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We determine which groups Z/MZZ/NZ occur infinitely often astorsion groups E(K)tors when K varies over all quartic numberfields and E varies over all elliptic curves over K. 相似文献
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Dimitris Karlis Evdokia Xekalaki 《Annals of the Institute of Statistical Mathematics》1999,51(1):149-162
Poisson mixtures are usually used to describe overdispersed data. Finite Poisson mixtures are used in many practical situations where often it is of interest to determine the number of components in the mixture. Identifying how many components comprise a mixture remains a difficult problem. The likelihood ratio test (LRT) is a general statistical procedure to use. Unfortunately, a number of specific problems arise and the classical theory fails to hold. In this paper a new procedure is proposed that is based on testing whether a new component can be added to a finite Poisson mixture which eventually leads to the number of components in the mixture. It is a sequential testing procedure based on the well known LRT that utilises a resampling technique to construct the distribution of the test statistic. The application of the procedure to real data reveals some interesting features of the distribution of the test statistic. 相似文献
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混合模型已成为数据分析中最流行的技术之一,由于拥有数学模型,它通常比聚类分析中的传统的方法产生的结果更精确,而关键因素是混合模型中子总体个数,它决定了数据分析的最终结果。期望最大化(EM)算法常用在混合模型的参数估计,以及机器学习和聚类领域中的参数估计中,是一种从不完全数据或者是有缺失值的数据中求解参数极大似然估计的迭代算法。学者们往往采用AIC和BIC的方法来确定子总体的个数,而这两种方法在实际的应用中的效果并不稳定,甚至可能会产生错误的结果。针对此问题,本文提出了一种利用似然函数的碎石图来确定混合模型中子总体的个数的新方法。实验结果表明,本文方法确定的子总体的个数在大部分理想的情况下可以得到与AIC、BIC方法确定的聚类个数相同的结果,而在一般的实际数据中或条件不理想的状态下,碎石图方法也可以得到更可靠的结果。随后,本文将新方法在选取的黄石公园喷泉数据的参数估计中进行了实际的应用。 相似文献
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We extend to higher Gaussian maps two classical theorems by Giuseppe Gherardelli and Beniamino Segre which give a sharp lower bound on the rank and characterize the borderline case. 相似文献
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The equality of the Milnor number and Tjurina number for functionson space curve singularities, as conjectured recently by V.Goryunov, is proved. As a consequence, the discriminant in sucha situation is a free divisor. 相似文献
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The Bezout Number for Piecewise Algebraic Curves 总被引:1,自引:0,他引:1
The computation of the Bezout number, the maximum number of intersection points between two piecewise algebraic curves whose common points are finite, is considered. A piecewise algebraic curve is a curve determined by a bivariate spline function. It is found that the maximum number of intersections depends not only on the degrees and the differentiability of the spline functions, but also on the structure of the partition on which the spline functions are defined. 相似文献
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David Grant 《Compositio Mathematica》2000,122(2):151-164
We prove a conjecture of Duke on the number of elliptic curves over the rationals of bounded height which have exceptional primes. 相似文献
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Recently, differential geometric properties of embedded projective varieties have gained increasing interest. In this note, we consider plane algebraic curves equipped with the Fubini--Study metric from2 () and give an estimate for the diameter in terms of the degree, initiated in a paper by F. A. Bogomolov. 相似文献
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Siman Wong 《Compositio Mathematica》2001,127(1):23-54
We show that 17.9% of all elliptic curves over Q, ordered by their exponential height, are semistable, and that there is a positive density subset of elliptic curves for which the root numbers are uniformly distributed. Moreover, for any > 1/6 (resp. > 1/12) the set of Frey curves (resp. all elliptic curves) for which the generalized Szpiro Conjecture |(E)|
N
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12 is false has density zero. This implies that the ABC Conjecture holds for almost all Frey triples. These results remain true if we use the logarithmic or the Faltings height. The proofs make use of the fibering argument in the square-free sieve of Gouvêa and Mazur. We also obtain conditional as well as unconditional lower bounds for the number of curves with Mordell–Weil rank 0 and 2, respectively. 相似文献
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Emanuela Ughi 《European Journal of Combinatorics》1983,4(3):263-270
Several theorems are studied concerning the number of points of an elliptic curve with a Legendre form on a finite field, in order to analyse the distribution of regular and pseudoregular points in relation to a hyperbola in a finite affine plane. 相似文献
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Robert Bryant Herbert Edelsbrunner Patrice Koehl Michael Levitt 《Discrete and Computational Geometry》2004,32(3):293-308
The motion of a biomolecule greatly depends on the engulfing solution,
which is mostly water.
Instead of representing individual water molecules, it is desirable
to develop implicit solvent models that nevertheless accurately
represent the contribution of the solvent interaction to the motion.
In such models, hydrophobicity is expressed as a weighted sum of
atomic surface areas.
The derivatives of these weighted areas contribute to the force
that drives the motion.
In this paper we give formulas for the weighted and unweighted area
derivatives of a molecule modeled as a space-filling diagram made up
of balls in motion.
Other than the radii and the centers of the balls,
the formulas are given in terms of the sizes of circular arcs
of the boundary and edges of the power diagram.
We also give inclusion–exclusion formulas for
these sizes. 相似文献
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This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and integral. Received August 10, 1999, Revised December 27, 1999, Accepted January 14, 2000 相似文献
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空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持. 相似文献