A question regarding finding the minimal polynomial associated with a field extension .

Say we have the field extension $\Bbb Q(w,\sqrt[3]{5})$ over $\Bbb Q$, where w is the primitive cubed root of unity. I know that the minimum polynomial of $\sqrt[3]{5}$ is $x^3-5$. I want to figure out the degree of the extension;  I know we can use the tower law $|\Bbb Q(w, \sqrt[3]{5});\Bbb Q|=|\Bbb Q(w, \sqrt[3]{5});\Bbb Q(\sqrt[3]{5})||\Bbb Q(\sqrt[3]{5});\Bbb Q|=x.3$ as $x^3-5$ has degree 3  But how does one find the minimum polynomial of the extension  of degree x


Need a copy of the file /etc/apache2/sites-available/default-ssl.conf for apache2 on ubuntu 14.04 LTS

Inadvertently overwrote the contents of the default-ssl.conf file right after I installed apache2.  D'OH !!  Yes, I see the same request here [] BUT that was 3 years ago. In case the contents have changed, can someone please oblige me with a more recent version ?  Thanks kindly in advance.


Downgrade backup from SQL Server 2014 to SQL Server 2012

Im trying to restore my database on my server, but i got the following error:     The database was backed up on a server running version 12.00.2269.   That version is incompatible with this server, which is running   version 11.00.2100. Either restore the database on a server that   supports the backup, or use a backup that is compatible with this   server.   So I need to downgrade my backup file, but how can I do it? Do I need to install a new instance of SQL Server 2014? With the option "Tasks -> Backup" there is no option to select the version for the backup.  Thanks!


Is ther any logic that migth help while you create a Neural Network?

I am a newbie in Tensorflow and Keras and for the first moment I ask me the same few questions while I am creating my Neural Network. Even searching for some explanation of how to estructure, train, etc. Layers While you are structuring your model in a Neural Network I cant understand how people reach to an optimal number of layers and neurons, is ther any logic behind that having an amount of inputs says wicht amount of hidden layers and beurons use on each one? Activatin Functions Also there are many activation functions such as:  ReLu , the common one. Softmax Sigmoid Linear  And more, I listed the ones that I see more, I know there are more and derivations of ReLu function. But my question for this section of building your Model is, Are there any relation between the type of input and the activation function while you are building? Compiling & Training Finally, in the training section I know there are diferent parts you can tune to have done repercussion on the model training and therefore on the result. Such as, the batch_size, the number of epochs, the loss function, the optimizer, etc. Also you can still modify (optimizer)some of those elements or even create your own ones and use it (loss function). But what about the number of epochs and the batch_size? What meaning does they have? I read that the learning rate have a relation with the batch_size used, I mean, low learning rate works better with more batch_size and vice versa. I know my questions are quite ambiguous and quite general, but even seraching I still have them. Thanks for reading me.


How do I wrap a spring-form pan in foil so it doesn't leak when I bake in a water bath?

I have never found a spring-form pan that does not leak.  I have never been able to wrap a spring-form pan so that some of the water doesn't get into the pan.  I can wrap it so that a lot of the water doesn't come into the pan.  But it seems to me that there must be a method that works to keep the water out entirely.  I just haven't figured it out.  How can I wrap a spring-form pan in foil so that water from the bath doesn't leak into it?


Difference in boiling points ( temperatures) of 2 elements

In a chemistry class, students were learning about boiling point of various elements.Reuben has compiled a table that gives boiling points of each of various elements. The lowest boiling point is of Element X: – 200 degrees Fahrenheit. The highest boiling point is of Element Y: 550 degrees Fahrenheit Find the difference between the lowest and highest boiling point.    I know how to calculate the difference. -200 – 550 = -750. I am not sure if the answer is written as a negative or positive. Will the answer be – 750 F or 750 F ? Would greatly appreciate if you could explain what the correct answer is.


Python pyModis installation give error on windows 10 using pip install pyModis

I am using windows 10 operating system on my HP i7 machine with Python 2.7 installed. For windows, it is possible to install pyModis using pip by writing the following syntax in Windows PowerShell:   pip install pyModis   But it give me error like:     Failed building wheel for GDAL Failed to build GDAL Installing collected packages: GDAL   Running setup.py install for GDAL Complete output from command c:\python2.7\python.exe -c "import setuptools, tokenize;__file__='c:\\users\\oaamer\\ap       pdata\local\temp\pip-build-j1djwe\GDAL\setup.py';exec(compile(getattr(tokenize,   'open', open)(file).read().repl ace('\r\n', '\n'), file,   'exec'))" install --record   c:\users\oaamer\appdata\local\temp\pip-njzqtm-record\install-rec   ord.txt --single-version-externally-managed --compile:       running install       running build       running build_py       running build_ext       building 'osgeo._gdal' extension       C:\Users\oaamer\AppData\Local\Programs\Common\Microsoft\Visual C++ for Python\9.0\VC\Bin\cl.exe /c /nologo /Ox /MD / W3 /GS- /DNDEBUG   -I../../port -I../../gcore -I../../alg -I../../ogr/ -Ic:\python2.7\include -Ic:\python2.7\PC -Ic:\pytho n2.7\lib\site-packages\numpy-1.9.2-py2.7-win32.egg\numpy\core\include   /Tpextensions/gdal_wrap.cpp /Fobuild\temp.win32-2.   7\Release\extensions/gdal_wrap.obj       gdal_wrap.cpp       C:\Users\oaamer\AppData\Local\Programs\Common\Microsoft\Visual C++ for Python\9.0\VC\Include\xlocale(342) : warning C4530: C++ exception   handler used, but unwind semantics are not enabled. Specify /EHsc       extensions/gdal_wrap.cpp(2859) : fatal error C1083: Cannot open include file: 'cpl_port.h': No such file or director y       error: command 'C:\Users\oaamer\AppData\Local\Programs\Common\Microsoft\Visual   C++ for Python\9.0\VC\Bin\ \cl.exe' failed with exit status 2   how to fix that error i have tried so many times to fix read different blogs but did not find the possible solution as windows does not provide friendly environment.


Fresh Numbering for theorems and Lemma in new chapter

I am building a report document. I want to start the numbering of lemmas and theorem with 1 in every new chapter.  For example, I have 3 Lemmas and 2 theorems in Chapter number 1. Now, in chapter 2 I again want to start with lemma 1 and theorem 1. But I don't want the format like Theorem 2.1  Can you please tell me the packages and how to achieve the above?  Edit 1: I want to This type of format  Chapter 1     ----Section 1     --------thm 1     --------Lemma 1     ----Section 2     --------thm 2     --------thm 3     --------Remark 1     Chapter 2     ----Section 1     --------Lemma 1     --------thm 1     ----Section 2     --------thm 2     --------Remark 1  But using the command \renewcommand*{\thetheorem}{\arabic{theorem}} is not helpful for the Lemmas and Remarks. using the above command as \renewcommand*{\theremark}{\arabic{remark}} and similarly for lemmas either give an error or starts them with number 0. And sometimes ignores the command and starts with the number from the continuation itself i.e. If chapter 1 has 2 lemmas, then in chapter 2 it starts with lemma 3.  Edit 2: I have known  after @oliversm provided the answered this question.  Edit 3: Here is my implementation of what I am trying to say in Edit 1 as pointed out by @egreg  \documentclass[a4 paper, 12pt]{report} \usepackage{amsmath} \usepackage{amsthm} \usepackage{enumerate} \usepackage{hyperref} \usepackage{fullpage} \newtheorem{lemma}{Lemma} \newtheorem{remark}{Remark} \newtheorem{thm}{THEOREM}[chapter] \renewcommand*{\thethm}{\arabic{thm}} \renewcommand*{\theremark}{\arabic{remark}} \renewcommand*{\thelemma}{\arabic{lemma}} \begin{document} \chapter{Hello} \section{Hi} \begin{thm}       some statement \end{thm} \section{ More Section in this chapter} \begin{lemma}       Purpose of Lemma \end{lemma} \begin{proof}       some bizzare statements \end{proof} \begin{remark}       some useful statement \end{remark} \chapter{ Next one} \section{in person} \begin{lemma}        It is the another lemma in the new chapter \end{lemma} \begin{proof}        some tricky part \end{proof} \begin{thm}        Theorem using previous lemma \end{thm} \begin{remark}        exercise for reader \end{remark} \end{document}


java.lang.NullPointerException while creating BinaryTree from preorder and inorder

I don't know why this code is throwing a runtime error     static class TreeNode<E> {     E data;     TreeNode<E> right, left;          TreeNode(E data)     {         this.data=data;         right=left=null;     } }  inpte: To store inorder in a manually implemented LinkedList. preptr: To store preorder in a manually implemented LinkedList. num: To store the total number of nodes in the tree. TreeNode<E> construct(Node<E> inptr, Node<E> preptr, int num) {     TreeNode<E> tmp;     Node<E> q;     int i,j;          if(num==0)     {         System.out.println("No node to create the tree");         return null;     }                tmp=new TreeNode<E>(preptr.data); //error line     if(num==1)         return tmp;          q=inptr;     for(i=0;q.data!=preptr.data;i++)         q=q.next;          tmp.left=construct(inptr, preptr.next, i);          for(j=1;j<=i+1;j++)         preptr=preptr.next;          tmp.right=construct( q.next, preptr, num-i-1);                   return tmp; }  error thrown:  Exception in thread "main" java.lang.NullPointerException     at practiceCodes.PreAndIn.construct(PreAndIn.java:32)     at practiceCodes.PreAndIn.main(PreAndIn.java:104)


`.TXT` file association to Notepad++ "stopped working"

I recently formatted and then reinstalled everything, but oddly now, Windows 7 refuses to let me set Notepad++ as the default .TXT editor.  I try to set the "open with" file as usual:      right click a .TXT file    Open With... → Choose Default → Browse    paste "C:\Program Files (x86)\Notepad++\notepad++.exe"    ... but Notepad++ doesn't show up in the dialog (image below), and the file instead opens with lame old Notepad.exe.    However when I open "C:\Program Files (x86)\Notepad++\notepad++.exe" from the ![Windows Key][oldwinlogo]+R Run dialog, Notepad++ opens without a problem.  Also, certain files' context menu have Edit with Notepad++, which also works fine.     From my registry, in case it's relevant:  [HKEY_CLASSES_ROOT\.txt]   Default="txtfile"   Content Type="text/plain"   PerceivedType="text"  [HKEY_CLASSES_ROOT\.txt\PersistentHandler]   @="{5e941d80-bf96-11cd-b579-08002b30bfeb}"  [HKEY_CLASSES_ROOT\.txt\ShellNew]   ItemName="@%SystemRoot%\system32\notepad.exe,-470"     NullFile=""    I tried rebooting... Any ideas?    Edit: I had also tried the editing the Associations directly in NPP as admin, without success. Note that I'm using Windows 7.  (I just got all my N++ setting/themes/plugins/ftp/etc all painstakingly setup, and it was working fine until I tried it this morning, so I'm hoping for a fix other than reinstalling N++.)


How to know when and which user logged into the system under Mac OS X? Last is not enough!

In Mac OS X, if I don't touch it for a while, it will lock the screen and one must use password to unlock it, but this kind of log in is not recorded by last command. I want to know if anybody tried to break into my MacBook when I am not in front of it. Is there any way I can log such attempts?


"However difficult something is, …" or "However difficult something may/might be, …" ?

Does it make sense to follow an adjective phrase such as "however difficult" with the modal auxiliaries "may/might"? Isn't it a bit pleonastic, since "however" already contains the idea of either uncertainty, or irrelevance?  "However wealthy he was / However wealthy he might have been, she would not have married him if she had not been in love with him."  Does "he was" imply that his wealth was certain but irrelevant, and "he might have been", that it is/was a matter for conjecture and irrelevant, anyway?


Adding style to a published layer using GeoServer REST API with Node.js

Lets say I have a custom style in GeoServer and after I created a new layer, I want to add the style to that layer. I am using  link for documentation.  function editLayerStyle(layerName, body) { url = `http://admin:geoserver@IP:PORT/geoserver/rest/layers/{layerName}/styles`  return new Promise((resolve, reject) => {     request.post(url, {         body,         headers: { 'content-type': 'application/vnd.ogc.sld+xml' }     }, function (error, { statusCode }, body) {         if (error) {             return reject({ success: false, statusCode: statusCode, message: body })         }         if (statusCode === 201) {             return resolve({ success: true, message: 'Style added to layer' })         } else {             return reject({ success: false, statusCode: statusCode, message: 'Unknown Error' })         }     }) }) }  let layerName = 'layer_name' let body = ` <styles>     <style>         <name>{style_name}</name>    /// name of my style         <filename>{style_name.sld}</filename>  /// format of style     </style> <styles>`  try {     await editLayerStyle(layerName, body) } catch (error) {     console.log(error) }   I get the error even I tried to change the style and the content type.


GNOME shell Ubuntu 16.04 - How to disable notification area

I have just Installed GNOME Shell on Ubuntu 16.04.  There a area in layout I don't know what is it name exactly. This area in below picture (Area 1):    I think some Icon in area 1 should be in area 2 (taskbar) and I already install a test Ubuntu with Gnome shell in another PC, it exactly in taskbar.  My question is how to disable area 1 and how to move icon in area 1 to area 2 (taskbar)?


I’ve been flying around the two islands available at the start of the game for ages, but I’m aware that on mobile there’s a third large island called Snowstone. But I just can’t seem to find it anywhere.  In the races section there’s a few I haven’t unlocked, including one called ‘yeti scramble’, which I can imagine is on this island.  So how do you find Snowstone Island?


I've got a Germany 'visitor/business' visa with 12 days left after my trip.

So the visitor visa lasts for 30 days  and I only stayed in Germany for 18 days  Will I be able to plan my next tourist trip to France without applying for a tourist visa ?


I'm having problem with  (TFS) when viewing .cs files and need to delete the file association with .cs in Windows 7. At the moment I go to Control Panel -> Default Programs trying to do this, but it seems to have no way to delete other than change the current association. So, how can I do it?


Starting a Question with "Why Not . . ." Inappropriate?

Microsoft Word has underlined a question I typed starting with "why not." Something along the lines of:     Why not walk to the hall every morning before the sun has risen and while the streets are empty?   According to Word, this is a non-standard question.   Is it correct in a semi-formal article that's intended for the Internet audience? I thought it was standard enough.


Multi-regional site, same language - Google penalization

Let's suppose there is a company "acme", that ships products world-wide. They have multiple sites, for example there is a site for Australia - acme.com.au  and a site for UK - acme.co.uk. Both sites have lots of identical content on pages (index, about, some product pages...)  Will be these sites penalized in results of Google Search and what can be done if so?  Thanks


Show that every Cauchy sequence is bounded

I am supposed to prove, that every Cauchy sequence is bounded.   From the definition of Cauchy sequence:$\left ( \forall \varepsilon > 0 \right )\left ( \exists n_{0}  \in\mathbb{N} \right ) \left ( \forall m,n  \in\mathbb{N}:m,n\geq n_{0} \right )d\left ( x_{n},x_{m} \right )< \varepsilon $.  We can fix $ \varepsilon$: $\varepsilon=1$. Then $m\geq n$, so that $d\left ( x_{n},x_{m} \right )< \varepsilon $. Let p be point in a space...  I do not know how to continue, or if it is correct. I want to somehow include triangle inequality, but I am not really sure, if that is correct.  Any help?


Things in the design world seem to be getting flatter! I can produce infinite examples; iOS7, Windows 8 (and everything else in Windows 8), Pepsi, the Dropbox logo, even things outside the computer world; everything is flatter now.  When Windows XP was released, the trend was to give a curve to everything, and it looked better! Now, getting rid of those curves looks better!  Who governs this and why do flatter icons and logos look better now?        EDIT: And a newer trend of making things round is catching up:


Dual-Boot Ubuntu 14.04 and Windows 7 on FakeRAID Installation error - question marks "????..."

I am trying to install Ubuntu 14.04 on FakeRAID along Win7.  Win 7 has been already installed, and dmraid is running.  During the installation I choose to manually partition, this is the structure:  \dev\mapper\isw_gchdghhd_Volume0 \dev\mapper\isw_gchdghhd_Volume0Op1 - NTFS Win7 loader \dev\mapper\isw_gchdghhd_Volume0Op2 - NTFS Win7 partition \dev\mapper\isw_gchdghhd_Volume0Op3 - swap \dev\mapper\isw_gchdghhd_Volume0Op5 - ext4 mounted as \ \dev\mapper\isw_gchdghhd_Volume0Op6 - ext4 mounted as \home   There is another sequence similar to above marked as "linear".  I choose \dev\mapper\isw_gchdghhd_Volume0 as boot device.  When immediately after the installation begins, an error with question marks pops up, and the installation stops.


deleting properties from cloned object affect both objects?

I am trying to clone an object and delete 2 properties,  this.clone = Object.assign({}, this.purchaseOrder) console.log("0clone", this.clone) this.clone.client_purchase_order_items.forEach((order, index) => {     delete order.list_of_measures;     delete order.isReadOnly; }); console.log("purchase Order", this.purchaseOrder)   But its affecting cloned object and the which I used for cloning. I don't want to remove properties from this.purchase order. what should I do?


Ubuntu 14.04 won't go past the log in screen; update

I loaded Ubuntu on an older laptop with windows vista. I opted for the dual boot. the computer boots to the Grub menu and I pick Ubuntu it loads and goes to the log in screen. I log in and hit enter the screen goes black, a few lines of code pop up then it goes back to the log in screen. this is my first time with Ubuntu. I was able to go into vista fine. I decided to try to re-install Ubuntu thinking that it would overwrite what was on the computer but it just installed a second instance. The same thing happens with the log in screen on either instance and now I can't get into vista. I would like to use Ubuntu on that laptop but how do i get Ubuntu to continue past the login?  I looked at the listings of this being a duplicate question. I changed the install to a solo install of 14.04 Ubuntu. I get to the log in screen and still not able to log in as user or guest. I did ctrl-alt-f1 and logged in on the shell. I can run commands on the shell. I tried the chmod and chown command lines listed on the duplicate. when i shift back to the log in screen still no luck. I tried the install-session and that didn't work. I noticed that when I ran the sudo command the prompt stayed at $ instead of switching to #.   Have there been issues with Unity desktop on an Nvidia video card? what command line sequence do i use to download the Unity desktop with nvidia drivers?  I am using a compaq presario cq60 laptop.


What makes lead-free solder harder to use?

Soldering in a RoHS-compliant way normally means using a solder that does not contain lead - the metal that made up most part of common solder before.  Handsoldering using lead-free solder seems to be harder. Possibly it also makes industrial soldering methods "harder" (as opposed to just different)?   What are the practical difficulties that arrise in comparison to using "classic" solder?   What causes these difficulties? How can they be handeled or worked around?


DHL Notification - Receive package without ordering

Today, I receive a notification from DHL that a company named Brand Addition Gmbh Hagen, that they have sent me a package. I have neither heard of the company, nor ordered anything from them. I also dont expect any package at the moment. This company knows my full name (which i dont use for online shopping) and my address. Can anyone please tell me if this has ever happened to you and if this is a scam? I´m thinking about not receiving the package and it will be automatically returned to the company after 7 days.


USB Flash drive partition encryption for OSX, Windows and Ubuntu

Is there a filesystem and encryption combination that works across the 3 operating systems? Assume OSX High Sierra, Windows 10, 16.04. Bonus round if you have successfully done this before (please state in reply).  Read / Write access is required.  It would be best if I could encrypt the flash drive so that it is not easily accessed if it were lost.  That being said it makes sense to select a combination of filesystem and encryption that works across the three platforms in my environment (if possible)


I'm making a map.  I want the player to create a stone button but they are on adventure mode so i need a command that makes it possible to be placed on something so when they make the button it can be replaced with a button that can be placed on dirt.


Prove that there exists such a set of $n$ positive integers

Prove that for any positive integers $m$ and $n$ , there exists a set of $n$ consecutive positive integers each of which is divisible by a number of the form $d^m$, where $d$ is some positive integer not equal to $1$.  I don't know how to approach this question.


p-value, intuition about type-I error=$\alpha$

In hypothesis testing consider this situation:  Define $\alpha=P\{\text{type I error}\}=P\{\text{ Rejecting } { H_0}\text{ when } H_0\text{ is true}\}$.  Also define $p-$value like this  What is the probability of observing a data which is similar to the one on hand, or more extreme, if $H_0$ happens to be true. This probability will be called the $p-$value.  How do I get some inutition about this: A test with a small $p-$value indicates that the null hypothesis is less plausible than the alternative hypothesis and in this case $H_0$ is rejected.


I am trying to create a regex for a currency in USD starting with any number of digits followed by 2 digits following a decimal point followed by a digits within round brackets. I want just the part before the round brackets. Like $179.29 (3). Output should be $179.29.


I’m an undergrad Interested in rigid body mechanics. I’ve already covered the material on kleppner’s book as well as Goldstein’s and I’m still doing some problems from Morin’s. I want to know where to find even more advanced material.


How can I remove a hline in a specific column?  I wish the first line did not have the hline  \begin{table}[h!] \resizebox{\columnwidth}{!}{% \centering \begin{tabular} {|c|c|c|c|c|c|c|c|c|c|c|c|c|}      \hline        \multirow{2}{5em}{Atividades} & \multicolumn{12}{|c|}{Meses 2019}\\       \hline       & Jan & Fev & Mar & Abr & Mai & Jun & Jul & Ago & Set & Out & Nov & Dez  \\      \hline       1 & X & X & &  &  & & &  &  & & & \\      \hline      2 & & & X & X & &  & &  &  & & &  \\      \hline      3 & & & & X  &  &  & &  &  & & & \\      \hline      4 & & & & X  & X &  & &  &  & & & \\      \hline      5 & & & &  &  & X  & &  &  & & & \\      \hline      6 & & & &  &  & X  & &  &  & & & \\      \hline \end{tabular} } \caption{Cronograma} \label{tab:Cronograma} \end{table}   Thanks


How to use __name__ == "__main__" to write a python script?

I have spent days to finish a simple python script, it layout like following:  import sys  several functions  infile = sys.argv[1]  # input file inconfig = sys.argv[2]  # input file outfile = infile.split(".")[0] + "_new.fxs" # output file  inputfile = open(infile, "r") inputconfig = open(inconfig, "r") outputfile = open(outfile, "w")  tmp_dict = getdict(inputconfig) # using a function named getdict  tmp_buffer = transblock(inputfile, tmp_dict.keys()) # using a function named transblock outputfile.write(tmp_buffer)  inputfile.close() inputconfig.close() outputfile.close()   By now, I use   python script.py inputfile inputconfig   in command window to run it. Yes, it works as expected.  I would like to learn more, could anyone show me how to use the symbol  __name__ == "__main__":   to coding this out as a expert? I means something like this:  import sys  several functions  if __name__ == "__main__":     statements     ...


Suppose $A=\{S\;|\;S \subset \mathbb R^n, S\text{ is Lebesgue measurable}\}$. What is the cardinality of $A$? Is it the same as the cardinality of all of the real numbers?


Checkers only repetitive moves left to opponent

If opponent only can move between the two diagonal squares in the "open" corner, does he lose? How many times can he makes these fruitless moves?


When iterating JSON with Javascript for...in, the final key returned is "remove"

This is a strange occurrence to be sure. First off, I'm using Chrome version 23.x and have not tried to reproduce this in other browsers yet.  I receive a JSON array from the server of the form:  JSON  { "layout":0, "caption":"Work History", "cols":[    {"field":"company","label":"Company Name","hidden":false,"order":-1,"validationType":2,"list":[]},       {"field":"date_start","label":"From","hidden":false,"order":-1,"validationType":1,"list":[]},    {"field":"date_end","label":"Until","hidden":false,"order":-1,"validationType":0,"list":[]},    {"field":"position","label":"Title","hidden":false,"order":-1,"validationType":2,"list":[]},    {"field":"description","label":"Description","hidden":false,"order":-1,"validationType":0,"list":[]},    {"field":"project","label":"Project","hidden":false,"order":-1,"validationType":64,"list":[]}    ] }   Then, I attempt to loop over the cols objects with Javascript"  Javascript  for (var c in json.cols) {     console.log("col name: " + c); }   Google Chrome's console prints the following:  Output  col name: 0 col name: 1 col name: 2 col name: 3 col name: 4 col name: 5 col name: remove   There should only be 6 outputs, first of all. Second, where does this final "remove" key come from? Why is it listed?


Strange Recurrence: What is it asymptotic to?

So I have the following recurrence relation for the growth rate of an algorithm:  $T(n)$ = time taken by algorithm to solve problem of size n:  $$T(n) = T(n-1) + T(\lceil(n/2)\rceil)$$  Clearly this does not obey any polynomial law but now my question is what does it obey?  I merely want an asymptotic equivalence.  My guess is subexponential since this is faster than polynomial but clearly slower than any exponential form.  What though is the question....


Currently in our game we use a 4 directional movement. Some abilities are triggered on mouse click and "fired" in the direction the player has clicked. For this, I have split the screen in 4 sectors (like 2 diagonal cuts) to determine in which general direction the player has clicked.  Back then, I found a short helper class for this:  public static class Triangle {     private static Vector2 topLeft = new Vector2(0, 0);     private static Vector2 topRight = new Vector2(Orbs.graphics.PreferredBackBufferWidth, 0);     private static Vector2 bottomRight = new Vector2(Orbs.graphics.PreferredBackBufferWidth, Orbs.graphics.PreferredBackBufferHeight);     private static Vector2 bottomLeft = new Vector2(0, Orbs.graphics.PreferredBackBufferHeight);      //Return true if p1 and p2 are on the same side of BA     private static bool SameSide(Vector2 p1, Vector2 p2, Vector2 A, Vector2 B)     {         // Convert points to Vector3 for use the Cross product, which is Vector3-only         Vector3 cp1 = Vector3.Cross(new Vector3(B - A, 0), new Vector3(p1 - A, 0));         Vector3 cp2 = Vector3.Cross(new Vector3(B - A, 0), new Vector3(p2 - A, 0));         return Vector3.Dot(cp1, cp2) >= 0;     }      //Return true if the point p is in the triangle ABC     private static bool PointInTriangle(Vector2 p, Vector2 A, Vector2 B, Vector2 C)     {         return SameSide(p, A, B, C) && SameSide(p, B, A, C) && SameSide(p, C, A, B);     }      public static string GetAndSetPlayerOrientationByClickedSector()     {         Vector2 playerCenter = new Vector2(//getPlayerCenter);         Vector2 mouseWindowPos = Microsoft.Xna.Framework.Input.Mouse.GetState().Position.ToVector2();          if (PointInTriangle(mouseWindowPos, topLeft, playerCenter, topRight))             return "North";          if (PointInTriangle(mouseWindowPos, topRight, playerCenter, bottomRight))             return "East";          if (PointInTriangle(mouseWindowPos, bottomRight, playerCenter, bottomLeft))             return "South";          if (PointInTriangle(mouseWindowPos, topLeft, playerCenter, bottomLeft))             return "West";          return "";     } }   Now, we are extending our movement in eight directions and therefore I need to extend this helper class to return the diagonal directions (SouthEast and so on) as well.  I am not even sure if this is doable properly with this approach, but I guess I only need to define the points of the additional triangles. Any suggestions on how to solve this are welcome.


How do I remotely wake my Mac over Wi-Fi?

I am running a server on my Mac mini at home (using the OS X Server app). I would like to access my home network using it's VPN server, but I understand that I can only do this while it's awake. I have already configured my Mac's server to use its IP address for Wi-Fi (for some DNS settings etc), and so connecting it via ethernet would mean that I would have to change quite a few settings...  I'm running OS X Mountain Lion 10.8  How can I do this without having to connect my Mac to my router via ethernet?  I've searched the site and can't find an answer that makes sense to me since they appear out-dated.


What is the perception of students who take a gap year between their graduation and starting graduate school?

I am an undergraduate mathematics major, entering my fourth year. I plan on applying to graduate school, but I have not yet taken the GRE exams, and there a few key courses (Topology and Algebra in particular) that I have not taken yet, so I am hesitant to take the Advanced Math GRE too soon. (If you're wondering why I haven't taken Topology and Algebra yet, it's because I was trying to secure a CS degree, which sidetracked my mathematical studies last year. It was a healthy branching out experience, and one that helped me realize my true academic passion.)  My main question: what is the perception of students who take a gap year between their graduation and starting graduate school?  I think I will take the GRE tests this fall, a) for practice and b) if I score high, then I might as well apply sooner rather than later. However, I ask this question to gauge how much energy I should put into preparing for the tests this fall. If I hear, "You should really do your best to avoid any gap in your education," then I will work my butt off in preparation for the tests. But if I hear, "It's totally okay take a gap year before going into graduate school," then I would give myself more freedom in terms of my non-standardized-exam studies, extracurriculars, and in general social activities. I figure the answer to this question won't be as cut-and-dry as I hope, but any advice would be appreciated!  Just to clarify, my gap year would not consist of me sitting at my desk taking practice GRE exams all day... That would be a pitiful use of my time. I definitely plan working either as an intern or a research assistant at a successful organization. It seems like the general consensus is that taking time off is okay, and potentially beneficial, assuming you actually do something in that gap.


Hyperref adds vertical space to equation environment

When the length of the text prior to an equation environment approaches \textwidth, hyperref adds an extra vertical space, as illustrated by the following snapshot:    The corresponding code is  \documentclass[12pt,fleqn]{article} \usepackage{a4} \usepackage{amsmath} \usepackage{hyperref}  \textwidth = 16cm \setlength{\parskip}{1.5ex plus0.5ex minus0.5ex} \setlength{\parindent}{0em}  \begin{document} Suppose $\vec{T}$ is a lower triangular matrix. Then $\vec{T}^{T}$ is upper triangular. By Lemma 2.23921, \begin{equation}     \det(\vec{T}) = \det(\vec{T}^{T}) = [\vec{T}]_{11}[\vec{T}]_{22}\dotsb[\vec{T}]_{nn}, \end{equation} as required. \end{document}   Note that it seems to affect the equation environment only.  Since there is no apparent way to predetermine the occurrence the problem in the source code,  I will have to manually scan the output text for the affected parts and replace equation with other math environments, such as gather, to circumvent the problem; clearly, this approach is suboptimal.  So, the question is, why does it only affect the equation environment but not other math environments? Is there a way fix this?


How does electrical current have energy? (when electrons move very slowly through circuit )

I'm interested to know how electric current carries energy. I understand that the huge amount of electrons pass at one point through conductor, but they move slowly. So I do not understand how much energy they have.


Where to install the pgflibraryqrr.shapes files when using MiKTeX in Windows

I am trying to run the code found , but I get the error. I did not find the pgflibrary 'pgflibraryqrr.shapes.openrectangle.code.tex'.....  I put the files in the directory   C:\Program Files (x86)\MiKTeX 2.9\tex\generic\pgf\libraries\shapes  and did a Refresh FNDB in MiKTeX but I could not get the file to compile.  Can you tell me where I need to put the tikzlibraryqrr.shapes.openrectangle.code.tex file?  Thanks.  Here is the original code found :  \documentclass{book} \usepackage[explicit]{titlesec} \usepackage{fourier} \usepackage{tikz} \usepackage{epigraph} \usepgflibrary{qrr.shapes.openrectangle}  \definecolor{mybluei}{RGB}{0,173,239} \definecolor{myblueii}{RGB}{63,200,244} \definecolor{myblueiii}{RGB}{199,234,253}  \tikzset{ mynode/.style={   rounded corners=30pt,   shape=open rectangle,   open rectangle fill=myblueii,   open rectangle sides=#1,   } }  \titleformat{\chapter}[display]   {\normalfont\huge\sffamily}   {}   {20pt}   {%   \begin{tikzpicture}[remember picture,overlay]   \node[     anchor=west,     rectangle,     minimum height=4cm,     text width=\paperwidth,     xshift=-\the\dimexpr\oddsidemargin+1in\relax,     outer sep=0pt,     fill=myblueiii] (titlerect) {};   \node[     anchor=south west,     xshift=2cm,     text width=\textwidth]      at ([yshift=5pt]titlerect.south west) {\fontsize{30}{36}\selectfont#1};   \node[     mynode=nw,     anchor=south east,     fill=myblueii,     inner xsep=1.5cm,     outer sep=0pt,     font=\color{white},     minimum height=30pt]      at (current page.east|-titlerect.north)      {\bfseries\MakeUppercase{\chaptertitlename}\ \thechapter};   \end{tikzpicture}%   } \titleformat{name=\chapter,numberless}[display]   {\normalfont\huge\sffamily}   {}   {20pt}   {%   \begin{tikzpicture}[remember picture,overlay]   \node[     anchor=west,     rectangle,     minimum height=4cm,     text width=\paperwidth,     xshift=-\the\dimexpr\oddsidemargin+1in\relax,     outer sep=0pt,     fill=myblueiii] (titlerect) {};   \node[     anchor=south west,     xshift=2cm,     text width=\textwidth]      at (titlerect.south west) {\Huge#1};   \end{tikzpicture}%   } \titlespacing*{\chapter}   {0pt}{-20pt}{60pt}  \setlength\beforeepigraphskip{1.5\baselineskip} \setlength\afterepigraphskip{2\baselineskip} \setlength\epigraphwidth{6.8cm} \setlength\epigraphrule{0pt} \renewcommand\epigraphsize{\large} \renewcommand\textflush{flushright}  \let\oldepigraph\epigraph \renewcommand\epigraph[2]{%   \oldepigraph{\color{mybluei}\itshape #1}{#2}}   \begin{document}  \chapter{From the Ground Up!} \epigraph{In theory there is no difference \\ between theory and practice. \\ In practice there is.}{Lawrence ``Yogui'' Berra,1925 \\ New York Yankees baseball player} \chapter*{A test unnumbered chapter}  \end{document}


Inequality involving inner product and norm

If $\|\cdot \|$ is the norm induced by the inner product $\langle,\rangle$, how to prove the following interesting inequality? $$\langle x,y\rangle(\|x\|+\|y\|) \leq\|x+y\|\,\|x\|\,\|y\|$$  This is a exercise in my textbook which is available only in portuguese called "Topologia e Análise no Espaço $\mathbb{R}^n$". The above inequality is obvious when $\langle x,y\rangle \leq 0$, but I don't know how to proceed to prove the other case.


Find all integers $x$ and $y$ such that $4y^2=x^7+1$.    I first subtract one from both sides to get $4y^2-1=x^7$, which can be factored into $(2y+1)(2y-1)=x^7$. From here, I can not proceed.   Any ideas?


What is a method for importing/exporting DXF files with QGIS? I work in an engineering field and we use CAD and specialist design programs, and often go through several iterations during a project. I am having trouble interchanging data between QGIS and DXF formats.  I export several layers from QGIS in DXF format and load them into cad.  Essentially I xref the exported DXF files into CAD, and then draw over the top of them in CAD, as I find it quicker and more accurate.  The files line up OK, but need to be scaled and transformed to match the coordinates in QGIS.  I then detach the xref's, save the new DXF with line work on a single layer.  The DXF file coordinates match the QGIS coordinates. I can't seem to get the new DXF to import back into QGIS.  I would like to be able to export and import a particular data table several times as the project develops. Screenshot 1 - I exported the pink polygons and edited them in CAD.  I then imported the DXF file back in but nothing came in - see "entities".  Screenshot 2 - Attribute table of imported layer.


How can I find the following problems using elementary trigonometry?  $$\lim_{x\to 0}\frac{1−\cos x}{x^2}.$$  $$\lim_{x\to0}\frac{\tan x−\sin x}{x^3}. $$  Have attempted trig identities, didn't help.


$(xy + 1)(yz + 1)(zx + 1) $ is a perfect square if and only if each factor is

Show that if $x, y, z$ are positive integers, then $(xy + 1)(yz + 1)(zx + 1)$ is a perfect square if and only if $xy + 1, yz + 1, zx+1$ are perfect squares.


I am working on a project which runs on ArcGIS platform using VB.NET. It is to model a sub-surface fault plane (currently a plane rectangular model with some dip) and then to find required distances from various points on surface of the earth. These distances are not necessarily nearest distances.   One idea I got and decided to use is TIN network.   I want to know if this is productive given that the number of points I know on surface would be only 5.   Is there any better option to model this?   And one more point I want to remind is that we can not model perfectly vertical faults using that.


Help! Most of my project doesn't show, but still renders

Please see the attached video, I've got no clue what happened.


An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$

I am looking for an example of a group $G$ where the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$, but $G$ is not an abelian group. I've started do some calculations in the group $D_{4}$ (I gave up!) Do you know where I can find that example? Is it possible find such example without doing a lot of calculations?  Thanks for your help!


Eclipse Neon freezes and crashes computer on Ubuntu 16.04

I did a fresh install of Ubuntu 16.04 (64 bit, 4.4.0-31-generic) and downloaded the eclipse neon installer and installed eclipse (not as root) in the ~/opt/ directory I created. Eclipse works fine and I am programming in Java, but after a little while (sometimes a few minutes, sometimes 30 minutes) eclipse suddenly crashes. My mouse moves but I can't click anything anywhere. About 10 seconds later the mouse also crashes and stops moving and the computer becomes unresponsive, and which point I have to hold the power button to turn off the laptop and start it up again.   Any ideas what this might be or possible fixes? I've tried reinstalling eclipse (by removing the installation directory and reinstalling), I've redownloaded the installer again also but no luck. I haven't experienced this problem with other applications yet so I'm presuming it's an eclipse problem.  I've installed openjdk-8-jre and openjdk-8-jdk.  EDIT: Apparently it's been marked as a duplicate question as what to do when Ubuntu crashes, but this issue has been arising while using eclipse. I'm not asking what I should do when it crashes, I'm asking what I should do to stop it crashing in the first place.


If $E_1, E_2$ are connected and $A_1\subseteq E_1$ and $A_2\subseteq E_2$ then $(E_1\times E_2)-(A_1\times A_2)$ is connected

Let $E_1$, $E_2$ connected metric spaces. Let $A_1\subseteq E_1$ and $A_2\subseteq E_2$ proper subsets. Show that the complement of $A_1\times A_2$ $$(E_1\times E_2)-(A_1\times A_2)$$ is connected.  I have tried to perform the test using the result that says if $A, B$ are connected and $A\cap B\neq \varnothing$ then $A\cup B$ is connected.  Note that  $$(E_1\times E_2)-(A_1\times A_2) = \left[E_1\times(E_2-A_2)\right]\cup\left[(E_1-A_1)\times E_2\right]$$ So it suffices to prove that the sets $E_1\times(E_2-A_2)$ and $(E_1-A_1)\times E_2$ are related and non-empty


Is there a way to format a grid in markdown?

I want to add a grid in one of my answer, but I can't find the format to do that. Is it possible ?


Ralink MT7601U (148f:7601) Wi-Fi adapter installation

I am trying to install a Ralink wifi adapter in Ubuntu Desktop 14.04.  The system is not detecting the wifi.   lsusb lists the device as:  Bus 002 Device 004: ID 148f:7601 Ralink Technology, Corp.  I have the rt2800 USB driver listed in "/etc/modules"; Following some instructions on the web, I tried this command:  echo 148F 7601 | sudo tee /sys/bus/usb/drivers/rt2800usb/new_i  lsmod | grep rt2800 returns the following:  rt2800usb              26581  0  rt2x00usb              20041  1 rt2800usb rt2800lib              83150  1 rt2800usb rt2x00lib              48886  3 rt2x00usb,rt2800lib,rt2800usb mac80211              545990  3 rt2x00lib,rt2x00usb,rt2800lib crc_ccitt              12627  1 rt2800lib


I am trying to create a Cholorpleth map using Processing and geoJSON. I am having difficulty cycling through my HashMap to check the property that will dictate the intensity of the polygons color.  Currently this is my code:  void draw() {   map.draw();   for (int i = 0; i < countyMarkers.size(); i++) {    Marker county = countyMarkers.get(i);    String pop = countyData.get("pop").toString();    println(i + "pop: " + pop);    }   What I would like to do is loop through my HashMap countyData and get the population of each entry. Use an if statement to compare it to a value and then assign it the color based on the statement that is true.  My HashMap can be seen here:  {name=Carlow, pop=54,612} {name=Cavan, pop=73,183} {name=Clare, pop=117,196} {name=Cork, pop=519,032} {name=Donegal, pop=161,137} {name=Dublin, pop=1,273,069} {name=Galway, pop=250,541} {name=Kerry, pop=145,502} {name=Kildare, pop=210,312} {name=Kilkenny, pop=95,419} {name=Laois, pop=80,559} {name=Letrim, pop=31,796} {name=Limerick, pop=191,809} {name=Longford, pop=39,000} {name=Louth, pop=122,897} {name=Mayo, pop=130,638} {name=Meath, pop=184,135} {name=Monaghan, pop=60,483} {name=Offaly, pop=76,687} {name=Roscommon, pop=64,065} {name=Sligo, pop=65,393} {name=Tipperary, pop=158,754} {name=Waterford, pop=113,795} {name=Westmeath, pop=86,164} {name=Wexford, pop=145,320} {name=Wicklow, pop=136,640}   I am relatively new to working with this type of data so I am at a loss as to where I am going wrong. I think my logic is correct I am just not sure how to implement it.  I'd appreciate any help on the issue.  Currently this line -> println(i + "pop: " + pop);   Outputs the last entry of the hashmap over and over.  This is the output I am getting  0pop: 136,640 1pop: 136,640 2pop: 136,640 3pop: 136,640 4pop: 136,640 5pop: 136,640 6pop: 136,640 7pop: 136,640 8pop: 136,640 9pop: 136,640 10pop: 136,640 11pop: 136,640 12pop: 136,640 13pop: 136,640 14pop: 136,640 15pop: 136,640 16pop: 136,640 17pop: 136,640 18pop: 136,640 19pop: 136,640 20pop: 136,640 21pop: 136,640 22pop: 136,640 23pop: 136,640 24pop: 136,640 25pop: 136,640   I populate my HashMap using this method.  void getCountyDetails(List<Marker>m) {     countyData = new HashMap();   for (Marker county: countyMarkers) {     countyData.putAll(county.getProperties());     println(countyData);   } }   Modified code here      Set<String> keySet = countyData.keySet();   for(String pop : keySet){      String value = countyData.get(pop).toString();      println("population:" + value);    }   Now It is outputting:  population:Wicklow population:136,640 population:Wicklow population:136,640 population:Wicklow population:136,640 population:Wicklow population:136,640 population:Wicklow population:136,640 population:Wicklow population:136,640 population:Wicklow population:136,640 population:Wicklow population:136,640 population:Wicklow population:136,640   It still does not seem to be iterating through each entry in the HashMap  New way Of populating HashMap  void getCountyDetails(List<Marker>m) {     countyData = new HashMap();   int i = 0;   for (Marker county: countyMarkers) {     countyData.put(i,county.getProperties());     i++;   } }


Lists with Parent Child Relationshiips - add records

I am creating a CRM system in SharePoint 2010, and I would like to be able to have the main list have the customers, and then sub lists with contact information, notes information, task information and libraries.  I would like to have a page that shows the profile of the customer with webparts of each of the associated items, and when I add an item, I want it to automatically know who the customer is and associate it to the correct customer.


everybody!  I have a list of 250 genes whose expression was measured in 21 samples. I want to discover which gene pairs are positively correlated. So, I performed Pearson correlation for these genes using the "rcorr" function of the Hmisc package (R). The output gives me the r and p-values. What I want to know is: do I have to perform p-value correction, like Bonferroni or FDR? In the case of an affirmative answer, which R package would be the best option to perform this task?  Thank you!


I'm stuck with a problem for an upcoming abstract algebra exam. Here it is:  Prove that if $N$ is a subgroup of a group $G$ and $[G\::\:N]=2$, then $N$ is normal in $G$.  I know that the fact that the index is two means that there are exactly two cosets of $N$ in $G$, but I'm stuck from there. Thanks for any help!


C++ static member of class template -- linker warning "multiple definition"

Let's say for some reason, I want to have a class template MyTemp with some static data member smDummyVar :  Mytemp.h  #ifndef MY_TEMP_H #define MY_TEMP_H  template<class T> class MyTemp{ ... private:    static int smDummyVar;    ... };  #include "MyTemp.cpp"  #endif //MY_TEMP_H   Mytemp.cpp  ... template<class T> int MyTemp<T>::smDummyVar = 0; ...   Since the compiler requires that the definition and declaration of a template be at the same place, so I include MyTemp.cpp in MyTemp.h .  Now: I want to use MyTemp at many places and create objects using the template:  case1.cpp  #include "MyTemp.h"  void dummyfunc1(){     MyTemp<int> myTemp1; }   case2.cpp  #include "MyTemp.h"  void dummyfunc2(){     MyTemp<int> myTemp2; }   I won't get any error from the compiler, but I'd get warning from the linker:  "multiple definition for MyTemp<int>::smDummyVar" ... defined in invalid_group(case1.o) ... rejected in favour of symbol defined in ...(case2.o)   Question: how can I get rid of this warning ?  Thanks a lot in advance for your help !  ====================================  inspired by one of the answers in this thread  I found the following solution:  i. remove #include "MyTemp.cpp" in MyTemp.h  ii. specialized.h  #include "MyTemp.h" typedef MyTemp<int> MySpecialized;   iii. specialized.cpp  #include "MyTemp.cpp" template class MyTemp<int>;   iv. give specialized.cpp to cmake file  v. include specilized.h in case1.cpp and case2.cpp  the "multiple definition" warning issued by the linker will go away.  Thank you guys for helping !


How to obtain a consolidated system wide history irrespective of users or powers?

If I am a normal user and I type  history   I get a set of commands typed by me in the terminal.  Now I make myself the sudo su (su stands for super-user here and not substitute user)  sudo su   I am typing again the history from the same terminal  history   I get a different set of commands which I had typed early.   I am working in a personal workstation.No one else handles the workstation. There are no users enrolled in the workstation other than me. Even if I obtain su (super-user) privileges, i am going to be using with those privileges also.  Hence I would like to obtain a consolidated system-wide same history irrespective of superuser or normal user.  How to achieve this?


Where to load scripts or css from CDN, head or body?

Where should I put the code for CDN scripts or styles? In the head element or before the closing body tag?


I have a very simple code to insert data into database, also checks if already has same data in table  [HTML]        <title>nickname</title>
input nickname
     <form action="foo.php" method="post">         <input type="text" name="nickname" />         <input type="submit">     </form>     [PHP]  //foo.php if(isset($_POST['nickname']) && !empty($_POST['nickname'])) {     $nickname = $_POST['nickname'];      //Object Oriented way     $servername = "localhost";     $username = "root";     $password = "foo_bar";     $dbname = "nickname";      //check connection     $conn = new mysqli($servername, $username, $password, $dbname);      if($conn->connect_error) {         die("cannot connect:".$conn->connect_error);     }      $sql = "SELECT * FROM nickname WHERE nickname='$nickname'";     $result = $conn->query($sql);      if($result->num_rows > 0) {         echo "nickname exists!";     } else {         $sql = "INSERT INTO nickname(nickname) VALUES(".$nickname.")";         $conn->query($sql);         echo "welcome $nickname!";     }      $conn->close();  } else {     echo "please input your nickname"; }   I am still learning how to use MySQL, what am I doing wrong? especially this line  $sql = "INSERT INTO nickname(nickname) VALUES(".$nickname.")"; $conn->query($sql);   the data in the variable is not inserted to table, nothing happens. but if I replace $nickname to plain text the data is inserted.  edit why is this a duplicate? the question is not even about "how to prevent sql injection"


Math in subsection title and incorrect PDF sections' sidebar

I have a subsection named \subsection{$Rp_{\widehat{Y},*}(\mathcal{P})$ has property bla and bla}. I would like to keep this as title of my subsection, but it creates problems.  My code is the following.  \documentclass[a4paper,12pt,oneside]{article}  \usepackage{amsthm} \usepackage{amssymb} \usepackage{amsmath,amscd} \usepackage[english,italian]{babel} \usepackage{latexsym} \usepackage{graphicx,subfigure} \usepackage[a4paper,top=30mm,bottom=30mm,left=30mm,right=30mm]{geometry} \usepackage{tikz} \usetikzlibrary{matrix,arrows,decorations.pathmorphing} \usepackage{hyperref} \usepackage{accents}  \usepackage[babel]{csquotes} \usepackage[maxnames=99,style=alphabetic,backend=bibtex]{biblatex}  \begin{document}  \subsection{$Rp_{\widehat{Y},*}(\mathcal{P})$ has property bla and bla}  \end{document}   If I keep it like this, it compiles giving multiple warnings about "Token not allowed in a PDF string". In this case the main problem is that the sidebar index of sections of the outcome PDF carries "RpY"0362Y,*P bla and bla" instead of the correct title with the math.  Furthermore, if I replace \widehat by \hat, it gives the error "Tex capacity exceeded", and it does not compile.  If I replace \subsection{$Rp_{\widehat{Y},*}(\mathcal{P})$ has property bla and bla} (or the version with \hat) with \subsection[just text]{$Rp_{\widehat{Y},*}(\mathcal{P})$ has property bla and bla} then I get no error. On the other hand, I still don't get what I want in the sidebar, since I would really like the math to be there as well.  How can I have the PDF compiling correctly and carrying the right math on the sidebar as well?


Why does Ubuntu detect two screens when I have only one?

which is annoying, because when I take screenshot it takes screenshot from both screens (from an existing one and a non-existing one).


Looking for a rigorous linear algebra book

I'm a mathematics undergrad student who finished his first university year succesfully. For this post, it should be interesting to note that I already took a course in group theory.  I also had a course in linear algebra where we treated the following topics:  1) Vector spaces; basis; span; linear dependency; direct sum   2) Linear transformations, matrices, rank  3) Linear varieties, system of linear equations  4) Determinants  5) Eigenvalues and eigenvectors, diagonalisation, triangalisation, cayley-hamilton,  6) Euclidean spaces: inner products, norm, hermitian transformations, orthogonal basis, Gramm-Schmidt, orthogonal transformations  7) Prehilbert spaces  8) Isometries  9) Bilinear forms and quadrics in $2$ and $3$ dimensions  Now, I want to revise these topics, but it would be too boring to reread these books again, so now I look for a book that has all these topics, but also some additional requirements:   Focus on intuition (e.g. connections between linear algebra and geometry). This is a hard requirement for me, since there was no attention given to this in the course I took) Additional topics such as Jordan form of matrices, quotient vector spaces, ... Good exercises (preferred with solutions somewhere) The book must be rigorous   In the course I had, we mainly discussed finite-dimensional vector spaces, but I am also interested in a theory of infinite dimensional vector spaces.  Can someone hint me towards a good book that would suit me? If I have to add any information, please leave a comment and I will edit my post.  Thank you for your time.


Hide an object from reflecting in the ocean modifier

I'm new to Blender and just following . I wanted to put a bit of my own stamp on it and got this grid set up at the top to give it an 80s vibe:  But its making a mess of my ocean. I want to have the pink grid object in the top to be hidden from being reflected in the ocean modifier plane below. I tried searching and looking for how to hide an object, turn off the shadows, etc. I thought maybe I could add a plane in between that would work as a one way mask - you can see the orange plane outlined which has a holdout material shader applied to it and backface culling on so I can see through this side, but it didn't stop the ocean still getting a peek. Can anyone point me in the right direction? Is it possible? (Update, I've been using Eevee to render this)


The chart produced by below code is too wide. How can I make it small enough to fit the page?  \documentclass[12pt]{article} \usepackage{pgfgantt}   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document}  \begin{ganttchart}[vgrid={draw=none,draw=none},%             %today=15,%             %today offset=.5,%             %today label=Heute,%             %progress=today,%             bar incomplete/.append style={fill=red},%             progress label text=  {\quad\pgfmathprintnumber[precision=0,verbatim]{#1}\%}%             ]{1}{36} \gantttitlecalendar*[compress calendar,time slot format=isodate]{2015-11-1}{2018-10-30}{year, month} \\ \gantttitlelist{1,...,36}{1}\\ \ganttgroup{Total Duration}{1}{36} \\  %%%%%%%%%%%%%%%%%Phase-1 \ganttgroup{Phase 1}{1}{12} \\ \ganttbar{Scope Reading}{1}{2} \\ \ganttlinkedbar{Literature Review}{2}{5} \ganttnewline \ganttlinkedbar{Define Scope of Review}{5}{6} \ganttnewline \ganttlinkedbar{Search for Relevant Literature}{6}{10} \ganttnewline \ganttlinkedbar{Classify the Documents}{10}{12} \ganttnewline %%%%%%%%%%%%%%%%%Phase-2 \ganttgroup{Phase 2}{12}{24} \\ \ganttlinkedbar{Solver Analysis $\&$ Formulation}{10}{15} \\ \ganttlinkedbar{Development of source code}{15}{16} \ganttnewline \ganttlinkedbar{Purchase Equipment}{16}{18} \ganttnewline \ganttlinkedbar{Design Experimental Procedure}{18}{20} \ganttnewline \ganttlinkedbar{Run Experiments}{20}{21} \ganttnewline \ganttlinkedbar{Analysis of Experimental Data}{21}{24} \ganttnewline  %%%%%%%%%%%%%%%%%Phase-3 \ganttgroup{Phase 3}{24}{36} \\ \ganttbar{Solving Validation and Conclusion}{24}{27} \\ \ganttlinkedbar{Publications $\&$ Workshops}{27}{30} \ganttnewline \ganttlinkedbar{Defence of Study Work}{30}{33} \ganttnewline \ganttlinkedbar{Thesis Writing}{33}{36} \ganttnewline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{ganttchart} \end{document}


EM wave generation from different frames of reference

Take 2 observers and a charged particle,  Observer S is stationary to the particle and sees the electric field and no magnetic field as he is stationary to the particle.  Observer A decides to accelerate and decelerate over and over back and forth in front of the particle.  From A's frame of reference, it can be said, by the equivalence principal, that the particle is accelerating and decelerating in A's frame of reference and therefor should emit a EM wave.  So A sees a Em wave come off the particle.  But wait, S does not see any such thing, other than A moving back and forth...  What am I missing?? Thanks! Eric


How can I pipe the output of *all* entered shell commands into another? (e.g. pipe everything into 'lolcat')

Good Afternoon,  (OS X user)  I am specifically trying to pipe the output of every shell command I type into the ruby gem 'lolcat' (which makes the output to the terminal rainbow colored).  Is there a way to do this without explicitly aliasing command individually? I was thinking perhaps there might be a way to pipe anything before the return key is pressed , but I am not sure how to do this.  Your assistance is appreciated, as I am tired of looking at just one color in my terminal.


Why does going close to absolute zero take out friction?

I read in a physics book that when you get close to absolute zero, a liquid stops having friction. Why is that (if it’s even true, that is)?


Electric force much stronger than gravitational force?

It is commonly said that the electric force is much stronger than the gravitational force.  Indeed, Coulomb's constant $k_e$ is much larger than the gravitational constant $G$ but they are measured in different units so it is not a reasonable comparison.  With other units, it could be reversed.    Consider two electrons in space far from any matter.  There will be a tiny gravitational attractive and a much larger electric repulsion.    Consider two protons.  The electric repulsion will be the same.  The gravitational attraction will be much larger (than for the electrons) but still much smaller than the electric repulsion.    So, those observations support that the electric force is stronger.  However, now consider two neutrons.  The gravitational attraction is slightly greater than for the protons.  There is no electric repulsion or attraction.    Is there some absolute sense in which the electric force is stronger?


This seems to be a gotcha for me, I couldnt figure this out  >>> from collections import Counter >>> tree = [Counter()]*3 >>> tree [Counter(), Counter(), Counter()] >>> tree[0][1]+=1 >>> tree [Counter({1: 1}), Counter({1: 1}), Counter({1: 1})]   Why does updating one Counter updates everything?


I have come across this proof that is a bit tricky to me. The value of An is making it pretty hard. Prove if $\lim\limits_{n\to \infty} S_n = S$, then $\lim\limits_{n\to \infty} A_n = S$ where $A_n = \frac{S_1 + S_2 + \cdots + S_n}{n}$ ? I was thinking to use $\varepsilon-N$ definition but am pretty stuck.


Which literary device swaps ideas between clauses?

While thinking of an appropriate inscription for my dad’s headstone, the following phrase came to mind: “He served his country with honor, and honored his wife with love.” Can this sentence be described as being an example of any particular kind of literary or poetic device?


Weird selection problem, selected the unselecting one

I have no idea why I select goes wrong like this. Especially when I meet the situation is that I did not even touch any of its, it still selected by me.  Would anyone meet the same problem as like I do? and how to solve this, please?  I reinstalled and re-download the newer one, still the same. (using 2.79 and 2.79a)


Today I installed sound card drivers of my motherboard (Asus P6T SE), and now I have started hearing the things that are happening on my screen. When I scroll, or change windows, basically cause a redraw on screen, I hear noises kind of resembles each action. And I am not on drugs.  What causes this and how can I fix that?


Given a sample $ X_1,X_2 \dots X_{100}$ and the density function   $ f(x;\theta) = \frac{1}{\pi \cdot \left(1+\left(x-\theta \right)^2\right)}$ , find Fisher information for  $\hat{\theta}_{MLE.}$ My attempt: $L(\theta;x_1,x_2\dots x_{100}) = \prod _{i=1}^{100}\left(\frac{1}{\pi \cdot \left(1+\left(x_i-\theta \right)^2\right)}\right)\:$ $l$ = $\log(L) = -100*\ln(\pi)-\sum^{100}_{i=1}(\ln(1+(x-\theta)^2)$. $\frac{\partial }{\partial \theta}\left(\log(L)\right) = \sum_{i=1}^{100}(\frac{2(x_i-\theta)}{1+(x_i-\theta)^2}$ $\frac{\partial^2 }{\partial^2 \theta}\left(\log(L)\right) = \sum_{i=1}^{100}-\frac{2\left(-θ+x_i\right)}{1+\left(x_i-θ\right)^2}$ fisher's information : $I(\theta) = -E[\frac{\partial^2 }{\partial^2 \theta}\left(\log(L)\right)$ but I don't how to find the expected value, I tried to simplify it but that didn't help.


I have a power supply that buzzes when nothing is connected and is silent when there is a power drain. What could it be?  It's a PC power supply that I used to power an LCD through its 12 V line.


Trapping region for Nonlinear ODE system?

I need to find a trapping region for  $u'=-u+vu^2$  $ v'=b-vu^2$  with $b>0$.  I don't know what theory to use or in wich book I can find some examples to find optimal trapping regions.  Thank you very much.


How do I set conditions in QGIS (ie. temperature map, show only areas that meet certain condition (avg temp 9-21 celsius) ?  basically, I want my map to show only areas that meet the condition (certain temperature, certain hours of sunlight per years...) stuff like that. Would also be cool if I could overlap those.


What is it when we work on something too much to see any new errors?

Whether I write a long paper or presentation, or am reviewing one, after looking it it many times, it seems impossible to notice any additional issues. For example, I am helping a client prepare a document for external audit. I am one of the internal auditors asking for information to put in the document and reviewing to ensure that it meets the needs of the external audit. After many working sessions and revisions, I can no longer see any issues. My friends and co-workers say the same thing. That's one reason why we always have a 2nd (and 3rd) person review everything after it is "done". Every new reviewer finds something new. What is it called when we can't stop "reading between the lines", or whatever it is that keeps us from seeing more?


Whenever I try to install something, I get the same error:  Reading package lists... Error! E: Encountered a section with no Package: header E: Problem with MergeList /var/lib/apt/lists/repo.mongodb.org_apt_ubuntu_dists_bionic_mongodb-org_4.0_multiverse_binary-amd64_Packages E: The package lists or status file could not be parsed or opened.   I've tried to do the following:  sudo rm -r /var/lib/apt/lists/*     sudo apt-get clean && sudo apt-get update   which was the solution proposed in many places, but it didn't work. Does anybody know how to fix this?


Remove top and bottom margin in tabular (around lists)

If I create a table with several (short) lists, currently I'm using a table construction with enumitem to (almost) remove the left margin. Now I still have a rather large margin at the top and the bottom (above and below) of the itemize lists.   Is there any way I can instruct either the itemize list or the table to remove this margin as well?  Code example:  \begin{tabular}{|m{3cm}|p{5.5cm}|p{5.5cm}|}    \hline     Category 2 &     \begin{itemize}[leftmargin=*]         \item A         \item B     \end{itemize} &     \begin{itemize}[leftmargin=*]         \item C         \item F     \end{itemize} \\    \hline \end{tabular}


Can I create an iTunes account without a credit card?

I am trying to create a iTunes account for my younger cousin, but he does not have a credit card (he's too young). Tried Google, seems outdated on this issue.


When do two functions become equal?  I have stumbled over this definition of equality of functions in elementary real analysis.     Let $X$ and $Y$ be two sets. Let $f:X\rightarrow Y$ and $g:X\rightarrow Y$ be two functions. $f=g$ iff $f(x)=g(x)$ for all $x\in X$.   Of course, this definition is so standard and I have no problem with it. However, as far as I know, this definition is actually a theorem. It can be proved in ZFC set theory. A function is just a set of ordered pairs (with some conditions). Two sets are equal if they have the same elements (the Axiom of Extensionality). With this assumption, one can prove the above definition. However, the proof does not require that the ranges of $f$ and $g$ have to be the same.   Suppose that the ranges are different, let's say $f:\mathbb{R}\rightarrow\mathbb{R}$ defined by $f(x)=x$ and $g:\mathbb{R}\rightarrow\mathbb{C}$ defined by $g(x)=x$. If we consider these functions as sets of ordered pairs, then they are just the set $\lbrace (x,x):x\in\mathbb{R}\rbrace$. Thus they are equal by the Axiom of Extensionality. However, the equality also requires that if objects $a$ and $b$ are equal, then any property which is true for $a$ is also true for $b$. In this case, we know that $f$ is a surjective, but $g$ isn't. Thus $f$ should not be equal to $g$ and hence a contradiction. But this is not a proof by contradiction to show that the ranges must be equal, everything assumed here is just axioms of ZFC and what is equality itself. So it looks like it is inconsistent.  I have searched similar questions in this website, but there is no question or answer that relate to this. The most related answer would be $f$ and $g$ must have the same range so there would be no problem. But logically, this is just an additional assumption to restrict the ability to compare two functions. If they don't have the same range, then you can't compare it, or there will be a paradox. The problem for this answer is, it doesn't solve the above paradox. It just restricts itself to the situation that the paradox won't arise, but the inconsistency is still there.  Lastly, I found another way to solve this problem in a set theory book. In the book, when one considers surjection, one have to specify which set the surjection is over. For example, one has to say whether it's surjection over $\mathbb{R}$ or surjection over $\mathbb{C}$. In this case, the paradox won't arise because $f$ and $g$ are both surjective over $\mathbb{R}$ and not surjective over $\mathbb{C}$. Thus the surjective property are the same for $f$ and $g$. The only problem for this answer is, if one consider the property of 'surjection over its range' instead, then this property is true for $f$ but not for $g$, which implies that $f\neq g$ again.  When do two functions become equal in general? Can anyone clarify this for me?  Thank you in advance.


Too quick with the Close button for "Unclear what you're asking"

All too often I see questions getting closed by direct moderator action for "Unclear what you're asking", when it's obvious that English is not the asker's native language.  In many of those cases, with about 30 seconds of thought and careful interpretation, I'm able to figure out what the user is trying to ask and make an edit to clarify it on their behalf.  Often I can summarize the intent of the question in just one or two sentences.  I don't think I have any magical translation superpowers, so if I can do that, it follows that others can too.  But for some reason they hit the Close button instead.  So I guess I'm asking if mods can just take a little more time before hitting the Close button, and at least make an effort to interpret the question first (or give the community a chance to do so - often this happens within 5 minutes after the question has been asked).  I know that sometimes it's hopeless, and I'm not saying bad questions should get a free pass just because the asker isn't a native English speaker.  But we need to understand that not everyone is fluent in English and have a little patience with them.  Asking them to clarify the question often won't help, because they've already expressed it as clearly as they are able within the confines of their limited grasp of the language.  A question that shows thought and an attempt to solve the problem shouldn't be closed simply because of the author's lack of English skills.  The edit button is there for a reason.  Whenever I make an edit to clarify a question like that, I put my attempted translation at the top, then leave the original wording below in case I got it wrong and someone else (or the OP) has a different interpretation.  I clearly mark my translation and the original question so it's obvious which is which.  I rarely spend more then a minute on this, but by the time I've finished editing the question I find that it's already been closed, and now the OP can't get the answers they're looking for until (and unless) the question gets reopened (which often doesn't happen, or by the time it gets reopened the OP has already given up in frustration).  Slow down and think before hitting that Close button.  Try to interpret the question first, and submit an edit to help clarify it if you can.  If you can't, wait a while to give the community a chance to do it - someone else might have better interpretive skills than you do.  If a day goes by and the question still hasn't gotten a better translation, THEN consider the Close button.  But consider it carefully - don't use it unless it's absolutely necessary.


can't change associated app for file (from Property) to Notepad++

I don't know, even after reinstalling the Windows the same happens - I can't change  the associated program from right click > Properties when I want to change that to Notepad++ (for others, it works).  Even after I click "OK", it still doesn't work (is not changed):    Any known bugs for this?


In Star Wars: The Last Jedi Supreme Leader Snoke says that      it was he himself who was connecting Rey and Kylo Ren via the force, minutes before Kylo Ren killed him.   But later on, on the planet Crait, Rey sees Kylo when she is about to board the Millenium Falcon. She closes the door in the apparition's face. How did this happen?      Wasn't Snoke, who was connecting them, dead?


Finding an equation for a circle given its center and a point through which it passes

No idea how to do this, I used to have these conic shapes committed to memory but I forget them already.   I am supposed to find an equation for the circle that has center $(-1, 4)$ and passes through $(3, -2)$.  I tried graphing it, but it didn't help since the point was not in a straight line with the center and I have no idea what the diameter is.


Openlayers 3 connecting to a wms feed with a different projection

I am trying to incorporate a wms feed in the British national grid projection (EPSG:27700) into a openlayers 3 project. I initially had used this wms layer in an openlayers 2 application using the following syntax:  new OpenLayers.Layer.WMS(         "ukimage",         "http://www.linktowms",         {             "LAYERS": 'ukimage',             "STYLES": '',             format: state.image_format         }, {     buffer: 0,     displayOutsideMaxExtent: true,     isBaseLayer: true } );   But I am having trouble converting this over to openlayers 3. I first tried setting the map projection to British national grid (view: new ol.View({ projection: 'EPSG:27700'}) as I had in the openlayers 2 app, but this produced the error  TypeError: h.B is not a function    and a white map.   When I try and use proj4 to convert the projection to EPSG:3857 as described here:  I get the same error:   TypeError: h.B is not a function    and again a white map.   my wms request is generally a varient of:  new ol.layer.Image({       source: new ol.source.TileWMS({         url: 'http://www.linktowms',         params: {'LAYERS': 'ukimage'},       })     }),   (I tried adding projection but that didn't help)  I am trying to work out if the image is even getting loaded from the WMS feed, but the syntax seems to have changed significantly from openlayers 2, instead of the properties and functions that have rather descriptive names, there are a now lots of short functions with names like Ua and Ig, which leaves me a bit in the dark as to what's actually going on when I try and inspect the layer with firebug.  I don't mind what projection the application is in, as I can re-project my other layers to match the basemap, so basically any way of using this EPSG 27700 WMS layer in openlayers 3 would be great.


Why can't I send a large file to a FAT32 formatted USB Drive?

Why can't my USB drive accept a large file, as in bigger than 3.50 gb, when it is formatted in FAT32?  My drive is a (16 gb) drive, but when I tried to send an ISO file to it while it was formatted in FAT32, it didn't accept it and showed a message that the file was too large. I reformatted my usb in NTFS and sent the ISO file again. This time the file was transferred successfully.  So why didn't it work when it was formatted in FAT32?


I'm a beginner QGIS user and am struggling with creating a grid. I've used the MMQGIS geometry import function to import data from the CSV file shown below but they pop up as points on QGIS. I want to make it into a grid so that I can pretty much have each of the points be in a box format. I've also tried to use the join function but am not sure what variable both the grid and the points have so that I can join them.


Why does subtracting a pointer value from an address result in gap of 8 times the pointer value?

In the following snippet, pointer addresses and values are referenced as the type size_t. However as the title says, the last subtraction does not make sense to me. It acts like, as if it subtracts the number multiplied with 8 instead of the actual value as seen in the int array.  #include <stdio.h> #include <stdint.h>  int main() {     int i[6] = {2, 0, 1, 0, 20, 24};      void *ptr = &i[2];      printf("%zu\n", ((size_t*)ptr));     printf("%zu\n", *((size_t*)ptr));     printf("%zu\n", ((size_t*)ptr) - *((size_t*)ptr)); }


Is the canonical morphism of sheaves $f^{-1}f_*\mathcal F\to \mathcal F$ an isomorphism?

Let $f:X\to Y$ be a closed immersion of topological spaces. Let $\mathcal F$ be  a sheaf of rings on $X$. Is the canonical morphism of sheaves $\varphi: f^{-1}f_*\mathcal F\to \mathcal F$ an isomorphism?


$n$ and $n^5$ have the same units digit?

Studying GCD, I got a question that begs to show that $n$ and $n^5$ has the same units digit ... What would be an idea to be able to initiate such a statement? testing $0$ and $0^5=0$ $1$ and $1^5=1$ $2$ and $2^5=32$  In my studies, I have not got "mod", please use other means, if possible of course.  I demonstrated in a previous period that $$2|n^5-n$$because $$n^5-n=(n+1)n(5n^4+5n+5)$$,  and$$5|n^5-n$$By Fermat's Little Theorem  Only I do not understand what should happen to the units of the two numbers are equal ... What must occur?


How do I Track Down a File's Location from Unity Search?

So my problem is that, while installing Eclipse, I created some desktop files in different locations, installing them all (I was trying to solve a bug, hence the need for repeatedly installing .desktop files. Somewhere along the line I must have created one in an alternate directory).  But anyways, my dilemma now is that when I search "Eclipse" from Unity Search I get two icons in the results. One is the one I wanted to use (i.e. the .desktop file with the correct settings, arguments), and the other is absolutely useless. However for the life of me, I can't figure out where the useless entry is located. I've tried just using Nautilus's search to find .desktop files, but it only gives me the correct .desktop file. I have no idea where the .desktop with the incorrect information is located; the only way I can locate it is through the search bar of Unity.  I'm reasonably sure that I've created a soft link to it in my bin; not sure though. Anyways, my question here is whether there's some way to locate files from Unity search. Dragging the result into Terminal doesnt seem to work, and the search feature is supremely unhelpful concerning file paths.  [Subquestion with no real answer]: I'm also looking for a better desktop environment. I really hate having to make .desktop files just to get a program into the Unity toolbar, and long for just being able to drag-and-drop a program in like Windows. Any help here?  Anyways, thanks!


Is the $ L^1$ norm continuous in the following sense?

Suppose I have $f \in L^1\cap L^\infty$, and I want to take the following limit $$\lim_{h\to0} \int|f(x+h)-f(x)|dx$$  Does this follow from the dominated convergence theorem? Since $|f(x+h)-f(x)| \leq |f(x+h)|+|f(x)|$, and $\|f(x+h)\|_{L^1(\mathbb{R})}<\infty$ and $\|f(x)\|_{L^1(\mathbb{R})}<\infty$, we then have $$\lim_{h\to0} \int|f(x+h)-f(x)|dx =  \int\lim_{h\to0}|f(x+h)-f(x)|dx = 0$$?  I'm not convinced, and I think a better argument would be to involve the density of continuous function in $L^1$. If the approach in this post does not work, can anyone explain why?


sudo must be owned by uid 0 and have the setuid bit set: what does it mean?

sudo fdisk -l  sudo: /usr/bin/sudo must be owned by uid 0 and have the setuid bit set   How to access permission to sda ( Primary HDD )


Need help finding a 1970-1980s (maybe early 90s) dark Space-SciFi Anime

For years I have been trying to find a anime scifi movie that I saw as a child. First and foremost, it is a movie. It is somewhat dark, maybe even towards horror but somewhat also adventurous. The main protagonist is a woman. A specific detail I recall that might help you identify this is that in a particular scene, this woman is isolated in a spaceship and there are odd things there, because first you see her I believe floating but asleep, and a scene later she has this weird headcrab (similar to ) on her face, but it looks more like a scrambled egg monster, really weird stuff. That is all that I can sort of recall. I have seen this in Europe around 1992-1995 ish, but back then in Europe we usually had movies and anime etc that were considerably older (late 70s, 80s), that is why I suggested even late 70s, 80s to early 90s. It was definitely dark, weird, had odd monsters like this headcrab thing that was suddenly on the girl’s head inside the space ship where she appeard to be completely alone.


Can I use my credit card a day before due date?

Payment due date of my credit card is on March 4th. And I already paid full amount of balance on Feb 26th. If I use my credit card today, which is March 3, should I pay another one by March 4?  (Hi,jamesqf. Even though I already paid, I thought I had to pay it again because it was the amount I used before the payment due date date.)


Generating a DEM and DSM from correct LiDAR point classification

I have downloaded classified LAS data from    I am trying to generate accurate DEM and DSM for further analysis. I created a LAS dataset with a projected CRS of  NAD_1983_UTM_Zone_19N in meters and the z CRS in meters as well. My question is on which classifications do I choose for the DEM and DSM. Here is the filter options I have in my dataset:     According to unh LiDAR data report class 2 is ground.     What I have done so far:  DEM I chose the class 2 points and used the las dataset to raster.   DSM In the predefined settings I chose first return and used the las dataset to raster tool.   Is this an accurate way of generating these two rasters? Do I not have to take into account the the unassigned class 1, noise class 7, reserved 11, reserved 17, reserved 18?  Additionally (I can ask this as a separate question if it gets requested to), when using the las dataset to raster tool the sampling value is defaulted to 10. I would like to change it to 2 or 3 (would be meters) to match the LiDAR resolution. I also plan on using the generated DEM and DSM for a least cost path analysis and I want them to be higher resolution. Will making the sampling_value 2 or 3 throw off the results or should I leave it at 10?


I am trying to empty an array passed to a function within javascript:  var a = [1,2,3];  function emptyArrayNo(ar) {     // the following does not empty the global array     ar = []; }  function emptyArrayYes(ar) {     // any of the following 3 methods empties the global array     ar.length = 0;     //ar.splice(0, ar.length)     //while(ar.length > 0) {ar.pop();}  }  emptyArrayNo(a); console.log(a); // returns [1,2,3]  emptyArrayYes(a);  console.log(a); // returns []   All the three methods within emptyArrayYes() seem to work, which I think is due to the reference to the array passed not being modified within the function. However when we set the array to [] within the function, I believe the reference changes therefore causing issues i.e. not being seen at the global scope. Can someone please clarify what is going on here? Thanks.


Can ArcGIS automatically round labels for a raster symbolised according to a classification?

I'm looking for a way to automatically adjust the reported precision of the label field for a float raster rendered in ArcGIS according to a classified symbology. Currently, the a classified raster symbology label is reported at the class break precision (8 decimal places).  I don't want to modify the class breaks itself, just round the reported break (e.g. to 2 decimal places) for producing a map layout.  I know I can modify the label manually but I don't want to have to do this for every class break and for multiple rasters.  Is there a setting automatically adjust the label?


I am having a difficult time with the following question. Any help will be much appreciated.     Let $A$ be an $n×n$ real matrix such that $A^T = A$. We call such matrices “symmetric.” Prove that the eigenvalues of a real symmetric matrix are real (i.e. if $\lambda$ is an eigenvalue of $A$, show that $\lambda = \overline{\lambda}$ )


I am using python to parse a JSON file, I know it is because of this ¥,   that I got this error when I was using json.loads  UnicodeDecodeError: 'utf8' codec can't decode byte 0xa5 in position 106: invalid start byte   But how do I get around it? Do I decode and encode again?  ¥ is the Chinese currency sign, but I am not sure which code category it belongs to.  Thanks!  update:  ====================  I think my question should be, If you see this symbol, how do you guess the encoding.  An answer to this question maybe:  If you see ¥, then "utf-8" won't work, try "latin-1" instead.  Is this understanding correct?


Can we get an indication comments are hidden between the comments?

When there are several comments some of them get hidden, which I don't mind, except when comments in the middle are hidden and I don't realize it till I get to the end. Then I have to unhide the comments and try to figure out which ones I haven't read.  The comments stay in order as they should so you can follow them but when you hide random ones in the middle you can loose the context of the comments until you unhide them all.  I have a couple of ideas that could help with this.  Put the Show X more comments at the top of the comments instead of the bottom  Put some indicator that there or hidden comments between these two  Comment this is the first comment Comment this is the second comment ... Comment this is the fourth comment, comment three is hidden indicated by the dots Comment this is the fifth comment ... Comment this is comment number nine, comment 6, 7, and 8 are hidden    Where the dots equals some indicator that there are hidden comment between two comments  Finally you could highlight the newly shown comments when you hit the unhide comments link like you do when you post your question.  Update  Just wondering if this could get a second look? Seems the community really likes the idea, and Jeff is ultimately who made the decision not to do it.


Can't sign up for meta.apple.stackexchange.com

I'm having difficulty signing up for meta.apple.stackexchange.com. When I click "signup" and choose my Google account, I'm taken back to the question without the typical flow of allowing access to Gmail info.  When I click on "comment", I'm asked to sign in with Google, but I'm immediately blocked for suspicious activity:    I don't think I've ever been blocked on the SE sites, and I know I have not offended anyone on Apple SE (yet?).  Should I be using Safari instead of Firefox? Or should I be using a different finger to press ENTER?  Or am I doing something else wrong?


Prove that time for planet to fall into the Sun equals $\left( \frac { 1 }{ 4\sqrt { 2 } } \right)$ of the planet's period

If a planet was suddenly stopped in its orbit supposed to be circular, show that it would fall onto the sun in a time $\left( \frac { 1 }{ 4\sqrt { 2 }  }  \right) $ times its time period.   I am getting stuck with this problem. I have applied conservation of energy and I think it may solve it. Please help. Here's my research on the problem:   Firstly, ${ T }^{ 2 }=\frac { 4{ \pi  }^{ 2 }{ r }^{ 3 } }{ GM } $. Assuming $v$ to be the velocity of the planet at a distance $s$ from the sun, we get: $\frac { m{ v }^{ 2 } }{ 2 } +\left( \frac { -GMm }{ s }  \right) =-\frac { GMm }{ r } $, where $r$ is the radius of the planet's orbit.


How Can I View All The Reputation Gained/Lost For One Specific Question

If I would like to view all of the reputation I have gained or lost due to one specific question of my own, how can this be done?  Is it possible for someone with, say, 421 rep on the site in question?


I'm looking for how to get FTPS working properly via FileZilla Server on an Azure VM running Windows 2012.  I've opened port 990 and configured FTP over TLS in FileZilla.  I have opened port 990 in both the firewall and the Azure portal interface and still cannot connect.  I'm attempting to connect using FileZilla client using FTPS login.  Has anyone succeeded in configuring an FTPS server (other than IIS) on an Azure VM?  I need separate user accounts and the ability to assign separate folders to save files to.  Any ideas?


How do I delete a previous recipient's email address from Mail?

I am trying to delete a friend's old email address so it doesn't automatically pop up when I enter his name while addressing an email. I have removed it manually from the address book, but it still shows up in Mail.  How do I stop this happening?


Is damage from multiple damage types cumulative for death and massive damage?

Scenario 1: A grimlock hits Alice with a Spiked Bone Club, dealing 5 bludgeoning damage, plus 2 piercing damage. Alice's HP was 12.   Using the optional Massive Damage rules on page 273 of the DMG, does this count as more than half the HP from a single source, or less than half, but twice?  Scenario 2: Assume the same grimlock hits Bob with the same attack, this time rolling 6 bludgeoning damage, plus 3 piercing damage. Bob's Max HP is 8, and he had 1 HP remaining before he was hit.  Using the Instant Death rules on page 197 of the PHB, does the character die, or are the two damage types tracked separately? Does the character have to make a death saving throw for the second part of the damage?


What does "end to end" mean in deep learning methods?

I want to know what it is, and how it is any different from ensembling?  Suppose, I want to achieve high accuracy in classification and segmentation, for a specific task, if I use different networks, such as CNN, RNN, etc to achieve this, is this called an end to end model? (architecture?) or not?


Let $t_n$ denote the $n$th triangular number. For what values of $n$ does $t_n$ divide $t_1^2+t_2^2+ \cdots +t_n^2$.  The hint says that because $t_1^2+t_2^2+ \cdots +t_n^2 = t_n(3n^3 + 12n^2 + 13n + 2)/30$, it suffices to determine those $n$ satisfying $3n^3+12n^2+13n+2 \equiv 0$ (mod 2*3*5). However, I don't see how to get $t_1^2+t_2^2+ \cdots +t_n^2 = t_n(3n^3 + 12n^2 + 13n + 2)/30$ this equiation in the first place. Also, I'm trying to solve the congruence $3n^3+12n^2+13n+2 \equiv 0$ for each mod 2, 3, 5 respectively but I have been unable so far to find the $n$ that satisfies these congruences. I would greatly appreciate any help.


how to create non linear presentation using beamer or prosper

8eamer prosper produces slides like power-point. Is it possible to produce non-linear presentation like the one produced by prezi?


Say I have a closed form expression for a divergent series and I can calculate as many terms in it as I want. What options have I got to obtain a meaningful result for this divergent series?


If $11 \gamma = \pi$ then prove that   $  \sec(\gamma) \sec(2\gamma) \sec(3\gamma) \sec(4\gamma) \sec(5\gamma) = 32. $   I could not use the relation $11 \gamma = \pi$.


My goal is to download all attachments of a given Case. I was managed to perform the needed queries to and I have a pointer to the ContentVersion object I need. They problem is that I don't know how to download the attachment. I believe I need the VersionData field, which holds the file in binary format. Another limitation that I have is that I'm using a Linux environment by means of its CLI prompt. I already made an authentication to SF by using SFDX API provided by SalesForce, but I cannot find a way to combine SFDX API with REST API's GET command to fetch the needed file so it will be downloaded to my Linux machine. Please advise. Uri


I want to perform a line density analysis for my line data, based on an attribute.   The heatmap option (kernel density analysis) seems to be only possible for point data.  I have tried to convert my line data into points, and create a heatmap, but the attributes for the weight were lost on the conversion.  This is a line density analysis performed with ArcGIS. I was looking to do the same with QGIS.    Is it possible to perform a similar line density analysis in QGIS?


I would like to estimate the log growth consumption for a database with full recovery model  for a particular transaction/group of transactions which is filling up my log drive. I would like to forcast this before a transaction is run.Is there a way to find this out in SQL Server(any version) Thanks in advance.


prescription.prescriptionDate gives me a proper date object prescription.prescriptionExpirationDate gives me a number (7, 14) Please keep in mind I am trying to get this done in-line. I am trying to add the number 7 or 14 into the date object and it should give me a new date object with the 7 or 14 days added into it. I am definitely doing something wrong as I get this error: TypeError: Cannot read property 'getDate' of undefined  Here's my code: <Typography variant="body2" component="p">     {new Date(prescription.prescriptionDate).setDate(prescription.prescriptionDate.getDate() + prescription.prescriptionExpirationDate).toDateString()}    </Typography>  Here's the code that works, to prove that I do get infact the prescription.prescriptionDate value correctly. <Typography variant="body2" component="p">         {new Date(prescription.prescriptionDate).toDateString()}        </Typography


I am  using ASP.net 3.5. A call to a Webmethod using JQuery returns valid JSON data. However when I call the same webmethod to populate a html table using the datatables.net JQuery plugin, I get back the entire html of the page.  **WebMethod:**  <WebMethod()> _          Public Shared Function GetData() As String         Dim a As String = "{""aaData"": [['Trident','Internet Explorer 4.0']]}"         Return a     End Function   **Successful JQuery call:**  $("#Result").click(function() {     $.ajax({       type: "POST",       url: "Default2.aspx/GetData",       data: "{}",       contentType: "application/json; charset=utf-8",       dataType: "json",       success: function(msg) {         // Replace the div's content with the page method's return.         $("#Result").text(msg.d);        }     });   }); });   Unsuccessful JQuery call:  $(document).ready(function() {     $('#example').dataTable({         "bProcessing": true,         "bServerSide": true,         "sAjaxSource": "Default2.aspx/GetDate",         "fnServerData": function(sSource, aoData, fnCallback) {         $.ajax({         "dataType": 'json',         "url": sSource,         "data": aoData,         "success": fnCallback         });         }     }); });   Any thoughts on why the second call returns html? I tried adding  contentType: "application/json; charset=utf-8", to the second ajax call. I get an error.


Answers should be sorted strictly according to upvotes and not give precedence to the accepted answer

Upvotes are almost always a much better indicator of a good answer than an answer actually being accepted by the question's author. Often times the question's author will accept a poor answer. Thus, the first answer to be displayed to the public should not necessarily be the accepted answer.   We want to cater to the general public who will be viewing the discussion. We want to show them the most relevant answers first. The answers that are most relevant to the general public are the ones with the most upvotes, not the answer that the question's author accepted. The collection of people who are voting almost surely do a better job of ranking answers than the single question's author. Afterall, these voters represent the general public that we are trying to cater to.


"Service Battery" warning briefly appeared on brand new rMBP. Should I take it back?

I bought a retina macbook pro yesterday and noticed a "Service battery" warning. It was there for a few hours and now has gone. Should I take it back to the store or do you think it's safe to ignore?  Update: The following day, the laptop battery was completely drained after being 100% the night before (and fully powered down). The "Service battery" warning also re-appeared. I took it back and it was just swapped it for a new one.


Why does cd-ing to // set PWD to //, but more slashes just gives /?

On my ubuntu box I accidentally just did cd // and noticed that my current path changed to //. ls showed the contents of my root directory.  When I try cd /// (or any other number of slashes) I'm just taken directly to the root.  I'm sure this isn't something I need to worry about in any way during every day life but I was wondering if there was some interesting curiosity about why it behaves this way.


Hilbert polynomial of an hypersurface in projective space

Let $X$ an hypersurface in $\mathbb{P}^{n}$ of degree $d$. I would like to prove that the Hilbert polynomial of $X$ is  $\qquad \qquad \qquad \qquad \qquad \qquad p(n)= \begin{pmatrix} n+r \\ n \end{pmatrix} - \begin{pmatrix} n+d-r \\ n \end{pmatrix} $  In the book "Geometry of Algebraic Curves Vol. II", Arbarello, Cornalba, Griffith, p. 7, I read that this result can be proved by taking the cohomology of the following exact sequence  $ \qquad \qquad \qquad \qquad \qquad 0 \longrightarrow \mathcal{O}_{\mathbb{P}^{r}}(n-d) \longrightarrow \mathcal{O}_{\mathbb{P}^{r}}(n) \longrightarrow \mathcal{O}_{\mathbb{P}^{r}}(d) \longrightarrow 0 $  Nevertheless, I am not able to compute $p(n)$.


Creating a seperate reference section with all non-cited Literature

I want to create a regular reference section with all the literature I cited in my document but also a separate one with a custom title (uncited literature) where All the keys should be listed that I haven't cited. Is there a (simple) way to do that?


How can I import a .c4d static model (Cinema 4d) on Blender? Is there any plugin could help me? I didn't notice anything on Internet.


How to draw the Mean Value Theorem graphic with TikZ?

(Edited 2014-03-23) Can anyone give a TikZ solution to my question?  I want to add an illustration of the Mean Value Theorem (Lagrange) like this:   \begin{center} {\Huge \shadowbox{\textbf{Teorema del Valor Medio (Lagrange)}}} \end{center}  \[\frac{{f(b) - f(a)}}{{b - a}} = f'(c)\]   Basically, I need the axis with the x and y labels, the function, the secant, the tangent and something that is missing in the picture: f(a), f(b) and f(c).  I made the picture that I want to make with TikZ with GeoGebra:


Compiz extra animations download Ubuntu 14.04 not working ( burning animations ETC)

I have installed Ubuntu 14.04 on my Dell Latitude yesterday. I wanted some cool window animations so I installed CompizConfig and also (at least, that is what I have tried to do), installed the extra animations that are available. I used the terminal with the following command to install the extra package:  sudo apt-get install compizconfig-settings-manager compiz-plugins-extra   When I finally had set up everything, I wanted to use a burning effect on the closing animation,however, I couldn't even find that animation in the list! What I have seen is that I have to turn on Animation addon to use those animations, but I don't have that option.  Is there any way to get the extra effects on compiz with Ubuntu 14.04? Or are the effects removed because they were unstable?


Why are two definitions of ellipses equivalent?

In classical geometry an ellipse is usually defined as the locus of points in the plane such that the distances from each point to the two foci have a given sum.  When we speak of an ellipse analytically, we usually describe it as a circle that has been squashed in one direction, i.e. something similar to the curve $x^2+(y/b)^2 = 1$.  "Everyone knows" that these two definitions yield the same family of shapes. But how can that be proved?


is there a way to get Flash 11 on ubuntu 13.04?

I am trying to play my games but not being able to play all of them because of no flash 11. Is there anyway to fix this?


I am a US citizen and on my way to Canada this weekend, by car.  Do I need a passport to get back into USA or will my birth certificate and drivers license do the trick? Virginia