一簇Lorenz映射的混沌行为与统计稳定性

该文研究一簇Ｌｏｒｅｎｚ映射犛犪：［０,１］→［０,１］（０＜犪＜１）犛犪（狓）＝狓＋犪　狓∈ ［０,１－犪）｛（狓＋犪－１）／犪　狓∈ ［１－犪,１］．从拓扑的角度考虑了犛犪的混沌行为,证明了：犛犪有稠密轨道;犛犪的周期的集合犘犘（犛犪）＝｛１,犿＋１,犿＋２,…｝,其中犿为使犪犿＜１－犪成立的最小正整数;犛犪的拓扑熵犺（犛犪）＞０;几乎所有（关于Ｌｅｂｅｓｇｕｅ测度）的点狓的Ｌｙａｐｕｎｏｖ指数λ（犛犪,狓）＝λ犪＞０．从统计的角度讨论了犛犪的稳定性．我们用下界函数方法证明了犛犪是统计稳定的,并且狌犵犪（犃）＝∫犃犵犪（狓）ｄ狓（犃∈犅）为犛犪的唯一绝对连续（关于Ｌｅｂｅｓｇｕｅ测度）不变概率测度．同时,不变密度犵犪在参数扰动和随机作用的随机扰动下是稳定的．     

半线性抛物方程可变号解的全局存在和爆破

该文研究了如下柯西问题狌狋＝狌狓狓＋ （狋＋１）－σ／２狘狓狘σ狘狌狘狆－１狘狌狘，　狓∈犚，狋∈犚＋ ，狌（狓，０）＝狌０（狓），　狓∈犚｛ ．其中参数σ≥０，狌０（狓）在犚上犽次变号，满足某种速降条件．证明了：如果ｍａｘ｛σ，１｝＜狆≤１＋２犽＋１，那么所有非零解在有限时间内爆破；如果狆＞ｍａｘ｛σ，１＋２犽＋１｝则存在一个非零全局解．     

一类线性errors－in－variables模型的参数强相合估计及其a．s．收敛速度

本文讨论了如下一类线性ｅｒｒｏｒｓ－ｉｎ－ｖａｒｉａｂｌｅｓ模型——多元线性结构关系模型β′ｘｋ＋α＝０，ξｋ＝ｘｋ＋εｋ．｛ｋ＝１，２，…，ｎ．其中，｛ｘｋ：ｋ＝１，２，…，ｎ｝为一组ｉ．ｉ．ｄ．的ｍ维随机向量，｛εｋ：ｋ＝１，２，…，ｎ｝是ｉ．ｉ．ｄ．的随机误差，Ｅ（ε１）＝０，Ｖａｒ（ε１）＝σ２Ｉｍ．且｛ｘｋ：ｋ＝１，２，…，ｎ｝与｛εｋ：ｋ＝１，２，…，ｎ｝相互独立．在一些条件下，我们证明了估计量β，α，σ２的强相合性、唯一性，并给出了估计量的收敛速度为ｏ（ｎ－１－１ｑ），这里ｑ∈［１，２）．对于Ｅ（ｘ１）ｕ１和Ｖａｒ（ｘ１）Ｖｘ的估计也得出了同样的结果     

关于相关收敛函数序列的一个命题

本文在［１］，［２］的基础上，给出了满足ｇｎ（ｘ）＝Ｃｏｆｎ（ｘ）＋Ｃ１ｆｎ－１（ｘ）＋…＋Ｃｋｆｎ－ｋ（ｘ）的相关函数序列｛ｆｎ（ｘ）｝和｛ｇｎ（ｘ）｝的极限间制约关系的一个命题，从而得到一种判断函数序列一致收敛并且求其极限函数的方法。     

关于МОХОНЪКО不等式的精确性

证明了如下定理：设Φ（ｚ）＝∑ｎｕ＝１∏ｔｉ＝１ｆａｕｉ０ｉ…ｆ（ｋｉ）ｉａｕｉｋｉ∑ｍｖ＝１∏ｔｉ＝１ｆｂｖｉ０ｉ…ｆ（ｋｉ）ｉｂｖｉｋｉ其中ｆｉ（ｚ），（１≤ｉ≤ｔ）是亚纯函数，ａｕｉｊ，ｂｖｉｊ为非负整数，则有Ｔ（ｒ，Φ）≤∑ｔｉ＝１｛［Ｓｉ＋ｏ（１）］ｍ（ｒ，ｆｉ）＋［△ｉ－ｕｉ＋ｏ（１）］Ｎ（ｒ，ｆｉ）＋（△ｉ－Ｓｉ）Ｎ（ｒ，ｆｉ）｝ｒＥ∈Ｌ．它是МОХОНЪКО的一个定理的精确改进．     

向量自激门限自回归（VSETAR）序列的遍历性

本文主要考虑二维自激门限自回归模型：Ｘ（ｔ）＝Ｉ［Ｘ（ｔ－１）∈Ｒｉ］ＡｉＸ（ｔ－１）＋ε（ｔ），其中Ａｉ（ｉ＝１，２，３，４）为２×２系数矩阵，｛ε（ｔ）｝为二维ｉ．ｉ．ｄ序列。我们得到｛Ｘ（ｔ）｝为遍历的四个充分条件。     

几类不具有捏制轨道系列完整性的单峰函数族

本文证明，存在着由单峰函数构成的Ｃｏ－函数族｛ｆλ），｛ｇλ｝及具有下列性质：（ｉ）各ｆλ均是分段线性的单峰平顶函数，各ｇλ及均是Ｃ∞－单峰平顶函数．但族｛ｆλ｝，｛ｇλ｝及均非一致平顶；（ｉｉ）族｛ｆλ｝及｛ｇλ｝均满足一致的Ｌｉｐｓｃｈｉｔｚ条件，但在峰顶处均非一致地可微；（ｉｉｉ）族在峰顶处一致地可微，但不满足一致的Ｌｉｐｓｃｈｉｔｚ条件；（ｉｖ）当０≤λ≤７／８时捏制序列Ｋ（ｆλ），Ｋ（ｇλ）及以均不大于ＲＬＣ，当７／８＜λ－≤１时Ｋ（ｆλ），Ｋ（ｇλ）及Ｋ均不小于ＲＬＬ（ＲＬＲ）∞，因而族｛ｆλ｝，｛ｇλ｝及均不具有捏制轨道系列的完整性．本文的结果解答了文［５］中提出的两个猜测．     

关于不可约复矩阵的可逆性

本文推广了不可约复矩阵可逆性的一个经典结果──Ｂｅｔｔｅｒ推论，证明了如下定理：一个ｎ×ｎ不可约复矩阵Ａ是可逆的，如果它满足下列条件之一：某α∈［０，１］，且对至少一个。成立严格不等式，其中Ｎ＝｛１，２，…，ｎ｝，Ｒｉ∑ｊ∈Ｎ－（ｉ）｜αｉｊ｜，Ｃｉ＝∑ｊ∈（ｉ）｜αｊｉ｜，（ｉｉ）｜αｉｉαｊｊ｜≥ＲｉＲｊ，且对至少一对（ｉ，ｊ）成立严格不等式，同时Ａ有两行其非零非对角元的个数不小于２。     

On the Cluster Set C [S_n/(2nφ(n))~(1/2)] in 2-type Banach Space

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｈａｖｅｏｂｔａｉｎｅｄｔｈｅｆｏｌｌｏｗｉｎｇｔｈｅｏｒｅｍｓ．Ｔｈｅｏｒｅｍ１　Ｌｅｔφ（ｘ）ｂｅａｉｎｃｒｅａｓｉｎｇｆｕｎｃｔｉｏｎｏｎ［０，＋∞），φ（ｘ）→＋∞ａｎｄφ（ｘ）ｘｂｅｎｏ－ｉｎｃｒｅａｓｉｎｇ（Ｗｈｅｎｘｉｓｌａｒｇｅｅｎｏｕｇｈ），ａｎｄｌｅｔＢｂｅａｓｅｐａｒａｂｌｅＢａｎａｃｈｓｐａｃｅ，ＸｂｅａＢ－ｖａｌｕｅｄｒａｎｄｏｍｖａｒｉａｂｌｅ，ｉｆｉ）Ｘ∈ＷＭ２０ｉｉ）Ｘτ－ＥＸτ∈ＣＬＴ，τ＞０，ｗｈｅｒｅＸτ＝ＸＩ｛ｙＸｙ≤τ｝ｉｉ…     

关于Fibonacci三角形的一个结果

关于Ｆｉｂｏｎａｃｃｉ三角形的一个结果湖北黄冈师专教学系袁明豪本文对文献［１］中的猜想给出部分结果．根据文［１］，先引出下列定义定义１Ｆｉｂｏｎａｃｃｉ数列｛Ｆｎ｝定义如下：我们把｛Ｆｎ｝中每一项叫做一个Ｆｉｂｏｎａｃｃｉ数．定义２边长为整数且面积也...     

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 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.     

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].