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     

新题征展(18)

Ａ　题组新编 １．已知ｆ（ｘ）＝　满足ｆ（０）＋ｆ（４）＝Ｆ（ａ＋３）,（１）求ａ的值;（２）当ｆ～（－１）（２Ｘ）＋１＞ｋｆ～（－１）（ｘ）恒成立时,求ｋ的取值范国;（３）若三个互不相等的正数ｍ、ｎ、ｔ成等比数列,问ｆ（ｍ）、ｆ（ｎ）、ｆ（ｔ）能否成等差数列？ ２．设双曲线　　＝１（ａ＞０,ｂ＞０）的 右顶点为Ａ,Ｐ是双曲线上的一个动点（异于顶点）,从Ａ引双曲线的两条渐近线的平行线与直线 ＯＰ分别交于Ｑ和Ｒ两点,则 （１）｜ＯＱ｜、｜ＯＰ｜、｜ＯＲ｜成＿数列; （２）｜ＯＱ｜＋ ｜ＯＲ｜—２｜ＯＰ｜…     

AVERAGE σ-K WIDTH OF CLASS OF Lp（R^n） IN Lq（R^n）

ＡＶＥＲＡＧＥ　σ－Ｋ　ＷＩＤＴＨ　ＯＦ　ＣＬＡＳＳ　ＯＦ　Ｌ_ｐ（Ｒ~ｎ）ＩＮ　Ｌ_ｑ（Ｒ~ｎ）ＡＶＥＲＡＧＥσ－ＫＷＩＤＴＨＯＦＣＬＡＳＳＯＦＬ_ｐ（Ｒ~ｎ）ＩＮＬ_ｑ（Ｒ~ｎ）￥ＬＩＵＹＯＮＧＰＩＮＧＡｂｓｔｒａｃｔ：Ｔｈｅａｖｅｒａｇｅσ－Ｋｗｉｄｔ...     

分次Morita对偶，Morita对偶与Smash积

设Ｃ和ｒ都是群，是Ｇ－型分次环，是Γ－型分次环．是双分次模，Ｒ＃Ｇ是Ｒ的Ｓｍａｓｈ积，Ａ＃Γ是Ａ的Ｓｍａｓｈ积。令Ｗ＝（＿ｇＵ＿（σ－１））＿（ｇ，σ）即（ｇ，σ）位置取＿ｇＵ＿（σ－１）的元素的｜Ｇ｜×｜Γ｜矩阵的全体组成的集合，且每个矩阵的每行和每列的非零元只有有限个，按矩阵运算，Ｗ构成（Ｒ＃６，Ａ＃Γ）双模。则＿ＲＵ＿Ａ定义了一个分次Ｍｏｒｉｔａ对偶当且仅当＿（Ｒ＃Ｇ）Ｗ＿（Ａ＃Γ）定义了一个Ｍｏｒｉｔａ对偶。     

欧氏空间中关于点集的对称变换

欧氏空间中关于点集的对称变换韩志勤（沈阳建工学院１１００１５）考察Ｒ２中关于点的中心对称，关于直线的反射变换和关于圆的反演变换．Ｒ２中关于点Ｐ０（ａ，ｂ）的中心对称变换是ｆ１：Ｒ２→Ｒ２为（ｘ１，ｘ２）→（２ａ－ｘ１，２ｂ－ｘ２）．容易看出，ｆ１为Ｒ...     

一类离散型奇异积分算子

设｛αｋ｝∞ｋ＝－∞为正数缺项序列，满足ｉｎｆｋαｋ＋１／ｄｋ＝α＞１，Ω（ｙ′）为Ｂｅｓｏｖ空间Ｂ０，１１（Ｓｎ－１）上的函数，其中Ｓｎ－１为Ｒｎ（ｎ２）上的单位球面．本文证明：若∫Ｓｎ－１Ω（ｙ′）ｄσ（ｙ′）＝０，则离散型奇异积分ＴΩ（ｆ）（ｘ）＝∑∞ｋ＝－∞∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）和相关的极大算子ＴΩ（ｆ）（ｘ）＝ｓｕｐＮ∑∞ｋ＝Ｎ∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）均在Ｌ２（Ｒｎ）上有界．上述结果推广了Ｄｕｏａｎｄｉｋｏｅｔｘｅａ和ＲｕｂｉｏｄｅＦｒａｎｃｉａ［１］在Ｌ２情形下的一个结果     

一类非自治迭代泛函微分方程

本文研究了一类非自治迭代泛函微分方程ｘ′（ｔ）＝（ｘ２（ｔ）－ｔ２）ｆ（ｘ（ｘ（ｔ）））（其中ｆ∈Ｃ（Ｒ，Ｒ），单调递增，ｚｆ（ｚ）＞０，ｚ≠０）满足初始条件ｘ（σ）＝σ＞０，或满足初始条件ｘ（σ）＝－σ＜０的解的性态、解的存在性及延拓问题．     

脉冲中立型时滞微分方程解的振动性

本文讨论一阶脉冲中立型时滞微分方程［ｙ（ｔ）＋Ｐｙ（ｔ－σ）］′＋Ｑ（ｔ）ｙ（ｔ－σ）＝０，ｔ０，ｔ≠ｔｋ，ｋ＝１，２，…，ｙ（ｔ＋ｋ）－ｙ（ｔ－ｋ）＝ｂｋｙ（ｔｋ），ｋ＝１，２，…，｛（Ｅ）这里τ，σ，Ｐ均为常数，τ＞０，σ＞０，Ｑ（ｔ）∈Ｃ（［０，∞），Ｒ＋），ｂｋ＞－１，ｋ＝１，２，…．分三种情况，Ｐ－１；－１＜Ｐ＜０；Ｐ＞０给出了方程（Ｅ）所有解振动的充分条件．     

1999年普通高等学校招生全国统一考试数学(理工农医类)试题及解答

第Ⅰ卷（参考公式,略）１．选择题（１）如图,Ｉ是全集,Ｍ、Ｐ、Ｓ是Ｉ的３个子集,则阴影部分所表示的集合是（　　）．　（Ａ）（Ｍ∩Ｐ）∩Ｓ　（Ｂ）（Ｍ∩Ｐ）∪Ｓ　（Ｃ）（Ｍ∩Ｐ）∩Ｓ　　　（Ｄ）（Ｍ∩Ｐ）∪Ｓ（２）已知映射ｆ：Ａ→Ｂ,其中,集合Ａ＝｛－３,－２,－１,１,２,３,４｝,集合Ｂ中的元素都是Ａ中元素在映射ｆ下的象,且对任意的ａ∈Ａ,在Ｂ中和它对应的元素是｜ａ｜,则集合Ｂ中元素的个数是（　　）．　（Ａ）６　　（Ｂ）５　　（Ｃ）４　　（Ｄ）７（３）若函数ｙ＝ｆ（ｘ）的反函数是ｙ＝ｇ（ｘ）,…     

The Inner Radius of Univalency of the Rhom busDom ain

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＮａｒｒａｔａｔｉｏｎｏｆｔｈｅＴｈｅｏｒｅｍＩｆｆｕｎｃｔｉｏｎｆｉｓａｎａｌｙｔｉｃｉｎｄｏｍａｉｎＤａｎｄｆ′（ｚ）≠０ａｔｐｏｉｎｔｚ，ｗｅｄｅｆｉｎｅｔｈｅｓｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅｏｆｆａｓＳｆ（ｚ）＝（ｆ″（ｚ）ｆ′（ｚ））′－１２（ｆ″（ｚ）ｆ′（ｚ））２．（１．１）　　Ｆｏｒａｌｏｃａｌｌｙｕｎｉｖａｌｅｎｔｈｏｌｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎ，ｉｔｓＳｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅｉｓｃｌｅａｒ．Ａｔｐｏｌｅｓ，ｔ…     

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.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

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.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

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].