l********e
发帖数: 3632 | 1 首先Riemannian Curvature是内蕴(intrinsic)的量，不需要通过嵌入高维的欧氏空间
来理解。如果你一定要好通过嵌入来理解，那么Riemannian Curvature tensor就是大
空间曲率和这个流形第二基本形式(second fundamental form)的差（其实这个有点投
机，应为第二基本形式就是这么定义的）。
如果取流形M tangent space里面的basis，那么曲率差不多可以理解为切向量沿M上闭
曲线平行移动的误差（参考和乐群hololomy group的定义）。
最后：一个d-dimensional manifold只有1个scalar curvature function。不是d个。
不过我想你帖子里可能所指的是principal curvature吧？
Ric其实就是sectional curvature的和，直观上理解控制了沿着某个方向的测地球面的
面积元。而scalar curvature就是控制了测地球的体积元。Ric控制面积，就是Gromov
的伟大发现了。
我觉得还是一句话，对于黎曼曲率最好用内蕴的方式理解，一直将流形 |
|
R********n
发帖数: 519 | 2 考虑一个d-dimensional的黎曼manifold M嵌入在一个D-dimensional的欧式空间里面，
在给定的一点p，我想观察manifold的curvature。
我一个很初等的理解是，是不是可以在点p的tangent space里面取一组基，然后看
manifold在这组基中的每一个basis上弯曲的情况？这样我就能得到d个sclar
curvature。
这个和Ricci curvature有什么关系呢？
我理解的Ricci是，也是要取tangent space的一组基e_i，然后对任意的v,mapping v到
\sum_{i} R(e_i,v)e_i,其中R(e_i,v)是Riemannian curvature tensor
谢谢:-) |
|
c*******s
发帖数: 179 | 3 稍微有点糊涂.
max principal curvature k1> min principal curvature k2. 包括符号吗? 还是只
是|k1|>|k2|. 对于elliptic convex surface, k1>k2>0. 对于elliptic concave
surface, 是 k2|k2|). |
|
c*******s
发帖数: 179 | 4 正在做surface evolution的问题，用于3D object segmentation.
1. max principal curvature k1> min principal curvature k2. 包括符号吗? 还是只
是|k1|>|k2|. 对于elliptic convex surface, k1>k2>0. 对于elliptic concave
surface, 是 k2|k2|).
2. 对于一个3D elliptic sphere的上下两部分，例如下面的两个图中的突起部分，应
该一个是convex, 另外一个是concave吧。当用k2>0搜索符合条件的点，然后在进行
surface evolution, concave部分也有deformation. 能帮助解释一下吗？ |
|
j****e
发帖数: 140 | 5 【 以下文字转载自 Quant 讨论区 】
发信人: jejune (孑孓), 信区: Quant
标 题: given level, slope and curvature, what will be the curve?
发信站: BBS 未名空间站 (Fri Oct 26 15:59:40 2007)
i need a curve that has given level, slope and curvature at a given point and pass anthoer pont.
what would be the simplest way to construct such a curve? |
|
c*******s
发帖数: 179 | 6 被一个问题困惑了一段时间.
按照定义: maximum principal curvature K_max>K_min.
但是,看别人的文章,理解的好象是:|k_max|>|k_min|. As for convex shape, both
k_max and k_min are greater 0, so k_max>k_min>0. While as for concave shape,
k_max<0 and k_min<0, then k_max
这样的话,两个理解就有矛盾了. 哪位给解释以下 |
|
m*f
发帖数: 8162 | 7 如果知道每一点上的主次pinciple curvatures和directions，第一和第二基本型, 有办法解析求
解Grad(H)吗？谢谢
感觉就是(k0 * v0 + k1 + v1)/2，where k0, k1是主次曲率，v0, v1是主次向量， 但是又不确定，sigh... |
|
R********n
发帖数: 519 | 8 非常感谢～～！
你的解释读了很多遍，一直想着看懂了再来回帖:-)。虽然没完全理解，但对我认识
manifold curvature起了很大的帮助
Gromov |
|
j****e
发帖数: 140 | 9 i need a curve that has given level, slope and curvature at a given point and pass anthoer pont.
what would be the simplest way to construct such a curve? |
|
f**n
发帖数: 155 | 10 You can search for active contours and deformable models. Curvature is an
important term in them. |
|
t*******r
发帖数: 22634 | 11 认真起见，俺刚才重新去 wiki 查了 “Riemann curvature tensor”
（btw 我前面随便灌水是凭记忆随手写的），wiki 这么说的：
In the mathematical field of differential geometry,
the Riemann curvature tensor, or Riemann–Christoffel
tensor after Bernhard Riemann and Elwin Bruno
Christoffel, is the most standard way to express
curvature of Riemannian manifolds. 。。。 。。。 。。。
It is a central mathematical tool in the theory
of general relativity, the modern theory of gravity,
and the curvature of spacetime is in principle
observable via the geodes... 阅读全帖 |
|
c*******d
发帖数: 353 | 12 In the book 'differential geometry' by Kreyszig, a result is frequently used
about the principal curvature k1, k2. For example, we know that gaussian
curvature K=k1*k2.
When lines of curvature (curves with principal curvature as tangents)
coincide with coordinate curves, it can be shown k1 = b_1^1, the first
element of a mixed tensor with degree 2 and 1 covariance indice. (p.131)
The author then equate k1 = b_11/g_11, k2=b_22/g_22. And this result is used
in several places. Here is what I am hav |
|
Y****N
发帖数: 8694 | 13 【 以下文字转载自 Faculty 讨论区 】
发信人: Highly (高妹), 信区: Faculty
标 题: 我为尹希教授做的专访
发信站: BBS 未名空间站 (Wed Sep 23 14:31:24 2015, 美东)
Interview with Dr. Xi Yin
--- By Fiona Rawsontile, Sept 2015
This interview was inspired by an earlier interview of Dr. Yin I saw on the
Internet, which made me think that we can’t expect someone who normally
writes for entertainment to understand a physicist. To “provoke” a
scientist, we need another scientist. So I volunt... 阅读全帖 |
|
H****y
发帖数: 2992 | 14 Interview with Dr. Xi Yin
--- By Fiona Rawsontile, Sept 2015
This interview was inspired by an earlier interview of Dr. Yin I saw on the
Internet, which made me think that we can’t expect someone who normally
writes for entertainment to understand a physicist. To “provoke” a
scientist, we need another scientist. So I volunteered (to myself) and sent
an invitation to Dr. Yin, who was recently promoted to Professor in Physics
at Harvard Uni... 阅读全帖 |
|
S*******t
发帖数: 3956 | 15 （作为年仅31岁就晋升哈佛正教授的青年才俊，尹希教授最近得到了很多关注。其中一
篇关于他的专访进入了一名同是美国大学华裔教授的女科学家的视线。因为觉得这样的
采访不过瘾，她突发奇想，想亲自采访一下尹希。于是就有了这个我们今天看到的两名
科学家之间的对话。这位女教授使用了化名，这是她出版自己几部科幻小说的笔名。对
，没错，这位女教授同时也是一个女文青，已经写了几本书，还都是英文，Amazon 就
能买到。感兴趣的不妨找来看看。很可能有一天，她也会成为传奇式的人物。那今天这
篇采访就会成为另一段佳话。）
Interview with Dr. Xi Yin
--- By Fiona Rawsontile, Sept 2015
Translated by Slow Rabbit
This interview was inspired by an earlier interview of Dr. Yin I saw on the
Internet, which made me think that we can’t expect some... 阅读全帖 |
|
x********u
发帖数: 12 | 16 关于近期Fano流形上构造Kähler-Einstein度量的工作
最近公布的Fano流形上构造Kähler-Einstein度量的工作，是Kähler几
何近年来引人注目的进展，专家们正在验证。若验查无误，将证明丘成桐关于Fano流形
的构想与猜测是正确的。Donaldson的稳定性条件是其中的关键步骤，还需在代数几何
上把此概念搞清楚，这样丘猜测就为深刻理解Fano流形奠定了基础。由于近期发生了一
些混淆不清的事件，我们将相关工作的公开记录做了客观、学术的分析，望有助于澄清
事实。本文主要涉及文献的比较，阅读本文无需是专家，数学专业本科高年级学生或研
究生可读懂绝大部分。欢迎关于数学上的批评与指正。
本文分三个部分：
1) 陈-Donaldson-孙的报告与文章
2) 田的报告与文章
3) 结论
I. 陈-Donaldson-孙的报告与文章
在最近的一系列文章中，陈秀雄-Donaldson-孙崧（CDS）宣布解决了Kähler
几何中悬置多年的问题。
丘成桐猜测：设M为一紧致K... 阅读全帖 |
|
S*******t
发帖数: 3956 | 17 【 以下文字转载自 Faculty 讨论区 】
发信人: SlowRabit (慢吞吞的小白兔), 信区: Faculty
标 题: 翻译：高妹对尹希教授的专访
发信站: BBS 未名空间站 (Sat Sep 26 11:16:17 2015, 美东)
（作为年仅31岁就晋升哈佛正教授的青年才俊，尹希教授最近得到了很多关注。其中一
篇关于他的专访进入了一名同是美国大学华裔教授的女科学家的视线。因为觉得这样的
采访不过瘾，她突发奇想，想亲自采访一下尹希。于是就有了这个我们今天看到的两名
科学家之间的对话。这位女教授使用了化名，这是她出版自己几部科幻小说的笔名。对
，没错，这位女教授同时也是一个女文青，已经写了几本书，还都是英文，Amazon 就
能买到。感兴趣的不妨找来看看。很可能有一天，她也会成为传奇式的人物。那今天这
篇采访就会成为另一段佳话。）
Interview with Dr. Xi Yin
--- By Fiona Rawsontile, Sept 2015
Translated by Slow Rabbit
Thi... 阅读全帖 |
|
R********n
发帖数: 519 | 18 研究中牵涉到相关概念，但自己认识还很少，谢谢大家:-)
一个几何结构，如果global的来说，curvature都是常数，那么是不是这个结构
一定是hyper-sphere? 比如circle，sphere，etc
另外，一个几何结构，如果只是要求local的curvature是constant，那这个是？
比如一个Riemannian manifold，加上local curvature constant，能够得到？
谢谢！^_^ |
|
R********n
发帖数: 519 | 19 谢谢你的回答:-)，赞！
就是说sectional curvature而言，其实就是你说的这3种情况
局部和全局我可能表达得不好，恩，是不是有这么一种情况，就是一个manifold，局部
曲率变化比较慢，可以认为近似constant,但是全局还是有变化的，不是不变的？~~这
是从应用出发的一个猜想，不知道是否合适
也谢谢你说的内蕴和外蕴曲率，我的理解是是不是内蕴曲率就是在manifold上面观察自
己，而外蕴则是嵌入到一个更高维空间，比如欧式空间，然后再观察。
所以你的意思是曲线的内蕴曲率是0，只有在外维空间来看，才有positive or
negative的曲率
我觉得从自己的应用出发，外蕴曲率对于很重要，我在欧式空间来观察这个manifold，
比如1D curve在R^2 or R^3来观察。这样的话，global constant curvature和local
constant(or local approximate constant curvature)d
的结论是不是还是和前面一样呢？
更进一步，一个高维Riemannian manifold，嵌入到R^N中间，怎么观察 |
|
g****a
发帖数: 1520 | 20 【 以下文字转载自 WaterWorld 讨论区 】
发信人: xiaoshushu (songshu), 信区: WaterWorld
标 题: 关于近期Fano流形上构造KE度量的工作(转载)
发信站: BBS 未名空间站 (Sat Aug 31 10:30:12 2013, 美东)
关于近期Fano流形上构造Kähler-Einstein度量的工作
最近公布的Fano流形上构造Kähler-Einstein度量的工作，是Kähler几
何近年来引人注目的进展，专家们正在验证。若验查无误，将证明丘成桐关于Fano流形
的构想与猜测是正确的。Donaldson的稳定性条件是其中的关键步骤，还需在代数几何
上把此概念搞清楚，这样丘猜测就为深刻理解Fano流形奠定了基础。由于近期发生了一
些混淆不清的事件，我们将相关工作的公开记录做了客观、学术的分析，望有助于澄清
事实。本文主要涉及文献的比较，阅读本文无需是专家，数学专业本科高年级学生或研
究生可读懂绝大部分。欢迎关于数学上的批评与指正。
本文分三个部分：
1) 陈-Don... 阅读全帖 |
|
g****a
发帖数: 1520 | 21 【 以下文字转载自 WaterWorld 讨论区 】
发信人: xiaoshushu (songshu), 信区: WaterWorld
标 题: 关于近期Fano流形上构造KE度量的工作(转载)
发信站: BBS 未名空间站 (Sat Aug 31 10:30:12 2013, 美东)
关于近期Fano流形上构造Kähler-Einstein度量的工作
最近公布的Fano流形上构造Kähler-Einstein度量的工作，是Kähler几
何近年来引人注目的进展，专家们正在验证。若验查无误，将证明丘成桐关于Fano流形
的构想与猜测是正确的。Donaldson的稳定性条件是其中的关键步骤，还需在代数几何
上把此概念搞清楚，这样丘猜测就为深刻理解Fano流形奠定了基础。由于近期发生了一
些混淆不清的事件，我们将相关工作的公开记录做了客观、学术的分析，望有助于澄清
事实。本文主要涉及文献的比较，阅读本文无需是专家，数学专业本科高年级学生或研
究生可读懂绝大部分。欢迎关于数学上的批评与指正。
本文分三个部分：
1) 陈-Don... 阅读全帖 |
|
L*m
发帖数: 235 | 22 最近十年在annals of mathematics上发表或合作发表文章的华人全统计（不包括
terrence tao和一位mit本科毕业的abc华人），单位统计以现在作者单位为准
annals
2015年
A proof of Demailly’s strong openness conjecture
关启安（北京大学） 周向宇（中科院）
A solution of an L2 extension problem with an optimal estimate and
applications
关启安（北京大学） 周向宇（中科院）
Finsler metrics and Kobayashi hyperbolicity of the moduli spaces of
canonically polarized manifolds
杨世琪（普渡大学） Wing-Keung To（新加坡国立大学）
Construction of Cauchy data of vacuum Einstein field equations evolving to
black holes
黎俊彬（中山大学）... 阅读全帖 |
|
P*****s
发帖数: 375 | 23 A nice interview I just read is being shared with you guys here. :)
[ref]
http://fionarawsontile.blogspot.com/2015/09/interview-with-dr-x
Interview with Dr. Xi Yin
By Fiona Rawsontile, Sept 2015
This interview was inspired by an earlier interview of Dr. Yin I saw on the
Internet, which made me think that we can’t expect someone who normally
writes for entertainment to understand a physicist. To “provoke” a
scientist, we need another scientist. So I volun... 阅读全帖 |
|
f**d
发帖数: 768 | 24 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 |
|
q*******u
发帖数: 1405 | 25 【 以下文字转载自 Faculty 讨论区 】
发信人: Highly (高妹), 信区: Faculty
标 题: 我为尹希教授做的专访
发信站: BBS 未名空间站 (Wed Sep 23 14:31:24 2015, 美东)
Interview with Dr. Xi Yin
--- By Fiona Rawsontile, Sept 2015
This interview was inspired by an earlier interview of Dr. Yin I saw on the
Internet, which made me think that we can’t expect someone who normally
writes for entertainment to understand a physicist. To “provoke” a
scientist, we need another scientist. So I volunt... 阅读全帖 |
|
o*********1
发帖数: 2608 | 26 顺便普及下非欧几何。
对空间相对性的思考完全从数学开始的，主要的想法是空间是不是绝对的（或者说是不
是只有一个理想的空间模型：欧几里得空间－－－就是平常说的平直空间）。 这是从
欧几里德第五公设开始的。
结论：
19世纪， Bolyai和Lobachevsky证明了非欧几何的存在。高斯更是理论上提出了曲率和
内蕴几何， 然后由黎曼推广到高维。 这些数学家的工作从哲学层面上说， 我们生活
的空间可能是平直的，也可能是弯曲的。黎曼更是第一个将时间和空间一起考虑的人，
所谓时空。
爱因斯坦是天纵之才， 用黎曼的语言提出了广义相对论。 他的工作的意义应该从
Bolyai的话来理解：
Bolyai ends his work by mentioning that it is not possible to decide through
mathematical reasoning alone if the geometry of the physical universe is
Euclidean or non-Euclidean; this is a task for the physical... 阅读全帖 |
|
x****u
发帖数: 12955 | 27
You forgot those numbers were radar effective ranges of a cruise missile,
flying at under 50m height. That range is limited by the curvature of earth.
DF21D would be coming from direct over head. Curvature of earth would have
no effect on it. |
|
c***y
发帖数: 7 | 28 找到答案了，自问自答一下。万一有人有一样的问题。隐形眼镜处方费确实有其道理的。
Here is a typical contact lens prescription:
Eye PWR BC DIA Brand
OD (Right) -2.25 8.8 14.0 Acuvue
OS (Left) -3.00 8.8 14.0 Acuvue
Here are the definitions of the symbols used:
PWR/SPH Power or Sphere (Strength of Correction)
BC Base Curve (Curvature of the Lens)
DIA Diameter (Diameter of the Lens)
Brand Refers to the contact lens prescribed.
OD Right Eye Prescription
OS Left Eye P... 阅读全帖 |
|
t*******r
发帖数: 22634 | 29 这个主要是自然语言的歧义，还是得靠码工用 formal logics 出马。。。
养娃的三种方式，推养、放养、以及不养。
推养，其实就是 tightly constrained，然后你不断的移动
那个 constraint，于是被 constrained 就往前动。。。
放养，其实就是 loosely constrained。。。但是这样一来
被 constrained 在里面懒惰不懂咋办？OK，你还需要动态加上
一个合适的不断向前移动的 curvature tensor。。。
不养，就是 no constraint，no curvature tensor。。。
比如黑人区街上娃。。。 |
|
z****u
发帖数: 3461 | 30 http://www.ncbi.nlm.nih.gov/pubmed/22401258
Phys Rev Lett. 2012 Feb 17;108(7):078101. Epub 2012 Feb 13.
Shape of a ponytail and the statistical physics of hair fiber bundles.
Goldstein RE, Warren PB, Ball RC.
Source
Department of Applied Mathematics and Theoretical Physics, University of
Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Abstract
A general continuum theory for the distribution of hairs in a bundle is
developed, treating individual fibers as elastic filaments with ra... 阅读全帖 |
|
D********g
发帖数: 533 | 31 you need thermo.
liquid: du=-S1dT+V1dP for chemical potential. Gibbs-Thomson relations says
the curvature has the relationship with partial molar pressure
P_curve - P_flat= \gamma \kappa (\gamma is surface tension while \kappa is
mean curvature.)
so
solid: du'=-S2dT+V2d(P+\gamma\kappa)
for melting, chemical equilibrium du=du'
-S1dT+V1dP=-S2dT+V2dP+V2\gamma d\kappa
(S2-S1)dT+(V1-V2)dP-V2\gamma d\kappa=0
normally, it is a isobaric process dP=0
\Delta S dT=V2\gamma d\kappa
for sphere \kappa =2/r ( |
|
t******a
发帖数: 140 | 32 田刚没动用职权把这篇给拒了？
http://annals.math.princeton.edu/articles/8339
Calabi flow, geodesic rays and uniqueness of constant scalar curvature K&#
228;hler metrics
From to appear in forthcoming issues by Xiuxiong Chen, Song Sun
Abstract
We prove that constant scalar curvature Kähler metric “adjacent” to a
fixed Kähler class is unique up to isomorphism. The proof is based on
the study of a fourth order evolution equation, namely, the Calabi flow,
from a new geometric perspective, and on the geome... 阅读全帖 |
|
L*m
发帖数: 235 | 33 近十年JAMS上的华人作者，JAMS上的文章相对更多，搜的没那么仔细，有可能不完全。
大家也看看有没有漏的
2015
Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics
with cone singularities
Xiuxiong Chen, Simon Donaldson and Song Sun.
Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle
less than 2π
Xiuxiong Chen, Simon Donaldson and Song Sun.
Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle
approaches 2π and completion of the main proof
Xiuxiong Chen, Simon Donaldson... 阅读全帖 |
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R**********n
发帖数: 523 | 34 http://lesniewski.us/papers/presentations/Bloomberg112505.pdf
page 34
or
http://arxiv.org/abs/0910.1671
We have embedded the classical theory of stochastic finance into a
differential geometric framework called Geometric Arbitrage Theory and show
that it is possible to:
--Write arbitrage as curvature of a principal fibre bundle.
--Parameterize arbitrage strategies by its holonomy.
--Give the Fundamental Theorem of Asset Pricing a differential homotopic
characterization.
--Characterize Geometric ... 阅读全帖 |
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x********i
发帖数: 905 | 35 http://iccm.mcm.ac.cn/dct/page/1
Invited Lectures
Group 1
Fan Qin: Cluster algebras and monoidal categorification
Fang Li: Positivity of acyclic sign-skew-symmetric cluster algebras via
unfolding method and some related topics
Cheng-Chiang Tsai: An attempt for affine Springer theory
Li Cai: The Gross-Zagier formula: arithmetic applications
Ming-Hsuan Kang: Geometric zeta functions on reductive groups over non-
archimedean local fields
Huanchen Bao: Canonical bases arising... 阅读全帖 |
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m********r
发帖数: 811 | 36 equivalence
To first order and in the x-a plane, for non-relativistic particles, a
homogeneous magnetic sector, with central angle A and radius of curvature R,
is equivalent to a cylindrical electrostatic sector of central angle A/n
and radius of curvature n*R. Determine n. |
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S***p
发帖数: 19902 | 37 Ricci curvature 当做场，量子化之后的，因为还有规范自由度，所以也是规范玻色子
这个规范自由度，gauge freedom?，我觉得从数学的角度很好理解一些，因为tangent
bundle 也是一种vector bundle（可以理解为定义在流行上的张量场）, 也可以定义
gauge transform（数学概念）,
Ricci curvature 从是tangent bundle来的张量场。 |
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c*******9
发帖数: 9032 | 38 Summation of Tesla's Dynamic Theory of Gravity
An excerpt from: Occult Ether Physics
by William R. Lyne
From: Don Allen
d**[email protected]
According to Tesla's lecture prepared for the Institute of Immigrant Welfare
(May. 12, 1938), his "Dynamic Theory of Gravity" was one of two far
reaching discoveries, which he "...worked out in all details", in the years
1893 and 1894. The 1938 lecture was less than five years before his death.
More complete statements concerning these discoveries can ... 阅读全帖 |
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m********e
发帖数: 1156 | 39 我还算有知的，无论深度还是广度，奈何世界上的知识太多。
有人贴出老爱的几百篇论文，我一看大多数是德文，不知道，无法判断。
您瞅一眼，看看有多少是真正的科研论文？
1913 Einige Argumente für die Annahme einer molekular Agitation beim
absoluten Nullpunkt Annalen der Physik(ser. 4), 40, 551–560, link
Some Arguments for the Assumption of Molecular Agitation at Absolute
Zero
1913 Déduction thermodynamique de la loi de l'équivalence
photochimique Journal de physique (ser. 5), 3, 277–282
Thermodynamic Deduction of the Law of Photoche... 阅读全帖 |
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l***y
发帖数: 1166 | 40 Dynamic theory of gravity
引力的动态理论
Tesla published a prepared statement on his 81st birthday (July 10, 1937)
critiquing Albert Einstein's theory of relativity. The following is a
portion of that statement:
特斯拉在他81岁生日的时候（1937年6月10日）准备了一份发表声明，批评爱因斯坦的
相对论。以下是发表声明的一部分：
"... Supposing that the bodies act upon the surrounding space causing
curving of the same, it appears to my simple mind that the curved spaces
must react on the bodies, and producing the opposite effects, straightening
out the curves. ... 阅读全帖 |
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i*******n
发帖数: 166 | 41
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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f*******d
发帖数: 339 | 42 Not sure what do you mean. There is no negative curvature
around massive
particles on a rubber sheet, the curvature there is also
positive, and
away from the massive particle it is asymptotically flat.
I live in Columbus. |
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l**n
发帖数: 67 | 43
I've already said and agree that the curvature near the
contacting point between the big massive body and the rubber
sheet is positive. This is because it is locally part of
a sphere if we assume the big massive body is a sphere.
We all agree at this point.
I also agree it is asymptotically flat far away from the
massive body but the question arises here that i will argue
the curvature goes to zero from some negative value not
positive value.
A easily thought of model of the rubber sheet will b |
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f*******d
发帖数: 339 | 44 I did not check the calculation in detail, but this model is
not necessarily
the correct one for a rubber sheet under particle anyway,
even if there is
a negative curvature, it does not prove anything.
Intuitively, I can't
see why (as you argued) curvature must going from positive
(near the center)
to negative and then back to zero at infinity, instead of
directly approach
zero.
In any case, the rubber sheet is just a way of
demonstration. |
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r***l
发帖数: 36 | 45 don't do filtering seperately along two directions.
google for mean curvature flow, it can be done without parameterization.
you can also look for modified version of it, which can keep features better,
especially since your shape is tube-like, it means the two principal
curvatures
are quite different (one being almost 0), so you have to take the
anisotropy into account. there are quite some papers on this.
needed
along
me
and |
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n*******4
发帖数: 2285 | 46 这是Nova的一集。
http://www.pbs.org/wgbh/nova/transcripts/3412_samurai.html
RICHARD VINCI: When the smith plunges it into water, the two different parts
of the sword are both contracting. The part with low carbon—this is the
part inside the core of the blade—is able to contract pretty much like it
would like to, because there's really not much carbon in there to be trapped
. So it shrinks a lot. The part on the outer surface though, is filled with
carbon, and so it's really prevented from shrinking as... 阅读全帖 |
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c*********d
发帖数: 9770 | 47 On September 8, 2004 60 Minutes aired a report on President Bush's Air
National Guard service, based on notes from the personal records of the late
Lieutenant Colonel Jerry B. Killian. These consisted of multiple memos
regarding Bush's failure to attend a physical and meet other standard
requirements. Lieutenant Killian had died in 1984 and CBS relied on the
opinion of handwriting analysts and document experts who believed the
material was authentic.
"Documents obtained by the CBS News program "... 阅读全帖 |
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