math.ceil(this.counter));         },         complete: function() {             oldCount = newCount;         }     }); }


Why English does not have diacritics to distinguish between words with different meanings and pronunciations

It just occured to me that there are words in English that have two different meanings, two different pronunciations and are written exactly the same.  For example "present" can be interpreted as the tense when pronounced   /ˈprezənt/ or as a synonym of "demonstrate" when /priˈzent/  Other examples from the top of my head: "read", "live".  I don't think I have seen that in any other language. In most languages you can't tell the spelling of a word by hearing it, but you call articulate it correcly when you're reading it. It seems that in English you can't do either of those.  Did English ever have accent marks to distinguish between those? How did it end up like that?


Combine two json sections into one json object

I would like to combine topData and bottomData into completeData.  var topData = {     "auth": "1vmPoG22V3qqf43mPeMc",     "property" : "ATL-D406",       "status" : 1,     "user" : "test001@aaa.com",     "name" : "Abraham Denson" }  var bottomData = {     "agent" : "pusher@agent.com",     "agency" : "Thai Tims Agency",     "agentCommission" : 1000,     "arrival" : "arrive 12pm at condo",     "departure" : "leaving room at 6pm", }  var completeData = topData.concat(bottomData)   Since these are not arrays, concat wont work here.  Can this be done without making foreach loops?


Constructors without parameters giving me errors

I have created a class Book that store 3 variables(string title, int pages, float price). I also have created 3 constructor but the null constructor keeps giving me errors. (58: error: request for member 'pages' in 'b1', which is of non-class type 'Book()') (61: error: request for member 'Info' in 'b1', which is of non-class type 'Book()')  #include <iostream> #include <string>  class Book{     public:      std::string title;     int pages;      private:      float price;      public:      Book(){          title = "";         pages = 0;         price = 0;     }      Book(std::string bookTitle){          title = bookTitle;         pages = 0;         price = 0;     }      Book(std::string bookTitle, float bookPrice){          title = bookTitle;         pages = 0;         price = bookPrice;     }      void Info()     {         std::cout << "Title: " << title << std::endl;         std::cout << "Pages: " << pages << std::endl;         std::cout << "Price: " << price << std::endl;     }      void Pricing(float bookPrice)     {         price = bookPrice;     }      };  int main() {     Book b1();     b1.pages = 100; //first error      Book b2("Mathimatics");     b2.pages = 200;      Book b3("Algebra", 50);     b3.pages = 300;      b1.Info(); //second error     b2.Info();     b3.Info();  }


I can’t find my minecraft files in Windows 10 with Linux

There’s something wrong with my Windows boot. But before I reinstall Windows 10, I need to backup my Minecraft saves with Linux.  So I use Linux live USB mount into Windows system disk, but I can’t find my .minecraft folder! The folder should be in Local/Users/Andare/AppData/Roaming. There’re many other folders. But I didn’t find .minecraft. And I tried to search .minecraft, but I got no results! Could the folder be hidden?


Is there no electric field inside a conductor?

I came across this statement while studying electric currents and I am confused:  "There is no electric field inside a conductor. Hence no current can flow through it".  Is there a fallacy in this statement?  Any help would be appreciated.  The conductor being discussed is ideal. What is the driving force for the current in this case?


Are polygons stored clockwise or counterclockwise in a shapefile?

I'm working with polygon coordinates in QGIS using PyQGIS using ESRI shapefiles as input data.   Are the polygon vertices (I am referring only to the outer boundary in the case of polygons with holes) stored as clockwise or as counterclockwise in a shapefile or can be in mixed order?   Is the order always the same or can be different depending on the source of the data: digitizing, converting from other sources as *.csv files, etc.?


Peano axioms in FOL - numbers lower than or equal to another

@Moderators: I apologize because this is very similar to my previous post, but I didn't post the exact axioms there from the beginning (I did quite a major change after receiving a reply).. please delete the previous one () if there are any problems.  Happy New Year,  I am trying to define natural numbers in first-order logic in order to use them in an Automated Theorem Prover. I have tried the Peano axioms on the Wikipedia page with/without multiplication (I don't really need it and thought removing it would make proving faster). I'd like to make the prover "know" (deduce that) the only three numbers lower than or equal to 2 are 0,1,2, but I can't seem to be able to do it. More precisely, I'd like the foolowing statement to be provable (NOTE: 2 is just an example, I'd like it to work for any natural number):  $$\forall x(nat(x) \to (leq(x, s(s(0))) \to (x=0) \lor (x=s(0)) \lor (x=s(s(0))) ))$$  My prover has equality implemented. I define 1,2,3 (where 0,1,2,3 are 0-arity functions.. or I assume I can call them constants) as: $1 = s(0)$ ($equal(1, s(0)$ is what I actually write in the prover) $, 2 = s(1), 3 = s(2)$   My axioms are pretty much these:  $$nat(0)$$ $$\forall x(nat(x) \to nat(s(x))$$ $$\forall x,y(nat(x)\land nat(y) \to nat(add(x,y))$$ $$\forall x( nat(x) \to s(x) \neq 0)$$ $$\forall x,y (nat(x) \land nat(y) \to (s(x)=s(y) \to s=y))$$ $$\forall x(nat(x)\land x\neq 0 \to \exists z (nat(z) \land x = s(z)))$$ $$\forall x(nat(x) \to add(x,0) = 0$$ $$\forall x,y(nat(x)\land nat(y) \to add(x,s(y)) = s(add(x,y)))$$ $$\forall x,y(nat(x)\land nat(y) \to (leq(x,y) \leftrightarrow \exists z(nat(z)\land y = x + z )))$$ (Maybe for the purpose of this question it would have been better to write the last axiom as "forall x,y leq(x,y) <-> nat(x) /\ nat(y) /\ exists z .....")  I know they look quite ugly.. in my prover I'm actually able to type something like this (using what I understand are called "sorts"): $\forall[nat(x)](P(x))$ instead of $\forall x(nat(x) \to P(x)$ so it looks cleaner and easier to follow.


How would you explain Moment Generating Function(MGF) in layman's terms?

What is a Moment Generating Function (MGF)?  Can you explain it in layman's terms and along with a simple & easy example?  Please, limit using formal math notations as far as possible.


Find all real numbers $x$ for which $$10^x+11^x+12^x = 13^x+14^x.$$   I thought about taking the logarithm of both sides, but didn't see how that would help. How can we make the equation simpler?


How to atomically increment a custom field?

We are creating custom IDs for Accounts by incrementing an integer field in a custom class. The issue is that if two or more new Accounts are created in close sequence/simultaneously the following code will assign duplicated numbers rather than an incremented number for each:  public static void SetCustomId(Account account) {            CustomObj__c customObj = CustomObj__c.getOrgDefaults();      account.CustomAccountId__c = String.valueOf(Integer.valueOf(customObj.CustomCounter__c));     customObj.CustomCounter__c = customObj.CustomCounter__c + 1;      update customObj; }   Is there a way in Apex to lock a process so that a shared resource is used sequentially? In Java, C#, C++ etc. this is pretty easily done via a critical section if it's a single process or a Mutex if multiple processes access the same resource. Is there anything like this supported in Salesforce? Solutions beside Apex code/triggers would be fine as long as they meet the spec.   EDIT:  It is important that the object creates be sequential and not generate errors due to lockouts.


Why is $\mathbb Q $ (rational numbers) countable?

By definition, a set $S$ is called countable if there exists an bijective function $f$ from $S$ to the natural numbers $N$.  If we take a function $g\colon\mathbb{Z\times N\to Q}$  given by $g(m, n) = \frac{m}{ n} $ to "construct" rational numbers, $g$ would only be a surjection from the countable set $\mathbb{Z\times N}$ to $\mathbb Q$. It's not injective, or is it?


What can cause "Android OS" process to use high percentage of battery?

I've read a bunch of forum posts about the Android OS battery drain bug. This is where the 'Android OS' process is showing large percentages in the battery statistics.  For me, I'm running 2.3 Gingerbread. I don't use bluetooth or GPS. I'm on 2G most of the time. Some days I get 40 hours out of a battery. On these days in the battery usage settings, the 'Android OS' process uses about 3% of battery. However other days I get about 8 hours with similar use. On these days the 'Android OS' process uses about 35% of the battery. I really want to find out what causes this.  The fixes suggested so far are:   Reboot (Temporary). Turn off and remove battery for a couple of minutes. Reset battery stats. Change WIFI sleep policy. Use a task manager Flash stuff to the phone. Revert to older versions of the OS (not really a fix).   Does anyone know the definitive cause of this problem and the correct fix? Or is it possible there are multiple issues that cause this so different things will work for different people?  Here are some of the threads:


Is there a 1-1 correspondence between symmetry and group theory?

The professor in my class of mathematical physics introduces the definition of groups and said that group theory is the mathematics of symmetry.   He gave also some examples of groups such as the set of all real numbers under addition.   My question is what symmetry are we talking about here when we consider the set of all real numbers under addition?


How do I access the internet with an infected computer that WILL NOT let me?

Im trying to fix my friends Toshiba laptop. She has Windows 7, no anti-virus and is infected with a virus. The computer shows no connection problems; but I cannot access the internet or download a disc to clean it up. I want to use esetnod32 and malwarebytes. I`m not as tech savvy as most of you, but I can hold my own. Melissa.


I'm running macOS Sierra 10.12.2 and am trying to get Python's IDLE to work properly with Tcl/Tk. This is the error message I'm getting when I open IDLE:  Python 2.7.13 (default, Dec 18 2016, 07:03:39)  [GCC 4.2.1 Compatible Apple LLVM 8.0.0 (clang-800.0.42.1)] on darwin Type "copyright", "credits" or "license()" for more information. >>> WARNING: The version of Tcl/Tk (8.5.9) in use may be unstable. Visit http://www.python.org/download/mac/tcltk/ for current information.   Visiting the link in the error message, I read the documentation and installed Tcl/Tk version 8.5.18.0 from  source. Perhaps it is important to note that I'm running a brew install of Python 2.7.13. After I installed the DMG for 8.5.18.0, the bash terminal and Python are not recognizing the Tcl/Tk upgrade (Note that it is recognizing Tcl/Tk (8.5.9) instead of 8.5.18.0. How can I get IDLE and the upgraded python install from homebrew to recognize the upgraded Tcl/Tk 8.5.18.0? In other words, how can I resolve the warning message?


I have written this program to make the value of a in b and the value of b in a. For this I created temp as a temporary variable and this is my program: #include <stdio.h>  int changevalue(int a, int b) {     int temp;     temp = a;     a = b;      b = temp; }  int main() {     int a;     int b;     a = 10;     b = 20;      printf("the value of a is %d \n and b is %d",a,b);     changevalue(a,b);     printf("the value of a is %d \n and b is %d",a,b);     return 0; }  But the values of a and b did not change . Where is the problem?


How to check the logs to see what process created a file?

The file dead.letter keeps appearing in my home folder. I want to know what process is responsible for this, but there is no information on the creator of a file in the file itself. However, I believe it should be possible for it's creation to recored in the log somewhere on the system.  Cheerio, thanks!


Online master's degree in CS at the Georgia Institute of Technology

I am a working student (working in software engineering) and this year I'll be completing my CS Bachelor's degree in Italy. I am doing the online degree as I can't attend lectures, due to my job.   I would like to continue my studies with a Master's Degree in CS so I googled a bit and found out that  I am interested in.   Here in Italy the online degree has the same value as the on-campus degree: we take exams on campus, study online with videos and materials provided by the professor, we have conference sessions with the professors for any questions or we can go visit them in their office. The exams are exactly the same as the on-campus degree, so are the professors.  I was wondering if this is the case in the USA and if doing an online degree will be a limit for me to pursue, in a remote future, a PhD. Should I move to the USA to study (I can work remotely) or I can study here, in Italy, and just go to the USA to take exams?


I'm getting some cryptic (for me) errors and warnings when I compile.  On the advice of darn near every internet resource I could find, I dug into the .log file.  The trouble is, I don't know how to interpret what I see.  I don't want to take up people's time so, where can I find a Reading LaTex .log Files for Beginners document?


Where to ask about programming language recommendations?

I'm looking to ask a question about recommendations for a language and/or framework which I can use to write a cross-platform program requiring OpenGL support. Where exactly should I ask this?  I tried 'Software Recommendations', but it got down-voted by at least one person, presumably as it's not really a question about software. I can't ask it in Stack Overflow, due to the strict 'no opinions' question policy there.  Any help much appreciated.


Rational points on the elliptic curve $y^2=x^3 -x$

I've been trying to find rational points on the elliptic curve $y^2=x^3 -x$ but I can't find anything else apart from $(-1,0), (0,0), (1,0)$. I have like an 'edgy' proof that it may not be possible to find rational points on this curve(apart from the ones already mentioned), but I'm unsure about it. Can anyone help?


If X has a countable base, then every base contains a countable base.

I need to prove that if X has a countable base, then every base contains a countable base.  I understand that this is a duplicate of another stack exchange question, but I do not know why a given element of the countable base can be expressed as the union of elements of the possibly uncountable base. I thought that the definition of base simply says that every element of the topology can be written in this way, but not necessarily every subset of the topology.


Level system of water tank?feedback of close loop?

I have attached a photo from animation from following link    this photo shows a float in a water tank, it appears to be close loop  controlsystem but how it is close loop system?where is feedback?


Integral of 1-form $\omega=\dfrac{-y \,dx + x \,dy}{x^2 +y^2}$ over a triangle.

I'm trying to evaluate the integral of the $1$-form      $$\omega=\dfrac{-y \,dx +x\,dy}{x^2 +y^2}$$   through the corners of a triangle with the vertices $A= (-5,-2)$, $B=(5,-2)$, $C=(0,3)$.  I've tried to use Green's theorem but it didn't work because the 1-form isn't differentiable on (0,0) so I had to parametrize the paths from each point and got three line integrals but it got so complicated at the end, so it doesn't seem to be the right solution or at least the one I'm supposed to calculate. Is there anyway else to evaluate the integral?


How to find out object's location coordinates?

For example I have a cube and I moved it to a certain location. I want to know if there is a way to find object's global location, so later I would be able to insert this location coordinates to another object.    So my Question is: Is there a way I can see the location of a certain object and if yes how can I insert this location coordinates to another object ?


jquery cannot deal with auto-generated DIVs

I have the following code you can test it on   html:
div 1

div 2

div 3

div 4
   css:   .expanded{     border-style:solid;     border-width:1px;     border-color:black;     background-color:yellow;     min-height:50px; }   javascript:  $('.sam').on('click',function(){         if ( $(this).hasClass('expanded') ){         $(this).removeClass('expanded');     } else {         $(this).addClass('expanded');      }  });  $(document).ready(function(){     //Im just test to write some divs after document ready     var output = '
div 5
';     $(output).insertAfter('.sam:last').fadeIn('slow');     var output = '
div 6
';     $(output).insertAfter('.sam:last').fadeIn('slow'); });   after running when click on the div1 , div2, div3 and div 4 it added/remove the .expanded class to the div but when clicking on the div5 and div6 which is generated by java and printed to the document it will not add/remove the class from them when I click into them.  any solutions?


Age old question: What's the meaning of 'word'?

An old question, for which I could find absolutely NO reference on the internet for many years. Perhaps I wasn't looking in the right places, but I have no clue about its usage either.  Then I stumbled upon this article just now that actually happened to address the same premise. I tried to figure out myself as a function of context but my better judgement was to seek expert advice. So here goes.  In the following excerpt I found in :     Ricky: Yo player let me get some of that valium!   Albert: **** off these are for my back spasms.   Ricky: Okay fine then I will tell your girlfriend about last weekend.   Albert: Fine, here you go a**hole.   Ricky: Word.   What exactly does word mean at the end? What are its connotations? Thanks :)


Can i use the same /home partition for multiple distro's partitons

Hello Unix/Linux Stackexchange. I have a mulri-part question about the /home partition. Thanks for taking the time to read and reply to all the questions below.   Is it possible to share the /home partition with two or more separate Linux partitions? For example can I use the same /home partition with an /Arch and /Debian partition?   If it is possible can I also use the same username for both or is it better to use different ones and share data between them?   I am also assuming that in this setup I would also need a separate /boot partition as well  is that correct?  Thanks!


PHP - Preg_match - verify presence of multiple words in any order

I'm trying to verify the presence of keywords in product titles from one of my affiliation deals. The issue I'm facing is that the keywords can be in a different orders and sometimes I have alternative keywords to test. Some examples: xiaomi Mi Laser projector 4K 19201080P Full HD Projector 5000 Lumens 2GB 16GB Projector Mijia 4K 19201080P Full HD Projector 5000 Lumens 2GB 16GB Xiaomi Mijia 4k projector Those are the same products and I'm trying to find a match that get them all. The following works if the order is respected: preg_match('/(xiaomi|mijia).*(projector)/', $input_line, $output_array);  but how I can make sure that I also capture the same keywords in a different order? I could repeat the operation a second time to have two alternatives in the same regex but it will quickly become unreadable. I would basically need something like (keyword1|keyword2|...)(keyword3|keyword4|...) in any order I'm not looking to extract the information, I'm just looking for match. Is there a clean way to do this with preg_match? Thanks!


Area 51 displays badge with docs-beta next to Stack Overflow with missing link

On  my badge shows Documentation Beta reputation next to Stack Overflow (where reputation is exactly the same), therefore it's showing on the top, despite I haven't edited a single page.    Secondly the link points to:        which is redirecting back to Stack Overflow user profile.  It's still fine having two of the same badges pointing to the same page, but is it necessary? Is it a bug or a feature? I think the fix would be either to correct the link, or if the documentation is part of Stack Overflow, then one icon should be enough, right?


Well, I want to install ubuntu but do not know how, I want to install using a Pendrive without dual boot, in the right manner, I've seen videos but only show how to install Ubuntu on the Pendrive and do not show what I do after this. thanks in advance.


This is the output after sudo apt-get -f install  The following packages will be upgraded:   libboost1.49-dev 1 upgraded, 0 newly installed, 0 to remove and 57 not upgraded. 21 not fully installed or removed. Need to get 0 B/9,182 kB of archives. After this operation, 24.6 kB disk space will be freed. Do you want to continue [Y/n]? Y (Reading database ... 580974 files and directories currently installed.) Preparing to replace libboost1.49-dev 1.49.0-3.2ubuntu1 (using .../libboost1.49-dev_1.49.0-4_i386.deb) ... Unpacking replacement libboost1.49-dev ... dpkg: error processing /var/cache/apt/archives/libboost1.49-dev_1.49.0-4_i386.deb (--unpack):  trying to overwrite '/usr/bin/inspect', which is also in package libboost1.53-tools-dev 1.53.0-6+exp3ubuntu8 No apport report written because MaxReports is reached already                                                               dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Errors were encountered while processing:  /var/cache/apt/archives/libboost1.49-dev_1.49.0-4_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1)


Pgfplots: Linewidth when using \ref in custom legend

I'm creating a custom legend for some pgfplots graph by drawing a node containing a shortstack. Inside the node I'm using \ref{} to insert correct line-styles in front of my text labels.  The problem is that while the lines in the graph are printed with line width=1pt, the lines from \ref are the standard thin size of pgfplots.  This does not happen when using the normal pgfplots legend setup (\addlegendentry), but this is not possible in this graph since the legend either needs to contain extra information or is a common legend for 2 different axis.   So how can I control the line width when using \ref?


$f(a+b)=f(a)+f(b)$. Prove that $f(x)=Cx$, where $C=f(1)$

A question from Introduction to Analysis by Arthur Mattuck:  Suppose $f(x)$ is continuous for all $x$ and $f(a+b)=f(a)+f(b)$ for all $a$ and $b$. Prove that $f(x)=Cx$, where $C=f(1)$, as follows:  (a)prove, in order, that it is true when $x=n, {1\over n}$ and $m\over n$, where $m, n$ are integers, $n\ne 0$;  (b)use the continuity of $f$ to show it is true for all $x$.  I can show the statement is true when $x=n$. As for $x={1\over n},{m\over n}$, I don't know how.


I no longer want Unity, and I want to switch to Gnome, I read  that you have to install gnome-session-fallback package.  To do this, however, when running:  sudo apt-get install gnome-session-fallback   I've got this output:  Reading package lists... Done Building dependency tree        Reading state information... Done Package gnome-session-fallback is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   gnome-session-flashback  E: Package 'gnome-session-fallback' has no installation candidate   So does this mean that I should install gnome-session-flashback instead of gnome-session-fallback to get Gnome? Also as I want to get the latest version of Gnome, which would be Gnome 3 and not 2, is this the correct package to install?    OS Information:  Description:    Ubuntu 15.04 Release:    15.04


Function that is both midpoint convex and concave

Which functions $f:\mathbb{R} \to \mathbb{R}$ do satisfy $$f\left(\frac{x+y}{2}\right) = \frac{f(x)+f(y)}{2}$$ for all $x,y \in \mathbb{R}$  I think the only ones are of type $f(x) = c$ for some constant $c\in \mathbb{R}$ and the solutions of the Cauchy functional equation $f(x+y) = f(x)+f(y)$ and the sums and constant multiples of these functions. Are there other functions which are both midpoint convex and concave?


python operator "*" with List， any others like it?

When using * to create list like:  >>> ll = [None] * 3 >>> ll [None, None, None] >>> ll[0] = 2 >>> ll [2, None, None]   And then using two dimension,   >>> ll2 = 3 *[ 3 * [None]] >>> ll2 [[None, None, None], [None, None, None], [None, None, None]] >>> ll2[0][0] = 2 >>> ll2 [[2, None, None], [2, None, None], [2, None, None]]   So, create list by operator *, if the element is object like list. It doesn't create new object, just use the referenced object.  Are there any other operators like this in Python?  Edit:  Sorry, My representation is bad.  What I want to know is, are there any other operators using like "*" will not create multiple reference.


solution doesn't work. I'm using Guest account right now.  I was just working on VirtualBox and listening to some music with Rhythmbox when suddenly my computer became laggy, and seconds later, everything disappeared except my cursor and wallpaper. I ran terminal using CTRL+ALT+T and typed startx, sudo startx, and the last one sudo shutdown -h now. After booting up my computer again I could not login to my user account, after typing my password and hitting enter, black screen for 2 seconds, and login screen again.


I have an enumerate list in this MWE.  \documentclass[]{beamer} \usetheme{Madrid} \setbeamertemplate{items}[circle]  \begin{document}  \begin{frame} \frametitle{Example} \begin{enumerate} \item First one \item Second one \item Third one \end{enumerate} In the above list, 2 and 3 are what more important. \end{frame}  \end{document}   I want "2" and "3" in the text to be the same as in the list, a blue solid circle with white numbers.  How do I do that? Thank you.


Preseed Ubuntu 16.04 not working (preseed file not found)

I've been trying to preseed my installation for 2 days now. I'm quite new in this topic, so execuse me if I'm asking noob questions. How do I use boot parameters, how do I know that my preseed file works. When is my preseed file loaded


Let $V$ be the set of real numbers. Regard V as a vector space over the field of rational numbers $F$ with the usual operations. Prove that this vector space is not finite dimensional. My attempt: Let $\beta$ be the basis of $V$ such that $\beta =\{\alpha_1, \alpha_2, ..., \alpha_n\}$. $\quad\therefore\;\forall\;\alpha\in span(\beta),\;\alpha = c_1\alpha_1 + c_2\alpha_2 + ..... c_n\alpha_n$ where $c_1, c_2, ...., c_n \in F$. Now I have to show there exists $\alpha \in V$ such that $\alpha \notin span(\beta)$ but I cant figure out which $\alpha$ will not belong in $span(\beta)$.


Why do plants have green leaves and not red?

I know plants are green due to chlorophyll.  Surely it would be more beneficial for plants to be red than green as by being green they reflect green light and do not absorb it even though green light has more energy than red light.  Is there no alternative to chlorophyll? Or is it something else?


Make sed work through 2 or more lines (all lines in this case) instead just one

I use Ubuntu 16.04 with Bash and I'm ought to enable http2 for a particular website I have on an Nginx environment.    Natively, the utility sed does its text-processing on the first instance in the first relevant line (using g argument would make it to process all instances on the first relevant line), but I desire to do a particular operation on 2 or more lines (all lines actually).  I took a look at man sed and found the -l argument that let's you specify number of lines to work with (if I understood correct), but I desire to work on all lines, without being dependent in particular amount of lines.  The particular case I'm having is that I try to unify these two sed operations into one:  s_a="/etc/nginx/sites-available/" $domain="example.com" sed -i "s/listen 443 ssl default_server;/listen 443 ssl http2 default_server;/" $s_a/$domain.conf sed -i "s/listen [::]:443 ssl default_server;/listen [::]:443 ssl http2 default_server;/" $s_a/$domain.conf   I could unify the two sed operations to something like:  sed -i "s/443 ssl default_server/443 ssl http2 default_server/" $s_a/$domain.conf   I assume that the safest way to make sure I cover all relevant lines in such convenient one line operation is to use some argument but I don't know if this can be done with the -l argument if at all, or I must use regex.


I have upgraded my Samsung Galaxy S4 to Android 5.0.1. It is full of bugs, but I don't wont to downgrade to Kitkat.  I have heard that Android 5.1 is available. Is it possible to get it for my S4?


Is there an idiom for being consistently unlucky through no fault of one's own?

Not quite sure how to word this, but I'm looking for an idiom or phrase/saying that describes when somebody who's done nothing to deserve it has hit a streak of bad luck. Wish I could be more descriptive, but that's about as well as I can elaborate on the idea.


I need to show that Every derivative $\delta : L \to L $ for finite semisimple Lie algebra $L$ over $\Bbb C $ is inner automorphism.  when Inner automorphism is defined by  $exp(ad_x)= \sum_{j=0}^{k-1}  ad_x^j/j!$   when $ad_x$ nilpotent with nilpotent degree of $k$  for all $x \in L$ when $ad_x:L \to L , ad_x(y)=[x,y] $


Lower spin than one half? Spin other than whole/half integer?

Someone asked me to explain why spin can't be lower than one half. All I could say was field geometry, that it's the minimum non-zero twist in a particle's field. Is that right? The follow up question they asked was, are angles quantised?


I used to close a running application by pressing ALT+F4. But, I realised that the application is still running and the correct way to close (quit) it is the combination of Ctrl+Q keys.  So, what is the purpose of ALT+F4 and how is it different from Ctrl+Q?


Merge all Language learning Stack Exchange sites together?

I'm confused by why there are so many separate sites for specific languages on here. Wouldn't it be better to just have one "Languages" Stack Exchange where you can indicate which language you're asking about with the tags? As it is, if I want to ask about ancient Greek dialects I have to post on the "Latin" Stack Exchange, and if I have a question about Ghandaran or Pali I have to go to the "Buddhism" one, and if I have a question about Klingon grammar I have to post on the Sci-fi and fantasy site (where it will most likely be closed as off-topic). As far as I know there's nowhere for me to ask about Toki or Ithkuil (although perhaps the Esperanto site might accept a question about these languages). Just wondering about the rationale for having so many separate sites. Is it possible to merge them all into one "Languages" site where any and every language would be on-topic?


package Annotaion_testng;  import java.util.concurrent.TimeUnit; import org.openqa.selenium.By; import org.openqa.selenium.WebDriver; import org.openqa.selenium.firefox.FirefoxDriver; import org.testng.annotations.BeforeClass; import org.testng.annotations.BeforeMethod; import org.testng.annotations.Test;  public class Login_case {    public String baseUrl = "https://www.eventerprise.com";   String driverpath = "C://Users//fizan//Documents//testing//webdriver_soft//fire_fox_driver//geckodriver.exe";   public WebDriver driver;    @BeforeMethod   public void f() throws InterruptedException {      System.out.println("opening firefox");     System.setProperty("webdriver.gecko.driver", driverpath);     WebDriver driver = new FirefoxDriver();     driver.get(baseUrl);     Thread.sleep(10000);   }    @Test   public void login(){     System.out.println("click on login link from header");      //code is failing from here     driver.findElement(By.xpath(".//*[@id='app']/div/div/div/header/div[1]/div[1]/div[2]/ul/li[4]/a")).click();      driver.findElement(By.id("email")).sendKeys("fijan@atyantik.com");      driver.manage().timeouts().implicitlyWait(1, TimeUnit.SECONDS);     //enter  password      driver.findElement(By.id("password")).sendKeys("atyantik@1234");      driver.manage().timeouts().implicitlyWait(1, TimeUnit.SECONDS);     //click on login button      driver.findElement(By.xpath(".//*[@id='eve-modal']/div/div[1]/div/div/div[2]/div/div/div/div[1]/div[2]/form/div[4]/button")).click();      driver.manage().timeouts().implicitlyWait(5, TimeUnit.SECONDS);      //click on log out from header      System.out.println("logging out");      driver.findElement(By.xpath(".//*[@id='app']/div/div/header/div[1]/div[1]/div[2]/div[1]/ul/li[7]/a")).click();     } }


Is there a way to suppress the warning for fopen (VS 2012 is suggesting I use fopen_s)? The following commands don't seem to work  #define _CRT_SECURE_NO_DEPRECATE #define _CRT_SECURE_NO_WARNINGS


Where has my `uniq` or `sort -u` line gone, with some unicode characters

What is going on in the following code snippet?  I'm not getting my expected output.     I'd think it was a bug, but it happens for 2 different programs (uniq and sort), so I suspect it is something to do with... well, I don't know what.. hence the question.     The first 3 (of 4) examples work, but the 4th fails!.    I would expect the same behaviour for any and all characters. ie. to print out 2 lines (from the 3 lines of input)... but in the 4th case, I only get 1 line (for both sort -u and uniq); the two identical lins just vanish!     I've converted the output '\n' to space for compactness of view.    I'm using uniq and sort from (GNU coreutils) 7.4 ... running on Ubuntu 10.04.3 LTS desktop.     The script:  {   locale -k LC_COLLATE   echo   for c1 in x 〼 ;do      for c2 in z 〇 ;do        echo -n "asis   : "; echo -e "$c1\n$c2\n$c2"          |tr '\n' ' ';echo       echo -n "uniq   : "; echo -e "$c1\n$c2\n$c2" |uniq    |tr '\n' ' ';echo       echo -n "sort -u: "; echo -e "$c1\n$c2\n$c2" |sort -u |tr '\n' ' ';echo       echo     done     echo   done }   The output:  collate-nrules=4 collate-rulesets="" collate-symb-hash-sizemb=2081 collate-codeset="UTF-8"  asis   : x z z  uniq   : x z  sort -u: x z   asis   : x 〇 〇  uniq   : x 〇  sort -u: 〇 x    asis   : 〼 z z  uniq   : 〼 z  sort -u: 〼 z   asis   : 〼 〇 〇  uniq   : 〼  sort -u: 〼   # In the last example (of 4) where did the '〇' go? .. U+3007 IDEOGRAPHIC NUMBER ZERO #


I want to make a cannon ball sink slowly into the ground

I want to make this giant cannon ball sink slowly into the ground.   I've attached a bone to the plane and animated it so it does this:   The problem is, I want other objects to fall into the hole after the cannon ball (like a diploma and a hat). After making the plane a passive rigid body object and the diploma and hat active, the active objects don't react to the ground plane's mesh deformation (even when I check all the animated/deform/deforming boxes in the passive object rigid body settings). Help!


Let $S^1 = \{z \in \mathbb{C} : |z| = 1\}$.  Take the loops $f,g : [0,1] \rightarrow S^1$, $f(t) = 1$, $g(t) = e^{2\pi it}$.  I know these represent different elements in $\pi_1(S^1, 1)$, but I don't see why $F(t,s) = e^{2\pi its}$ isn't a homotopy between $f$ and $g$.


Do you take the negative square root when you raise a number to the power of a half?

E.g. does $4^{1/2} =  \pm 2$ and if not, why?


Accidentally installed Ubuntu to my Intel Optane Memory (MEMPEK1J016GA)

I was attempting to install Ubuntu 18.04.3 LTS for the very first time without help from a tutorial and I managed to somehow install Ubuntu on my intel optane memory instead of my hard drive.   When I look at the disks, my hard drive "Acer" comes up as a removable drive - when it is a hard drive installed into the laptop.  I am wondering if it is possible to change my file-system location to my internal hard drive as my optane memory is only a small capacity.


When is `\[` preferred over equation* environment?

When is it preferable to use \[ instead of equation*? I find I often use the equation* environment in the following way:  \begin{equation*} some expression \end{equation*}   Should I instead be using the \[ as below?  \[ some expression \]


Ubuntu shows as first priority boot option but keeps loading into windows, which is second priority

I have already installed Ubuntu 20.04 and made it first boot priority on my computer (asus 2019 zenbook) but my computer keeps jumping into the second boot option which is Windows 10.


product of normal and lognormal variates

If x and y are uncorrelated normal variates, x*exp(y) will have a symmetric unimodal distribution with positive excess kurtosis. Has this distribution been named and studied?


Comment flag box stuck in top left, can't reach any option

When I try to flag a comment, the flag comment box is in the top left and I can't select any option.    This does not happen consistently. Sometimes it ends up in the correct place. Sometimes it jumps to the middle when I perform an action.  I'm using Firefox 56.0 here, but I've also seen the behaviour in a recent version of Pale Moon.


Control what can connect to systemd's rpcbind/portmap service (port 111)

systemd on my box is listening to port 111 for the  service.  Lets say I wanted to allow some other computers to connect to it, but not all. Is there any way besides a firewall to control what can connect to this service?  Poking around I see that the rpcbind binary is linked against the  tcp_wrappers-libs library, meaning it can use .  However, I don't know if systemd immediately hands connections to port 111 over to the rpcbind binary, or if it does some of its own processing first.  My system is a standard desktop install of Fedora 25.


How can I repair this graph when the graph is not continuous at the origin?

I want to draw graph of the function abs(\x^3)-3*abs(\x) with pgfplots. I tried  \documentclass[12pt]{standalone} \usepackage{pgfplots} \usepackage{tikz} \usepgfplotslibrary{fillbetween} \usetikzlibrary{patterns} \pgfplotsset{compat=1.9} \usepackage{fouriernc} \begin{document} \begin{tikzpicture} \begin{axis} [ declare function={Y(\x)=abs(\x^3)-3*abs(\x);}, axis line style = very thick,     axis lines = center,     xlabel=$x$,ylabel=$y$,         domain=-2.2:2.2,         ymin=-2.5,         ymax=2.5,         xmin=-2.5,         xmax=2.5,     samples=100,xtick distance=1, ytick distance=2,unit vector ratio*=1 1 1,     width=11cm,     grid=major,     grid style={gray!30}] \addplot [black, ultra thick,name path =B] {Y(x)}; \addplot [black, mark=*,only marks,samples at={-2,-1,1,2}] {Y(x)}; \node at (axis cs:-0.25, -0.25) {$O$} ; \addplot[color=black,dashed] coordinates {(-2,0)         (-2,2)         (2,2) (2,0)          };          \addplot[color=black,dashed] coordinates {(-1,0)         (-1,-2) (1,-2) (1,0)         }; \end{axis} \end{tikzpicture} \end{document}    The graph is not continuous at (0,0).


Do we use in or on when we want to talk about some action or event that takes place in/on the street?        This car has been parked [in/on] our street for a week now.   There's nobody [in/on] the street.   Let's go play [in/on] the street.   There was an accident [in/on] their street yesterday.   I guess I lost my necklace [in/on] the street.      And so on.


How to interpret TCP/ip fingerprint when scanning for OS?

I run the command : nmap -O ip_address to identify the os and I have the result below:  OS:SCAN(V=5.05BETA1%D=8/23%OT=22%CT=1%CU=42341%PV=N%DS=0%DC=L%G=Y%TM=4A91CB     OS:90%P=i686-pc-linux-gnu)SEQ(SP=C9%GCD=1%ISR=CF%TI=Z%CI=Z%II=I%TS=A)OPS(O1     OS:=M400CST11NW5%O2=M400CST11NW5%O3=M400CNNT11NW5%O4=M400CST11NW5%O5=M400CS     OS:T11NW5%O6=M400CST11)WIN(W1=8000%W2=8000%W3=8000%W4=8000%W5=8000%W6=8000)     OS:ECN(R=Y%DF=Y%T=40%W=8018%O=M400CNNSNW5%CC=N%Q=)T1(R=Y%DF=Y%T=40%S=O%A=S+     OS:%F=AS%RD=0%Q=)T2(R=N)T3(R=Y%DF=Y%T=40%W=8000%S=O%A=S+%F=AS%O=M400CST11NW     OS:5%RD=0%Q=)T4(R=Y%DF=Y%T=40%W=0%S=A%A=Z%F=R%O=%RD=0%Q=)T5(R=Y%DF=Y%T=40%W     OS:=0%S=Z%A=S+%F=AR%O=%RD=0%Q=)T6(R=Y%DF=Y%T=40%W=0%S=A%A=Z%F=R%O=%RD=0%Q=)     OS:T7(R=Y%DF=Y%T=40%W=0%S=Z%A=S+%F=AR%O=%RD=0%Q=)U1(R=Y%DF=N%T=40%IPL=164%U     OS:N=0%RIPL=G%RID=G%RIPCK=G%RUCK=G%RUD=G)IE(R=Y%DFI=N%T=40%CD=S)   Please can you help me how can I find the most likely OS on this scanned computer? How can I interpret this result... What suggests that the os may be Linux for example,and what suggests that it may be another os , for example Windows?  I am trying so much to understand it, but nothing til now... Please help me. Thanks in advance


If we run a workflow,Process Builder and a Trigger run simultaneously,Which one work first?


What's the meaning of this sentence below from Longman Dictionary of Contemporary English?     ▪ Blow me down if she didn’t just run off!     The Longman Dictionary says you use 'blow me' to show annoyance or surprise and is usually used in British English. But I still cannot figure out what it means and in what situation it can be used.


How do I delete a directory with hyphen in the name please?

Could someone help me delete a directory named -ltr I accidentally created this when trying to list items.   None of this works:  rm -R *-ltr* rm -R "-ltr" rm -R '-ltr'


How does Schengen 90/180 apply to long-stay visas?

My SO and I are currently staying in France under the country's visa long séjour, essentially a 1-year visitor visa. If we return to Europe after leaving when the visa expires we would naturally be covered by the Schengen visa for 90 days, which also begins the 180-day period. How do the rules for these two visas interact? For example, if we applied for another long séjour to begin at the end of our 90-day Schengen visa, does the Schengen period reset 90 days within the long séjour period? Will the French authorities frown on having visa types overlap like this? Our goal is to travel for around 2.5 years in Europe and then return home. We're American and can prove means and lodging for the entire period.


In The Universe in a Nutshell chapter 4, Hawking explains the warping of spacetime according to general relativity.  Near a massive but ordinary star, spacetime is warped such that the light emitted from the star appears to move slower when near the star, and appears to "speed up" to the constant speed of light c when away from the star, from the viewpoint of an outside observer.  Of course, we can't directly measure this experimentally because there is no way to measure the speed of light near a star from the reference point far away from a star. (Do I have this right?)  Hawking writes that this "slower" light is due to the warping of spacetime near the star, and this leads into the discussion of how spacetime and light behaves near a black hole.  I've always heard that light cannot escape a black hole due to the extreme gravity from the super-dense black hole (star).  And so it make sense that near an ordinary massive star, light can escape but "struggle" to do so, going "slower" near the star before "breaking free" and "speeding up" to what we see as the speed of light farther away from it.  (I use scare quotes as I realize these idioms are shortcuts for understanding relativity and not literally true.  Feel free to correct me if I am using them incorrectly.)  So which is it?  Is the light escaping from a massive star held back a bit by the pull of gravity, or by the warping of spacetime near it?   Or is it both, additively?  Or are both concepts two sides of the same coin in a way I am missing?


More Casual and Succinct Way to Say "John's Areas of Expertise"

I am creating a user profile page, and one of the sections will contain a list of the subject areas in which the user has had the most activity and up-votes e.g. User a has answered the most questions and/or received the most up-votes in categories x, y, z. The assumption is that categories where the user answered a lot of questions and received the most up-votes would be categories in which the user has a degree of expertise.   The section will list the categories under which the user's highest percentage of the above two took place.  I am struggling to find a succinct, natural heading for this section.   I am playing around with:   John's Top Subjects John's Areas of Expertise John's Expertise   ...but none of the above fit the scenario exactly, and all feel awkward and unnatural.  Looking for suggestions.


Reconstruction of "wavefunction" phases from $|\psi(x)|$ and $|\tilde \psi(p)|$

Consider a "wavefunction" $\psi(x)$, which has a Fourier transform $\tilde \psi(p)$  Suppose that we know, for each $x$, $|\psi(x)|^2$, and that we know, for each $p$, $|\tilde \psi(p)|^2$.  Have we enough information to reconstruct the "wavefunction" $\psi(x)$, that is, obtain the phase of the "wavefunction" for all $x$ (up to a global phase, we are only interesting to the relative phases between the $x$)?


The files .DS_Store and .DS_Store had a tree conflict error from Git in xcode 8

I'm using GitHub as project repository for ios project. But whenever I'm trying to pull project from xcode 8 I'm getting the following error:     The files .DS_Store and .DS_Store had a tree conflict   Any solution?


Is the gold and silver in the GLD and SLV ETFs leveraged?

There are various blogs and videos that indicate that the gold that GLD holds (via HSBC) and the silver that SLV holds (via JP Morgan) is leveraged 50 to 1 or 100 to 1.  For me there are some advantages to using these ETFs vs. one like CEF, and so I was wondering if this leverage is "fact or fiction".  Do you have any concrete knowledge or concrete references on this subject?  Or have you been able to wrap your head around this whole issue?


I'm having problems with my laptop keyboard - specifically, some keys don't work any more.  The problem started three months ago - just three months after I purchased this ASUS K42F - when the left Alt key got busted. I cannot forget that moment because I was editing something important in Photoshop that required the use of such key. I didn't bother to do something about it; I still have the right Alt key anyway.  I was surprised when two days ago, almost half of all the keys in random positions didn't work any more. I haven't spilled any liquids on the keyboard, and I know nobody else has either because I always put this laptop in a vault when I'm out (privacy is a problem here). I've tried everything, from scanning for viruses and spyware to using compressed air, but nothing has worked. I hope someone can help me with this before I'll be obliged to visit the seller whose location is very far from mine. I still have the one year warranty.


Mrs Reed forgets the number combination to her safe. The combination has $4$ numbers each is a $1$ digit number. The $4$ digits add up to $10$ and there are no zeros. How many times does Mrs Reed have to try to open her safe?  My attempt: ${9 \choose 3} = 84$ but the answer is $80$.


Is it possible to highlight the OP's name in the comments in Android app?


Problem on Linear Diophantine Equation over 3 variables

How to solve $ax+by+cz=d$ over integers where $a,b,c,d$ are integers?


Is there some tool for finding files in one directory but not in the other?

I would like to write a bash script to find those files in a directory but not in another directory.   Does the following script work? When does it not?  for i in "$1"/*; do     f=$(basename $i);     if [ ! -e "$2"/"$f" ]     then         echo $f     fi done   I heard diff  can find differences between the contents of two directories too. Can it also solve the same task?  Or some other tool?  Thanks.


Validity of conditional statement when the premise is false.

Is it just for convenience that mathematicians define that false statements imply anything?  If yes, why it would be defined like this?


Method to reduce added information in a question being written in comments

The problem  On EE.SE, but probably most SE sites, we have a common problem:  A (usually new) user asks an ambiguous question.  Other users ask for more information in comments to the question.  The OP writes additional information in more comments.  Many people aren't going to read a lengthy and tedious comment chain, so they continue to see just the ambiguous question.  Sometimes they ask for the same additional information someone else already did.  Experienced users are frustrated with the OP's lack of cooperation.    I think we've all seen this.  The root cause of the problem is that the new user answers comments with more comments, instead of adding pertinent information to the question itself.  The solution  Don't let users post comments to their own question.  There is really very little legitimate reason for doing this.  This site isn't a KaffeKlatsch, so comments aren't for chit-chat anyway.  Just about all comments to a question by the question author are to add information to the question.  This information belongs in the question.  If you really want users to still be able to comment on their own question, then at least pop up a message explaining that additional information to a question should be added to the question itself, and provide something to click on that opens the editor on the question instead.  Another alternative is to allow commenting on your own question after some rep level.  The message about adding information to the question should still pop up regardless.  Of course anyone that posted a comment to a question should automatically get notified when that question is changed.  The only times I remember that I've written comments to my own question were to ping someone that I added the information they requested to the question.  Similar discussions  I see that something similar was requested in .  However, that seeks to prevent someone from commenting on all their own posts, not just questions.  It is also trying to address a different problem.  The problem addressed here is real pertinent information to a question getting hidden in comments.  That problem isn't even mentioned as one of the issues in the question linked to above.  Example  See  at EE.SE.  The OP's use of "negative amplitude sine wave" was confusing and unclear.  Clarification was asked for in a comment.  The OP did answer, but that answer is buried in a comment.  I came along later, read the question, and asked about the same thing again.  In the end, the question was closed as unclear, because it was.  I doubt I'm the only one that often doesn't read comments to a question just to answer it or ask for more information.  I've found that comments are usually a waste of time, and they certainly aren't supposed to contain pertinent information to the question.  Of course the help explains what you should do, and there is no excuse for not having read the help before posting a question, but it is easy to think that you should reply to a comment with a comment.  By far new users commenting to their own question are responding to things asked by others in comments.  The current situation is a lot worse than new users getting a popup when trying to comment on their own question.  This propoal should be considered separately from the other, since it proposes something different, to address a different problem.


In Terminal, Option + click allows me to place my cursor at any point on the current line-- great for editing really long commands.  How can I do this in iTerm2?  Update: According to , the feature has been around since 0.7.0 (2003). I've also noticed that if I hold Command+Option, the cursor changes into the familiar cross like in Terminal...  but clicking still does not reposition my cursor.