2-year integral

Yes! This integral took me 2 years to figure out! Of course, I didn't just do this integral without doing anything else. I intensively spent several days 2 years ago on it and gave up. One year ago, I tried it ago and still failed. However, this integral is strongly related to my research. I borrowed its result from another research paper. If it is wrong, all of my research work should be modified, and some of them are even going to be useless. Therefore, I spent some time on it again these days. Excitingly, I finally figured it out!
Click to see this integral

film 2012 ( No any comment on the plot )

I went to the theater in the Butler plaza last Saturday. That was my first time to the theater in the US. Before that, I sometimes went to Gator night movies for free.
The theater here is nice and the ticket price is also inexpensive.

Science in the film 2012 is kind of absurd.
First, it says the the mantle of the earth is heated by the neutrinos. However, in reality, neutrinos barely interact with matter. There are tons of neutrinos filled in space. Neutrinos also penetrate our bodies quite frequently. Though, we don't feel that because those particles do not interact with us. That's also a reason that neutrinos are not easily detected even though they are believed to be everywhere. If neutrinos can heat the earth mantle as the film describes, we all will be burned to ashes by neutrinos before those earthquakes or volcano eruptions occur.
Second, geomagnetic poles can indeed reverse their orientation. However, they change gradually, ranging from tens of thousands to many millions of years. How can they change suddenly as they happen in the film? Well....probably, if the earth is heated thoroughly and loses it magnetism in a short time...

Anyway, the visual effects are good...

Uncertainty relations of angular momentum and the angular position

Recently I happened to read an article on the bbs ( bulletin board system ) about the uncertainty principle of the angular momentum and the angular position. The author was confused by some linkage between the quantum and classical limits, which is not so interesting to me. However, his confusion, at some point, brought me to reconsider the uncertainty relations between the angular momentum ( more precisely, Lz) and the angular position ( more precisely, the azimuthal angle ). First, there is an upper limit for the angle. This makes angle very different from the position in translational sense, which can span all over the space to infinity. Second, the angular momentum operator is no more Hermitian on the state \hat{phi}|n> where |n> is the eigenstate of Lz and \hat{phi} is the "physical" angle operator. There are two ways to get around it. One is to keep it as usual but carefully trace the boundary terms: Don't miss it! The other is to create an periodic angle operator which keep Lz always Hermitian. The latter approach seems more rigirous. However, the former way is very physically meaningful. I trid to find some research papers that discussed this issue. The most original seems to be written by Dr. Judge. He adopt the first approach. The report is only one page long. Excellent! I like a short article because I am not that patient. This is very interesting paper.
**** D. Judge, Phys. Lett. 5, 189 (1963)***

I read it and took notes below.
http://www.phys.ufl.edu/~chungwei/paper/uncertainty_angular.pdf

divergent series

1. zeta function regularization:

1+1+1+1+....... = -1/2

1+2+3+4+........= -1/12 ( not Abel summable)

1-2+3-4+........= 1/4 ( Abel summable )

2. geometric series:

1+2+4+8+...... = -1 ( Abel summable; not Borel summable )

1-2+4-8+.......= 1/3 ( Borel summable )

1-1+1-1+.......= 1/2 ( Grandi's series; Borel summable )

You think I am messing math up?

murmur as the opening of the blog

Yesterday, I stayed in the office until 23:40 and therefore missed the last train ( Le Guichet RER-B Station, France ) back to Palaiseau ( Paris direction ). I walked around, waiting for any possibility of the taxi passing me, but it never happened!

Le Guichet is a very small town. I thought it might be the reason that no any taxi went by, and therefore made a prompt decision to take the train to the next station - Orsay ( Opposite to the Paris direction), trying to seek any hope of getting a taxi. Orsay is also a small city but much prosperous than Le Guichet.

Prosperous? Maybe...more people were still in the town even though it was already 1 am. More people meant that around 1 - 2 persons per block in this city. I met 3 kind French people who enthusiastically called taxi for me, but they failed: Taxi drivers were reluctant to make money in the midnight here. Finally, they suggested me to go to the bus stop nearby to wait for the night bus.

I waited for the bus for 30 minutes and it finally came, which made me emotionally delighted and moved, mixed together......Wait! The bus driver told me that this bus went along the opposite direction to Palaiseau. Damn.....

Fortunately, one beautiful lady passed by and I asked her for the correct place to wait for the bus. Finally I got it. However, it was already 3am when I got back home.

I caught a cold again...damn it!

昨晚待到 23:30 才離開辦公室. 結果錯過末班列車回家到 Palaiseau ( 往巴黎方向 ). 我就四處晃晃, 看看是否能等到計程車. 結果等到半夜一點還是沒等到. 想說我所在的站 Le Guichet 是個小站, 所以等不到計程車. 於是心念一轉, 搭列車到下一站 Orsay ( 反巴黎方向 ).

想說 Orsay 比較大站一點點, 應該等得到計程車. 結果發現竟然也都是要自己叫車. 所幸遇到三位熱心的法國人幫我叫車. 但是最終還是失敗 --- 計程車司機似乎沒興趣在半夜賺錢. 後來他們建議我去附近搭夜間公車.

我等了30分鐘, 車終於來了. 內心真是感動又高興. 結果方向是錯的! 該死.....
所幸之後遇到一位美女. 我請教他該去哪裡搭公車. 經過他指引, 我總算找到正確搭車位置. 但是回到家的時候已經是半夜 3 點多了..好冷....

又感冒了. 該死!

我就來為此事作一首詩吧..展現我驚人的文采.
末班列車過, 它克吸難候, 心念一變動, 轉往奧賽Go.
熱心三路人, 它克吸狂call, 你爸不願去, 冷死你卡好. (後兩句閩南語發音)
公車尚可得, 兩刻鐘來到, 豈知方向反, 內心靠靠靠.
女神降人間, 嘆無投懷抱, 指引站牌處, 寅時回家到.

Guestbook

Welcome to leave your messages