Problem with table of contents and chapters
Creating unnumbered chapters/sections (plus adding them to the ToC and/or header)
$_POST empty on utf-8 characters Subsurf on a crown. How can I smooth some edges and keep others sharp? How can I smooth all crown but don't smooth the top of the crown? I did a subdivision surface, but this didn't work. All crown became smooth and changed form. if p is prime then 1920 divides $p^4-10p^2+9$ From a paper via Schneier on Security's  (emphasis mine):  In the case of AES-128, there is no known attack which is faster than the 2128 complexity of exhaustive search. However, AES-192 and AES-256 were recently shown to be breakable by attacks which require 2176 and 2119 time, respectively. While these complexities are much faster than exhaustive search, they are completely non-practical, and do not seem to pose any real threat to the security of AES-based systems. In this paper we describe several attacks which can break with practical complexity variants of AES-256 whose number of rounds are comparable to that of AES-128.  Is the implication here that AES-192 is stronger than AES-256? If so, in simple terms, how is that possible?  The attack exploits the fact that the key schedule for 256-bit version is pretty lousy -- something we pointed out in our 2000 paper -- but doesn't extend to AES with a 128-bit key.  Again, in simple terms, what does that mean? In practice, does this mean I should drop AES-256 in favor of its 128-bit counterpart, like Schneier recommends in the comments?  That being said, the key schedule for AES-256 is very poor. I would recommend that people use AES-128 and not AES-256. An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$. I want to prove:     For an integrable function $f(x)$ and periodic with period $T$, for every $a \in \mathbb{R}$, $$\int_{0}^{T}f(x)\;dx=\int_{a}^{a+T}f(x)\;dx.$$   I tried to change the values and define $y=a+x$ so that $dy=dx$ and the limits of the integrals are as we want, but I'm not sure how to use the fact that $f(x)$ is periodic.  Thanks a lot! "Speed" of Gravity and Speed of Light AutoHotKey: Calling one script from another script Inner join using an array column Having trouble indexing and executing a query in O (log n) time.  The query includes an INNER JOIN, an ORDER BY, and an equality operation. If I understand the laws of databases correctly, a query can be indexed and executed in O (log n) time (or thereabouts) if a non-equality operator is not used on more than one column. In this case, I believe the INNER JOIN does count as an equality operator and the non-equality operator would be the ORDER BY portion of the query. This table has upwards of 10,000,000 rows and needs to handle several reads and writes per second.  Using PostgreSQL. This is what the table looks like. As you can see, the column 'Names' is a list property and it is the column that the INNER JOIN goes against:  Age Names                       Date 34  ['carla', 'john', 'sam']    3/13/2011 26  ['json', 'cindy', 'joel']   3/13/2011 72  ['beth', 'amber', 'susie']  3/13/2011 14  ['john', 'jim', 'debie']    3/13/2011   This is the query that we are trying to do:  SELECT * FROM the_table WHERE Age==26 AND Names=='john' ORDER BY Date   My background is from using App Engine's Big Table, so I've used equality operators here to indicate that 'john' should be one of the names in the Names column. This would be an acceptable query in GAE's big table, it would execute in O (log N) time as all Big Table queries are reqyured to do. I am assuming there is a way to do this in PostgreSQL as well since PostgreSQL accepts list data types as columns.  Is this possible to do in PostgreSQL?  If so, how should the index be set up (we can't figure out how to set up an index that takes into account the three properties)? I am using Snow Leopard and Windows 7 with bootcamp. I would like to be able to save some files to my OSX partition from Windows. I would also like to have files (say, photos, source code, etc) that I can manage with both partitions. Is it possible to get the two partitions to "play nice"? Problems when adding a fillable PDF form if the page is rotated Set horizontal width on custom listings environment I want to create a custom listings environment and want to set its width as something like 90% of textwidth, centred.  Per an  for algorithms, the first thing I tried was to embed the listing in a minipage environment. However, . I found a way to still make standard environment work, but it requires to use the escape command every time before ending the environment.  The second thing I tried was this latter command, but as far as I can see, it doesn't offer a feature to set the width of the listing or centre it.  \documentclass{article} \usepackage{listings} \usepackage{lipsum}   \lstnewenvironment{queryl} %% APPROACH 1  {\lstset{frame=shadowbox,escapechar=`}}  {}  \newenvironment{query} %% APPROACH 2  {\begin{minipage}{4cm}\centering\begin{queryl}}  {\end{queryl}\end{minipage}}   \begin{document} %% APPROACH 1 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. \begin{queryl} begin { do nothing } end ; \end{queryl} Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.  %% APPROACH 2 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis.  \begin{query} begin { do nothing } end ;`%&lt;- needs escape-to-LaTeX character to work \end{query}  Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. \end{document}     One can note that for the first environment, the frame extends beyond the width of the text. Also, puzzlingly the minipage environment doesn't seem to want to centre and swallows space (though I guess I could perhaps at least get that to work with tinkering).  In any case, does anyone have any ideas on how to set a width for a custom listings environment and centre it without requiring use of the escape character each time to end the environment? How do I check if a string is a number (float)? What is the best possible way to check if a string can be represented as a number in Python?   The function I currently have right now is:  def is_number(s):     try:         float(s)         return True     except ValueError:         return False   Which, not only is ugly and slow, seems clunky. However I haven't found a better method because calling float in the main function is even worse. Multirow and Multicolumn with missing lines Why does friction play the role of centripetal force during the turning of a car? Prove that given $A\subseteq\mathbb{R}$, if has a maximum $a_0$, then $a_0$ must be the supremum.   In order to prove this, I have written the following:  Let $A\subseteq \mathbb{R}$, nonempty set because $a_{0}$ $\in A$ for hypotesis. Then, since $a_{0}$ $\in A$ is the largest element of the set $A$   (i.e. for each element $A$ of A we have that $ a\leq a_{0}$) $A$ is bounded above. Then, A has a supremum. Let $s$ be the least upper bound of $A,$ so we have that for each element $a$ of $A$, $a\leq s$, for being $s$ an upper bound. In particular, $a_0\leq s$, which implies that $s=a_0$.   Then, we have that $\sup(A)=\max(A)=a_0$, which is exactly what we wanted to prove.  Observation: this proof is true if $s \in A$   I'm not sure if my proof is correct. I will be thankful if someone tells me. Clamp velocity along local axis In the attached , I have a representation of a airplane/jet fighter (cube scaled at one end to indicate direction of flight). I am using torque to steer, and adding Linear Velocity along a local axis for thrust/brakes. What I want to know is how to clamp the velocity along the plane's local axis so when the plane steers, it does not simply keep flying in the direction that is was before it turned. I would prefer a solution with logic bricks, but if that is not possible, python would be acceptable. (it just needs to keep a speed relative to how long the thrust/breaks have been held no mater which direction it is pointing.) Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$, and $f$ be a function from $U$ into $U$.   Finally, let $F : P(U) \to P(U)$ be the function defined by  $$F(X) = \{f(x) | x \in X\}$$  For instance, if $f(x) = 13 − x$, and $X = ${1, 3, 4, 7}, then $$F(X) = \{f(1), f(3), f(4), f(7)\} = \{12, 10, 9, 6\}$$  Show that $F(A−B)$ is not necessarily a subset of $F(A)−F(B)$.    I am having trouble showing an example. Let's say:  $A = \{1,3\} , B = \{2,3\}$  $F(A) = \{f(1),f(2)\} = \{12,11\}$  $F(B) =\{f(2),f(3)\} = \{11,10\}$  Now, $F(A-B) = \{12,10\}$  $F(A)-F(B) = \{12\}$.  Hence, $\{12,10\} \nsubseteq \{12\}$ &lt;-- hmm..  By definition if $A \nsubseteq B$, there exist an $x \in A$ such that $x \notin B$. From my example, we have $x=10 \in A $ but $\notin B$. Is that sufficient?     I'm confused between the difference of $F(A-B)$ and $F(A)-F(B)$. "Authoring" versus "Writing" In my area of work the word author as a verb has become quite common. However, it seems to have a subtly different meaning than plain vanilla write. For example, one does not write software unit tests; one authors them.  Can anyone offer a clear distinction between the two words? Has author as a verb become a common usage outside of the field of computer software? As an extension to  on equiangular fisheye distortion, how can I calculate equidistant points around an ellipse (or 1/4 segment of) given it's aspect ratio? When it's circular, I can use a simple angle increment around the central point, but as the aspect ratio gets smaller, the length of the arc gets shorter and the angles are no longer equidistant. What is the best way to iterate over a dictionary? I've seen a few different ways to iterate over a dictionary in C#.  Is there a standard way?