Pointwise convergence, bounded variation, and lim inf's
Pointwise convergent and total variation
What did my neural network just learn? What features does it care about and why? I'm doing some web scraping and sites frequently use HTML entities to represent non ascii characters. Does Python have a utility that takes a string with HTML entities and returns a unicode type?  For example:  I get back:  &amp;#x01ce;   which represents an "ǎ" with a tone mark.  In binary, this is represented as the 16 bit 01ce.  I want to convert the html entity into the value  u'\u01ce' Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$. $Q$ is unitary, so $QQ^*=I$ If $A$ and $B$ are positive-definite, than $A=A^*$ and $B=B^*$. $A^*=(BQ)^*=Q^*B^*$ $A^2=AA=AA^*=(BQ)(Q^*B^*)=B(QQ^*)B^*=BIB^*=B^2$ $A^2=B^2$. I don't know how to use the fact that $A$ and $B$ are positive-definite to finish the proof. Is there any Sound enhancers/equalizer? Does someone know how to set a command block with a command inside using the setblock command?  I have created this code /setblock &lt;x&gt; &lt;y&gt; &lt;z&gt; command_block {TileEntityData:{Command:"testfor @p[_=1]"}} but it doesn't works.  Do someone know how to do that? Why did Slytherin House not get disbanded? GCD in a PID persists in extension domains Taking notes, I was going to write this:     therefore p′ is a shortest path.   But the topic is APSP which stands for "all pairs shortest paths" so I decided to just write SP instead and...  Is it written with a like this     therefore p′ is a SP   or with an like this (because in my head I would "read" the S)     therefore p′ is an SP Change Default Scrolling Behavior of UITableView Section Header Batch-Resizing images in OS X to a certain height Let's fix some terminology first. A category $\mathcal{C}$ is preabelian if:  1) $Hom_{\mathcal{C}}(A,B)$ is an abelian group for every $A,B$ such that composition is biadditive,  2) $\mathcal{C}$ has a zero object,  3) $\mathcal{C}$ has binary products,  4) $\mathcal{C}$ has kernels and cokernels.  A category $\mathcal{C}$ is abelian if it is preabelian and satisfies:  5) every monomorphism is a kernel and every epimorphism is a cokernel.  Define the coimage of a map to be the cokernel of its kernel, and the image to be the kernel of its cokernel. We have the following commutative diagram:    where $\overline{f}$ is the only existing map (because of universality of kernel and cokernel).  I'm having trouble proving the following:     A preabelian category $\mathcal{C}$ is abelian iff $\overline{f}$ is an isomorphism.   The converse is easily shown, I'm having trouble proving $\Rightarrow$... Align an object to a specific face I usually face this problem when I cut objects to make them printable in my 3D printer. As you may know, you need your object to have a nice base to be printed.  So I usually use bisect to cut an object to different pieces. As in this example:    and I need to rotate the top part to have a face as bottom:    I'll share my workflow in an answer, but I'm asking for a simpler solution, if there were any. This code is part of a larger code that generates an Arithmetic Quiz, although the code I have show below just saves the score that the user got on the test and their name. When saving the code it checks if the user has taken the quiz before. If the user has taken the quiz before it saves it as 'Older Score' or 'Oldest Score', however if the user has not taken the quiz before it generates a new row for them. Additionally it works out the average score and highest score for all users it has the data for. For my task I'm supposed to make the code as short as possible.  name = ""+first_name+" "+last_name rows_data = [] class_file_names = ['Class 1.csv', 'Class 2.csv', 'Class 3.csv'] scan = open(class_file_names[int(math_class)-1], 'r+') rows = csv.reader(scan) for row in rows:     rows_data.append(row) scan.close() class_file_names=['Class 1.csv', 'Class 2.csv', 'Class 3.csv'] csvfile=open(class_file_names[int(math_class)-1], 'w', newline="") fieldnames = ['Student Name', 'Oldest Score', 'Older Score', 'Latest Score', 'Average', 'Highest'] writer = csv.DictWriter(csvfile, fieldnames=fieldnames) writer.writeheader() nameFound=False for x in rows_data[1:]:     if x[0] == name:         x[3]=x[2]         x[2]=x[1]         x[1]=str(score)         x[4]=(int(x[1])+int(x[2])+int(x[3]))/3         x[5]=max(x[1],x[2],x[3])         nameFound=True     writer.writerow({'Student Name': x[0], 'Oldest Score': x[3], 'Older Score': x[2], 'Latest Score': x[1], 'Average': x[4], 'Highest' : x[5]})  if nameFound==False:     writer.writerow({'Student Name': name, 'Latest Score': score, 'Older Score': '0', 'Oldest Score': '0', 'Average': score, 'Highest': score}) csvfile.close() input("Test complete! Press anything to close.") What is the value of $1^i$? $\,$ 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. Are collective nouns always plural, or are certain ones singular? Lots of questions in the reopen queue Iterating each character in a string using Python In C++, I can iterate over an std::string like this:  std::string str = "Hello World!";  for (int i = 0; i &lt; str.length(); ++i) {     std::cout &lt;&lt; str[i] &lt;&lt; std::endl; }   How do I iterate over a string in Python? Proving a direct product of groups is a group Python - email header decoding UTF-8