文章与日志

在宇宙空间,碟子状结构是最常见的力学结构,大约1半的恒星都位于碟子状螺旋星系当中,而象太阳系这样有行星的碟子状恒星结构,也越来越有迹象表明是普遍存在的.另外碟子的构型也出现在很多其他地方,如白矮星和黑洞,因此碟子一定引力的常见力学结果.

用红外眼睛朝银河系中心望去:

CREDIT: IPAC/CALTECH/2MASS/NASA

如果有可能在远处俯视银河这个大盘子:

CREDIT: CHRIS BUTLER
宇宙可见结构的演化,最主要的研究方法是计算机模拟.

可以肯定的是坊间流传的洗髓经不会早于宋明,不过其理路尚可,用于补足作为动功的易筋经是堪任的.
下面我剔除无用累赘之语,径直述说其理路,或有益于时人.
洗髓经属于所谓静功范畴,即:心象的建立-驱动生理功能构建-心象的泯灭-基于新生理功能的心象建立.这么一个循环的进步过程.
因此作为静功的入门,即腾出心力来专事于把握自体的心象之建立,也就是所谓放松与安静的实质.
但平常人的心力总是消耗或者说系绊在日常心理上,常用的两种解脱方式是:
1.替代法,即用本质仍然属于日常心理范畴的操作,例如数息,念诀,行气之类,来强制替代日常心理流,而该操作能够引导到心象的建立.
2.智慧法,集中运用人的思维,或者笼统地说智慧的能力,令人走上自我反省观照之路,以求截断日常心理之根源.

Cosmological Parameters from Eigenmode Analysis of Sloan Digital Sky Survey Galaxy Redshifts

原文

We present estimates of cosmological parameters from the application of the Karhunen-Loève transform to the analysis of the 3D power spectrum of density fluctuations using Sloan Digital Sky Survey galaxy redshifts. We use mh and fb = b/m to describe the shape of the power spectrum, 8gL" align="middle"> for the (linearly extrapolated) normalization, and to parametrize linear theory redshift space distortions. On scales k 0.16hMpc–1, our maximum likelihood values are mh = 0.264 ± 0.043, fb = 0.286 ± 0.065, 8gL" align="middle"> = 0.966 ± 0.048, and = 0.45 ± 0.12. When we take a prior on b from WMAP, we find mh = 0.207 ± 0.030, which is in excellent agreement with WMAP and 2dF. This indicates that we have reasonably measured the gross shape of the power spectrum but we have difficulty breaking the degeneracy between mh and fb because the baryon oscillations are not resolved in the current spectroscopic survey window function. ©2004 American Institute of Physics

Brane Inflation: From Superstring to Cosmic Strings

S.-H. Henry Tye
Laboratory for Elementary Particle Physics, Cornell University, Ithaca, NY 14853

Brane inflation, where branes move towards each other in the brane world, has been shown to be quite natural in superstring theory. Inflation ends when branes collide and heat the universe, initiating the hot big bang. Cosmic strings (but not domain walls or monopoles) are copiously produced during the brane collision. Using the COBE data on the temperature anisotropy in the cosmic microwave background, the cosmic string tension µ is estimated to be around 10 –6 > Gµ > 10–11, while the present observational bound is 7 × 10 –7 > Gµ. This implies that the anisotropy that seeds structure formation comes mostly from inflation, but with a small component (< 10%) from cosmic string effects. This cosmic string effect should be testable in the near future via gravitational lensing, the cosmic microwave background radiation, and/or gravitational wave detectors like LIGO II/VIRGO. ©2004 American Institute of Physics

最直接的分析集合的方法，是赋予集合一种测量方式，使得可以进行基本的分析。
进行分析需要对象满足两个基本要求：无限的与有序的。满足这两点的基本模型就是实数集合，因此要对一般集合进行分析，一般的方法，就是赋予集合以测度,也就是用函数的方法，测量集合而得到一个实数值。

无限的存在，大概是人的第一个惊奇。数数给我们的经验是，计数不是最终目的，明确地描述行为本身才是目的。
描述所需要面临的第一个问题是获得对象，最基本的对象观念，就是集合。
描述“加1”背后的集合，就获得了人类的第一个数学对象-自然数集合。

关于无限的第二个惊奇，是发现哪怕是运用自然数，即可找到不同于自然数的其他无限形式，“日取其半，以至于无穷”，还好，我们可以使用集合观念来把握那样的无限：