Z_2-商的秩为r的超椭圆纤维化曲面的斜率

设Ｓ是一般型的相对极小曲面，ｆ：Ｓ→Ｃ是亏格ｇ的超椭圆纤维化．本文中我们证明了如果 Ｓ的代数基本群的垂直部分的极大挠 ２商为，那么其斜率且等号成立仅当 Ｓ上的超椭圆对合所诱导的二次复盖的分歧除子 Ｒ仅有（ｒ＋１→，＋１）（当ｒ为偶数）型奇点，或（ｒ＋２→ｒ＋２）（当ｒ为奇数）型奇点．     

De Sitter空间中紧致类空超曲面的积分公式及其Goddard猜想的应用

本文对ｄｅＳｉｔｅｒ空间Ｓｎ＋１１（１）中紧致类空超曲面建立Ｍｉｎｋｏｗｓｋｉ型公式，并给出其到ｒ－次（ｒ＝１，２，…，ｎ－１）平均曲率为常数超曲面的应用．当ｒ＝１时，我们得到Ｍｏｎｔｉｅｌ的结果．     

截断和的弱大数律

投｛Ｘｎ，ｎ≥１｝ｉ．ｉ．ｄ．，Ｘｎ，１≤Ｘｎ，２≤…≤Ｘｎ，ｎ是Ｘ１，Ｘ２，…，Ｘｎ的次序统计量．对非负整数ｋ，ｒ，ｋ＋ｒ≤ｎ，令．本文研究当ｋ＝ｋｎ，ｒ＝ｒｎ满足ｍｉｎ（ｋ，ｒ）→∞，ｍａｘ（ｋ，ｒ）→０时截断和Ｓｎ（ｋ，ｒ）的弱大数律．设βｎ＞０，Ｃｎ∈Ｒ，文中给出了依概率收敛的充要条件．     

Lorentz空间中常平均曲率类空超曲面

本文证明了ｎ＋１维Ｌｏｒｅｎｔｚ空Ｌｎ＋１中以Ｓｎ－１（ｒ）为边界的紧致常平均曲率类空超曲面只有 Ｂｎ（ｒ）和超伪球面盖．对于 Ｒｎ＋１中的紧致常平均曲率超曲面，当高斯映照像落在一个半球面内时，得到相应的唯一性结果．     

Baskakov-Durrmeyer型算子同时逼近的强逆不等式

本文对Ｂａｓｋａｋｏｖ－Ｄｕｒｒｍｅｙｅｒ型算子Ｍｎ（ｆ，ｘ）证明了，当１＜ｐ∞时，存在某一正数ｍ，使得ω２φｆ（２ｒ），１ｎｐＭ（‖Ｍ（２ｒ）ｎｆ－ｆ（２ｒ）‖ｐ＋‖Ｍ（２ｒ）ｍｎｆ－ｆ（２ｒ）‖ｐ＋１ｎ‖ｆ（２ｒ）‖ｐ，φ２（ｘ）＝ｘ（１＋ｃｘ）     

数学问题解答

１９９８年９月号问题解答（解答由问题提供人给出）１１５１设Ｓｎ＝１＋１２＋１３＋…＋１ｎ，求Ｓ１９９９的整数部分．解当ｒ为自然数时，显然有：ｒ＋１２＋ｒ－１２２＜ｒ＜ｒ＋１＋ｒ２，∴ｒ＋１－ｒ＜１２ｒ＜ｒ＋１２－ｒ－１２．在上式中令ｒ＝３，４，…，ｎ...     

变换图的直径及Brualdi猜想

设Ｒ＝（ｒ１，ｒ２…ｒｍ）及 Ｓ＝（Ｓ１，Ｓ２，…，Ｓｎ）为两个正整数向量，满足Σｍｉ＝１ｒｉ＝Σｎｊ＝１ｓｊ＝ Ｋ．记Ｇ（Ｒ，Ｓ）为（０，１）－矩阵类 Ｕ（Ｒ，Ｓ）的变换图．Ｂｒｕａｌｄｉ在文山中给出了 Ｇ（Ｒ，Ｓ）的直径厂（Ｇ（Ｒ，Ｓ））的一个上界：ｍｎ／２－１，并猜想Ｄ（Ｇ（Ｒ，Ｓ））≤ｍｎ／４．本文通过对有向图围长的研究得到了Ｄ（Ｇ（Ｒ，Ｓ））的一个新的上界：１／２ｍｎ－１／６ｔ（ｔ－１）（４ｔ＋１），其中Ｔ＝　　．     

奇异半线性发展方程的局部Cauchy问题

本文在Ｂａｎａｃｈ空间Ｅ中讨论如下问题ｄｕｄｔ＋１ｔσＡｕ＝Ｊ（ｕ），０＜ｔＴ，ｌｉｍｔ→０＋ｕ（ｔ）＝０，其中ｕ：（０，Ｔ］Ｅ，Ａ是与ｔ无关的线性算子．（－Ａ）是Ｅ上Ｃ０半群｛Ｔ（ｔ）｝ｔ０的无穷小生成元，常数σ１，Ｊ是一个非线性映射ＥＪ→Ｅ．它满足局部Ｌｉｐｓｃｈｉｔｚ条件．我们证明了当其Ｌｉｐｓｃｈｉｔｚ常数ｌ（ｒ）满足一定条件时．问题（Ｓ）有局部解，且在某函类中解唯一．设Ｊ（ｕ）＝｜ｕ｜γ－１ｕ＋ｆ（ｘ）（γ＞１），Ｅ＝Ｌｐ，ＥＪ＝Ｌｐγ时得到了与Ｗｅｉｓｌｅｒ［２］在非奇异情形类似的结果．     

关于ψ（z）f（z）f‘（z）的值分布

本文研究有穷圆内ψ（ｚ）ｆ（ｚ）ｆ＇（ｚ）的值分布，其中ｆ（ｚ）为非常数亚纯函数，ψ（ｚ）为非零亚纯函数，并对平面上这样的函数，若Ｔ（ｒ，ψ）＝Ｓ（ｒ，ｆ），得到Ｔ（ｒ，ｆ）〈９／２Ｎ（ｒ，ｆ）＋１／２Ｎ（ｒ，１／ψｆｆ＇－１）＋Ｓ（ｒ，ｆ）。     

最佳L2局部逼近存在唯一的充分必要条件

本文给出了最佳Ｌ２局部逼近的存在唯一性定理，设ｆ∈Ｌ２（０，δ），Ｓｎ＝ｓｐａｎ（ｕ０，ｕ１，．．．Ｕｎ－１）Ｃ＾ｎ－１（０，δ），且ｄｅｔＷｎ（ｕ０，ｕ１，．．．ｕｎ－１；０）≠０，那么，当ｘ→０时，网（Ｐｘ（ｆ，Ｓｎ）收敛于Ｓｎ中某元素Ｐ０（ｆ，Ｓｎ）的充要条件为：ｆ＝Ｐｎ－１＋ｈ，其中Ｐｎ－１（ｔ）＝ｎ－１∑ｉ＝１ａｉｔｉ（ｈ，１）ｘ＝０（Ｘ＾ｎ），ｘ→０，且Ｐ０（ｆ，Ｓｎ）＝ＵＷ＾－１ｎＡ     

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].