发帖数: 1 | 1 QUANTUM SPACE ELEMENTS (QSE)
INTRODUCTION
This is a non-mathematical proposal introducing a cosmological model that is
cyclic, deterministic and infinity-free. For the purpose of achieving this
objective a number of new concepts are introduced. The framework of this
proposal is structured over a number of assumptions, leading to various
considerations of cosmological concerns. Furthermore, verification methods
are suggested of both, observational and mathematical nature.
ASSUMPTIONS
Space is dis... 阅读全帖 |
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p*****k
发帖数: 318 | 2 i recall that unless the step size of the random walk shrinks to zero, i.e., a Brownian motion, it does not have a limiting distribution (for BM, it's simply diffusion on a closed surface, thus uniform). so i would naively think the answer to (2) is no. i will try (1) when i get more time. |
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D**u
发帖数: 204 | 3 Is there a link (or name of the theorem) that the limiting distribution does
not exist (or is not uniform)?
., a Brownian motion, it does not have a limiting distribution (for BM, it's
simply diffusion on a closed surface, thus uniform). so i would naively
think the answer to (2) is no. i will try (1) when i get more time. |
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r******r
发帖数: 138 | 5 not ok... |.,.| is not defined...
plane, then take the remainder of |An-A1|/(2pi) where Ai = (alpha_x,alpha_y)
radian, and calculate the corresponding |
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y*a
发帖数: 7 | 6 It actually has a very elegant ansewer:
E[ |x_n-x_0|^2] = 2*R^2 - 2*R^2*cos(theta)^n
where theta = a/R, a is the distance walked each time (in this case, a=1
meter)
and it converges to 2*R^2 when n --> infinity.
Also if let R --> infinity, the result approaches n*a^2, whihc is the result
for a 2-D random walk on a flat plan.
Simple vector analysis can get you the answer. |
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D**u
发帖数: 204 | 7 correct.
Here is a (trivial) generalization of the problem. If in stead of a fixed
theta for each step, the k-th step has theta_k, then
E[ |x_n-x_0|^2] = 2*R^2 - 2*R^2* cos(theta_1) * ... * cos(theta_n)
result |
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D**u
发帖数: 204 | 8 Thanks for the link. I haven't yet read it because I haven't found a online
full version that I can access. |
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p*****k
发帖数: 318 | 9 i agree with you guys' result.
DuGu, here is a copy of the paper. not sure if it's helpful though:
http://ifile.it/p56kcvz |
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J*****n
发帖数: 4859 | 10
你这个表达式能在详细的解释一下么？
谢谢。
result |
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y*a
发帖数: 7 | 11
Sure. Here is my derivation:
if x_i is the location vector originated from the center of the sphere, then
we have
x_i = R * p_i, where p_i is the unit vector in the same direction as x_i
then
R*p_i+1 = R*cos(theta)*p_i + R*sin(theta)*t_i --- (1)
where t_i is an random unit vector with a uniform distribution
in all directions that are perpendicular to p_i. and
theta = a/R, where a is the distance walked each time ( in this question, a
= 1 meter).
from (1) we have
p_n = p_0 * (cos(theta))^n +
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D**u
发帖数: 204 | 12 Very nice. Another way to look at is to compute E(x_0*x_n) instead of computing
E((x_n-x_0)^2) directly.
Notice that
E(x_n|x_(n-1)) = cos(theta)*x_(n-1) where theta=a/R. (1)
so
E(x_n|x_0) = cos(theta)*E(x_(n-1)|x_0)
= ... = cos(theta)^n * x_0. (2)
Then using (2) we have
E(x_0*x_n) = x_0 * E(x_n|x_0) = cos(theta)^n * x_0 * x_0
= cos(theta)^n * R^2.
So
E((x_n-x_0)^2) = E(x_n^2+x_0^2-2x_0*x_n)=2R^2 - 2E(x_0*x_n)
= 2R^2 (1 - cos(theta)^n).
then
a |
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y*a
发帖数: 7 | 13 Thank you for sharing!
That is a really nice way to arrive at the answers.
computing |
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M*********l
发帖数: 214 | 14 Portfolio optimization under elliptical distributions?
里雾里。这里有高手详细指点一下吗？用简单的语言平铺直叙吧。数学公式等的我都懂
，wiki我也看了，不用重复。多谢了 |
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p******i
发帖数: 1358 | 15 plot 一下是个圆或者是椭圆。。。
这个是我的理解 |
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i*******n
发帖数: 166 | 16
Not a good example. Even you and your girl walk on a
spherical shell with zero mass (so no gravity at all),
you twocan also meet each other. So your example has
nothing to do with the gravity.
I think spatial curvature != gravity. The space-time
curvature generates the gravity effect. |
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S***y
发帖数: 186 | 17 SUBROUTINE SB(LMAX,Z,JL)
INTEGER::LMAX
COMPLEX::JL(0:LMAX),Z
INTEGER::L
COMPLEX(KIND=8)::DJL(0:LMAX),NORM
DJL(LMAX)=(0.0D0,0.0D0)
DJL(LMAX-1)=(1.0D0,0.0D0)
DO L=LMAX-2,0,-1
DJL(L)=(L+L+3)*DJL(L+1)/Z-DJL(L+2)
END DO
NORM=DJL(0)
DJL(0)=SIN(Z)/Z
NORM=DJL(0)/NORM
DO L=1,LMAX
DJL(L)=DJL(L)*NORM
END DO
JL=DJL
END SUBROUTINE SB
This subroutine tabulates Spherical Bessel Function in JL(0 |
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d*n
发帖数: 137 | 18 Integrals and series
volume 3: more special functions
A.P.Prudnikov, etc
Mathematical methods for physicists
G.Arfken, etc,
P754 |
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w****o
发帖数: 20 | 19 The main atomic difference between C and other group IV elements is that C has
no inner shell (except 1s2 which is spherical and extremely tightly bound),
but for Si and Ge they have bigger inner shells. When valence electrons
(s2+p2) hybridize to form either sp2 or sp3 structures, the inner shell
electrons will have an effect, serving as a perturbation to bridge/facilitate
the outer-shell hybridization (the diagonal element in the Hamiltonian
matrix). So for Si and Ge, sp3 hybridization is ener |
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o******r
发帖数: 259 | 20 网上已经有matlab 和 c的混合编程，
我就来写个mathematica 和 C/C++的混合编程吧，只图方便
- observer
mathematica的数学运算在有些方面比 matlab 要全一些，symbolic computing就不
用说了，
比如我感兴趣的 non-square的矩阵求逆， mathematica可以直接做，
matlab还要自己调svd,剔除无效singular value，再算逆矩阵，
还有spherical harmonics，mathematica 可以直接求
当然matlab和mathematica 我两个都用，
我比较喜欢的是用mathematica和matlab完成那些公式函数太多的运算，
调函数的方式在matlab和mathematica下效率是优化过的，所以不慢
而剩下的“苦”活就由我用c/c++来写好了
以下基于mathematica 5.0 的 mathlink 和 VC6，
mathlink支持很多接口，包括tcp/ip, 也就是装mathematica的机器可以不在本地
mathematica 好象没有做成 matlab那样， |
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H******e
发帖数: 333 | 21 我之前没学过这个，但现在做一个东西需要这个分析。
我查了半天资料，加上我手上现在的书相关的介绍不太多。
我想麻烦大家问一下，就是在做one-way repeated ANOVA之前需不需要有什么
assumption？
还是说直接在SAS里面用proc ANOVA的statement就可以了？
我在网上查有的说对于assumption需要先做Mauchly's sphericity test。
但是对于这个test的结果分析没有，或者说这个test是对应用proc GLM做one-way
repeated ANOVA的。
我是新手，这是第一学期，还是老师告诉我要用这个的。
但现在对这里非常confuse，希望高人们可以帮帮我。
谢谢 |
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w*********y
发帖数: 7895 | 22 我是半桶水。据我了解的是，做任何TEST都要看看其数据是否符合该TEST的
ASSUMPTION。如果你的数据不符合MAUCHLY'S SPHERICITY TEST的话，确实
应该用PROC GLM。 |
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H******e
发帖数: 333 | 23 关键是我不知道MAUCHLY'S SPHERICITY TEST是test的啥，汗一个
我看的资料上都是说需要做这个test，但没有说test啥。。。也没说如果不符合怎么处
理。如果符合怎么处理 |
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p**********l
发帖数: 1160 | 24 What we learnt during a lecture was to use sphericity test to test if the
within subject variance-covariance matrix has a type H ( Huynh & Feldy)
structure, or others call it HF structure.
Covariance matrix is of type H iff its quadratic form with an orthogonal
contrast matrix.
H0: = sigma^2 I.
Ha: = unstructured form.
If the test is nonsignificant, use univariate test for within-subject
effects and since they are more powerful then the multivariate test.
If the test is signifi |
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G**7
发帖数: 391 | 25 BTW, I only have 2 levels of repeated measures. |
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G**7
发帖数: 391 | 26 BTW, I only have 2 levels of repeated measures. |
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S********f
发帖数: 36 | 27 Spherical surface samples are measured for their radii (R) and imaged by a
camera. The image is not a numerical value, but m different quantities (Q1,
Q2,..., Qm) are derived from it using different models. Now if I want to
analyze the correlation between R and each Qi (i = 1,..., m), should
Bonferroni correction be applied to adjust the significance level? Thanks! |
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G***s
发帖数: 10030 | 28 在这里想请教一个问题，用repeated measures，Sphericity test被reject了，然后用
multivariate test,书上写的还要查homogeneity or variance和normality这两个
assumption，但是在ucla的tuitor网站说这两个也被violate了，到底要check哪些
assumption？
Repeated measures ANOVA carries the standard set of assumptions associated
with an ordinary analysis of variance, extended to the matrix case:
multivariate normality, homogeneity of covariance matrices, and independence
. Repeated measures ANOVA is robust to violations of the first two
assumptions. Violations of i... 阅读全帖 |
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f**d
发帖数: 768 | 29 这是一本计算神经科学的优秀著作，全文拷贝这里（图和公式缺），有兴趣的同学可以
阅读
如需要，我可以分享PDF文件（－－仅供个人学习，无商业用途）
From Computer to Brain
William W. Lytton
From Computer to Brain
Foundations of Computational Neuroscience
Springer
William W. Lytton, M.D.
Associate Professor, State University of New York, Downstato, Brooklyn, NY
Visiting Associate Professor, University of Wisconsin, Madison
Visiting Associate Professor, Polytechnic University, Brooklyn, NY
Staff Neurologist., Kings County Hospital, Brooklyn, NY
In From Computer to Brain: ... 阅读全帖 |
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i****x
发帖数: 17565 | 30 谢谢
看来我看的没错，就是两个万向轴捏一起，根本原理是把摩擦对半分
那要是能把三个万向轴捏在一起，岂不是能更顺滑。。。
spherical |
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w*******y
发帖数: 60932 | 31 Link:
http://www.frys.com/product/5975474
Control
* AF modes : Single-shot AF, Automatic AF, Continuous AF, (AF/MF selectable)
* Drive Mode : Single-shot, Continuous, Self-timer, Bracketong; Cont./ WB,
Remote Commander
* Exposure Compensation : ?2EV (in 1/3 EV steps)
* Exposure settings : Auto, Auto Flash Off, Program Auto (P), Aperture
priority (A), Shutter priority (S), Manual (M)
* Focus Area : Wide (Up to 9 active focus points), Spot, Local (9 local
areas selectable)
* Focus Features : Manua... 阅读全帖 |
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t*******e
发帖数: 21 | 33 You didn't get the main point of his research. Spherical conformal mapping
is quite old in his research (not to mention geometry image, although highly
quoted), his later on contributions in graphics include conformal
structures for general surfaces, hyperbolic structures, ricci flow...
标 题: Re: 想起当年的禁水令
发信站: BBS 未名空间站 (Wed Aug 23 03:47:22 2006)
来 源: 71.130.
你来帮忙继承troy的事业吧？
撮 |
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o******r
发帖数: 259 | 34 I told you I've already skipped that part :)
I read those papers 1,2 years ago when Gu was still in UFL, after he
graduated under Yau's advisory.
Gu's spherical conformal mapping method was adopted in a paper of mine.
That's why I write above to credit him.
I'm more application oriented, especially on 3D shape classification/match
stuff now.
Conformal structures for general surfaces, has limited usage in this
direction.
Though Gu wrote a classification paper base on them, I still think they are |
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t*******e
发帖数: 21 | 35 You didn't get the main point of his research. Spherical conformal mapping
is quite old in his research (not to mention geometry image, although highly
quoted), his later on contributions in graphics include conformal
structures for general surfaces, hyperbolic structures, ricci flow...
标 题: Re: 想起当年的禁水令
发信站: BBS 未名空间站 (Wed Aug 23 03:47:22 2006)
来 源: 71.130.
你来帮忙继承troy的事业吧？
撮 |
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o******r
发帖数: 259 | 36 I told you I've already skipped that part :)
I read those papers 1,2 years ago when Gu was still in UFL, after he
graduated under Yau's advisory.
Gu's spherical conformal mapping method was adopted in a paper of mine.
That's why I write above to credit him.
I'm more application oriented, especially on 3D shape classification/match
stuff now.
Conformal structures for general surfaces, has limited usage in this
direction.
Though Gu wrote a classification paper base on them, I still think they are |
|
t*******e
发帖数: 21 | 37 You didn't get the main point of his research. Spherical conformal mapping
is quite old in his research (not to mention geometry image, although highly
quoted), his later on contributions in graphics include conformal
structures for general surfaces, hyperbolic structures, ricci flow...
标 题: Re: 想起当年的禁水令
发信站: BBS 未名空间站 (Wed Aug 23 03:47:22 2006)
来 源: 71.130.
你来帮忙继承troy的事业吧？
撮 |
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s*****t
发帖数: 1994 | 38 A Twisted Meteor Train
Credit and Copyright: Jimmy Westlake (Colorado Mountain College)
Explanation: Did this meteor leave a twisting path? Evidently. Meteor trains that twist noticeably are rare - and even more rarely photographed - but have been noted before. The underlying reason for unusual meteors trains is that many meteors are
markedly non-spherical in shape and non-uniform in composition. Meteors, usually sand sized grains that originate in comets, will disintegrate as they enter the Ear |
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