Is it true, that a compact (topological?) manifold without boundary is a boundary of another compact manifold? Intuitively it looks like for most manifolds there must be some relation similar to $\mathbb{S}^n=\partial D^{n+1}$.  It looks like a very trivial question, though I can not find any reference.  Thanks.
What are some examples of manifolds that do not have boundaries and are not boundaries of higher dimensional manifolds?  Is any $n$-dimensional closed manifold a boundary of some $(n+1)$-dimensional manifold?
Got a bunch of .mp4 videos (info shows H.264 Video + AAC Audio) that are chapters of a larger video.  I'd like to merge them, but not sure which is the best way.  I don't have Quicktime Pro, but I'll get it if that's the best way to do this.  Edit: Just to clariify this is Mac OSX 10.6 I'm on. Are there functions or packages in Mathematica to sort subsets in lex order, colex, revlex, etc.? wrong numbering for subcaption in scrbook When using the scrbook document class in combination with the subcaption  package, the numbering of subfigures seems broken. Consider:  \documentclass{scrbook} \usepackage{xcolor} \usepackage{caption} \usepackage{subcaption} \captionsetup{%   format=hang,%   font=small,%   labelfont={sf,bf},%   aboveskip=0.2\normalbaselineskip,%   position=top } \pagestyle{empty}  \begin{document} \begin{figure}   \caption{Black}   \label{fig1}   \centering \rule{2cm}{2cm} \end{figure}  \begin{figure}   \caption{More figures}   \label{fig2}   \centering   \begin{subfigure}{.3\textwidth}     \centering     \caption{Blue}     \label{fig2a}     \color{red}\rule{2cm}{2cm}   \end{subfigure}   \begin{subfigure}{.3\textwidth}     \centering     \caption{Green}     \label{fig2b}     \color{green}\rule{2cm}{2cm}   \end{subfigure}   \begin{subfigure}{.3\textwidth}     \centering     \caption{Blue}     \label{fig2c}     \color{blue}\rule{2cm}{2cm}   \end{subfigure} \end{figure}  Figure \ref{fig1} shows a black box. Figure \ref{fig2} shows colored boxes, where Figure \ref{fig2a} shows a red box, Figure \ref{fig2b} shows a green box, and Figure \ref{fig2c} shows a blue box. \end{document}   This results in the following display:    Clearly, the figure numbering in the text references is off by one for the subfigures. Instead, if I change the document class to article, it looks fine:     Why does this happen, and how can I prevent it? Is there a difference between "" and {} in BibTeX? Allow only alphanumeric characters for a UITextField TOC entries and labels for included PDF pages I am embedding full pages from another PDF document (using the pdfpages package), but I would like to be able to declare my own section headings before each embedded document (for e.g. hyperlinking / TOC purposes). pdfpages has an experimental feature which lets me do this, but the problem is that I want to put all of these embedded documents inside a section, so I need to insert a section heading and a subsection heading on the first document I embed. Unfortunately pdfpages doesn't seem to be able to do this. Is there a way for me to do this?  Edit: Thank you for the suggestions. I am also in need of something similar for general labels — at the moment I am abusing the addtolist option of \includePDF but the objects I'm labelling aren't really figures or tables. When I cut a layer using marquee tool, I get blur edges to cut side. How do I get sharp edges after cut? I am using rectangular marquee tool to cut a portion of the layer in photoshop cs5, but after cutting, the edges are not sharp, I get blur edges.      how can I get sharp edges? Let me add or change edit summary during edit window (grace period) Would a female Jedi be referred to as Jedi Mistress instead of Jedi Master? Likewise would a Sith female be referred to as a Sith Lady instead of a Sith Lord? I'm trying to compute the infinite series $\sum_{n=0}^{\infty} ne^{-n}$.  I know the answer is $e/(e-1)^2$, but I don't understand how to find this result.  Thanks for the help! How to populate the geometry column in a PostGIS table? After loading a polygon shapefile into PostGIS, the geometry column (geom) is blank for several features. In one case, only a single feature has the geometry calculated and all others are blank. I'm using the PostGIS SHP and DBF loader v.2.0. I am creating a spatial index, and using COPY rather than INSERT. I have loaded several other point datasets and they geom column is populated just fine... (Otherwise, things are working just fine for the polygons: when I create a new feature, the geometry is calculated / geom field populated...etc.) Have I done something wrong when importing the data?  Solution by @ThomasG77 (in comments) PgAdmin3 [doesn't] display features that are too complex but they are present.  You can try SELECT length(ST_astext(the_geom)) from your_table to confirm or you can find &quot;true&quot; empty geometry with SELECT * from your_table WHERE the_geom IS NULL;. How do the PHP equality (== double equals) and identity (=== triple equals) comparison operators differ? What is the difference between == and ===?  How exactly does the loosely == comparison work? How exactly does the strict === comparison work?  What would be some useful examples? how to disconnect main service drop at service panel when upgrading to a 200 amp service panel with service drop coming from bottom underground do I need southern California Edison to come disconnect and then reconnect or can I just do it on my own. I do have a permit. Quickest way to rename files, without retyping directory path How to start X windows inside "Bash on Ubuntu on Windows" After installing the new feature (still "Beta") called  that is a feature subset of Windows 10 Anniversary edition, I get the following message when trying to start X-Windows using startx :    What do I need to tweak / configure in order for X-Windows to launch?  I noticed that xauth was already installed, however I had to install the rest of the framework as follows :  apt-get install xorg openbox Add "paragraphs" to Markdown help Like balpha once , a &lt;br&gt; line break (newline) should be used in very few cases, and surely is not the same as a new &lt;p&gt; paragraph. Still  only explains line breaks, not paragraphs:      Some sites  an additional &quot;New paragraphs only occur when there is a blank line. A single carriage does not create a new paragraph.&quot;, but I feel that's not very clear*, and the emphasis is still on line breaks while it should be on paragraphs:      So: As a minimum, please add (rephrase) a note about the blank line, and maybe use &quot;Only when really needed [...] force&quot;:  Paragraphs and line breaks Simply use a blank line between two paragraphs to start a new &lt;p&gt; paragraph. Only when really needed, end a line with two spaces to force a &lt;br/&gt; line break: How do I love thee?__     Let me count the ways   I'd even prefer an explicit example, simply as I think &lt;p&gt; should be favoured over &lt;br&gt; in most situations:  Paragraphs and line breaks Simply use a blank line to start a new &lt;p&gt; paragraph: First sentence in the first paragraph. Another sentence. And a third. Maybe making this multiple consecutive lines of text, but still one paragraph.  The second paragraph.  Only when really needed, end a line with two spaces to force a &lt;br/&gt; line break: How do I love thee?__     Let me count the ways   Alternatively, slightly change the existing &quot;Linebreaks&quot;† part, and above that add a standalone section, :  Paragraphs A paragraph is simply one or more consecutive lines of text, separated by one or more blank lines: A blank line is any line that looks like a blank line. A line containing nothing but spaces or tabs is considered blank.  Normal paragraphs should not be indented with spaces or tabs.  Line breaks Only when really needed, end a line with two spaces to force a &lt;br/&gt; line break: How do I love thee?__     Let me count the ways   And: maybe even add a section &quot;Paragraphs&quot; to the inline post help on top of the editor? I'm not sure which help tab should then be shown  though.  * Also note how not all sites highlight the two spaces with a different background color. † Yes, I think &quot;line break&quot; likes a space too... I'm currently making a Minesweeper in C#. I've already done the basics (generating minefield, rules and ui) but I don't know how I should implement when the user clicks a cell and the cell has no mines nearby and clicks nearby cells with also no mines nearby, like this:    And after click    This is my current code on this:  if (MineField(x,y) == false) // If the clicked cell isn't a mine {     if (GetNeighbours(x,y) == 0) // GetNeighbours returns the amount of mines in the closest 8 cells     {         // To be honest, no idea...     } } Why did Voldemort hide two Horcruxes in Hogwarts? Getting hybrid graphics to work nvidia-prime GT650M I recently made the switch to Ubuntu. Everything on my laptop works fine except my hybrid graphics card. It is Intel graphics combined with Nvidia GeForce GT650M. I tried Bumblebee, but primusrun doesn't work (segmentation fault, core dumped) and optirun works with glxspheres64, but steam games look worse with optirun than with Intel graphics (e.g. Surgeon Simulator 2013 runs fine with Intel and hangs a lot with optirun)   I tried Nvidia Prime, but it gives me a black screen on startup after install, so I can't do anything and have to power off my PC with the power button. I also tried nvidia-prime 0.5 on Ubuntu 14.04, and then I get 'low-graphics mode' and I can't get to Unity. How does a wizard or bard learn new spells?