Mapping of texture changes when using subsurf modifier
UV mapping not filling faces
Should I upgrade my body or lens first? accessing loop variable within a loop Are there any reputable studies on spanking? Can you terminate more than one common on the furnace C terminal? Hide Command Window of .BAT file that Executes Another .EXE File Natural Sort in MySQL Vector spaces for the irreducible representations of the Lorentz Group EDIT:  The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain unanswered.  The definition of a representation is a map (a homomorphism) to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the   $(0,0)$ Representation $(\frac{1}{2},0)$ Representation  $(0,\frac{1}{2})$ Representation $(\frac{1}{2},0) \oplus (0,\frac{1}{2}) $ Representation $(\frac{1}{2},\frac{1}{2})$ Representation infinite dimensional Representation? New messages flagged blue bubble does not go away I've just started using matlab-prettifier.    Since the line \begin{lstlisting}[style=Matlab-editor] is a lot to type, I created my own environment:  \newenvironment{myMP}      {\begin{samepage}\begin{lstlisting}[style=Matlab-editor]}      {\end{lstlisting}\end{samepage}}   I've used this syntax many times before, but in this case it doesn't work.  Is there any reason why I can't enclose the lstlisting inside my own one?  Here's sample code, illustrating the problem.  \documentclass{minimal} \usepackage[framed]{matlab-prettifier}%For matlab code \newenvironment{myMP}      {\begin{samepage} \begin{lstlisting}[style=Matlab-editor]}      {\end{lstlisting} \end{samepage}} \begin{document} \begin{myMP} matlab word \end{myMP} \end{document}   When I run this with pdflatex it returns a *, indicating that the environment wasn't closed properly.  Thanks! How to verify iOS app integrity? If I write an app for iOS and it's accepted by the AppStore, how do I know if the app is actually the app I compiled and has not being substituted/altered by, say, a "Man in the middle" style interception/attack? Is there a way to do a checksum either after the fact or from inside the app itself? How can I show or hide boot messages when Ubuntu starts? Is there a way to easily turn on/off showing the boot messages (loading the services) when Ubuntu starts? Is it something in Grub2?  I am running 10.04. A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$ It seems to me, perhaps naïvely, that Aristotle resolved  well, when he said that,      Time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles,    and that Aquinas clarified the matter for the (relatively) modern reader when he wrote      Instants are not parts of time, for time is not made up of instants any more than a magnitude is made of points, as we have already proved. Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time.     For me, any further attempts at explanation and resolution, such as Russell's, (bar rather tenuous appeals to connections with quantum physics) simply reiterate, and rather labour Aristotle's initial erudite explanation.  What serious arguments exist that counter Aristotle's objection, if any, and why is Aristotle's objection not considered a resolution to this paradox? Should black holes be considered two-dimensional or three-dimensional? Remove duplicate fields in a given column (after ID check) Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$. I want to prove that:  $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$. Thesis chapter headings, any suggestions? I've found a thesis with really beautiful chapter headings that I would like to use. What package am I going to need and how would I go about creating a heading that looks like the one below. Also, if you have or know of any nice headings do please share! Plot showing discontinuity where it shouldn't To show that Fermat number $F_{5}$ is divisible by $641$. How can I show that  $F_{5}=2^{2^5}+1$ is divisible by $641$. Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$. This is something I've been trying to work out this evening.      Let $R$ be the ring of continuous real-valued functions on $[0,1]$ with pointwise addition and multiplication. For $t\in [0,1]$, the map $\phi_t\colon f\to f(t)$ is a ring homomorphism of $R$ to $\mathbb{R}$. I'm trying to show that every ring homomorphism of $R\to\mathbb{R}$ has this form.   Suppose otherwise, that there is some $\phi\neq\phi_t$, and thus there is some $f_t\in R$ such that $\phi(f_t)\neq \phi_t(f_t)=f_t(t)$. Define $g_t=f_t-\phi(f_t)1\in R$. Here $\phi(f_t)1$ is the constant function sending $[0,1]$ to $\phi(f_t)$. Then $g_t(t)\neq 0$. My first small question is why does $\phi(g_t)=0$? It seems only that $\phi(g_t)=\phi(f_t)-\phi(\phi(f_t)1)$.  I would like to conclude that there are only finitely many $t_i$ such that $g(x)=\sum g_{t_i}^2(x)\neq 0$ for all $x$. Then $g^{-1}=1/g(x)\in R$, but $\phi(g)=0$, contradicting the fact that homomorphisms map units to units. How can we be sure there are only finitely many $g_{t_i}$ such that the sum of their squares is never $0$? Thanks.