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f*********g
发帖数: 632 | 3 Equations of higher degree
Some of the ideas described here can be generalized to equations of higher
degree. The basic ideas for solving the sextic using Klein's approach to the
quintic were worked out around 1900. For algebraic equations beyond the
sextic, the roots can be expressed in terms of hypergeometric functions in
several variables or in terms of Siegel modular functions.
http://library.wolfram.com/examples/quintic/main.html
示（Klein 和Poincare的结果）（应该是自守函数，如理解有误，请千万不吝指教） |
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发帖数: 632 | 4 The Siegel theta function is implemented in Mathematica as SiegelTheta[Omega
, s].
This function was investigated by many of the luminaries of nineteenth
century mathematics, Riemann, Weierstrass, Frobenius, Poincaré. Umemura has
expressed the roots of an arbitrary polynomial in terms of Siegel theta
functions (Mumford 1984).
http://mathworld.wolfram.com/SiegelThetaFunction.html
the |
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s*********l
发帖数: 103 | 6 The result in the book is correct.
It seems a special case of Weingarten Equations.
http://mathworld.wolfram.com/WeingartenEquations.html
Make sure your computation of g^cv is correct.
(is it the inverse of the matrix form of the first
fundamental form?) |
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c******m
发帖数: 599 | 8 计算器不行, iphone上有著名的wolfram的 alpha app |
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发帖数: 1039 | 9 我平时做作业是在网上用的这个wolfram的alpha app， 如果没有其他办法，那就麻烦了 |
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t******g
发帖数: 1136 | 10 我输入：
Get["/path/to/Polyhedra.m"]
输出：
$Failed
我输入：
FileNames["*.m",$Path,Infinity]
出来一个很长的list, 的确有这个文件：
"C:\Program Files\Wolfram \
Research\Mathematica\7.0\AddOns\LegacyPackages\Graphics\\
Polyhedra.m",
是不是我装mathematica 没有装对？或者应该修改当前目录？
该怎么修改当前目录呢？
谢谢指点。 |
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l********e
发帖数: 3632 | 15 wolfram alpha is much useful |
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B**e
发帖数: 60 | 17 You mean n(n-1)/2 edges, right, which is the number of edges a complete
graph with n nodes can have. For the genus of a complete graph, please
follow the link below.
http://mathworld.wolfram.com/GraphGenus.html
a |
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d******0
发帖数: 471 | 20 Order of importance:
Fields medal.
Wolf Prize
Steele Prize
Bôcher Prize,
Cole Prizes
Fulkerson Prize
http://mathworld.wolfram.com/MathematicsPrizes.html
The most prestigious mathematical award is known as the Fields medal. In
rough order of importance, other awards are the $100000 Wolf Prize of the
Wolf Foundation of Israel, the Leroy P. Steele Prize of the American
Mathematical Society, followed by the Bôcher Prize, Cole Prizes in
algebra and number theory, and the Delbert Ray Fulkers... 阅读全帖 |
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B*********h
发帖数: 800 | 25 ☆─────────────────────────────────────☆
scarface (人生犹如一场电影) 于 (Thu Jan 11 20:54:55 2007) 提到:
2 cylinders each with radius 1 intersect at right angles and their centers a
lso intersect. What is the volume of the intersection?
☆─────────────────────────────────────☆
alexx (panda in love~八胖~饲羊员~水木十年) 于 (Thu Jan 11 21:01:47 2007) 提到:
http://mathworld.wolfram.com/SteinmetzSolid.html
a
☆─────────────────────────────────────☆
scarface (人生犹如一场电影) 于 (Thu Jan 11 21:08:49 2007) 提到:
sigh,看不懂 |
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p*****k
发帖数: 318 | 30 few minor additions to solutions by swordmans:
(1) tighter bounds could be got by using eq.(13) on this page:
http://mathworld.wolfram.com/Erfc.html
[ (x+sqrt{x^2+8/pi})/2, (x+sqrt{x^2+4})/2 )
(3) one wants the even n terms, which is hyperbolic cosine,
hence e^(-lambda)[e^(lambda)+e^(-lambda)]/2=p, which gives:
lambda = [log(2*p-1)]/2 |
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p*****k
发帖数: 318 | 31
seems to me it's related to Bessel functions. see e.g.,
http://mathworld.wolfram.com/BesselDifferentialEquation.html
Eq.(6)
with alpha=3/8, beta=i/2, gamma=2, and n=3/16
so the general solution is:
x(t)=t^(3/8)*[C1*I_{3/16}(t^2/2) + C2*I_{-3/16}(t^2/2)],
where I is the modified Bessel function |
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l******i
发帖数: 1404 | 39 首先感谢楼主贡献，
如果可以的话，希望楼主最好能在帖子标题里加上问题的类别和关键词，
例如该帖名字可为：【Probability Problem】一道面试题
这样方便我们工作人员整理，谢谢啦。
我已经把标题改了。
关于楼主给的题目本身：
If X1 and X2 are two independent standard normal random variables,
then Z = X1·X2 follows the "product-normal" distribution
with density function fZ(z) = K0(|z|)/π,
where K0 is the modified Bessel function of the second kind.
See details here:
http://mathworld.wolfram.com/NormalProductDistribution.html |
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m****9
发帖数: 492 | 40 是在wolfram|alpha算的嘛？请教怎么用wa算cutoff？面试时候要算出这个实在有点困
难，我只能答道Pcutoff选B了。 |
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O*********2
发帖数: 31 | 42 OK, Had a look at wolfram|alpha and it seems indeed numerical solution. It
has sth like “find roots of an equation using Newton's method” |
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k*****e
发帖数: 4 | 44 http://www.stephenwolfram.com/scrapbook/
1959: Born August 29 in London, England
1967-1972: Dragon School, Oxford
1968-1976: Won various prizes for English, science, math, etc
1972: Won scholarship to Eton College
1972-1976: King's Scholar, Eton College
1972-1973: Wrote unpublished book on particle physics
1973: Started programming Elliott 903C computer
1973: Did first scientific computer experiments
1974: Wrote first scientific paper
1975: Published first scientific paper
1975: Won schola |
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s******i
发帖数: 870 | 49 Watson, James L (ed.) 1984. Class and Social Stratification in Post-
Revolution China. Cambridge
University Press.
Li, Yi. 2005. The Structure and Evolution of Chinese Social Stratification.
University Press of America.
Firebaugh, Glenn. 2003. The New Geography of Global Income Inequality.
Harvard University Press.
Origin
Eberhard, Wolfram. 1962. Social Mobility in Traditional China. Netherlands:
E.J. Brill.
Ho, Ping-Ti. 1976. The Ladder of Success in Imperial China: Aspects of
Social Mo |
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s******i
发帖数: 870 | 50 附录一：中国社会分层研究英文文献
Watson, James L (ed.) 1984. Class and Social Stratification in Post-
Revolution China. Cambridge University Press.
Li, Yi. 2005. The Structure and Evolution of Chinese Social Stratification.
University Press of America.
Firebaugh, Glenn. 2003. The New Geography of Global Income Inequality.
Harvard University Press.
Origin
Eberhard, Wolfram. 1962. Social Mobility in Traditional China. Netherlands:
E.J. Brill.
Ho, Ping-Ti. 1976. The Ladder of Success in Imperial China: As |
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