Is it possible to define a group structure on arbitrary set?
How to define binary operation on arbitrary set in order to create a group structure.
How does the reparameterization trick for VAEs work and why is it important? How does the  for variational autoencoders (VAE) work? Is there an intuitive and easy explanation without simplifying the underlying math? And why do we need the 'trick'? How to move boot and root partitions to another drive How to add field history and product as a related list of opportunity in vf page I am trying the below code to add field history and product as a related list of opportunity in vf page, but its not working .  &lt;apex:relatedList list="OpportunityFieldHistory"/&gt; &lt;apex:relatedList list="Product"/&gt;   Can anyone tell me what is the correct way to write it.  Regards    Edit:  There are two Standard objects that have Opportunity history information,  and . The relatedList component works fine with a value of OpportunityHistories for the list attribute, but an error is thrown when using the value of Histories, even though the SObject describe information shows "Histories" as the child relationship name.   &lt;apex:relatedList list="OpportunityHistories"/&gt; &lt;!-- Works fine --&gt; &lt;apex:relatedList list="Histories"/&gt;            &lt;!-- Error --&gt; FasterCsv doesn't show any result in my view in Ruby on Rails? CSS3's attr() doesn't work in major browsers How to find roots of $X^5 - 1$? How to find roots of $X^5 - 1$? (Or any polynomial of that form where $X$ has an odd power.) Question on the correlation between two dependent variables I'm working on this question and it's stumping me.     Let $S_n = X_1 + \ldots + X_n$ (with $n&gt;=1$) be a random walk with $X_1, \ldots, X_n$ be iid RV's.   $$ E(X_k)=\mu,\,{\rm Var}(X_k)=\sigma^2.  $$   Find the covariance of $S_n$ and $S_m$   Can anyone help out? I am trying to use the equation: $${\rm Cov}[S_n, S_m] = E[S_nS_m] - E[S_n]E[S_m]$$  but can't quite figure it out. How to blacklist kernel modules? How do I disable loading of unnecessary kernel modules. Kernel 3.2.4 Unemployed person applying for UK visa GET and POST methods with the same Action name in the same Controller What are the practical implications of a name change for international travel and activities abroad? I am considering a name change, which seems to be a relatively straightforward action, when one remains in the same country: certain documents are replaced with new ones bearing the new name, and others are presented together with the name change document.  However, I travel internationally multiple times per year, and I often change temporary residence from one country to another. So I often deal with immigration and similar things. Furthermore, I have a lot of things going on like work and studies.  Quite obviously, if I change my name, I would often have to produce a proper translation of the name change document, which may include notarized translation thereof with apostille or, for example, traduction assermentée in France.  However, it would be great to hear about experiences of people, who have dealt with this issue first-hand, so I can weight the disadvantages against advantages of this correctly. In particular, I would like to know if anyone has encountered unforeseen difficulties with this, and how people rate the overall difficulty of such experiences. delete vs delete[] operators in C++ Tweak showlabels/showkeys - wrap the label Why is sample standard deviation a biased estimator of $\sigma$? According to the Wikipedia article on  the sample SD   $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$  is a biased estimator of the SD of the population. It states that $E(\sqrt{s^2}) \neq \sqrt{E(s^2)}$.   NB. Random variables are independent and each $x_{i} \sim N(\mu,\sigma^{2})$   My question is two-fold:   What is the proof of the biasedness? How does one compute the expectation of the sample standard deviation    My knowledge of maths/stats is only intermediate. Why taking components of a component of a vector is invalid? What is the difference between OpenOffice and the newly created LibreOffice? What is the difference between OpenOffice and LibreOffice? I understand that LibreOffice is another fork that is going to be developed. I have used OpenOffice since v1 and am wondering if there is a definite advantage to uninstalling and trying LibreOffice. I have a database which contains 5 tables. Each table contains 24 rows and each row contains 4 columns.  I want to display these records in Excel sheet. The heading of each table is the name of the table, but I am unable to merge the columns for heading.  Please help me. Italics/roman in BibTeX I use a BibTeX style which automatically italicises booktitles (using \emph). I have certain entries which contain italicised words in the title. I would like these to appear non-italicised (in roman) in the final PDF output. Using any of \emph or \textit or \textrm on these items doesn't seem to make any difference -- the whole title still appears in italics.  Minimal .bib entry  @PHDTHESIS{klein1974, author = {Klein, Jared S.}, title = {The Particle \emph{u} in the {R}igveda}, school = {Yale}, year = {1974}, address = {New Haven, CT}, timestamp = {2009.12.04} }   Minimal .bbl entry generated by sp.bst:  \bibitem[{Klein(1974)}]{klein1974} Klein, Jared~S. 1974. \newblock \emph{The particle \emph{u} in the {R}igveda}. \newblock New Haven, CT: Yale dissertation. How do I install VMware player on a Mac os X? I went to their site, and downloaded a .bundle which automagically turned into a .txt file after downloading.   Long story short, I can't run the txt file because I guess Mountain Lion Mac os X isn't a strict Linux box and is missing some core components to do that type of installation.  Does anyone know how to install VMware? How did Asuna and Kirito survive? In the last episode of Aincrad arc of Sword Art Online, how did Asuna survive even though her avatar disintegrated after being attacked by Kayaba? Also Kirito was stabbed by Kayaba as well. How did he survive?  Was it in the novel on how they really survived?