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Small summation problem

Posted November 20th, 2008 by Mgccl
in

\sum _{i=1}^{n-2}\sum _{j=1}^{n-1-i} (n-i-j) = 2\sum _{i=a}^{b}\sum _{j=c}^{d} (n-i-j)
n is even.
Find a,b,c,d, where a,b,c,d are all linear combination of n/2, i and 1.

I stumbled though this problem because I was trying to solve a even harder one
2\sum _{i=a}^{b}\sum _{j=c}^{d} (n-i-j)f(i,j) = \sum _{i=1}^{n-2}\sum _{j=1}^{ n-1-i} (n-i-j)|f(i,j)| where f(i,j) = -f(j,i)

I don't know the difficulty of this question, but I don't have any technique for solving problem like this. So I did exactly what the question asked. Decompose the variables into linear combinations of n/2, i and 1 and brute force all the solutions.
2\sum _{i=k_1\frac{n}{2}+c_1}^{k_2\frac{n}{2}+c_2}\sum _{j=k_3\frac{n}{2}+m_1i+ c_3}^{k_4\frac{n}{2}+m_2i+c_4} (n-i-j) = \sum _{i=1}^{n-2}\sum _{j=1}^{ n-1-i} (n-i-j)

There are a lot of solutions. I put an restriction on all the coefficients. But I found a particular nice one:
2\sum _{i=1}^{\frac{n}{2}}\sum _{j=1}^{\frac{n}{2}-i} (n-i-j) = \sum _{i=1}^{n-2}\sum _{j=1}^{ n-1-i} (n-i-j)

And... I don't like my current MimeTex system. The output equations looks ugly.
I need to find other servers. Currently MathBin is nice and fast, but it is created to be a pastebin. Ahh. I want a delicate server. Or leech from CodeCogs LaTeX Equation editor. Wordpress one is good. but blocked in China.

Mathematica 7 released

Posted November 19th, 2008 by Mgccl
in

As a Mathematica user(MUHAHAHA, that's what's so good about having a parent work at a research institution. MUHAHAHAHA!!!), the release of Mathematica 7 is an exciting news.
Mathematica has becoming Photoshop for math. In the future I will edit photos by typing equations instead of mouse gestures. Love this thing.
Can't wait to get my hands on it...
While it is good. I can't help to notice Mathematica 7 is way bloated and a released too soon. Consider Mathematica 6 was released only a year ago. Does anyone really need speech output system for Mathematica? lol.

I can get my own copy if I gold USAMTS. The last problem for this round is quite hard consider I use the naive and obvious sum up all area and divide method. Still searching for nice identities.

Fuck intel. No more.

Posted November 16th, 2008 by Mgccl
in

Since my Intel has already been sent, and just today I realized what I forgot to do.
I forgot to create a cover page for my research paper.
Big screw up for me.
But, Screw Intel.
This is how Intel get started

"hey. we want to make a contest judge people's research paper. What do you think? So we can judge people by how they do in their research. In their real scientific talent."
"How about instead of just research paper, we want them to make the paper looking good with cover pages + and a 20 page form with more information than college application + 5 essays about themselves which we would not even care to read + some recommendations. So we can judge people in every way instead of what the contest is really about, finding a person who does science and does it good."
"Brilliant!"

Fuck it.

"Humm, this research paper doesn't have a cover page."
"Disqualify him."

The end.

Best xkcd comic not shown on xkcd

Posted November 8th, 2008 by Mgccl
in

This was drawn for The New Yorker's Cartoon-Off
I loved this one. In fact this is the best one I have seen recently(like the past 6 months).

Higher dimensional string as a 1 dimensional string in higher dimensional space?
That's what I thought. Correct me if I'm wrong.
2 dimensional manifolds can knot in 4 dimensional space right?

Noddles named after me?

Posted November 7th, 2008 by Mgccl
in

As I read my RSS, I saw the article "Friday Recipe: Shanghai Xu Chao Mien"

My name is Chao Xu. In Chinese pronunciation, my name is Xu Chao(family name first).
In my Facebook, I added the middle name Mein after my name.
LOLed when I saw this article.

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