遗传算法收敛率的下鞅分析

通过鞅论分析来给出遗传算法的收敛率 ,这种分析方法的优势在于它不依赖于染色体的编码形式如常用的二进制形式 ,也不依赖于转移矩阵及其特征值的分析 ,它只以概率来给出遗传算法的收敛率 ,在形式上更加简单明了 ,这是鞅分析优于其它分析如马尔可夫链分析的独特优势 .本文分别对在一定条件下收敛的杰出遗传算法和整体退火遗传算法给出了收敛率的概率形式o( 1- mNn · sNn)和o 1N +N0+( 2 - cN0n - mN0n)e(Δ-δ) /Tn .     

关于A-收敛

设A={ai}（i=1）∞S_（e_1）~＋,其中S（e1）＋={x=（x（n））∈e1：‖x‖=1且x（n）≥0对任意的n∈N}.Banach空间X中的序列{x_n}称为A-收敛于x∈X是指对任意的ε〉0,→0当i→∞,其中A（ε）={n∈N：‖x_n-x‖≥ε}.这篇文章中,我们证明了该收敛可以用一个有限可加的概率测度加以刻画.我们对A-收敛与统计收敛的关系进行了讨论,证明了A-收敛为统计收敛完全取决于A的w~＊-拓扑性质.     

α-混合随机序列最近邻密度估计的强相合收敛速度

设{Xi）i=1^∞是一维平稳序列，具有公共的未知密度f（x），在{Xi}i=1^∞是α-混合的条件下，给出了f（x）基于前礼个观测值{Xi}i=1^∞的最近邻密度估计的强相合收敛速度，当f（x）满足适当条件，收敛速度可达到0（n^-1/3（ln n）^4（1＋p）／3））．     

关于无穷积分收敛的必要条件的讨论

当无穷积分∫0^ ∞f(x)dx收敛时,若f（x)在[0, ∞]上一致连续,或者知lim x→ ∞f(x)存在,那么都有lim x→ ∞f(x)=0。     

关于2002年考研试卷中的一道级数题

见到 2 0 0 2年的数学考研试卷 ,总的感觉是较为适中。从四套试卷的整卷看 ,都是较好的 ,但数三的幂级数题错了 !数三卷的二 ( 2 )题 :设幂级数 ∞n=1anxn与 ∞n=1bnxn的收敛半径分别为 53 和 13 ,则幂级数 ∞n=1a2nb2nxn的收敛半径为 ( A) 5;( B) 53 ;( C) 13 ;( D) 15。其参考答案是 ( A)。我们试举一个反例如下。例 1　设 ∞n=1anxn = ∞n=1( 35) nxn;而令 bn =3 n,当 n为奇数 ;bn =1 ,当 n为偶数 ,即 ∞n=1bnxn=3 x +x2 +3 3x3+x4 +… +3 2 k- 1x2 k- 1+x2 n +…　　这样 , ∞n=1anxn 的收敛半径是 53 ;而 ∞n=1bnxn 的收敛半径是…     

极限lim x→＋∞f（x）=0的一个充分条件的探讨

从无穷积分∫＋∞ a f（x）dx收敛与无穷远极限lim x→＋∞f（x）=0之间的关系展开论述,研究在广义积分∫＋∞ a f（x）dx收敛的前提下,无穷远极限lim x→＋∞f（x）=0的一个充分条件．在此基础上,适当减弱条件得到该条件的推广形式,为更好的解决无穷远极限lim x→＋∞f（x）=0的问题提供更一般的方法．     

Banach空间中渐近非扩张映射的不动点迭代

设D是一致凸Banach空间X的非空闭凸子集 ,T∶D→D是渐近非扩张映射且kn ≥ 1 ,∑ ∞n =1(kn- 1 ) <∞ .设T的不动点集F(T) ≠ ,T是全连续的 (X满足Opial条件 ) ,{xn},{yn},{zn}由定义 2给出 ,如果 ∑∞n =1cn <∞ ,∑ ∞n =1c′n <∞ ,∑ ∞n =1c″n <∞ ,且下列条件之一满足 :(i)b″n ∈ [a ,b] ( 0 ,1 ) ;b′n ∈ [0 ,β];bn ∈[0 ,α],αβ β <1 ;(ii)b′n ∈ [a ,b] ( 0 ,1 ) ;b″n ∈ [a ,1 ];bn ∈ [0 ,b];(iii)bn ∈[a ,b] ( 0 ,1 ) ;b′n ∈ [a ,1 ],则 {xn},{yn},{zn}强收敛于T的不动点 .( {xn}弱收敛于T的不动点 ) .     

新Dirichlet级数Σ_(n=0)~∞a_ne~(λns)的收敛横坐标

本文给出新Dirichlet级数Σ_(n=0)~∞a_ne~(λns)的收敛横坐标σ_c、一致收敛横坐标σ_u和绝对收敛横坐标σ_a的定义.通过指数λ_n和系数a_n的关系去估计三个横坐标,并补充证明两类Dirichlet级数Σ_(n=0)~∞a_ne~(λns)和Σ_(n=0)~∞a_ne~(-λns)的收敛条件是一致的.     

样本均值幂级数的收敛性

摘要设X_1,X_2,…为iid.,EX_1=0,0相似文献   

无穷限反常积分收敛时被积函数的极限状态

根据无穷限反常积分∫a^＋∞f（x）dx收敛的柯西准则和定积分的性质,讨论被积函数f（x）当x→∞时。的极限状态,并得出当无穷限反常积分∫a^＋∞f（x）dx收敛且f（x）在[a,＋∞）上连续,或者无穷限反常积分∫a^＋∞f（x）dx绝对收敛时,存在数列{xn}∩[a,＋∞]且xn→＋∞（n→∞）,使limn→∞xnf（xn）=0.     

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

正~~     

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].