I've been wondering about this for years.  It seems like a pretty obvious question, so I'm surprised not to have found it addressed among the other Tolkien minutiae on this site.  Hopefully I haven't missed it, but anyway, here goes...  In Tolkien's Middle-Earth writings, Evil cannot create things, only twist and warp what already exists.  Thus, Orcs are twisted Elves, Trolls are twisted Ents, etc.  So then, what's the original source for Dragons?  They look pretty original to me!  The only template that seems even remotely possible is the Eagles, as they're both powerful fliers, but the connection seems very remote indeed.  Also, as twisted copies Orcs and Trolls are markedly inferior to Elves and Ents respectively, but I'm not aware of any text describing Dragons as inferior to Eagles.

All that I know of Smaug is that he (she?) came out of nowhere to attack and conquer Erebor. Where exactly did he come from? In fact, what are the origins of dragons? Did Ilúvatar create them or did they come from somewhere else?


Hi i have some data which coming out from database in form of table like this, first i match some data with searching and then display it on page now  i need to download it as csv file format please help me check my code and i'm new in php. please check image too for the reference and please please help me  //import.php // echo "
"; //print_r($_POST);die(); $keyword = $_POST['keyword']; $csvname = $_POST['csv_file'];  ?>

             id	             title	             count

  <?php  $row = 0; if (($handle = fopen("idata.csv", "r",)) !== FALSE) {     while (($data = fgetcsv($handle, 1000, ",")) !== FALSE) {            $num = count($data);         // echo "
 $num fields in line $row:

\n";         $row++;         for ($c=0; $c < $num; $c++) {             // echo $data[$c] . "
\n";             $query = "SELECT * FROM wm_article WHERE id = '".$data[$c]."'";             $exec = mysqli_query($conn, $query);             $details = mysqli_fetch_array($exec);             $description = $details['title'] ." ".$details['description'];              //echo $description ;              //  $regex = "/royal/";              //  if (preg_match_all($regex, $description, $match))             //  {              //      print_r ($matches[0]);             //  }               if(preg_match_all("/\b".$keyword."\b/i", $description, $match,PREG_OFFSET_CAPTURE, 3)){                 // echo count(explode('royal', $description));                 // echo "
";print_r($match);     ?>
  <?php echo $details['id'];?>	  <a href ="<?php echo $details['url'];?>" target ="_blank"><?php echo $details['title'];?>	  <?php echo count($match[0]); ?>
    <?php                 }         }     }  } ?> <?php    ?>

What is the most efficient way to convert a MySQL query to CSV in PHP please?  It would be best to avoid temp files as this reduces portability (dir paths and setting file-system permissions required).  The CSV should also include one top line of field names.


Following along in tutorials I see the blur filter being used. I am using Blender 2.69 and I can't locate it visually or even with a search. Actually, there is no "Filters" category at all.  Do I have to download something to get it?

I have been following  tutorial until I started adding nodes. The problem is that he has completely different nodes than I have. Even nodes that are created at start are different (I have Material and Output and he has Render Layers and Composite). Have I missed something or should I use different nodes than he?


Does Tarski-Grothendieck set theory can prove the consistency of ZFC?

Does TG () prove that ZFC2 (second-order ZFC) has a model? Does it at least prove the consistency of ZFC2?


This bicycle was given to me and I'm not sure was the make of it I've tried look in the serial number up on Google but I came up with nothing so hopefully you can help me with trying to figure out what kind of bike this is the Serial number is SNHFD10K02145

I have a bike I'm trying to sell because it's just been sitting in my basement. It looks as if someone primered it and the only thing I found was a serial number. Is there like a website I can look up more info on the bike using just that number?


I am interested to know how the  tool works in QGIS 3. I am choosing to use this rather than the  tool which works of the "center of mass" methodology because this creates a point outside the area of the polygon which is not suitable for my needs.  The QGIS documentation does not seem to explain the calculation used but I would like to know so I can test whether it is suitable for my analysis and so I can incorporate an error with my calculations.

The PostGIS documentation states that ST_PointOnSurface returns "a POINT guaranteed to lie on the surface". It seems like this function could be trivially implemented to give results that satisfy the documentation but provide little real-world utility, though I'm certain that PostGIS provides a non-trivial implementation.   provides a nice comparison and contrast of ST_Centroid with ST_PointOnSurface and says that "[ST_PointOnSurface] is substantially more computationally expensive than the centroid operation".  Is there a more thorough explanation of how ST_PointOnSurface is calculated? I've been using ST_Centroid, but have encountered some edge cases in my data where the centroid is outside the geometry. I believe that ST_PointOnSurface is the correct substitute, but the function name and documentation leave room for uncertainty.  Further, is the computational expense of ST_PointOnSurface incurred even if the centroid does lie within the geometry already?


I have up-voted a question in Meta Webmasters Stackexchange. That question is available in home page under Hot Meta Post list. But my count has not been updated. Why it’s not updating quickly? If it will take time means what’s the approximate time duration?  Screenshot for reference:

I often click on the questions in the "Hot Meta Posts" section of the sidebar. Today when I clicked on one of the questions I noticed that it had already been deleted.     I view this as a bug, though you could also view it as a feature request I suppose. I do not think that a deleted Meta question should still be considered "hot".


I have exported my maple mathematical matrices to latex and now I want to show those equations in Powerpoint presentation. I have installed MathType in MS Powerpoint that converts basic latex codes or equation to mathtype but not the matrices. For example If if paste below code into Mathtype it gives error;   Error: This equation has exceeded the maximum width and/or height allowed. Remember mathtype is not a word processor.     Latex Code that I want to convert to Mathtype:  \begin{equation} T_{R,A_1}= \left[\begin {array}{cccc} \cos  \psi_{{1}}  \cos  \delta_{{1}}  &-\sin  \psi_{{1}}  &\sin \ \delta_{{1}}  \cos  \psi_{{1}}  &-\sin  \delta_{{1}}  \cos   \psi_{{1}}  r-\sin  \psi_{{1}}  {\it k5}+{\it k2}\\ \noalign{\medskip}\cos  \beta   \sin  \psi_{{1}}  \cos  \delta_{{1}}  +\sin  \beta  \sin  \delta_{{1}}  &\cos  \beta   \cos  \psi_{{1}}  &\cos  \beta  \sin  \delta_{{1}}  \sin  \psi_{{1}}  -\sin  \beta   \cos  \delta_{{1}}  & T_2\\ \noalign{\medskip}\sin  \beta  \sin  \psi_{{1}}  \cos   \delta_{{1}}  -\cos  \beta  \sin  \delta_{{1}}  &\sin  \beta  \cos  \psi_{{1}}   &\sin  \beta  \sin  \delta_{{1}}  \sin \psi_{{1}}  +\cos  \beta  \cos  \delta_{{1}}   & T_1 \\ \noalign{\medskip}0&0&0&1\end {array}\right]  \end{equation}

Let's say I have a (comparatively) lovely-looking document in LaTeX, full of lovingly typeset, (relatively) complex equations. Now, let's say some barbarians come along one day and decide that the document has to be put into Microsoft Word (2007). ...after the usual mourning period associated with such events, let's say I value my job (more specifically, the bread it provides) enough to get all the text and tables formatted and references organised into the Word document. –...related questions  and – Now I'm looking at the equations with fear and dread. One option of course is to just lift screenshots from the original document, but this is painstaking if I need to refer to parts of the equation in the text. Also, I might need to edit equations on the fly. Anyone know of a free application which allows embedding LaTeX math into MS Word? I've looked at  and  which do roughly what I want... they build LaTeX images from source and embed them into the Word document, allowing to edit the source later... but both are commerical. ...any help in these troubling times will be greatly appreciated. EDIT: Just a note that  offers a 30-day free trial and is working out really nicely... but still, it's not free. Might be a good solution for those with short-term needs, or money.


Strictly speaking, a complex number is any number that can be represented in the form $z=a+bi$, even if $b=0$. This means that $5$ is technically a complex number. There are certainly advantages of this being the case: for example, the real numbers are a subset of the complex numbers. However, this makes it a little awkward to describe a polynomial that does not have real roots—if I say 'this quadratic has $2$ complex roots' then this is really true for any quadratic. I suppose I could say 'this quadratic has $2$ non-real roots', but this also feels a little awkward (though it may be my best option). With this in mind, is there a specific term for a non-real complex number?

Complex numbers include all real numbers. Is there a name for the subset of complex numbers which does not include any real numbers (i.e. where the imaginary component is nonzero)?


I am asked:     Let $F_{i}$ denote the $i$-th Fibonacci number.   Prove that $$\sum^{n}_{i=0}\binom{n}{i}F_{i}=F_{2n}$$   I have the base case and the inductive hypothesis, but I'm not sure what identity I need to make the jump from   $\sum^{n+1}_{i=0}\binom{n+1}{i}F_{i}=F_{2n}+F_{n+1}$ to $F_{2n+2}$, where $F_{2n+2}$ is the n+1 term.   Any tips?

I am stuck with the identity  $$ F_{2n} = \sum_{k=1}^n \binom{n}{k} F_k, $$  which happens to be formula . I am using induction, but so far without too much result.  $$ \sum_{k=1}^{n+1} \binom{n+1}{k} F_k = \\ F_{n+1} + \sum_{k=1}^n \binom{n+1}{k} F_k = \\ F_{n+1} + \sum_{k=1}^n \binom{n}{k} F_k + \sum_{k=1}^n \binom{n}{k-1}F_k =\\ F_{n+1} + F_{2n} + \sum_{k=1}^n \binom{n}{k-1}F_k, $$   I am stuck with the sum $ \sum_{k=1}^n \binom{n}{k-1}F_k$, because, on the other hand   $$ F_{n+1}+ \sum_{k=1}^n \binom{n}{k-1}F_k = F_{2n+1} $$  Which would conclude the proof. What am I missing?


I'm unable to create a new document in /var/www/  I followed this tutorial :-   and did as suggested, but still I'm unable to make a new document. Any suggestions ?

For some reason I can't change the file permissions of my var/www folder or anything else inside it. I've tried using gksu-nautilus to change the permissions but it doesn't work. When I open the properties window, and select a different level of permission for myself, it instantly switches back to the previous setting.  Any idea of how to fix this?


I have been looking deeper into different collection implementations and i wonder if there is any performance difference when implementing iterator on various List types(Like the previously mentioned in the title).   As we all know iterating over ArrayList is faster as opposed to LinkedList. However is the case same when we iterate over both using the iterator methods?  Also the case is reversed when adding and removing elements, then the LinkedList is faster, but if we implement listIterator which has better performance on the add/remove operations or do they equate for both lists and there is no difference.  I apologize if this question has been asked before, I wasn't able to find anything to help me.

I've always been one to simply use:  List<String> names = new ArrayList<>();   I use the interface as the type name for portability, so that when I ask questions such as these I can rework my code.    When should  be used over  and vice-versa?


Is it possible that after sending minor revisions my paper has gone for a fresh review again. I had received the following recommendation: accept subject to optional revision. The status has been showing " under review " for a month now.   Is it still with the associate editor or with the old reviewers. I got two referred comments and one guest editor comments  Sent my paper to ieee transaction

What steps does a manuscript typically go through from submission to publication (or rejection) in a typical journal? How are these steps referred to, in particular by editorial systems, and how long do they each typically take?  Note that this question is about the typical situation and hence not about:   Journals with an atypical workflow, e.g. those that allow for an instantaneous reviewer–author interaction. Exceptional steps or rare occurrences such as withdrawal or .   This is a canonical question on this topic as per . Due to its nature, it is rather broad and not exemplary for a regular question on this site. Please feel free to improve this question.


\begin{tikzpicture}[>=triangle 45,shorten >=1pt,auto,node distance=3cm] \node[state] (moderate) {moderate}; \node[state, minimum size=2cm] (above) [below right of=moderate, xshift=1cm, yshift=-3cm] {above}; \node[state, minimum size=2cm, xshift=-1cm, yshift=-3cm] (below) [below left of=moderate] {below}; \path[->] (moderate) edge [loop above] node {\texttt{t\_high = 0, t\_low = 0}} (moderate)     edge [bend left] node {\texttt{t\_high = 1}} (above)     edge [bend left] node[align=center, xshift=-2cm, yshift=1cm] {\texttt{t\_low = 1}} (below)     (above) edge [loop right] node {\texttt{t\_high = 1}} (above)             edge [bend right] node {\texttt{t\_low = 1}} (below)             edge [bend left] node[align=center, xshift=2.2cm, yshift=1cm] {\texttt{t\_high = 0,}\\\texttt{t\_low = 0}} (moderate)     (below) edge [loop left] node {\texttt{t\_low = 1}} (below)             edge [bend left] node[align=center] {\texttt{t\_high = 0,}\\\texttt{t\_low = 0}} (moderate)             edge [bend right] node {\texttt{t\_high = 1}} (above); \end{tikzpicture}    I'm trying to draw a state machine diagram with Tikz. However, the destinations of the arrows seem to be overlapping at the same point of the nodes. I would like them to space out evenly so that one can easily tell different arrows apart; how can I do that? Any help would be appreciated.  P.S. Is there a way to get these arcs flatter? They seem to be really "fat".

I'm trying to draw an automata as follows:  \begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=2.8cm]   \node[initial,state] (q1)      {$1$};   \node[state]         (q2) [right of=q1]  {$2$};   \node[state] (q4) [below right of=q2] {$4$};   \node[state, accepting]         (q3) [above right of=q4] {$3$};    \path[->]          (q1)  edge                 node {a} (q2);   \path[->]          (q2)  edge   [bend left]   node {b} (q3);   \path[->]          (q3)  edge   [bend left]   node {a} (q2);   \path[->]          (q2)  edge                 node {b} (q4);   \path[->]          (q4)  edge                 node {a} (q3); \end{tikzpicture}   However, the bending seems to be "too much", and it interferes with the two arrows to/from q4. In addition, I'd like the labels on those two arrows to be on the other side of the arrow. Sadly I couldn't find how to do it online so I turned to this page.


I'm using Entity Framework 6 , with Database First. The model is created using wizard from existing Sql server database. I'm using this code to do a deep clone :  Imports System.ComponentModel Imports System.Collections Imports System.Data.Entity.Core.Objects.DataClasses Imports System.Runtime.Serialization Imports System.IO Imports System.Reflection Imports System.Runtime.CompilerServices  Module Extensions  Private Function ClearEntityObject(Of T As Class)(ByVal source As T, ByVal bCheckHierarchy As Boolean) As T     If (source Is Nothing) Then         Throw New Exception("Null Object cannot be cloned")     End If     Dim tObj As Type = source.GetType     If (Not tObj.GetProperty("EntityKey") Is Nothing) Then         tObj.GetProperty("EntityKey").SetValue(source, Nothing, Nothing)     End If     If bCheckHierarchy Then         Dim PropertyList As List(Of PropertyInfo) = Enumerable.ToList(Of PropertyInfo)((From a In source.GetType.GetProperties             Where a.PropertyType.Name.Equals("ENTITYCOLLECTION`1", StringComparison.OrdinalIgnoreCase)             Select a))         Dim prop As PropertyInfo         For Each prop In PropertyList             Dim keys As IEnumerable = DirectCast(tObj.GetProperty(prop.Name).GetValue(source, Nothing), IEnumerable)             Dim key As Object             For Each key In keys                 Dim childProp As EntityReference = Enumerable.SingleOrDefault(Of PropertyInfo)((From a In key.GetType.GetProperties                 Where (a.PropertyType.Name.Equals("EntityReference`1", StringComparison.OrdinalIgnoreCase))                     Select a)).GetValue(key, Nothing)                  ClearEntityObject(childProp, False)                 ClearEntityObject(key, True)             Next         Next     End If     Return source End Function  <Extension()> _ Public Function ClearEntityReference(ByVal source As Object, ByVal bCheckHierarchy As Boolean) As Object     Return ClearEntityObject(source, bCheckHierarchy) End Function  <Extension()> _ Public Function Clone(Of T)(ByVal source As T) As T     Dim ser As New DataContractSerializer(GetType(T))     Using stream As MemoryStream = New MemoryStream         ser.WriteObject(stream, source)         stream.Seek(0, SeekOrigin.Begin)         Return DirectCast(ser.ReadObject(stream), T)     End Using End Function  End module   Now , I try to use this code like this :    Private Sub DoClone     Dim litm, newitm As MyObject     litm = context.MyObjects.FirstOrDefault     newitm = litm.Clone()     newitm.ClearEntityReference(True)     context.MyObjects.Add(newitm)     context.SaveChanges() End Sub   I get an error :     An unhandled exception of type   'System.Runtime.Serialization.SerializationException' occurred in   System.Runtime.Serialization.dll         Additional information:Type   'System.Data.Entity.DynamicProxies.MyObject_F2FFE64DA472EB2B2BDF7E143DE887D3845AD9D1731FD3107937062AC0C2E4BB'   with data contract name   'MyObject_F2FFE64DA472EB2B2BDF7E143DE887D3845AD9D1731FD3107937062AC0C2E4BB:'   is not expected.       Consider using a DataContractResolver or add any   types not known statically to the list of known types - for example,   by using the KnownTypeAttribute attribute or by adding them to the   list of known types passed to DataContractSerializer.   This is my model that I use :  Partial Public Class Myobject Public Property id As Integer Public property name as string Public Overridable Property chld As ICollection(Of chld) = New HashSet(Of chld)  Public Overridable Property chld1 As ICollection(Of chld1) = New HashSet(Of chld1) End Class  Partial Public Class chld     Public Property id As Integer     Public Property date1 as DateTime     Public Property quantity as Integer     Public Property ParentID as integer     Public Overridable Property MyObj1 As MyObject End Class  Partial Public Class chld1     Public Property id As Integer     Public Property nm as string     Public Property ParentID as integer     Public Overridable Property MyObj1 As MyObject End Class

I want to do something like:  MyObject myObj = GetMyObj(); // Create and fill a new object MyObject newObj = myObj.Clone();   And then make changes to the new object that are not reflected in the original object.  I don't often need this functionality, so when it's been necessary, I've resorted to creating a new object and then copying each property individually, but it always leaves me with the feeling that there is a better or more elegant way of handling the situation.  How can I clone or deep copy an object so that the cloned object can be modified without any changes being reflected in the original object?


I am using a customised set-up as shown below for my title and need some help reducing the space between the top of the page and the "title" which in my case is defined by a "chapter" environment.       \documentclass[12pt,a4paper]{report}     \usepackage[margin=0.75in]{geometry}     \usepackage[latin1]{inputenc}     \usepackage{amsmath}     \usepackage{amsfonts}     \usepackage{amssymb}     \usepackage{multicol}     \usepackage{titling}      \usepackage{xcolor}     \usepackage[explicit]{titlesec}      \setlength\columnsep{50pt}     \setlength{\droptitle}{-5pt}     \author{The Doctor}     \title{\textbf{Mirko Vosk EDH}}       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     \titleformat{\chapter}       {\normalfont\LARGE\bfseries\fontfamily{uncl}\selectfont\filcenter}{}    {0em}{#1}      \titleformat{\section}       {\normalfont\LARGE\bfseries\fontfamily{pbk}\selectfont\color{red}\filcenter}{}{0em}{#1} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     \begin{document}     \chapter{``Rush of the Wild" R/G \, Aggro}      \begin{multicols}{2}     \section*{``Base" Creatures=04}         \begin{itemize}             \item 02 Rakdos Cackler (B/R) [2/2]             \item 02 Kalonian Tusker (GG) [3/3]         \end{itemize}      \end{document}   I would like for the document to be one page without changing my margins and shrink the space between title and top of page. Thanks!

I want to decrease the vertical space between the top of the page and the chapter heading. I have tried to follow the instructions for titlesec but I am not successful. I have tried the following two setups without any changes occuring.  First:  \documentclass[12pt]{report}   \usepackage[compact]{titlesec}   \begin{document}   \chapter{Characters}  The origin of the group determinant begins with Richard Dedekind in the late 1800's. He began to explore the idea after studying the discriminant in a normal field [A]. He made several observations about the group determinant, but was only able to prove some of them.   \end{document}   Second:  \documentclass[12pt]{report}   \usepackage{titlesec}   \titleformat{\chapter}[display]   {\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}   \titlespacing{\chapter}{0pt}{0pt}{0pt}   \begin{document}   \chapter{Characters}    The origin of the group determinant begins with Richard Dedekind in the late 1800's. He began to explore the idea after studying the discriminant in a normal field [A]. He made several observations about the group determinant, but was only able to prove some of them.   \end{document}


Method 1   public static synchronized Database getInstance(){    if(INSTANCE == null){      INSTANCE = new Database();    }    return INSTANCE; }   Method 2  private static final Database INSTANCE = new Database();     public static Database getInstance(){         return INSTANCE;     }   Which is the better choice ?

What is an efficient way to implement a singleton pattern in Java?


hi I have canon 550D and have 2 leses 18-55 / 55-250; going thru the sharpness and quality i am thinking to purchase 40mm / 50mm lense. as per me the quality of images of existing lenses are not that much sharp what it needs to be.  Can anybody advice me (1) Is it right to go for 40mm / 50mm lense (2) if yes, which one?

So I'm about to buy my first DSLR (definitely a Canon, probably the 700D) and my original plan was to buy the one with the included 18-55mm f/3.5-5.6 kit lens.  At the same time I was thinking about picking up the 50mm f/1.8 on account of the fact that it's cheap and I love taking photos of people with a shallow depth of field.   A couple of friends who are big into photography both suggested that the kit lenses aren't that good and produce blurry, distorted and drab imagery. They also both suggested that I should use the money saved by just getting the body to offset the cost of a decent prime lens.  At this point their views differed:   One suggested that I should get the Canon EF 40mm f/2.8 STM. This works out at only £12 more expensive than the kit. They said it takes much better photos than the 50m f/1.8 for only a small amount more and it's very light. Another suggested that I go directly to the Canon EF 50mm f/1.4 as it's a lens that I'll never ever need to replace. This works out at £150 more expensive than the kit, although I can take (very small) comfort in the fact that I'm saving £80 by not buying the f/1.8 as a stepping stone to the f/1.4.   Both also suggested that once I'd had some lessons, learnt how to use the camera and absolutely must have a zoom lens, then I save up and look to buy something decent at that point in time, rather than use the kit lens.  Should I drop the kit lens and pick up a decent prime? Will I be missing out on some types of photography without the kit lens? Or should I start off with the kit and nifty-fifty and upgrade each component over time?


Goals:   Have a single nginx reverse proxy for all sub-sites (running on other ports). BLOCK all direct connections, and instead; route through nginx.   Problem(s):   502 gateway errors when trying to access https://www.example.com/site1/ (connect() failed (111: Connection refused) while connecting to upstream)   Setup:   example.com running on port 80 (nginx). site1 and site2 running on ports 8001 and 8002 respectively.   nginx config:      worker_processes 1;      events { worker_connections 1024; }      http {         sendfile on;          upstream site1 {             server 127.0.0.1:8001;         }          upstream site2 {             server 127.0.0.1:8002;         }          server {             listen 80 default_server;             server_name _;             return 301 https://$host$request_uri;         }          server {              listen 443 ssl;             listen [::]:443 ssl;             gzip on;             access_log on;             log_not_found on;             error_log  /var/log/nginx/error.log error;             server_name example.com www.example.com;             charset UTF-8;             root /var/www/html;             error_page 404 /404.html;              ssl_prefer_server_ciphers on;             ssl_certificate /etc/ssl/server.crt;             ssl_certificate_key /etc/ssl/server.key;              location /site1/ {                 proxy_set_header X-Original-Request $request_uri;                 proxy_set_header X-Real-IP $remote_addr;                 proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;                 proxy_set_header X-Forwarded-Proto $scheme;                 proxy_pass http://site1;             }              location /site2/ {                 proxy_set_header X-Original-Request $request_uri;                 proxy_set_header X-Real-IP $remote_addr;                 proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;                 proxy_set_header X-Forwarded-Proto $scheme;                 proxy_pass http://site2;             }         }     }   Facing a few problems regarding setting up my nginx reverse-proxy. Any help in this regard is much appreciated. Many thanks.

This is a  about Connection Refused    We see a lot of questions to the effect      When I try to connect to a system I get a message      Connection refused      Why is this ?


I have Toshiba Satellite c850 B516 with Original Win8 installed. I accidentally formatted the internal hard disk. There is no serial number written on the bottom of my laptop. How can I recover my original Win8 even if all my personal data is lost.

My new laptop came preinstalled with Windows 8. Naively, as I am, I just formatted the harddrive and installed fine old Ubuntu. Now I want to install Windows 8 for dual boot again, but I have no DVD and to download the ISO one needs a product key. That key is not on the back of the laptop anymore but somewhere on the mainboard.  Is there any way to recover the product key from the mainboard using Ubuntu?


There are many documentaries, forums, blogs and more dedicated to . I have been frantically searching for an answer to my question however none of my sources have clarity to the matter of hand. I would really love a clear explanation to: What exactly is Dark Matter? Please help me to have a clear understanding.

What evidence is there that dark matter isn't one of the known types of neutrinos?  If it were, how would this be measurable?


I know chicken isn't edible raw, but how long can it stay outside the refrigerator without gaining bacteria to where you can't even cook it?

If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?


There are linker errors to Symbols defined by SFML, but i cannot see how they occur despite that I linked the lib. I'm using make, which I currently learn and I want to build a minimalistic dev-environment with it.  Give a holler if you need anymore information than the following. I'd just like to minimize the questions size.  XXX@XXX ~/Documents/dev/cpp/proj/beep $ make clean                                                                                rm -f build/*.o build/release/*.o build/debug/*.o build/test/*.o XXX@XXX ~/Documents/dev/cpp/proj/beep $ make tests //test obj first g++ -std=c++14 -Wall -pthread -Iinclude   -c test/Packager.ut.cpp -o   build/test/Packager.ut.o -g3 //now the src obj  g++ -std=c++14 -Wall -pthread -Iinclude   -c src/ClientAddress.cpp -o build/debug/ClientAddress.o -g3 g++ -std=c++14 -Wall -pthread -Iinclude   -c src/Packager.cpp -o build/debug/Packager.o -g3   g++ -std=c++14 -Wall -pthread -Iinclude   -c src/Package.cpp -o build/debug/Package.o -g3 Built debug object files. //now the first test itself g++ -std=c++14 -Wall -pthread -Iinclude  -lsfml-network  build/test/Packager.ut.o build/debug/ClientAddress.o build/debug/Packager.o build/debug/Package.o -g3  -o bin/test/Packager.ut  build/test/Packager.ut.o: In function `main': /home/XXX/Documents/dev/cpp/proj/beep/test/Packager.ut.cpp:69: undefined reference to `sf::IpAddress::IpAddress(char const*)' build/debug/ClientAddress.o: In function `nw::udp::ClientAddress::ClientAddress()': /home/XXX/Documents/dev/cpp/proj/beep/src/ClientAddress.cpp:21: undefined reference to `sf::IpAddress::IpAddress(char const*)' build/debug/ClientAddress.o: In function `nw::udp::operator==(nw::udp::ClientAddress const&, nw::udp::ClientAddress const&)': /home/XXX/Documents/dev/cpp/proj/beep/src/ClientAddress.cpp:33: undefined reference to `sf::operator==(sf::IpAddress const&, sf::IpAddress const&)' ...   and so on ... every mentionings of sf:: inside the files are quoted  I get the same error pattern if I try to compile the other tests (for ClientAddress for example)  Of course i now want to know what i linked wrong how there. As you can see the lib is linked with -lsfml-network. I also checked the SMFL installation, so it is at least less likely a lib file gone missing from standard directory.  I guess there is an error in my usage of g++ , compiling and linking orders or smth.  My project tree:  >bin ----mainexec --->test     ----.ut >build --->debug     ----.o --->release     ----.o --->test     ----.ut.o >src ---- .cpp >include ---- .h >test ---- .ut.cpp   As a second part of the question, I'd like to ask if there is a better way to build tests, because I simply link every src-obj with my test-obj, even if there are way more src-obj linked than it actually needs. It should work and I do not have to maintain my test dependencies all the time, which later would be very cumbersome. What is common ?

Why does the order in which libraries are linked sometimes cause errors in GCC?


I'm trying to merge the polygons (administrative boundaries) in a dataset untill they reach a minimum value. Lets say that the polygon dataset consists of the number of people per polygon and I need each polygon to contain at least 100 people. In that case I want the polygons with a value less than 100 to merge with an adjecent polygon, preferably in this order:   merge polygon with one adjecent polygon that contains less than 100 people if adjecent polygons of less than 100 people are not available, merge with a polygon that contains 100 or more people. if after the merge the minimum number is not reached yet, repeat the process untill no more adjecent polygons are available.  The end result should be a polygon dataset in which as many polygons as possible have at least 100 people per polygon.   I hope this discription is clear enough. Let me know if you need more info.   I'm using ArcMap 10.2.1. I already tried the dissolve tool, but this doesn't have the option to dissolve based on a minimum value. I saw that during an edit session in ArcMap you can merge polygons manually, but I found no way to do this in a model or a python script. If necessary I'm open to use other tools such as QGIS or SpatiaLite.

I have a shapefile with 3800 polygons representing the smallest administrative areas in Ireland. Many of these, in rural areas, have tiny populations, under 100 people. In urban areas, all would have adequate populations.  For each area I have a population figure, and various other attributes, all of which can be intelligently summed to give valid results for areas produced by combining the smaller areas.  I need to merge the areas to get say, 500 or 600 areas of reasonable population. I need to leave the larger (in population) areas alone, where possible. I would greatly prefer to do this automatically. This is necessary for model fitting purposes, primarily.  I've looked at a number of the dissolve questions here:   'Batch Dissolve Polygons based on Attributes in QGIS or FWTools' I think would require me to know which areas to merge, when this is what I need to calculate. 'Practical way of managing polygons and unions of them' and 'How do dissolve polygons from shapefile using open source tools?' have the same issue.   Any suggestions?


I got stucked in this problem and get no clue to solve this. Can any one please help me? Thanks     Suppose $X$ is an inner product space. If for every bounded linear function $f$, there exists $z \in X$ such that $$f(x) = <x, z>$$ for all $x \in X$. Prove that $X$ is a Hilbert space.   I can't find any way to relate the complete of space $X$ with the existence of $z$. Please help me solve this. I really appreciate.

Let $H$ be a vector space equipped with an inner product $(\cdot, \cdot)$ and $f:H\to H',\ f(x)=(\cdot,x)$ surjective. Now, why $H$  is a Hilbert space? The other direction is clear by Riesz' representation theorem but what about this?


QGIS 2.8.1 Win7 64 bit installed with osgeo4w-setup.  I’m trying to run GRASS commands on a LIDAR raster layer but I get the following message:     Missing dependency.... GRASS not installed in your system` message each time.   GRASS appears in the processing tools pane and the “Processing options” for GRASS shows the Msys and GRASS folders locations correctly (which was a problem for a similar questioner). I note that GRASS has been 7.0 stable since mid February but osgeo4w-setup only shows GRASS 6. All manuals refer to a ‘GRASS plugin’ but none seem to be listed now.   Is there 'best-practice' way of installing GRASS functionality in QGIS 2.8 on Windows7 64 bit?  As a supplementary question is it possible to install a GRASS add-on that is not part of the core GRASS setup (I need  for LIDAR visualisation of archaeological features)?

I am quite new to QGIS and working with the external applications such as GRASS.  When trying to launch a GRASS tool from the processing toolbox I get the following error:     Missing dependency. This algorithm cannot be run :-(   This algorithm   requires GRASS to be run. Unfortunately, it seems that GRASS is not   installed in your system, or it is not correctly configured to be used   from QGIS    Click here to know more about how to install and configure   GRASS to be used with QGIS   When I am using GRASS from the Plugins menu it works. I have GRASS 6.4 installed to my system and running, GRASS 7 installed, but it doesn't run, probably due to some known El Capitan issue. Anyhow, GRASS 6.4 should be working. Moreover, there is also the GRASS that comes with the QGIS installation.  Unfortunately I messed up the path to GRASS that was originally set in Processing -> Options before I even tried if the original setup works. I tried really every possible path I could think of, to the GRASS-6.4 installation in my applications folder (/Applications/GRASS-6.4.app) and to the GRASS folder in the QGIS installation (/Applications/QGIS.app/Contents/MacOS/grass), I don't get the GRASS tools to working. I reinstalled QGIS to restore the original settings, but obviously I have to delete the particular settings before (but where?), because the path was still as I set it before reinstallation.  SAGA is working from the processing toolbox.  So, long story short:   Any suggestions what could be the issue? Anyone experiences with running GRASS via processing toolbox with QGIS 2.8 on El Capitan? It would be already a great help if someone could give me the original path to GRASS set at "Processing" --> "Options"


I've recently removed the Windows partition  keeping Ubuntu as single OS. The way I did it was through an Ubuntu Live boot-drive, using the Try Ubuntu option. In Gparted I simply removed the referred partition. This is what Gparted shows:  /dev/sda1..fat16....39.19 MiB  unnallocated..unnallocated..281.78 GiB  /dev/sda4..(KEY)..extended..183.94 GiB  ../dev/sda6..ext4..180.03 GiB  ../dev/sda5..(KEY)..linux-swap..3.91 GiB  unnallocated..unnallocated..1.02 MiB    My problem is that I can not expand my ext4 partition. My goal is to make the unallocated space usable. Can anyone help me?  I would like to clean up this partitions too, keeping just what I use.

How can I expand/resize my extended partition (sda3) with unallocated free space to the left of it? I want this to be able to expand my / partition (sda5).


I'm trying to make a simple summation of an array of 10 numeric elements. I get a totally incorrect result, which only occurs with an array of certain values, otherwise works well.    var sum = 0; var values = [14, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4]; for (var i = 0; i < values.length; i++) {   var v = values[i];   sum += v; } console.log(sum);     The expected result is 0, but I get oddly -2.22! At other times, I have achieved results with so many decimal places, which I had to round up. But in this case, with these numbers, that kind of bug is absurd.

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


Is there a simple way to save a QGIS project and all associated files to a zip folder so that another person could unzip the folder and open the project?    Or is there a better way to share a project with another person?

I was wandering if there was a way to save a specific project with all layers as dependent files to make it easy to share with collaborators.  for example, create a zipped or non-zipped folder containing the same structure as the project :  Root_folder/ my_project.qgs     \____________myfolder                      \___Layer 1                      \___Layer 2                      \___Layer 3     \____________myfolder2                      \___Layer 4                      \___Layer 5                      \___Layer 6     \____________myfolder3                      \________myfolder4                                      \___Layer 6                                      \___Layer 7                      \___Layer 8   If it does not exists, would it be tricky to develop regarding the current API ?


Someone please explain me how the below code prints 8.800000095367432.  class Test { public static void main(String[] args) {     Double object = new Double("2.4");     int a = object.intValue();     byte b = object.byteValue();     float d = object.floatValue();     double c = object.doubleValue();      System.out.println(a + b + c + d );  } }   Dear Pavel,The question in another link regards to javascript. I was wondering how is it in Java.  To make it more clear, The below one prints 6.4   Double object = new Double("2.4");         int a = object.intValue();         byte b = object.byteValue();         double c = object.doubleValue();          System.out.println( a+c+b);   Where as,   Double object = new Double("2.4");     int a = object.intValue();     byte b = object.byteValue();     double c = object.doubleValue();     float d = object.floatValue();     System.out.println(a + c + b + d);   prints 8.800000095367432.


Normally, if using itemlize we should get the following appearance:  There are following methods: \begin{itemlize}     \item Method A     \item Method B \end{itemlize}   There are following methods:   Method A Method B   However, I want no new line after the first line, like:   How can I do this?

I've created a new environment called 'Example' like this:  \newenvironment{example}     {\textbf{Example:} \begin{itemize}}     {\end{itemize}}   The environment works fine, but the items are starting after the Example: text. Is it possible to start with the first item on the same line as the Example: text and vertically aline the rest of the items with the first item?


I am trying to get the headers of few web sites with curl , and send mail when i get errors like 404,403,500,503 but i keep getting this error  Error:    line 7: [: -eq: unary operator expected   Code:  # !/bin/sh  NOW=$(date +"%H:%M_%m-%d-%Y")  web() {     res=$(curl -I -s "$1" -o test/"$1_log_$NOW" | grep HTTP/1.1 | awk {'print $2'})     if [ $res -eq 500 ]     then       echo "Error $res on $1" |mail -s "Error $res at $1 "mail@something.com      fi }   I manage to do what i wanted but i changed a lot of the script :  #!/bin/sh  NOW=$(date +"%H:%M_%m-%d-%Y")  web() {  res=$(curl -I -s $1  | grep HTTP/1.1 | awk {'print $2'}) if [[ "$res" == 500 ||"$res" == 403 || "$res" == 404 ||"$res" == 503 ]] then   echo "Error $res on $1" |mail -s "Error $res at $1 " somethng@domain.com   fi echo "$res" > /home/user/test/"$1_log_$NOW"  } web domain1.com

The following code gives      [: -ge: unary operator expected   when   i=0  if [ $i -ge 2 ] then     #some code fi   why?


When I refer to a table in text, the \ref{<labeloftable>} statement produces the chapter number in which the table resides, instead of the number of the table.  Any help would be welcomed!

\documentclass{article} \usepackage{algorithm}  \begin{document} \setcounter{section}{54} \section{A section with no label} \begin{algorithm} \label{myalg} \caption{An algorithm with the label `myalg'.} \end{algorithm} Reference to myalg: \ref{myalg}. \end{document}   With this code, the reference givens 55 (the section number); if I move the label after the caption command, I get the correct reference (1).  Why should this be the case? I find it confusing: when thinking about an algorithm as an environment, you expect to be able to label it right after you began it. At the very least I would expect some kind of error or "??" to appear, rather than the previous environment or reference-able entity being used.


Each time I look video in regards to quantum physics there is almost always one point where they claim small matter can be represented by a wave function (can be everywhere but the item in question has an higher % of being at a specific location than far away) until it is observed (now seen as a particle).  In practice, what is considered as an "Observer"?  Is consciousness essential to the observer role?  Example1: Let's say X is not observed (so in the wave function state), then a device is placed to determine the location of X but the result is never looked at by a conscious being (assuming a human) .  Is X considered observed so now represented by a particle?  Example2: Same example as 1 but now a conscious being looks at the result of the device.  I assume X is now being considered observed therefore it is now represented as a particle.

My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.  What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally?


I recently purchase an 512 SSD notebook and I verify that there was much less space than I thought.   I checked at the disk size (not partition size neither file system space) and I found that the disk itself does have only 476,81GB.     What is the cause for it? Where are the missing space? The SSD is Samsung mzmte512hmhp.

From all the hard drives I have bought, they never seem to be as large as the advertised size; from 320 GB down to 290 GB, from 500 GB down to 450 GB, etc. Is there a technical reason for this?


Why has the speed of light in a gravitational field always the same value $c$ when measured locally?   More precise: When you are far away from any masses, that means when the spacetime is flat, and you measure the speed of a light ray that passes you, you will always get the same value $c$. Now suppose you are in a static gravitational field at a fixed position, and do the same. Why do you also measure the same value $c$? (Please note: You are not in a free falling system where gravity vanishes)

Regarding the paper, what does Einstein means when he says:     "If we call the velocity of light at the origin of co-ordinates $c_0$, then the velocity of light $c$ at a location with the gravitation potential $\Phi$ will be given by the relation: $c = c_0\cdot\left(1+\frac{\Phi}{c^2}\right).$ The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of"   relativity"   Does the velocity of light is constant only into a space where the gravitation potential is constant either?


I created a navbar in my header and aligned it with another element so that they were centered. However, after adding an image to the header, one of the elements is no longer centered:    #header nav {   display: inline; } #header {   background: #5D6D63;   padding: 28px 0 26px;   position: fixed;   top: 0;   left: 0;   z-index: 1000;   width: 100%; } #header nav ul {   float: right;   margin: 0px;   margin-right: 100px; } li {   list-style-type: none;   float: left;   margin-left: 46px; } a[href^="#"] {   color: #fff;   font-size: 20px;   font-weight: bold;   letter-spacing: -1px;   text-decoration: none } a[href="#top"] {   margin-left: 100px; }    Name

Link 1

Link 2

Link 3

         The issue is the vertical alignment of the Name anchor tag. It should be centered with the the github image and the navbar. If I remove the github image, it works fine and it is aligned. Why is the github image causing the Name anchor tag to be pushed down a few pixels?  Here are pictures to show it misaligned (with image) and aligned (without image)

Why won't vertical-align: middle work?  And yet, vertical-align: top does work.   span{   vertical-align: middle; }
      Doesn't work.


Can we change the wording of the "marked as duplicate" template?    I don't think we should say "ask a new question".   If the cited answers actually don't fully address my question, but that fact isn't clear (as opposed to someone did some hasty tagging without seeing that my question is different) then I should fix my question to make it clear, not leave a useless question hanging around and ask another.   Instead of "please ask a new question", it should say "please edit your question to make it clearer".

The new closed-as-duplicate banner says:     This question has been asked before and already has an answer. If those answers do not fully address your question, please .   I think it should instead say     This question has been asked before and already has an answer. If answers there do not fully address your question, please  or  to the pre-existing one.   — to discourage re-re-asking the same question. (I also changed "those answers", which has no plural , to "answers there", which doesn't need one.)    As of September 19, 2013, the original text quoted above has returned here.


Is there a way to construct a PLL cicruit which locks on to an input signal's phase but provides an output signal with different duty cycles?

I am looking to build a circuit to control five different FET drivers individually. The input signal would be a single shot from a function generator, which should produce five output signals, with the same frequency and phase but the duty cycles need to be individually controllable. Basically, I am trying to replace five function generators (synchronized to the same clock) with one single function generator and a circuit board due to limited resources. The outputs need to have only two levels i.e pulse wave  EDIT: Olin's suggestion (using a MCU) or a FPGA seem to be the best options but any analog alternatives are much appreciated. Thanks :)


I would like to view the output of echo in vim, and save to a file after having a look at it. I have tried echo $PATH | vim, but I get the following error:  Vim: Warning: Input is not from a terminal Vim: Error reading input, exiting...  Vim: Finished.   What can I do?

I'd like to start vim on a non existing file, named f, with the content c. Both f and c are arbitrary and I'd like to not have to put anything in the vim config to fill new buffers with c.  Basically, I would like to combine  $ echo c | vim -  with  $ vim f  Is there a flag to vim which lets me achieve this?


I am using dual monitors (equal) and have recently switched to 11.10.  When I used 10.04, the top panel with indicators, etc. was showing only on my left monitor, leaving the entire space of the right monitor available for app windows.  In 11.10, the top panel is duplicated on the second monitor. IMO, it makes no good, just wastes precious desktop space.  Is there any way to make the top panel to show only on one monitor?  Thanks in advance!

How do I remove top bar on secondary monitor??


Prove that $\mathbb{N}\times\mathbb{Q}$ is countably infinite. I understand that I somehow have to show that a bijection exists between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{Q}$, I’m just struggling to see a way of labelling the set in such a way that no elements are missed.

How can I prove that the Cartesian product of two countable sets is also countable?


In Kleppner & Kolenkow's  (Amazon link), the general gyroscope motion including  was derived using the approximation condition $\Omega T \ll 1$ where $\Omega$ is the precession angular velocity and $T$ is the period of nutation.  How does one describe the gyroscopic motion if the the condition for the approximation is not satisfied? How does one describe the general gyroscopic motion if    the angular momentum of precession is not negligible and  if the gyroscope spins very slowly around its axis, $\omega$ is low?   In general I want to find the formula for most general gyroscope motion. If I let $\omega$ go to zero then I should get the special case of a pendulum.

Can you tell be how to set the equations to describe the motion of this machine in movie "Contact":     This is  with , am I right?


How can I center all the contents in the page, and make the order be right-to-left, because the alignment is to the left and the order is left to right.  here is the code:  Edit Center parent div       .grid-item {   float: left;   width: 270px;   min-height: 260px;   max-height: 260px;   background-color: whitesmoke;   margin-bottom: 10px;   border: solid 5px #bfbbd9;   padding: 7px; }

1

2

3

4

How can I horizontally center a
 within another
 using CSS?

Foo foo


I have a colleague here in my project, who is deeply against the use of instanceof operator, because it "generates a lot of overhead", what is the reason for that? Is it true?  Is there another way to check the type of the Object instead of using it?   Because I find it very useful in some occasions.

I am working on an application and one design approach involves extremely heavy use of the instanceof operator. While I know that OO design generally tries to avoid using instanceof, that is a different story and this question is purely related to performance. I was wondering if there is any performance impact? Is is just as fast as ==?  For example, I have a base class with 10 subclasses. In a single function that takes the base class, I do checks for if the class is an instance of the subclass and carry out some routine.   One of the other ways I thought of solving it was to use a "type id" integer primitive instead, and use a bitmask to represent categories of the subclasses, and then just do a bit mask comparison of the subclasses "type id" to a constant mask representing the category.  Is instanceof somehow optimized by the JVM to be faster than that? I want to stick to Java but the performance of the app is critical. It would be cool if someone that has been down this road before could offer some advice. Am I nitpicking too much or focusing on the wrong thing to optimize?


I am running on Ubuntu (I was on W8 before), but I need to go back to Windows.  I'm trying to boot from a live-DVD and a FlashDrive, but without luck. Ubuntu doesn't give me any boot option. If I press Esc at the startup screen, i only get this options:  *Ubuntu Advances Options EFI/ubuntu/MokManager.efi efi/EFI/ubuntu/MokManager.efi System setup  I have an Acer Aspire v5-571. Thanks a lot!

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


There is a lot of hype being generated by the distributed storage solutions:        They (supposedly) offer low-cost storage, and also pay for people to share their storage for others to use.  However, it is extremely difficult to find out how much it costs in everyday money to use these systems (or how much one would get paid), as they are based around their own crypto-currencies (which prices are often quoted in Bitcoin to add further obfuscation). The duration of storage adds further complexity to making a comparison.  As such, it's extremely difficult to know how much each service costs or pays out individually, and even more difficult or to make a fair comparison between them.  In my searches, people are looking for some real-world figures and/or a way to calculate them - but they are not readily available.  I would like to ask a question along the lines of:     How can I work out which is the cheapest storage solution [of the three], based on storing 1TB of data for a month?   I tried to ask the analogous question with respect to earnings  but it was closed as off-topic.  I feel that this question would add value in clarifying very murky waters, but I'm not sure where to post it, or even if it would be on-topic for any SE site.  If it's not on-topic for SE, any pointers as to where to ask it outside?

I have a question about a problem I'm having installing optifine with forge on minecraft.  Is there a place where I could ask this question?  I asked this on gaming, but I just got downvoted and told it is the wrong place.  The question is here:


Assume the mass of star 2 is 4 times the mass of star 1. Compare the radius of the orbit of star 1 to that of star 2.   Possible answers:  R1:R2=1:4   R1:R2=1:2   R1:R2=2:1   R1:R2=4:1   R1:R2=16:1   What's the answer?  I guess I'd use the gravitational force formula:  $ F = G\cdot \frac {m1 \cdot m2}{r^{2}} $  But I don't see how the $r$ from the formula, which is the distance between the two stars can be related to what the question is essentially asking - radius of the orbit of the smaller star.  And when the question says: "Compare the radius of the orbit of star 1 to that of star 2"  Wouldn't it mean that the bigger star (2) will stay stationary, and the smaller star would orbit around it? Or will they both orbit each other? I guess the latter.  If so, wouldn't they orbit each other the same way? e.g. always remain the same distance from each other?

Two particles with initial positions and velocities $r_1,v_1$ and $r_2,v_2$ are interacting by the inverse square law (with G=1), so that  $$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$ $$ {d^2r_2\over dt^2} = - { m_1(r_2-r_1)\over |r_1-r_2|^3} $$  (the inverse square law along the line of separation). What is the complete solution of these differential equations? What is the position of the two objects as a function of time?  After reading a lot on Wikipedia, I've come to the definition of center of mass and relative coordinates:   $$R(t) ~=~ \frac{m_1 r_1 + m_2 r_2}{m_1+m_2}$$  $$\ddot{r}(t) r(t)^2 ~=~ (m_1+m_2)G$$  Where $R$ is the center of mass, and $r$ is the displacement between the particles... Is this correct? How do I proceed to solve the differential equation?


At one time, it seems that I made a mistake in something, and the object I was creating went far.    Then, even I scroll the mouse wheel to zoom it, it gradually stops zooming, and eventually stops.  Someone can help?  Thank you.

I often find that I can zoom in to a point, but then cannot zoom any more, even when there is a lot of room to zoom to the meshes on the scene.   This is particularly annoying in the following scenario:  I often land up left clicking on the scene and the 3D cursor shifts there. I use Shift+C to shift the 3D cursor back to the origin. However, this also centers the view on the cursor and shifts the view to show all objects, and sometimes this zooms things way out – at this point, if I try to zoom in, I can zoom in to a point (using the pinch/zoom on trackpad), but then it stops zooming in.   How do I zoom in after that? Is there anything else I am doing wrong in this case?


I'm currently working closely with a professor on a research project as an undergrad student. I always address her by her last name: Dr.xx. However, this makes me feel distant from her.. I am wondering by which point I could call her by first name?   Here is some background info: I got to know her in person by taking a class taught by her and then started working together on this project at the end of last term. We had meetings together for a few times and exchanged a few emails back and forth. She always addressed herself by her first name in the email but I insisted called her Dr.xx to show my respect. However, some of her grad students in the lab are calling her by first name...  Thanks!

I have worked with my adviser for a few months as a graduate student. Everyone, including her other graduate students, seems to call her by her first name. She never expressed a preference to me, so I've been calling her "Dr. Smith". She signs her emails with her first name.  I am worried that I am being awkward. I don't mind calling her "Dr. Smith", but during meetings where other students are present, it would be jarring to call her "Dr. Smith" while other students use her first name in the same conversation. So far, I have managed to avoid this issue by choosing my words very strategically to avoid directly addressing my adviser at all.  I don't wish my adviser to think that I am making some sort of statement by being unnecessarily formal. On the other hand, I don't wish to appear too informal either. Apart from that, once you've addressed someone by their title for several months, unceremoniously switching to their first name out of the blue seems like it would be very strange.  Is there any tactful way of resolving this predicament, besides waiting and hoping for the adviser to express a preference? I am in the US.


Please forgive me if I am making some very big mistake by asking a silly question like this. By no means do I want to disrespect any of the intellectual people here on Stack Overflow.  I read a few question and answers on Stack Overflow and found that people with very high reputation get upvotes very easily even if the answers are not worthy to get so many of the upvotes.  An example of such a post is this question:-   I know that the obvious answer could be "yes" but that's just an example.  In this I found that people have  given upvotes and also the answer was accepted, just because it's Jon Skeet, the most reputed and most intelligent guy of the world, who has answered.  If some other guy who had less reputation had answered this in a similar manner, then we can very easily see that people would have downvoted and voted to delete the answer. Or the community or other moderators would have deleted the answer.  Why is this sort of behavior present?  P.S. Jon Skeet: Sir please don't get me wrong. I respect you the most on this planet and by no means do I doubt your intelligence. I took you just because all of us respect and appreciate you, and maybe many can understand what I am trying to convey easily. And if by any means I am disrespecting you then please forgive me. But trust me that's not intentional or personal.  EDIT:-  To mark another example as pointed by someone in comments:-    So how come this answer deserves 117 reps ;) Just becasue the person who is answering it has high reputation.  Trust me there are many more which you people can find as your reputations are higher and I have few restrictions because of less rep. But that's how I have seen it.

It's not that I feel bitter when somebody else's answer is upvoted above my own, but it's when a user with a high rep answers a question and their answer seems to attract an immediate barrage of upvotes.  Now I'm not saying that these votes are always unwarranted, but by simply observing this behavior, I think the system seems flawed.    The concept of reputation (or at least one of the concepts) is to give users a sense of trust in the reputed user's answers.  But this should be trust, not blind faith.  I know that this problem doesn't exist for every question asked on SO, but it's definitely present.  I'm sure this is a contentious question, as it might seem overly critical, but does anybody else agree with me and, if so, does anybody have any thoughts on how this problem could be alleviated? It's a great shame when a new or less active user's answer is stifled by the reputation-rich user's answer.


I have ubuntu 16.04. I want to add  sudo modprobe -r psmouse && sudo modprobe psmouse proto=imps   to my startup applications.  I added it succesfully but it isn't running with the startup.  I think because of the password requirement.  Please help me as I want it to run along with start of my laptop.  Is there any other way or is there a way to fulfill my above requirements? Please let me know....

I have been having several issues with my touchpad since upgrading to 12.04LTS.  I believe it is an issue with the Elantech driver.  I have found that the following commands fix my problem, however, the changes seem to be reverted when I reboot.    modprobe -r psmouse modprobe psmouse proto=imps   Is there a way I can make these changes permanent?


I have an Acer Aspire Revo R3600 , intel atom CPU 230 @ 1.6 GHZ, 1G Ram, 120G hard disk and currently running window xp (but in the system properties, it says 895 ram only).  it is slow and so I would like to install ubuntu os on it to improve the performance but not sure what version of ubuntu I should install.  I only found previous literature that people installed Ubuntu version 9.x in this machine written in 2009.  now that ubuntu has higher version.  Can someone advise what is the ubuntu version I should install given this machine spec? anyone tried it?  also, does this version support other lanugage (chinese)?

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


I will be pursuing masters from UT Austin this fall.I have mailed professors for the position of  a teaching assistant. Some of them replied and some did not.  What should I write in the followup email to the professors who did not respond.  Thanks!

When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation)


In episode 4 of season 7 Daenerys with Drogon attacks some of the Lannister soldiers, but then goes on the burn the whole supply line. This may make sense if you expect to lose the batte and you want to destroy your enemy's supplies. However, I think she was fairly confident she would win, so why not save the grain and take it for her own army?   Alternatively, she could have distributed it to the commonfolk and gain major points. Given that she wants the people to believe in her, which is why she did not attack the castles with her dragons, why burn food when winter has arrived? The people will probably not be happy about that.

During Game of Thrones S07E04 we saw a battle take place during the last 10 minutes of the show.     During this battle we see Dany flying around burning everything.  I do understand it is not good TV to have her kill everyone in one pass (she could have flown over the line formed and burned them all at once) but that's beside the point.  The bigger issue is, she complained they lost all their food in the attack the Lannisters did.  Not only did she kill the army, she also made it a point to purposely fly over the caravans and burn them too instead of letting those be for spoils of war.   There was no point to purposely burning the food.  The Lannisters were clearly outnumbered and were easily killed with nowhere to run.  They had no way of sneaking out any of the food either.  She could have left them alone to bring them back since the Dothraki were mounted.  Attaching them to a few horses who lost their masters wouldn't be that big of a deal.  So why did she do it when it was something she even stated they needed?


I want to ask why is $$0! = 1$$ the same as $$1! = 1.$$   As a student I was lost and when I tried to ask the question the teacher said this will be done in complex analysis.  I know here I will thirst my quest by the help of people who understand it.   I know We define $n!$ as the product of all integers k with $1\leq k\leq n$. When $n=0$ this product is empty so it should be 1.   I was just wondering if for factorial we take:  $$6! = 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$$ $$5! = 5\cdot 4\cdot 3\cdot 2\cdot 1$$  In normal multiplication any number multiplied by $0$ = $0$  hence $$0! = 0\cdot 0 = 0$$ hence $$1! = 1\cdot 1 = 1$$  I am confused by this help Thanks.  But then the factorial rule of $0!$ being $1$ is misleading because $0$ x emptyset = emptyset why would it be 1?

How can I prove  from first principles that $0!$ is equal to $1$?


Let's say you were in a race, and you finished 5th. One of your friends comes to you and asks "What was your ___ in the race?".  Or, 'G' is the 6th letter in English alphabet.  Someone asks you what is the ___ of 'G' in English alphabet.  What should come in place of "___" in those sentences?  I thought of "order" maybe, though it doesn't sound correct. Maybe, it shouldn't be asked as in the examples, and should be asked in a different way.

I want to make a question having an answer as follows:     5 is the third prime number.   The bold part is the answer. How to phrase the question?


The WinSXS folder on my PC currently holds over 6.9GB of data, which is a few hundred files inside the folder named like amd64microsoft-******.  I have read, and read but just can’t seem to find an trustworthy answer on the following questions:   What does MRT.exe do?

A Vista virtual machine I use only has a 10 GB virtual hard disk -- and I'm worried about it running out of space over time. I used  to check for the culprits..  And the primary culprit is that /winsxs or "Windows Side-By-Side" folder.  What is the Windows Side By Side folder? Well, that's .  All of the components in the operating system are found in the WinSxS folder – in fact we call this location the component store.  Each component has a unique name that includes the version, language, and processor architecture that it was built for.  The WinSxS folder is the only location that the component is found on the system, all other instances of the files that you see on the system are “projected” by hard linking from the component store.  Let me repeat that last point – there is only one instance (or full data copy) of each version of each file in the OS, and that instance is located in the WinSxS folder.   So looked at from that perspective, the WinSxS folder is really the entirety of the whole OS, referred to as a "flat" in down-level operating systems.  This also accounts for why you will no longer be prompted for media when running operations such as System File Checker (SFC), or when installing additional features and roles. That explains why the folder starts off big, but not why it gets larger over time – the answer to that question is servicing.   In previous versions of Windows the atomic unit of servicing was the file, in Windows Vista it’s the component.  When we update a particular binary we release a new version of the whole component, and that new version is stored alongside the original one in the component store.  The higher version of the component is projected onto the system, but the older version in the store isn’t touched.  The reason for that is the third part of why the component store gets so large.  Lots of other people :  A coworker recently received his every two year work laptop refresh and was in the middle of loading his new laptop with Vista. For some reason, his hard drive C: was partitioned to only 25GB and the rest of the space reserved for a much larger drive D:. Anyway, after loading many Windows Updates, he was left with hardly any drive space left on C:, and for some reason, the WinSxS directory had ballooned to over 8GB. While I knew what the WinSxS (Windows Side-by-Side) directory was for, I wasn't quite sure why that directory would explode in size so fast with normal operating system updates.  I don't really care about having all these duplicate files for safety, but I do care about the VM exploding due to an out of disk space error. So.. can /winsxs be safely pared down in any way? ..  Administrators should not, for any reason, take it upon themselves to clean out the /winsxs directory - doing so may prevent Windows Update and MSI from functioning properly afterwards.  Preventing accidental deletion from the directory is accomplished by putting a strong security descriptor on the directory that inherits to its children.  If this /winsxs folder gets any larger, I'm going to have to re-image this virtual machine.. which I really don't want to do!


I am making a map and I want to be able to give points to players, which I have down (using the scoreboard command). But I want to be able to see if a player has a specific score and reward them with a diamond helmet.     Also, I want to replace the item on their head with the diamond cap, not just use /give to give it to them. If you can give me the command or set of commands that would be great! I'm using 1.9.2.

What if I want to make a command like this:  execute @e[score_A=10] ~ ~ ~ summon Creeper   So that the entity must have a score of 10 (not less, not more)?  Does it even exist that or a [score_A_max=] argument?  I know about scoreboard players test, but i guess it is not the case to use it.


I recently installed an application (VueScan) on Ubuntu 20.04. Works great but I noticed there is no icon in the Gnome app launch menu.  I have to execute the program from the terminal. Once the application (VueScan) is up and running, it works great but I noticed that the icon in the dock is missing too. Any way I can add a missing icon for an app in the dock and create an app icon in the Gnome app launch menu?

Looking for a utility that allows me insert an item into the list of applications that GNOME knows about.   For example: I have downloaded Eclipse EE (I have some very special plugins that I need to work with, and those plugins don't "like" the version available in the default repository). I'm using GNOME 3, on Ubuntu 11.10. So I want to execute Eclipse w/o opening a terminal and running it.   It must be something very simple.


Like the subject states, Has anyone tried something like this to IRCC before? just need some form of Clarification and stuff.  Edits  I am applying for a Tourist visa. Just Visit and come back home, Want to make Canada my second home.

I would like to know if there is a possibility for me to get  a tourist visa for Canada.   I have no invitation letter from anyone from Canada. I have travelled to the UK last year (July 2018) and I also visited Europe (Nov 2017).  Should I apply without having an invitation letter, or do I have to wait until I arrange invitation letter somehow?  If I should apply without having invitation letter then how much funds should I keep on my personal and current account?  I have an IT company here in India.


The goal is to collect the MAC address of the connected local NIC, not a list of all local NICs :)   By using socket and connect (to_a_website), I can just use getsockname() to get the IP, that is being used to connect to the Internet.   But from the IP how can I then get the MAC address of the local NIC ?   Main reason for the question is if there are multiple NICs.

I need a cross platform method of determining the MAC address of a computer at run time.  For windows the 'wmi' module can be used and the only method under Linux I could find was to run ifconfig and run a regex across its output.  I don't like using a package that only works on one OS, and parsing the output of another program doesn't seem very elegant not to mention error prone.   Does anyone know a cross platform method (windows and linux) method to get the MAC address?    If not, does anyone know any more elegant methods then those I listed above?


I have got the following code:  DateTime start = DateTime.Now; Thread.Sleep(60000); DateTime end = DateTime.Now;   and I would like to calculate the difference in minutes between start and end. How am I supposed to do it? For the example above, the result should be '1'.  Thanks in advance!

I need to find a bottleneck and need to accurately as possible measure time.  Is the following code snippet the best way to measure the performance?  DateTime startTime = DateTime.Now;  // Some execution process  DateTime endTime = DateTime.Now; TimeSpan totalTimeTaken = endTime.Subtract(startTime);


I'm using a Minecraft give command generator since I can't format the commands myself. What I'm trying to do is:  /give @p diamond_sword{Damage:1000} 1   or  /give @p minecraft:diamond_sword{Enchantments:[{id:sharpness,lvl:2000}]}   But every time I try that command I get the error: Unknown item name  I have no idea what to do with this issue or where to search about it.  I'm trying all these on my Minecraft Bukkit Server version 1.14.4.

Recently I've been messing around with making a few minigames, and have used a few plugins to help make it easier to create and run them. However, a newer one I'm making requires me to use the /summon command in order to spawn zombies. However, no matter what I put in, I can't spawn hostile mobs. All other entities still spawn perfectly fine. Strangely, the /spawnmob command which comes with Essentials can summon hostile mobs fine. I would rather use /summon since it's more customizable though. Here's a list of plugins I have installed.   Essentials EssentialsChat HolographicDisplays PermissionsEx setspawn [A plugin I have made, just a simple timer] Vault VoxelSniper WorldEdit WorldGuard   Please let me know if you have any ideas on what I'm doing incorrectly or isn't functioning the way it should.


I have a hard drive filled with files, and I need to find a specific file without knowing its name. All I know is that the file contains a list of email addresses. Is there any way I can locate it?

I am trying to locate a file that (should) contains the string "1896.345", somewhere under /home/dir/.  Any ideas of how I can do it? Thanks


Consider a polynomial $p \in \mathbb{R}[x]$ of degree $n$ and with no real roots. Prove that$$\int_{-\infty}^{\infty}\frac{(p'(x))^2}{(p(x))^2+(p'(x))^2}dx$$converges, and is less or equal than $n^{3/2}\pi$ My approach Now let $x_1, x_2, \dots, x_n$ be the roots of $p$. By Cauchy-Schwarz $$(\sum_{k=1}^{n}{\frac{1}{x-x_k}})^2\leq n\sum_{k=1}^{n}{\frac{1}{|x-x_k|^2}}$$ I don't know what to do next. If I am wrong kindly provide a detailed answer in the answer section. I have shown what I have thought of or what I have done . Can anyone confirm if my thought process is right? Just a reminder... This question has been lying unanswered for a long time Thank you.

$ p(x)\in\mathbb{R[X]} $ is a polynomial of degree $n$ with no real   roots. Show that: $$\int\limits_{-\infty}^{+\infty}\dfrac{(p'(x))^2}{(p'(x))^2+(p(x))^2}\,dx \leq n^{3/2}\pi.$$   It's easy to see that the degree of $ p$ has to be even. For $n=2$ this integral is at most $2\pi$. For $n>2$ the maximum value of this integral is obtained when all the imaginary parts of the roots of $p(x)$ tend to $0$, but I couldn't go further.    Any help would be appreciated, thanks.    Edits by David Speyer: It seems very likely now that the optimum bound is $n \pi$, not $n^{3/2} \pi$. As pointed out in the comments below, and further in , this is the value we get in the limit where $p$ has double roots on the real axis.   It seems likely that  moving the roots of $p$ away from the real axis can only make the integral less. Write the roots of $p$ as $a_j \pm i b_j$, so $p(x) = \prod ((x-a_j)^2 + b_j^2)$ and  $$\frac{p'(x)}{p(x)} = \sum \frac{2 (x-a_j)}{(x-a_j)^2 + b_j^2}.\quad (\ast)$$  So making the $b_j$ larger tends to make $p'(x)/p(x)$ smaller, which makes the integral smaller. But this argument is not rigorous, because the terms of $(\ast)$ can have both positive and negative sign, so it could be that making the individual terms closer to $0$ makes the absolute value of $(\ast)$ larger.  I don't see how to beat this issue easily.  Thus, I'm putting up a bounty for proving or disproving   $$ \int_{-\infty}^{+\infty}\dfrac{(p'(x))^2}{(p'(x))^2+(p(x))^2}\,dx \leq n\pi.$$


How to control fan speed in ubuntu 20.04 with fan control software

How can I control the computer's fan speed?  On Windows there is a wonderful program called .


I have a raster layer containing climatic monthly data:   rainfall maximum and minimum temperatures   There is one layer for each variable and month.  I want to extract the average and maximum values for all of these layers into an Excel sheet.  Is there a way to do this without having to manually extract each value for every raster layer?

I work with QGIS GDAL,I have many raster image 'geotiff' with one band for many dates, I want to create a table that contains statistics for all rasters that I have. I tried the algorithm 'raster layer statistics' in QGIS but it gives just an 'html' file for one raster in input, but what I need is to have as result a table that contains statistics for many raster of many dates. I want result like table (csv,txt format..) that gives:  dates mean min max..  Any help to do this with QGIS?


What can I do that all tabs stay in the foreground all the time?  Imagine you have two windows open; one is, for example, Google Chrome, this one is fullsize. The second one is a normal sized terminal. If I do something in the terminal it's in the foreground, but if I then click something in the browser, the terminal will go to the back. What can I do to hinder the terminal or any other window to going to the background when it loses focus?

I'm using Lubuntu 14.04 64 Bit and I need to have the "Always on top" feature so I can have any window always visible if I need to.  I've searched a lot up and down, but to my surprise I could not find anything.  Is it possible at all to have this feature ?


I work with a very large bibtex file when I write articles. The bib file is in version control and is collaboratively edited by a large group of scholars with similar interests. This creates a 'moving target', which means that if I go back to compile an article that was written years ago, some of its references may have been changed, so the result does not equal the original, as it would have compiled then. At the same time, creating multiple copies of this very large bib file would be very inefficient.  One solution is to simply save a pdf of the compiled document in version control (I do this currently, and will continue to do this). Additionally, I also wondered if it is not possible to just add the bbl file to version control. That way you don't need to access any bib file to compile the document as it was. Is this a valid approach? Any drawbacks? Other suggestions?

My colleague asked me to write a page for a paper he writes. I wrote the page in LyX, compiled it to LaTeX, and sent him the TeX files. Then he reminded me that I forgot to send the .bib file with all the references.  But, my .bib file is huge - it contains over 1000 references (I have a global BiBTeX file for all my papers). The page I wrote uses only about 20 of them.  Is there an automatic way to extract from the bib file, only the records relevant to the current paper?


Given $f$ entire function on $\mathbb C$ and $f$ one-one. Is it true that $f$ is linear?  At least among polynomials the only such functions are linear!

Can we prove that every entire one-to-one function is linear?


In the context of differential geometry, we have a smooth vector field $X$ and an integral curve of $X$ called $\gamma$ such that $\exists\ t_0 \in \mathbb{R}$ with $\gamma'(t_0) = 0$. The exercise asks to prove that under those conditions, $\gamma$ is constant.  Invoking the Picard-Lindelöf theorem of existence and uniqueness of differential equations that can easily be proved.  I was wondering if there was another, more indirect and "by hand" way.  Thanks!  PS: I don't think this is a duplicate question, as it's not the same to have an integral curve into an arbitrary manifold as it is to have one to $\mathbb{R^n}$. Of course, given Anthony's answer, I can see that this specific question can be answered by reducing it to the other case. But there could also be another answer that takes a different approach.

Let $U$ be an open subset of $\mathbf R^n$ and $V:U\to\mathbf R^n$ be a differentiable vector field on $U$. Let $\mathbf p\in U$ be a singular point of $V$, that is, $V(\mathbf p)=\mathbf 0$.     Then the only integral curve which starts at $\mathbf p$ is the constant curve.   I know that one could simply use the theorem of "uniqueness of integral curves" and in fact adapt the same proof for this particular case.  But is anybody aware of a simple argument for this?


Is there the Lunatic Cultist on Terraria 1.2.11979? I defeated the Golem but the Cultist won't spawn.

I'm a mobile Terraria player and I have heard of hard mode, and gotten it. Now I also heard of expert mode but I can't seem to find anyway to get it. How can I get expert mode on mobile Terraria?


Which of the following notation is a correct definition of the square function?   $f(x) \triangleq x^2$ $f(x) := x^2$ $f(x) = x^2$ $f(x) \equiv x^2$   While this question is similar to , the aforementioned question and its answers do not address the usage if these symbols in the context of function definition.

I'm interested in knowing what is the meaning of the various equality symbols: $=,\sim, \cong,\approx,\equiv$.  For example, the speed of a car $V$ in m/s: what would be the meaning of each of these statements? $$V = 30\\ V\sim 30\\ V \cong 30\\ V \approx 30\\    V \equiv 30$$


I'm making school web application which will be for testing users SQL knowledge and they have to enter SQL queries in form textarea and execute it on server mySQL. the problem that occurred to me is that I can't do prepared statements or binding or white-list on unknown dynamic queries(entered by user) and this makes the application SQL injection vulnerable.  How can I prevent SQL Injection on this type of queries(allowed will be SELECT, DELETE, INSERT, UPDATE) without affecting the final compare result?  Maybe I'm missing some PHP function which can do that? or I have to create a SQL parser which will check user queries for possible SQL injections? I'm not trying to do anything fancy, I just need basic protection for my application.  I use CodeIgniter as Framework, but I don't think this will change anything.  How can I use PDO, statements,whitelists and other techniques, when user can enter queries like   select * from user where some_column = some_value (this is just example)   or query like  select * from user LEFT JOIN ..... having something > 5 ORDER by some_column   I can't predict their input and all possible combinations can contain injection vulnerability.  I receive on my end $_POST['SQL_user_query'] which contains string of SQL query, I can't use on it prepared statement.  EDIT: what i want is that is to prevent the users to do destructive things with my database and gain information about the tables, because after they submit the query the web application also will show the result from the query under the  input textarea and if they make injection that can show sensitive information.

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


I was searching through the internet for an equation that defines the path followed by a racing line, when I came across the following formula on StackExchange . However, I could not understand what kind of maths is being used in the proof submitted by this user:  I created this account, but couldn't comment on the user's proof, so I decided to post it as a question. I would appreciate it if someone was able to explain to me just what kind of maths was used to solve the problem.  I understand that it involves trigonometry, but I can't seem to figure out exactly how he used it to solve this problem and how he applied trigonometry to solve it, as I don't think I have advanced that far in maths. I am not sure how I am supposed to apply trigonometry here because I honestly cannot understand how each he (or she) transitions from the first equation to the second and then to the third.

I am in the process of designing a board game involving car chases, and I am stumped by the following problem:  A car will have a maximum speed through a constant radius speed turn, giving a maximum safe cornering speed for a given turn radius. But, if the car follows the racing line (an apex turn?), the radius of the turn is greater, and the car can take the turn faster  A simplified situation would be sufficient to cater to my needs (no need for curves of changing radius, etc), see i.stack.imgur.com/odIyF.jpg for an illustration    The radius of the racing line R(race) must be dependent on 3 factors: Outer radius: R(outer) Inner radius: R(inner) And the length of the turn in degrees.  From this I should get R(race)  R(inner) and R(outer) have the same center, and the center of R(race) must be somewhere on the line that bisects the turn (midpoint of the curve)  I would love to have a formula for the 90 degree turn, but preferably I would like a general solution, where the turn can be of any angle of turn (up to 180 degrees or more). Looking at my sketches, at 180 degrees of turn, the radius of the racing line will equal R(outer), while the radius will approach infinity, as the angle of turn becomes smaller and smaller  I have tried searching online for answers, but the formula I have dug up have given results I haven't been able to reproduce when mocking up on graph paper


I'm using Ubuntu 18.04.2 x64 installed on an internal SSD. The PC also has internal and external HDDs.  The problem is that any application that has been installed from Ubuntu Software doesn't have access to those HDDs.   E.g., I cannot save any file from Opera to them, and Inkscape cannot open/save the files from/to those HDDs.   I've tried changing the apps' permissions in Ubuntu Software itself but they are never saved.  How can I overcome such issues?

I have Ubuntu 18.04 LTS installed. I inserted USB-flash to my laptop. It was automounted to /media/username/DISKLABEL and opened in Nautilus. I can read and write objects to it. How can I access it from the application, which is installed as Snap? I tried snaps of the following applications such as gedit, arduino-mhall119, organize-my-files. All them show me errors if I navigate to /media folder:    Could not read the contents of Media Error opening the directory of '/media': permission denied  Output of active Snap  is below: $ snap interfaces  | grep -v ".*-$" Slot                             Plug :browser-support                 organize-my-files :core-support                    core:core-support-plug :cups-control                    gedit :desktop                         gedit,organize-my-files :desktop-legacy                  gedit,organize-my-files :gsettings                       gedit,organize-my-files :home                            arduino-mhall119,gedit,organize-my-files :network                         arduino-mhall119,gedit,organize-my-files,pulsemixer :opengl                          organize-my-files :pulseaudio                      organize-my-files,pulsemixer :unity7                          arduino-mhall119,gedit,organize-my-files :wayland                         gedit :x11                             arduino-mhall119,organize-my-files,pulsemixer gnome-3-26-1604:gnome-3-26-1604  gedit gtk-common-themes:gtk3-themes    gedit gtk-common-themes:icon-themes    gedit gtk-common-themes:sound-themes   gedit -                                arduino-mhall119:serial-port -                                gedit:avahi-observe -                                gedit:mount-observe  Updates:  connecting mount-observe to Gedit with snap connect gedit:mount-observe does not help. it seems that we need special Snap with support of  interface.


I am making a game where if the player is at half a heart I want to teleport them to a place. Is it possible to detect player health with command blocks? Thanks.

I am creating a mini-game in Minecraft, where I must check to see if the player is injured. The injured player will then be given an item. My guess is that the command would look something like /testfor @p[injured=true], but this command doesn't work. Is there a command for this?


I am making a scene with a particle effect system in it, and I am wondering how I can take away the glow from the object. It is really bright, and it is not intended to look like that. Thanks

I've setup a plane with a particle emitter system. When I render the footage and the particles are glowing. Where do I find the settings for that?


I have the following code:   Iterator<ggItem> iter = ggItemTimestampMap.keySet().iterator();  ggItem gg;  while (iter.hasNext()) {         gg = iter.next();         if (DateTime.now().isAfter(ggItemTimestampMap.get(gg).plusSeconds(10))) {              Log.v("ggItem 10 second limit:", gg.toString());              //If it hasn't been seen 10 seconds after its last timestamp. Remove it from the ArrayList and remove it from the ggItemTimeStampMap HashMap.              ggItemTimestampMap.remove(gg); //TODO probable problem causer.              removeggItemFromList(gg);          }  }   I get a ConcurrentModificationException error on the iter.next(); call and am uncertain why?  I realize you cannot both access a hashmap of object keys and timestamp values and modify it at the same time, but doesn't the iterator counteract that?

We all know you can't do the following because of ConcurrentModificationException:  for (Object i : l) {     if (condition(i)) {         l.remove(i);     } }   But this apparently works sometimes, but not always. Here's some specific code:  public static void main(String[] args) {     Collection<Integer> l = new ArrayList<>();      for (int i = 0; i < 10; ++i) {         l.add(4);         l.add(5);         l.add(6);     }      for (int i : l) {         if (i == 5) {             l.remove(i);         }     }      System.out.println(l); }   This, of course, results in:  Exception in thread "main" java.util.ConcurrentModificationException   Even though multiple threads aren't doing it. Anyway.  What's the best solution to this problem? How can I remove an item from the collection in a loop without throwing this exception?  I'm also using an arbitrary Collection here, not necessarily an ArrayList, so you can't rely on get.


I have been playing with the series which I had been calling the 'Double Basel problem' for the past couple of hours $$ \sum_{n=1}^{\infty} \sum_{m=1}^\infty \frac{1}{{n^2 +m^2}}. $$ After wrestling with this for awhile, I managed to generalize a result demonstrated . This identity is: $$ \sum_{m=1}^{\infty}\frac{1}{x^2+m^2} = \frac{1}{2x}\left[ \pi \coth{\pi x} - \frac{1}{x}\right]. $$ Hence the original series becomes: $$ \sum_{n=1}^{\infty} \frac{1}{2n}\left[\pi \coth{\pi n} - \frac{1}{n} \right]. $$ I have no idea where to go next with this problem.  I seriously doubt that this series is convergent; however, I have been unable to prove it.  Can you prove that this series is divergent? If it converges what is its value?  Thanks so much!


For some reason I keep getting this strange restricted view only in solid & wireframe viewport mode. Doesn't appear in render preview. See the attached pics to see what I mean. Can anyone tell me what this is and how to remove it please. In solid preview: And in render preview:

When looking at my objects in 3d view I'm seeing a gray cone that seems to be hiding other objects.   Can anyone help me turn this off and explain what it is please.  Screenshots attached.


My solution is as follows: Let $d_1= (a,b) > 0$. Then by Bezout's identity, there exists integers $x_1$and $y_1$ such that, $d_1=ax_1+by_1$. Similarly let $d_2 = (a+c,b) > 0$ then there exists integers $x_2$ and $y_2$ such that, $d_2=(a+c)x_2+by_2$. Then since $b\mid c$ there exists integer $k$ such that $c=bk$ for some $k$. Note that, $d_2=(a+c)x_2+by_2$. Since $c = bk$ then, $d_2=(a+bk)x_2+by_2$ $\Rightarrow$ $d_2 = ax_2+b(kx_2+y_2)$, which is a linear combination in $a$ and $b$. Since $d_1 = (a,b)$, it divides any linear combination in $a$ and $b$. Thus $d_1\mid d_2$. Similarly, $d_1=ax_1+by_1$ $\Rightarrow$ $d_1=ax_1+by_1+cx_1-cx_1$. Since, $c=bk$ $\Rightarrow$ $d_1=(a+c)x_1+b(y_1-kx_1)$. Which is a linear combination in $a+c$ and $b$. Thus $d_2\mid d_1$. Since $d_1$ and $d_2$ are $\gcd$ of two integers, and $d_1\mid d_2$ and $d_2\mid d_1$, we conclude that $d_1=d_2$ as desired. Thank you for reading upto here. If there is any errors feel free to comment.

Given: $a = qb + r$. Then it holds that $\gcd(a,b)=\gcd(b,r)$. That doesn't sound logical to me. Why is this so?    Addendum by LePressentiment on 11/29/2013: (in the interest of  and averting a duplicate)  What's the intuition behind this result? I only recognise the proof and examples solely due to algebraic properties and formal definitions; I'd like to apprehend the result naturally.


I just created an SO account to offer some feedback to .  Although I can apparently post a whole answer, or even edit others' answers (okay, it's moderated, but still), I can't post feedback to the one answer on that page I wanted to.  I don't have anything to add further to the other answers already posted, but I wanted to post a likely explanation as to why the poster of the linked answer didn't get a flush.  (The calls to flush and close lack parens, so all you get is a reference to the function, not an invocation of it.)  The tips popup for the answers makes it clear that answers should answer the OP, not address other answers.  I don't want to edit the answer at hand (even if it would be accepted), because it's not my post.  Can I do anything, or should I wait until I've built up enough reputation?

Users with less than 50 reputation points cannot write comments on questions and answers that they don't own.  Why does this limit exist? But I want to contribute now. What should I do instead? But I can't write a good answer without more information! Shouldn't I be allowed to post comments if I have reputation on a different site? But I saw a new user posting a comment! How did they do it? Why do I need 50 reputation to comment on my own post?   See also:    in the Help Center


The higgs boson is an elementary particle so how it can decays into another elementary particle; the photon? And why the photon doesn't interact with the Higgs field?

Why don’t photons interact with the Higgs field and hence remain massless?


After upgrading from 16.04 to 18.04 I see there is a menu on top that supplies a way to quit the selected app, but this seems half implemented.     I would imagine the main (file++) menu could be exposed there like in previous versions of Ubuntu. Thus the following should be exposed there:    Is there a way to make this happen?

I installed the latest version of Ubuntu (17.10) , but the problem is, I can't find the menu bars of applications in the GNOME panel. For instance, the Chrome menu bar doesn't appear on the panel like in Ubuntu 17.04 and earlier versions.