I came upon this reading the python  on the super keyword:  If the second argument is omitted, the super object returned is unbound. If the second argument is an object, isinstance(obj, type) must be true. If the second argument is a type, issubclass(type2, type) must be true (this is useful for classmethods).  Can someone please give me an example of a distinction between passing a Type as a second argument versus passing an Object?   Is the documentation talking about an instance of an object?  Thank you.
In Python, what are metaclasses and what do we use them for?
What is the mechanism by which magnetic fields do work? I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example.   Do magnetic fields do work directly, or is it their induced electric fields that do work? How do I install minecraft 1.9 on mac? How to duplicate a div in JavaScript Splitting all polygon features in a shapefile into smaller equal width polygons I have a shapefile of thousands of polygon features, that i would like to break up into smaller pieces (i.e. break a square into 8 equal pieces). I have read all over these boards for the right solution and haven't found one yet unfortunately. I've tried parcel editor but that only allows you to manually edit one feature at a time, and I've tried fishnet but that doesn't run through each individual feature it just processes across the entire extent of the shapefile. I have the full license for ArcGIS so all options are game. Ultimately I would like to be able to split this initial shapefile of features into a specified amount of equal width slots that each would be their own feature in the resulting shapefile.  Any thoughts? Is complex conjugation needed for valid inner product? What are the benefits of using a conjugate linear inner product in a complex vector space vs a simple linear inner product?  That is, why do we demand that $(y,x) = \overline{(x,y)}$ as opposed to $(y,x)=(x,y)$?  Of course, this ensures that $(x,x)$ is real and thus makes an easy definition of norm, but is that necessary? I am sketching out my 2012 programming project, and Im planning to make a classic fantasy RPG game.  The world design, plots, characters and all that I can make, but being a avid tabletop role-player, I would love to use a stable and tested rpg system like Pathfinder, since its balanced and interesting.  Would there be a problem if I make a game (indie dev, but still planning on selling it) using the pathfinder license ? Do I have to purchase a license? And would I able to say that it's based on the Pathfinder ruleset, or should i keep that under wraps.  All big official D&amp;D games boast with that they are official, so doesn't this mean that unofficial games can exist too ?  It's not because I wan't to jump the lowest fence, and all storylines and the game setting will be by my own hand. But I love the Pathfinder system and actually think it could use some publicity as well.  If not, I guess I could make a Pathfinder-like system, with a few measely differences... But I would rather not, since it would feel a bit of a rip... Beamer, Babel and Tikz conflict I am preparing lecture notes in Turkish, and I have a digram for mathematical modelling procedure. But I cannot produce a good output for the following code. When I remove the first three packages, I get my desired output. However, I need to have keep them in my document. Would you help me in this direction?  \documentclass[10pt,notheorems]{beamer}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[turkish]{babel}  \usepackage{tikz} \usetikzlibrary{positioning,shapes,arrows}  \hypersetup{bookmarksdepth=4,bookmarksnumbered=true,bookmarksopen=true}  \usetheme{Warsaw} \usecolortheme{seahorse}  \begin{document}  \begin{frame}[fragile]{}{}  \begin{figure}   \centering   \begin{tikzpicture}     \node (rwp) [draw,fill=blue!20,text centered,minimum height=2em,rounded corners] {Ger\c{c}ek ya\c{s}am problemi};     \node (mm) [right=2cm of rwp,draw,fill=purple!20,text centered,minimum height=2em,rounded corners] {Matematiksel model};     \node (mc) [below=2cm of mm,draw,fill=green!20,text centered,minimum height=2em,rounded corners] {Matematiksel \c{c}{\i}kar{\i}m};     \node (rwq) [below=2cm of rwp,draw,fill=red!20,text centered,minimum height=2em,rounded corners] {Ger\c{c}ek ya\c{s}am tahminleri};     \path [draw,-&gt;] (rwp.east) -- node [above] {Form\"{u}lasyon} (mm.west);     \path [draw,-&gt;] (mm.south) -- node [right] {\c{C}\"{o}z\"{u}m} (mc.north);     \path [draw,-&gt;] (mc.west) -- node [below] {Yorum} (rwq.east);     \path [draw,-&gt;] (rwq.north) -- node [left] {Kontrol} (rwp.south);   \end{tikzpicture}   \caption{Modelleme s\"{u}reci}\label{s2ss2fig1} \end{figure}  \end{frame}  \end{document} Induction proof: $S$ contains powers of 2 and predecessors implies $S={\bf N}$ Let $S$ be a subset of $\mathbb{N}$ such that $$2^k\in S\quad\forall\ k\in\mathbb N$$ and, $$k\in S\Rightarrow k-1\in S\quad\forall\ k\ge2,k\in\mathbb N$$  Show by induction that $S=\mathbb N$. Find a parabola touches the line $y=x$ and $y=-x$ at $A(3,3)$ and $B(1,-1)$ If a parabola touches the line $y=x$ and $y=-x$ at $A(3,3)$ and $B(1,-1)$, then find the focus, axis of the parabola and its directrix.   What I thought: Since the 2 tangents are perpendicular,the origin must lie on the directrix and the line joining A and B is a focal chord. Don't know how to proceed from here.. Is it possible to test apex that relies on field history tracking? What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod&lt;T&gt;() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod&lt;T&gt;()?         GenericMethod&lt;myType&gt;(); // This doesn't work          // What changes to call StaticMethod&lt;T&gt;()?         Sample.StaticMethod&lt;myType&gt;(); // This also doesn't work     }      public void GenericMethod&lt;T&gt;()     {         // ...     }      public static void StaticMethod&lt;T&gt;()     {         //...     } } Prove the Radical of an Ideal is an Ideal I am given that $R$ is a commutative ring, $A$ is an ideal of $R$, and $N(A)=\{x\in R\,|\,x^n\in A$ for some $n\}$.  I am studying with a group for our comprehensive exam and this problem has us stuck for two reasons.  FIRST - We decided to assume $n\in\mathbb{Z}^+$ even though this restriction was not given. We decided $n\ne 0$ because then $x^0=1$ and we are not guaranteed unity. We also decided $n\notin\mathbb{Z}^-$ because $x^{-1}$ has no meaning if there are no multiplicative inverses. Is this a valid argument?  SECOND - We want to assume $x,\,y\in N(A)$ which means $x^m,\,y^n\in A$ and use the binomial theorem to expand $(x-y)^n$ which we have already proved is valid in a commutative ring and show that each term is in A so $x-y$ is in $N(A)$. The biggest problem is how to approach the $-y$ if we are not guaranteed unity. Does anyone have any suggestions?  Thank you in advance for any insight. A function takes every function value twice - proof it is not continuous I want to prove the following nice statement I've found:  A function $f: [0,1] \rightarrow \mathbb{R}$ takes every function value twice - proof it is not continuous  I've already found an answer to my question but one thing is still not clear to my mind. The answer I found was :   Whole post:  "Assume that you have a function $f$ that does take every real value exactly twice. Let $f(a) = f(b) = 0$ with $a &lt; b$. Let $c \in (a,b)$ be given, and assume without loss of generality $f(c) &gt; 0$. Then for every $0 &lt; \epsilon &lt; f(c)$ there exist $d \in (a,c)$ and $e \in (c,b)$ such that $f(d) = f(e) = \epsilon$. So on the intervals $[0,a)$ and $(b,1]$ our function cannot go any higher than zero. That means that $f$ should take every positive real value on the interval $[a,b]$. However the restriction of $f$ to $[a,b]$ is continuous from a closed interval to $\mathbb{R}$ and thus bounded. Contradiction."  Now everything is clear here except for:  "However the restriction of $f$ to $[a,b]$ is continuous from a closed interval to $\mathbb{R}$ and thus bounded. Contradiction."  Well I think know what Arthur is telling there: Because of the boundary there is always at least one function value that can't be taken twice by the function, e.g. just like the peak of $-x^2$.  But that is exactly where I was stuck before I started researching that issue. Is it really possible to just say it the way Arthur did? I thought that I'd have to further somehow prove the statement that boundary leads to that contradiction.    I hope that it is clear what I was trying to express here...  Anyways as always - thank you for your help!  FunkyPeanut Python: list items are not changed in for loop Formal basis for variable substitution in limits So we do a lot of variable substitution in limits at school. Stuff like $\lim\limits_{x\to5}\ (x+1)^2\ =\ \lim\limits_{y\to6}\ y^2$, where we define the substitution $y = x + 1$.  But I've never been clear on what exactly the theoretical basis for this is. What is the formula that you're actually applying when you do variable substitution? What are the formal conditions under which it is possible?  My conjecture would be the following:  For all continuous $f$, and all real $a$: $\lim\limits_{x\to a}\ (f\circ g)(x)\ =\lim\limits_{x\to g(a)}\ f(x)$, where $g$ is a continuous function  So to take my first example, $f$ would be $x^2$, $g$ would be $x + 1$, and $a$ would be $5$.  Am I in the right area? If this is correct, can it be proven using $\epsilon$-$\delta$? I had a half-hearted shot at it the other night and didn't get anywhere. opengl storing multiple indices into indices buffer After parsing collada files I found out that we have to load two(or more) indices each pointing to say a vertex or normal etc. like this (&lt;p>3 0 2 0 0 0&lt;/p>)  Is there a way to load (and use)these indices to indices buffer(ELEMENT_ARRAY_BUFFER) like this (vnvnvn...) ; where v is vertex pointer, n is normal pointer from the above. with vertices loaded to VBO1 like (vvvv...) and in VBO2 like (nnnn...). So that we dont have to repeat the normals in VBO2.  VBO like (vnvnvn...) is also ok. (and not something like this ), I'm not trying to use multiple indices buffer. I'm trying to put all the given indices into one index buffer and use them alternately.  (If I wasnt clear i will try for more clarification.) I need to periodically run a command that ensures that some text files are kept in Linux mode. Unfortunately dos2unix always modifies the file, which would mess file's and folder's timestamps and cause unnecessary writes.   The script I write is in Bash, so  I'd prefer answers based on Bash. Origins of the nose-bleed in anime/manga In a similar spirit to my , I wonder who was the first artist to feature a nose-bleed when thinking, shall we say, "provocative thoughts"?  Did it become popularized in anime/manga because of the popularity of the artist's work or because it is a common belief in japanese folklore? I read the definition of  as  $$W ~=~ \vec{F} \cdot \vec{d}$$  $$\text{ Work  =  (Force) $\cdot$ (Distance)}.$$ If a book is there on the table, no work is done as no distance is covered. If I hold up a book in my hand and my arm is stretched, if no work is being done, where is my energy going? SSH login without password with kerberos