How to Change Left-Right Audio Balance
Program to balance speaker output for surround sound 2.1?
I read a novel where several enemy alien species were stranded together on an interdicted planet.  They had to recycle everything and keep hidden. By "keep hidden" I mean make sure there is no evidence of their presence visible from space. They recycled everything and lived in camouflaged dwellings.  The younger generation was building a mixed culture community until the older home species showed up.  One of the alien races had a body made of rings or donuts of gases that mixed to express itself. Members of this species could be taken over and controlled by rings transferred from another member of the species.  The book may be 20 years old or more. PHP Error - Uploading a file As a follow up to my other , I would like to know whether the following is possible:  I have $20,000 in my brokerage account The price of a call option with $300 strike price is $5.00 (1 contract = 100 shares) I buy 20 contracts of these $300 calls (cost is 20 * 5 * 100 = $10,000) The price of the underlying goes up, making my option in-the-money  I decide to exercise my options. Exercising my calls means that I buy 20 * 100 = 2,000 shares of the underlying at $300 per share. However, I only have $10,000 left in my brokerage account and am unable to pay for the shares (2,000 * 300 = $600,000). What now? How does this work? Do brokers recognize that my position is profitable, and buy and sell the underlying for me as soon as I exercise my calls? In other words, do I need to worry about being able to pay for the shares of the underlying if I decide to exercise my options? Can I just take my profit without bothering with the shares at all? Picking coefficient in Inverse Distance Weighted method of QGIS? I'm using QGIS 1.8.0 to interpolate weather data. This is, I have a weather station located in say, A and C. With the Inverted Distance Weighting or Triangular Interpolation methods, I can know/interpolate information in B. When using the IDW method, I have to choose a coefficient.   Does anyone know in which range the coefficients should be?   Say from 1 to 10 or .1 to .99 or 100 to 1000?   Any ideas? Question statement is as in the title:     $\varphi:G\to H$ is a Lie Group Homomorphism, then $\ker \varphi$ has Lie algebra $\ker D_e \varphi$   Since $\varphi$ is a Lie group homomorphism, in particular it is continuous. As $H$ must be Hausdorff, every point set is closed, and hence $\{e\}$ is closed in $H$, which implies that $\ker\varphi = \varphi^{-1}(e)$ is closed as well.  So $N=\ker\varphi$ is an embedded Lie subgroup of $G$. Therefore, the inclusion $j:N\to G$ is a Lie Group homomorphism, and induces a Lie algebra homomorphism $D_e j :T_e N \to T_e G$. So I only need to show that $D_e j$ is in fact an isomorphism between $T_e N$ and $\ker D_e \varphi$.  But I'm stuck at this point. I know that for $X\in T_e N$, we have, for $f\in C^{\infty}(H)$,  $$ D_e\varphi (D_e j(X))(f)=D_e j (X)(f\circ \varphi)=X(f\circ \varphi\circ j)=0$$  So $D_ej(T_e N) \subset \ker D_e \varphi$.  At this point, I can either show inverse inclusion: that is, for every $X\in \ker D_e \varphi$, we can find $Y\in T_e N$ such that $D_e j (Y)=X$, or for all $f\in C^{\infty}(G)$, $Y(f\circ j)=X(f)$  Or I can somehow show that dimensions of the two spaces are the same.   But I can't proceed from here.  It'd be great if someone could help me The range of $T^*$ is the orthogonal complement of $\ker(T)$ How can I prove that, if $V$ is a finite-dimensional vector space with inner product and $T$ a linear operator in $V$, then the range of $T^*$ is the orthogonal complement of the null space of $T$?  I know what I must do (for a $v$ in the range of $T^*$, I have to show that $v\perp w$ for every $w$ in $\ker(T)$ and then do the opposite), but I don't know how to show that this inner product is zero. The Center of $\operatorname{GL}(n,k)$ The given question:  Let $k$ be a ﬁeld and $n \in \mathbb{N}$. Show that the centre of $\operatorname{GL}(n, k)$ is $\lbrace\lambda I\mid λ ∈ k^∗\rbrace$.  I have spent a while trying to prove this and have succeeded if $ k \subseteq \mathbb{R}$. So I imagine there is a nicer way to go about this. I have seen people saying take matrices where every element except one is zero in proving similar results but such matrices are not in $\operatorname{GL}(n,k)$ as they are not invertible.  What I have done.  I have said let $B \in$ Center then $B$ commutes with everything in $\operatorname{GL}(n,k)$. So take a permutation matrix, $P$ which swaps rows $i,j$ $P \neq I$. From this you can deduce that $B^T = B$ and that $B_{ii} = B_{jj}$. We can use the fact that $B$ is symmetric to find an orthogonal diagonalisation of $B$ by the spectral theorem.  This gives $QBQ^T = D \rightarrow B=D$. And as $B_{ii} = B_{jj}$ we can say $B = k * I$.   But the spectral theorem requires $B$ to be a real matrix.   How do I prove this for a general $k$?. I would like to create an alias to rm command in order to have a confirmation message after executing this command. So I am creating an alias like this alias rm='rm -i'. But as far as I know this is a temporary alias and it lives until you close the terminal.  As it is explained  to save alias permanently I need to execute ~/.bash_aliases or ~/.bashrc commands in terminal and add my alias there. But when I execute ~/.bashrc I get following error message :  bash: /home/bakhtiyor/.bashrc: Permission denied   When I run ~/.bash_aliases I get another error message like this:  bash: /home/bakhtiyor/.bash_aliases: File or directory doesn't exist.   What is the actual problem and how can I solve it? Why does the dock appear on the left when my screen is locked? The dock doesn't work correctly after I enter my password, either. Floor a date in SQL server In SQL Server, how do I "floor" a DATETIME to the second/minute/hour/day/year?  Let's say that I have a date of 2008-09-17 12:56:53.430, then the output of flooring should be:   Year:  2008-01-01 00:00:00.000 Month: 2008-09-01 00:00:00.000 Day: 2008-09-17 00:00:00.000 Hour: 2008-09-17 12:00:00.000 Minute: 2008-09-17 12:56:00.000 Second: 2008-09-17 12:56:53.000 Use Outgoing SSH to receive incoming SSH My ISP does not allow me to have a static IP address. As such I am unable to remotely SSH in my home machine. Is there a way I could SSH from my home machine to a server and SSH into the server from my remote laptop and bridge the two connections?  Cheers! I just came across this idiom in some open-source Python, and I choked on my drink.  Rather than:  if isUp:     return "Up" else:     return "Down"   or even:  return "Up" if isUp else "Down"   the code read:  return isUp and "Up" or "Down"   I can see this is the same result, but is this a typical idiom in Python? If so, is it some performance hack that runs fast? Or is it just a once-off that needs a code review? What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$? How to show every field is a Euclidean Domain. I'm having trouble proving this. This is what I have so far:  Let $F$ be a field. Let $v(x) \rightarrow 1$ for all $x$ not equal to $0$.  So if we let $x$ be in $F$ where $x$ not zero then we can write $x$ as: $x=qy+r$ for some $y$ in $F$. If $r$ not zero then $V(r)=1$.  Not sure what to do from here. I know eventually I'm supposed to get no remainder $(r=0)$ but I'm stuck at applying the definition and valuation map. Syntax highlighting with less, trouble with lexer I have installed python-pygments and using it for syntax highlighting with less as described by mankoff  I put a function in my .bashrc  cless () {     pygmentize -f terminal "$1" | less -R }   it is enabling syntax highlighting with less. But when I am going to open a file like /etc/fstab or /etc/apt/apt.conf a error saying  Error: no lexer for filename '/etc/apt/apt.conf' found   I found option to show pygmentize the lexer with -l at this . But what will be the appropriate lexer for such files? and how to use it? Your favourite application of the Baire Category Theorem Maximal ideals in the ring of real functions on $[0,1]$ Let $S$ be the ring of all continuous functions from $[0,1]$ to $\mathbb R$. How to prove that all maximal ideals of $S$ have the form $M_{x_0}=\{f\in S \mid f(x_0)=0\}$?   Thanks in advance. How can the following inequation be proven?  $$a^2 + b^2 + c^2 \ge ab + bc + ca$$ I was writing a program in C++ to find all solutions of ab = c, where a, b and c together use all the digits 0-9 exactly once. The program looped over values of a and b, and it ran a digit-counting routine each time on a, b and ab to check if the digits condition was satisfied.  However, spurious solutions can be generated when ab overflows the integer limit. I ended up checking for this using code like:  unsigned long b, c, c_test; ... c_test=c*b;         // Possible overflow if (c_test/b != c) {/* There has been an overflow*/} else c=c_test;      // No overflow   Is there a better way of testing for overflow? I know that some chips have an internal flag that is set when overflow occurs, but I've never seen it accessed through C or C++.    Beware that signed int overflow is undefined behaviour in C and C++, and thus you have to detect it without actually causing it. For signed int overflow before addition, see . How do I create a completely unattended install of Ubuntu? I need a CD or USB stick, that will install Ubuntu on a completely headless machine. Stick CD in and restart, no keyboard or screen should be involved.  There are a few obstacles:   The language selection menu when you first boot the CD. The fact that the CD menu waits. The installer's asking questions during installation.