无穷格点上长波-短波共振方程组核截面的分形维数估计

该文证明了无穷格点上长波-短波共振方程组核截面的分形维数估计.     

非自治耗散Schr\"odinger-Boussinesq 方程组紧致核截面的存在性$^$

讨论满足齐次Dirichlet边界条件的非自治耗散Schr\"odinger-Boussinesq 方程组解的长时间行为. 通过 对方程作适当的分解, 证明了方程组所生成的过程存在紧致核截面.     

非自治耗散Schrdinger-Boussinesq方程组紧致核截面的存在性

讨论满足齐次Dirichlet边界条件的非自治耗散Schrodinger-Boussinesq方程组解的长时间行为.通过对方程作适当的分解,证明了方程组所生成的过程存在紧致核截面.     

Re-Os核钟相关核素丰度的网络方程求解

~(187)Re-~(187)Os核钟是核纪年学中用来确定银河系年龄的重要核钟.分叉s-过程中元素~(187)Re和~(187)Os的丰度比对于研究~(187)Re-~(187)Os核钟问题起着决定性的作用.根据分叉s-过程网络路径图,给出了分叉s-过程网络方程组;利用四阶龙格库塔法计算出了网络方程组的数值解,进一步画出了分叉系统中各个元素随时间变化的丰度图.的研究及所获得的数值结果,对研究~(187)Re-~(187)Os核钟和银河系的年龄问题有一定的帮助.     

剩余格上Riean态的存在性

在good剩余格上研究Riean态的存在性。证明了good剩余格上Riean态的核是一个真弱正规滤子,但不是正规滤子。进一步,给出了good剩余格上Riean态存在的充分必要条件。此外,证明了可表示剩余格至多只有一个固定点。     

一类对偶积分方程组正则化为第一类含对数核的Fredholm奇异积分方程组解法

引入辅助未知函数及辅助未知函数的积分关系式,表示原未知函数,将对偶积分方程组退耦.应用Sonine第一有限积分公式,实现化为Abel型积分方程组,应用Abel反演变换并化简,正则化为含对数核的第一类Fredholm奇异积分方程组.由此给出奇异积分方程组的一般性解,进而获得对偶积分方程组的解析解,同时严格地证明了,对偶积分方程组和由它化成的含对数核的奇异积分方程组的等价性,以及对偶积分方程组解的存在性和唯一性.     

离散外微分与计算电磁学

计算电磁学的核心之一是数值求解Maxwell方程组.适当的离散方式是保证结果能真实反映物理现象的关键.为了在离散的过程中保持该方程组的几何性质,我们建立了基于棱柱网格的系数为R的格点规范理论,其离散曲率满足相应的Bianchi恒等式.通过适当定义离散微分形式之间的内积和棱柱网格上的Hodge星算子,我们由离散变分导出源方程和连续性方程,和Bianchi恒等式一起称为真空中的离散Maxwell方程组.这组方程是内蕴的,并具有规范不变性.     

用龙格-库塔法求解非线性方程组

本文介绍了一种求解非线性方程组的新方法龙格-库塔法。     

半伪补MS-代数的理想及同余关系

在半伪补MS-代数上引入核理想的概念,研究半伪补MS-代数的核理想性质,刻画了核理想生成的同余关系的结构,论证了核理想格与具有核理想的同余关系格是同构的。     

解非线性约束方程的拉格朗日全局投影方法

基于最优化方法求解约束非线性方程组的一个突出困难是计算 得到的仅是该优化问题的稳定点或局部极小点,而非方程组的解点.由此引出的问题是如何从一个稳定点出发得到一个相对于方程组解更好的点. 该文采用投影型算法,推广了Nazareth-Qi$^{[8,9]}$ 求解无约束非线性方程组的拉格朗日全局算法(Lagrangian Global-LG)于约束方程上; 理论上证明了从优化问题的稳定点出发,投影LG方法可寻找到一个更好的点. 数值试验证明了LG方法的有效性.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].