Link infinite series to finite series
Deriving Sum of a Geometric Progression
How to compute azimuth between QgsPointV2s? The  class has an azimuth() method but the new  class does not. What's the best way to compute the azimuth between QgsPointV2s? I couldn't find a convenient way to convert V2 to the old version, so my fallback is to construct a QgsPoint from the V2's x and y:   self.traj = QgsLineStringV2(...)     p_i = self.traj.pointN(self.i) # this returns a QgsPointV2 p_j = self.traj.pointN(self.j) a = QgsPoint(p_i.x(),p_i.y()).azimuth(QgsPoint(p_j.x(),p_j.y()))   Is there a better way? Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$ I am given the info that A is an invertible  m by m matrix and B is a m by n matrix. By solving for the null space $ABx=0$, I get $A^{-1}ABx=A^{-1}0$, therefore $Bx=0$. I concluded that the null spaces of A and AB must be equivalent, and therefore the nullity(AB) = nullity(B) = some number p. Therefore rank(AB) = n-p = rank(B)   (because both AB and B are m by n matrices).   Is this proof valid, specifically the null space step? Can you use another material as input to material nodes in cycles? Prove a differentiable function between banach spaces is continuous I really don't know where to start with this problem. It intuitively makes sense from basic calculus knowledge but I have absolutely no clue how to show it. , Will I be demoted to a lower league in Starcraft 2 if I don't play? I've just been promoted from platinum league to diamond and master pretty fast (in 4 vs 4). This was totally amazing for me but I'm afraid I will be demoted again to a lower league as fast as I came higher.   If I don't play any 4 vs 4 anymore, will they demote me to a lower league automatically or do they only do so, if I play? I am aware there are many questions similar to this on MSE but I am having trouble following any of the solutions given.   I have the function given by   $f(x) = \dfrac{xy}{x^2+y^2}\;$ for $(x,y)\neq (0,0)$ and $f(0,0)=0$  I have calculated the partial derivatives and found:   $$\frac{\partial f}{\partial x} = \frac{y(-x^2+y^2)}{(x^2+y^2)^2}, \quad \frac{\partial f}{\partial y} = \frac{x(-y^2+x^2)}{(y^2+x^2)^2}$$  Now I need to show the partial derivatives exist for $(x,y) = (0,0)$.  I am also asked to show it is not continuous at $(x,y)=(0,0)$, based on other answers I've seen it seems like this follows from solving the first part but I fail to see how that follows through as well.   I could just copy the solutions with my function in place as I have seen a lot of answers using the definition of the derivative, but realistically I do want to understand what the thinking behind this is.   Any help would be appreciated. reference variable In some text it is given that we can't assign constant values to a reference variable. When I executed such a program I could do it. Is there any condition we can't assign a constant value to a reference variable? 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. MySQL Error 1093 - Can't specify target table for update in FROM clause I have a table story_category in my database with corrupt entries. The next query returns the corrupt entries:  SELECT *  FROM  story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category INNER JOIN         story_category ON category_id=category.id);   I tried to delete them executing:  DELETE FROM story_category  WHERE category_id NOT IN (     SELECT DISTINCT category.id      FROM category        INNER JOIN story_category ON category_id=category.id);   But I get the next error:      #1093 - You can't specify target table 'story_category' for update in FROM clause    How can I overcome this? postfix - how to prevent users from sending with another users name Even though my postfix server cannot be used without authentification (open relay), sending mail in another users name after logging in is still possible like this:  EHLO domain.org auth plain eW91IGxpdHRsZSBkaXJ0eSBiYXN0YXJkIDstKQ== 235 2.7.0 Authentication successful mail from: otheruser@domain.org 250 2.1.0 Ok rcpt to: recipient@otherdomain.org 250 2.1.5 Ok data 354 End data with &lt;CR&gt;&lt;LF&gt;.&lt;CR&gt;&lt;LF&gt; Please send me your account info. . 250 2.0.0 Ok: queued as D40692A61AA quit   How can this be prevented? arccot limit: $\sum_{r=1}^{\infty}\cot ^{-1}(r^2+\frac{3}{4})$ Where are the evolutionary "inbetweeners"? The problem I've always had with evolution is the actual lack of variation between animals. More specifically, the lack of observable gradual change between species.  Take for example the hammerhead shark. It obviously has a strong connection with a normal shark, but where's the "half-hammerhead" shark? Where's the species that only has a SLIGHTLY wider head?  I really doubt that a single mutation on a normal shark resulted in a head shaped like that, it had to happen gradually. Right? As far as I understand, evolution works by random mutation in a child being somehow slightly beneficial to that animal so it get's to live longer and reproduce more, eventually resulting in it's genetic material in dominating the inferior ones before it. But if it was for whatever reason beneficial to have a slightly wider head, why don't all the sharks have slightly wider heads now? On the other hand, if it wasn't beneficial, how come the hammerhead still exists?  Furthermore, I feel like some characteristics of a certain animal can't really have gradual benefits. There's a lizard that shoots blood out of it's eyes. The original ancestor certainly didn't, and I'm sure that if it's child only bled slightly from it's eyes it wouldn't really help if much in life. So for it to actually become beneficial, it seems to me that there had to be a ton of lizards that had a disadvantage of bleeding slightly. In fact, there had to be so many that they evolved even further in the same direction and kept doing that until they bled so much it's an actual benefit (sorry for this turning so gross). So why did the inbetweeners survive long enough to evolve even more, and why did they THEN die out? What is the difference between a "link function" and a "canonical link function" for GLM In Windows 7, How to query times, when the computer was locked? Is there a way to get a list of the following times:  whenever windows is locked (using windows+l combo)  whenever windows is unlocked in the past week?   I've tried poking in the event log, to no avail. Many thanks! Can grep output only specified groupings that match? Say I have a file:  # file: 'test.txt' foobar bash 1 bash foobar happy foobar   I only want to know what words appear after "foobar", so I can use this regex:  "foobar \(\w\+\)"   The parenthesis indicate that I have a special interest in the word right after foobar.  But when I do a grep "foobar \(\w\+\)" test.txt, I get the entire lines that match the entire regex, rather than just "the word after foobar":  foobar bash 1 foobar happy   I would much prefer that the output of that command looked like this:  bash happy   Is there a way to tell grep to only output the items that match the grouping (or a specific grouping) in a regular expression? How can I change Win 10 protected registry entries? Is there a difference between "==" and "is"? My  has failed me.  In Python, are the following two tests for equality equivalent?  n = 5 # Test one. if n == 5:     print 'Yay!'  # Test two. if n is 5:     print 'Yay!'   Does this hold true for objects where you would be comparing instances (a list say)?  Okay, so this kind of answers my question:  L = [] L.append(1) if L == [1]:     print 'Yay!' # Holds true, but...  if L is [1]:     print 'Yay!' # Doesn't.   So == tests value where is tests to see if they are the same object? I know that IList is the interface and List is the concrete type but I still don't know when to use each one. What I'm doing now is if I don't need the Sort or FindAll methods I use the interface. Am I right? Is there a better way to decide when to use the interface or the concrete type? How to get function's name from function's pointer in Linux kernel? How do I change the default file manager back to Nautilus? A while back, I set my default file manager to Nemo. I like it a lot, but it constantly crashes. I remember editing a text file to set it as default, but I forgot which file it was. How do I switch back to the Nautilus file manager?