m*****k
发帖数: 58 | 1 我用的是c语言版的fftw3, 可能会不一样.
r2c 是有hermite symmetry. f(-k) = f(k)*, 它的相位是[0, 2\pi*(N-1)/N], r2c 就
会有f(n) = f(N-n). fftw偷懒, 只存了一半的系数, 后一半全是0, 不会有 (0,20,40
)这样的mode.可能是你的计数方式搞错了吧. |
|
a*****g
发帖数: 19398 | 2 英国教授发文章介绍《棋魂》和围棋数学
不错，英国人也开始意识到了围棋和数学相关性．
Symmetry Plus, a magazine for young mathematicians in the UK, published an
article about Hikaru no Go and math01 in its latest issue. Calin Galeriu, a
professor at Becker College, writes that go is a “board game with an
incredible amount of mathematical content.” Young people reading Hikaru
learn about area, the coordinate plane, deductive and inductive reasoning,
and more. The problem solving techniques Hikaru and his friends use for go
problems are sim... 阅读全帖 |
|
z*****n
发帖数: 7639 | 3 interference dominating是说接收天线的信号
里面白噪声只占噪声总量的很小一部分，大部分
噪声是其他基站的co-channel interference。
你提高基站发射功率，所有基站的功率都要相应
提高，不然cell symmetry就被violated。
所以提高发射功率，SNR不会有明显改观。 |
|
s******u
发帖数: 142 | 4 1. Barkhausen's criterion. Differential ring oscillator is very widely used,
Maneatis' PLL paper provides very good implementation. There are tons of
papers about diff ring osc.
2. One of the reason about symmetry is for jitter/phase noise improvement.
Hajimiri's paper describes it pretty clearly. Don't know if there's other
considerations.
3. It doesn't change from theory if Wx10, L remains. delay will not change
because current also increases by 10 times.
4. Don't know... waiting for solutions... 阅读全帖 |
|
s******u
发帖数: 142 | 5 1. Barkhausen's criterion. Differential ring oscillator is very widely used,
Maneatis' PLL paper provides very good implementation. There are tons of
papers about diff ring osc.
2. One of the reason about symmetry is for jitter/phase noise improvement.
Hajimiri's paper describes it pretty clearly. Don't know if there's other
considerations.
3. It doesn't change from theory if Wx10, L remains. delay will not change
because current also increases by 10 times.
4. Don't know... waiting for solutions... 阅读全帖 |
|
l********6
发帖数: 39 | 6 Professor Zhong Lin Wang’s group at Georgia Tech has a postdoctoral opening
in the field of piezotronics and piezo-phototroncis. Due to the
polarization of ions in a crystal that has non-central symmetry in materials
such as the wurtzite structured ZnO, GaN and InN, a piezoelectric potential
(piezopotential) is created in the crystal by applying a stress. Owing to
the simultaneous possession of piezoelectricity and semiconductor properties
, the piezopotential created in the crystal has a strong... 阅读全帖 |
|
a***u
发帖数: 9 | 7 If your Si wafer has a thick oxide layer on the top, the broad peak might be
due to the oxide. You can measure the oxide thickness with ellipsometry.
Si wafer is single crystalline. When you rotate the wafer, you will probe
translational symmetry along different directions. For polycrystalline sample
with isotropic orientation, you will see the same diffraction pattern when
rotating the sample. I think it will be more helpful to ask these questions to
people from materials science major. |
|
s*******e
发帖数: 2 | 8 我现在在读统计本科, 明年毕业以后想申请到美国读PhD.
现在有三门课可以选择读一门.Differential Equat, Groups and Symmetry,Real
Analysis. 单从学科的角度来说, 那门功课比较重要一些呢? 或者说大多数学校会要求申
请者在本科学过.
谢谢了! |
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t****e
发帖数: 48 | 9 看cornell教授brian greene的“the elegant universe”。里面提到在string theory中
有重大里程碑作用的mirror symmetry，一些数学家的工作起了很大作用。其中提到了
Gang Tian。当然这个镜像对称，首先是由物理学家提出并证明的，当时并没有一个数学
结构可以揭示它的数学意义。然后数学家们震惊了，去研究了。这是一个了不起的发现。
它像广义相对论一样再一次彻底改造了人们对时空结构的认识。问题是，是那个田刚吗？
我觉得不像。你们说呢？ |
|
n*******l
发帖数: 2911 | 10 Well, first thanks for the 包子。
Let me clarify my previous counterexample.
First the sum=1 is not essential, we can rescale anyway.
What you want to prove is
(P0) if p1+...+pn = q1+...qn and r= max(pi)/max(qi),
then p1^2+...+pn^2 <= r^c (q1^2 +...+qn^2).
Now if max(pi)=max(qi), then r=1 and what you want to prove becomes
(P) if p1+...p_{n-1} = q1+...+q_{n-1}
then p1^2+...+p_{n-1}^2 <= q1^2 +...+q_{n-1}^2.
Because of symmetry, if (P) is true, you must also have
q1^2+...+q_{n-1}^2 <= |
|
n*s
发帖数: 752 | 11 I have a matrix and it turns out
if lambda is eigenvalue, 2-lambda is also eigenvalue
is this a kind of symmetry? does it help solving the eigenvalue problem?
for example, does this property help in decomposing the matrix? |
|
n******t
发帖数: 4406 | 12 I just feel in this case symmetry is needed... |
|
c*******h
发帖数: 1096 | 13 搞统计的或者应用的很多人就用kl-divergence来衡量。对称不是很重要。
通常就是有一个基准（例如正态分布），然后看自己手上的分布离这个基准有多远
I just feel in this case symmetry is needed... |
|
S******y
发帖数: 72 | 14 每个方向都有自己的途径吧。
代数几何是： 抽象代数，一点拓扑，交换代数，同调代数， Hartshorne的代数几何，
之后就分方向了：1 曲线的向量丛的模空间理论，自己找书和文献学习，2高维代数几
何，Mori Program, 自己找书和文献学习，3. 几何不变量和计数代数几何，自己找书
和文献学习，4. 奇点解消，自己找书和文献学习。5量子场论,超炫理论，和Mirror
Symmetry，自己找书和文献学习，6 Toric Variety，自己找书和文献学习。7 代数K理
论，Motivation Cohomology，自己找书和文献学习。8算数代数几何，自己找书，看文
献，寻找重要的问题，思考，学习。等等吧。
学习的过程中要多做练习，自然检验了你的理解程度。 分析，代数的还好，代数几何
的是你做了很多东西，有的时候不知道自己做的对不对，要很小心。 导师和我都有这
种体会。
有的结论，事后想到有问题还要回去改正。 反复做好几遍。 |
|
|
w****1
发帖数: 4931 | 16 what do you want to talk about? |
|
p****o
发帖数: 13 | 17 Let's see. How about some simple stuff, like a galois deformation proof of
abelian reciprocity? I wonder where I can find the complete argument
involving iwasawa algebra etc. |
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b*******i
发帖数: 548 | 18 Galois deformation没办法证明互反律
实际情况都是反过来用class field theory计算universal deformation ring of
Galois representation
Iwasawa理论最好看Iwasawa本人的文章
比所有后来人做的都干净漂亮 |
|
e*******y
发帖数: 73 | 19 geometric L 是不是和数论没有什么关系啊 |
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r**a
发帖数: 536 | 20 另外，hitchin moduli space上面的那个mirror是不是已经被证实是对的了？我忘了是
否有这个结论了。印象里这里的mirror好像是两种hitchin fibration之间的一个对应
，具体的时间太长了想不起来了。
a
is |
|
w****1
发帖数: 4931 | 21
That can't be true. I have met two already.:) |
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p****o
发帖数: 13 | 22 Well, firstly there are many methods to prove this 1-d case which is
kronecker-weber. And it can be proved by the similar R=T argument using
taylor-wiles patching. But I dont know the details as I just heard it from
some experts.
I wonder if it will look like the usual argument in class field theory
starting from the local case and do some group cohomologies. |
|
t*******y
发帖数: 11968 | 23 Could anyone provide a good approach to explain the symmetry in the weights
of quadrature formulas? Thanks. |
|
e*******y
发帖数: 73 | 24 吃果果的互相吹捧!
这才是同行之间的正常关系嘛!呵呵
发信人: Symmetry (小林), 信区: Mathematics
标 题: Re: 田刚的案子现在什么结论？
发信站: BBS 未名空间站 (Tue Jan 13 02:04:39 2009)
以后的时代，就看你了。 |
|
D**u
发帖数: 204 | 25 来自主题: Mathematics版 - 几何不等式 Take square of both sides of the original equation. Some terms are canceled
out, and after some re-arranging of the remaining terms, the inequality
becomes:
(|X|*|X+Y+Z|+|Y|*|Z|)+(|Y|*|X+Y+Z|+|X|*|Z|)+(|Z|*|X+Y+Z|+|X|*|Y|)
>= |X+Y|*|X+Z|+|Y+X|*|Y+Z|+|Z+X|*|Z+Y| (1)
Now if we can prove
|X|*|X+Y+Z|+|Y|*|Z| >= |X+Y|*|X+Z| (2)
|Y|*|X+Y+Z|+|X|*|Z| >= |Y+X|*|Y+Z| (3)
|Z|*|X+Y+Z|+|X|*|Y| >= |Z+X|*|Z+Y| (4)
then we are done by adding up (2),(3)and(4).
By symmetry, (2),(3) a |
|
a****e
发帖数: 128 | 26 朋友在国内一所大学读博，急着发文章毕业，希望投的文章越快越容易接受越好，不管
档次，只求能按时毕业，但要求是ＳＣＩ期刊，请大侠们支支招，SCI收录的有哪些容
易接收的数学方面的期刊可以考虑呢？他文章的title是：
Sato's Backlund transformations, additional symmetries and ASvM formular for
the discrete ＫＰ ｈｉｅｒａｒｃｈｙ |
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n***p
发帖数: 7668 | 27 让我尝试着解释一下。 It is just about symmetry.
Let r =|y-x|. Then
\frac{\partial r}{\partial y_i} = (y_i-x_i)/r
and
\frac{\partial r}{\partial x_i} = (x_i- y_i)/r.
That is
\frac{\partial r}{\partial y_i}
= - \frac{\partial r}{\partial x_i}.
For any function f(r), if you take partial derivative in
y, it is just chain rule. Say
\frac{\partial}{\partial y_i} f(r)
= f'(r) \frac{\partial r}{\partial y_i}
= - f'(r)\frac{\partial r}{\partial x_i}
= - \frac{\partial}{\partial x_i} f(r).
When you take... 阅读全帖 |
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n***p
发帖数: 7668 | 28 首先呢，一个包子是10伪币， 这个我不太关心。
本着把问题讲清楚的原则，let me try again.
Because of the symmetry,
taking derivative in y = - taking derivative in x.
Hence
"take derivative to y, then let y=0"
= - "take derivative to x, then let y=0"
= - "let y=0, then take derivative to x".
This is why when you take partial derivatives m times, there must be
a constant C = (-1)^m.
let y=0" and "let y=0, then take derivative to x" are the same, i.e, why
"differentiation" commutes with "taking value", which is the critical... 阅读全帖 |
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x********i
发帖数: 905 | 29 The Witten equation, mirror symmetry, and quantum singularity theory
by Huijun Fan, Tyler Jarvis, Yongbin Ruan |
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g****a
发帖数: 1520 | 30 [转载]高山与小土沟：丘成桐与田刚(2012-07-31 21:17:01)转载▼标签： 转载
原文地址：高山与小土沟：丘成桐与田刚作者：baixiaosheng
高山与小土沟：丘成桐与田刚
送交者: 眼望钟山 2006年2月19日13:39:06
看了关于田刚学术上的不入流品，回想起丘先生的作风。感慨万分。丘先生与别人有很
多合作文章。听说主要都是他的IDEA，但他还是把他的师弟和学生的名字放在前面。不
少人凭此拿了教授位置。当然坏的副产品也有，那是有能力不强的人借此鸡犬升天。
根据丘成桐点名,田刚剽窃过的至少七个数学家,六个有名有姓
送交者: 丘证明 2006年2月17日18:04:48
丘成桐本人
哈佛大学数学系主任萧荫堂
A= Anderson, Michael
V= Viaclovsky, Jeffrey
N= Nadel, Alan Michael
T= Todorov, Andrey
还有一个年轻中国人,没有写出名字
丘成桐原文:
田的学术道德也很成问题。早在一九八六年年底，哈佛大学数学系一位教授就给我写信
，反映田的论文抄袭了他在学术会议上所做学术报告的内容。该教授提... 阅读全帖 |
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q*d
发帖数: 22178 | 31 有没有质量跟是否Abelian没关系,
而是看gauge symmetry是否自发对称破缺,
即是否引入Higgs机制. |
|
t**********o
发帖数: 26 | 32 田刚的学术腐败绝非偶然
萧荫堂1986年4月在哥伦比亚大学介绍关于Kahler-Einstein度量的工作，田刚在座
，然后到了1986年8月田刚写出一篇文章，完全用的就是萧荫堂在哥伦比亚大学讲座上
所介绍的思想和技巧，只不过写法上改头换面了一下。
Tian, Gang， On Kahler-Einstein metrics on certain Kahler manifolds with $
Csb 1（M）>0$. Invent. Math. 89 （1987）, no. 2, 225--246.
田刚企图将这一成果完全据为己有，他曾想自大的在文章里写上“Siu’s
technique does not work”这样的话，后来干脆在文章中只字未提萧荫堂的贡献。正
如萧在信中所指出的那样，田刚剽窃了萧的想法以后，剩下的计算其实就是在“钉马掌
”，可惜田刚还把马掌钉歪了，反而把一个简单的问题搞得很复杂，见如下萧的文章第
622页。
Siu, Yum Tong The existence of Kahler-Einstein metrics on manifolds w... 阅读全帖 |
|
x********i
发帖数: 905 | 33 Sarnak Awarded Wolf Prize
Peter Sarnak has been awarded the 2014 Wolf Prize in Mathematics. A
mathematician of extremely broad spectrum and far-reaching vision, Sarnak
has influenced the development of several mathematical fields, often by
uncovering deep and unsuspected connections. "By his insights and his
readiness to share ideas he has inspired the work of students and fellow
researchers in many areas of mathematics," the Wolf Foundation said. Sarnak
is the Eugene Higgins Professor of Mathem... 阅读全帖 |
|
m**********r
发帖数: 507 | 34 1. No. e.g., n=2 set Y1 = Y2 = X = Ber(1/2)
-> Y1|X is independent of Y2|X
(1) P(Y1=1, Y2=1|X=1) = 1 = P(Y1=1|X=1) P(Y2=1|X=1)
(2) P(Y1=1, Y2=0|X=1) = 0 = P(Y1=1|X=1) P(Y2=0|X=1)
(3) P(Y1=0, Y2=1|X=1) = 0 = P(Y1=0|X=1) P(Y2=1|X=1)
(4) P(Y1=0, Y2=0|X=1) = 0 = P(Y1=0|X=1) P(Y2=0|X=1)
similarly check ALL combinations of Y1 and Y2 conditioning on the event X=0
-> marginally, both Y1 and Y2 are Ber(1/2)
Thus P(Y1=1) * P(Y2=1) = (1/2) * (1/2) = 1/4
-> But Y1 is NOT independent of Y2, because
P(Y1=1, Y... 阅读全帖 |
|
x********i
发帖数: 905 | 35 2014: Alex Kontorovich for From Apollonius to Zaremba: Local-global
phenomena in thin orbits, Bulletin AMS, Vol. 50, 2013, pg. 187-228
2013: John C. Baez and John Huerta, for "The algebra of grand unified
theories". Bulletin Amer. Math. Soc. 47 (3): 483–552. 2010. doi:10.1090/
S0273-0979-10-01294-2.
2012: Persi Diaconis for The Markov chain Monte Carlo revolution,
Bulletin AMS, Vol. 46, 2009, pg. 179–205
2011: David Vogan for The Character Table for E8, Notices of the AMS,
Vol. 5... 阅读全帖 |
|
L*m
发帖数: 235 | 36 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 |
|
x********i
发帖数: 905 | 37 The Shaw Prize in Mathematical Sciences 2015 is awarded to Gerd Faltings,
Managing Director at Max Planck Institute for Mathematics in Bonn, Germany,
and Henryk Iwaniec, New Jersey Professor of Mathematics at Rutgers
University, USA, for their introduction and development of fundamental tools
in number theory, allowing them as well as others to resolve some
longstanding classical problems.
Number theory concerns whole numbers, prime numbers, and polynomial
equations involving them. The central p... 阅读全帖 |
|
a*****g
发帖数: 19398 | 38 英国教授发文章介绍《棋魂》和围棋数学
不错，英国人也开始意识到了围棋和数学相关性．
Symmetry Plus, a magazine for young mathematicians in the UK, published an
article about Hikaru no Go and math01 in its latest issue. Calin Galeriu, a
professor at Becker College, writes that go is a “board game with an
incredible amount of mathematical content.” Young people reading Hikaru
learn about area, the coordinate plane, deductive and inductive reasoning,
and more. The problem solving techniques Hikaru and his friends use for go
problems are sim... 阅读全帖 |
|
n*********3
发帖数: 534 | 39 I suddenly realize that Gauss's famous act of solving in a short time,
perhaps
less than a minute, the following problem
1+2+3+...+100=
is quite similar to Lookacar's solution below.
Both of them use symmetry to apply to math.
Maybe Lookacar is a genius.
Is he still fighting with those trivial matters? |
|
L*m
发帖数: 235 | 40 统计了近十余年来中国大陆高校在四大刊物上的发文，有些是挂名的，但不管如何，还
是都统计了。全名单如下
Annals of Mathematics
A proof of Demailly’s strong openness conjecture
Qi'an Guan（关启安 北京大学） Xiangyu Zhou（周向宇 中科院）
A solution of an L2 extension problem with an optimal estimate and
applications
Qi'an Guan（关启安 北京大学） Xiangyu Zhou（周向宇 中科院）
Construction of Cauchy data of vacuum Einstein field equations evolving to
black holes
Junbin Li（黎俊彬 中山大学） Pin Yu（于品 清华大学）
Special test configuration and K-stability of Fano varieties
Chi Li(李驰 普林斯顿大学 现stony broo... 阅读全帖 |
|
R**********n
发帖数: 523 | 41 https://www.msri.org/workshops/804
Elementary Introduction to the Langlands Program, by Edward Frenkel
September 21,2015 - September 22,2015
Location: MSRI: Simons Auditorium
Organizers
Edward Frenkel (University of California, Berkeley)
Speaker(s)
Edward Frenkel (University of California, Berkeley)
Description
One of the most fascinating and important developments in mathematics in the
last 50 years is the "Langlands Program", a collection of ideas that
provides a grand unification of many area... 阅读全帖 |
|
Q***5
发帖数: 994 | 42 来自主题: Mathematics版 - 权威语录 丘教授的mirror symmetry被人拿来做学习高代的“辅助内容”“自学”，还有个好评
：比一般破习题集档次高多了。
丘教授听到这赞誉，多半会感激涕零吧？
发信人: lookacar (美国名校发考题), 信区: Military
标 题: Re: 推荐几本线性代数习题集
发信站: BBS 未名空间站 (Mon Oct 12 10:10:35 2015, 美东)
让你人肉？我才不傻
我在大一就学习了邱的镜面对称（当时是作为高代的辅助内容自学的），这比一般破习
题集档次高多了
只不过后来读PhD搞得是分析，代数的不少东西生疏了。学过代数的都知道，代数这东
西一扔下来很容易就生疏，跟分析不一样 |
|
Q***5
发帖数: 994 | 43 来自主题: Mathematics版 - 权威语录 这个牛皮还不算太过分，但大家也要考虑到，人家是在学习丘教授的 mirror symmetry
之余，挤时间搞定群表示论的。而且所有这些是在学习高代的同时干的。
相当于一边学加减法，一边学微积分呀。
发信人: lookacar (美国名校发考题), 信区: Military
标 题: Re: 推荐几本线性代数习题集
发信站: BBS 未名空间站 (Sun Oct 11 17:32:37 2015, 美东)
纯数学专业大四才开群表，我大一就自学完了。等到我大四的时候早就把研究生一年级
的课全都学完了，而且开始写paper了 |
|
Q***5
发帖数: 994 | 44 来自主题: Mathematics版 - 权威语录 俺夸过你了，攒了那么多数学名称真不容易。不过，稍微一发挥就露馅。
比如你找的那个“mirror symmetry"绝对是很牛的东，可你这外行不知深浅，把这么牛
的东西和入门的高代放一起学，还拿来跟习题集比，一下就露馅了。
其实，做生物也不比别人低，干嘛这么自卑，冒充是学数学的。 |
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Q***5
发帖数: 994 | 45 来自主题: Mathematics版 - 权威语录 谦虚的好处之一是不必端“权威”的架子，可以随便引用WIKI。查了下，”镜面对称“
是研究calabi-yau 流形之间的关系的，而c-y 流形的介绍俺抄在下面了。大家可以看
看，想弄明白，需要多少准备知识吧。
一个大一，还在学入门的高代课的学生，能同时学习”镜面对称“？真正学过纯数学的
，再蠢也不会吹这种牛皮吧？也只有无知的外行，不知深浅，才敢那样大言不惭地吹牛
。因为对外行来说，高代就挺高大上了。
A Calabi–Yau manifold, also known as aCalabi–Yau space, is a special
type ofmanifold that is described in certain branches of
mathematics such as algebraic geometry. The Calabi–Yau manifold's
properties, such as Ricci flatness, also yield applications
intheoretical p... 阅读全帖 |
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Q***5
发帖数: 994 | 46 来自主题: Mathematics版 - 权威语录 丘教授的mirror symmetry被人拿来做学习高代的“辅助内容”“自学”，还有个好评
：比一般破习题集档次高多了。
丘教授听到这赞誉，多半会感激涕零吧？
发信人: lookacar (美国名校发考题), 信区: Military
标 题: Re: 推荐几本线性代数习题集
发信站: BBS 未名空间站 (Mon Oct 12 10:10:35 2015, 美东)
让你人肉？我才不傻
我在大一就学习了邱的镜面对称（当时是作为高代的辅助内容自学的），这比一般破习
题集档次高多了
只不过后来读PhD搞得是分析，代数的不少东西生疏了。学过代数的都知道，代数这东
西一扔下来很容易就生疏，跟分析不一样 |
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Q***5
发帖数: 994 | 47 来自主题: Mathematics版 - 权威语录 这个牛皮还不算太过分，但大家也要考虑到，人家是在学习丘教授的 mirror symmetry
之余，挤时间搞定群表示论的。而且所有这些是在学习高代的同时干的。
相当于一边学加减法，一边学微积分呀。
发信人: lookacar (美国名校发考题), 信区: Military
标 题: Re: 推荐几本线性代数习题集
发信站: BBS 未名空间站 (Sun Oct 11 17:32:37 2015, 美东)
纯数学专业大四才开群表，我大一就自学完了。等到我大四的时候早就把研究生一年级
的课全都学完了，而且开始写paper了 |
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Q***5
发帖数: 994 | 48 来自主题: Mathematics版 - 权威语录 俺夸过你了，攒了那么多数学名称真不容易。不过，稍微一发挥就露馅。
比如你找的那个“mirror symmetry"绝对是很牛的东，可你这外行不知深浅，把这么牛
的东西和入门的高代放一起学，还拿来跟习题集比，一下就露馅了。
其实，做生物也不比别人低，干嘛这么自卑，冒充是学数学的。 |
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Q***5
发帖数: 994 | 49 来自主题: Mathematics版 - 权威语录 谦虚的好处之一是不必端“权威”的架子，可以随便引用WIKI。查了下，”镜面对称“
是研究calabi-yau 流形之间的关系的，而c-y 流形的介绍俺抄在下面了。大家可以看
看，想弄明白，需要多少准备知识吧。
一个大一，还在学入门的高代课的学生，能同时学习”镜面对称“？真正学过纯数学的
，再蠢也不会吹这种牛皮吧？也只有无知的外行，不知深浅，才敢那样大言不惭地吹牛
。因为对外行来说，高代就挺高大上了。
A Calabi–Yau manifold, also known as aCalabi–Yau space, is a special
type ofmanifold that is described in certain branches of
mathematics such as algebraic geometry. The Calabi–Yau manifold's
properties, such as Ricci flatness, also yield applications
intheoretical p... 阅读全帖 |
|
Q***5
发帖数: 994 | 50 您的帖子当然高深，
做纯数学的投cell
发过四大的不会分离变量法解ode
高代还没学全就学习“mirror symmetry"
神啊！！！ |
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