平衡型与BP-最优设计

对Lu和Sun[1],Lu等[2]中提出的E(d2)准则进行了扩展,定义了一个新准则,用以评价和构造因子设计.对一个含有k个因子的因子设计,定义了"平衡型"向量B=(B(1),B(2),…,B(k)),其中B(m)表示与m平衡(即强度为m的正交性)的接近程度,m=1,…,b,而B(2)=E(d2).这个新准则(称为"最近平衡准则"),顺序最小化向量B的各个分量.对B(m)得到了下界LB(m),m=1,…,b.证明了当试验单元间的Hamming距离都相等时,平衡型向量的各分量同时达到其下界.试验单元间的Hamming距离都相等的等水平设计称为"正则表".饱和的等水平正交表构成了正则表的一个子类.对2≤q≤7给出了一些q-水平正则表的结果,其中某些是新的.正则表可进一步用于构造具有好性质的设计.     

t-可约二部分竞赛图的得分表偶

设 T_(m,n)是 m×n 二部分竞赛图,(X,T)是 T_(m,n)的顶点集合 V(T_(m,n)的有序分划,其中|X|=m,|Y|=n.设 X={x_1,x_2,…,x_m},Y={y_1,y_2,…,y_n}.顶点x_1,x_2,…,x_m 在 T_(m,n)中的得分依次为 a_1,a_2,…,a_m,a_1≤a_2≤…≤a_m;y_1,y_2,…,y_n 在 T_(m,n)中的得分依次为 b_1,b_2,…,b_n,b_1≤b_2≤…≤b_n.记 A=(a_1,a_2,…,a_m),B=(b_1,b_2,…,b_n).有序向量偶(A,B)称为 T_(m,n)的得分表偶.反之,给定有序非负整向量偶(A,B),其中 A=(a_1,a_2,…,a_m),a_1≤a_2≤…≤a_m,B=(b_1,b_2,…,b_n),b_1≤b_2≤…≤b_n,是否存在 m×n 二部分竞赛图 T_(m,n),使得(A,B)是 T_(m,n)的     

含有给定k-正则子图的[a,b]-因子

设G是一个图,并设n,k,r,a和b是整数且满足k≥1,k≤a＜b和n≥3.对于G的给定的k-正则图H,如果G是K1,n-free图,且G的最小度至少是((n(a+1)+b-a-(k+1))/(b-k))「(ab+b-a-k)/(2(n-1))」-(n-1)/(b-k)(「(an+b-a-k)/(2(n-1))」)2-1,那么G有一个[a,b]-因子F使得E(H)(∈)E(F).类似地,也得到了关于图G有一个r-因子含有G中给定的k-正则子图的度条件.进一步,指出这些度条件是最佳的.     

关于本原射影Reed-Solomon码的深洞

本原射影Reed-Solomon码是数字通信领域中的一类重要的极大距离可分码.在本原射影ReedSolomon码的译码过程中,人们通常采用极大似然译码算法.对于一个收到的向量u∈F_q~n,极大似然译码算法关键在于确定向量u关于码C的错误距离d(u,C).熟知d(u,C)≤ρ(C),其中ρ(C)为码C的覆盖半径.若d(u,C)=ρ(C),则称u为码C的深洞.本文得到了本原射影Reed-Solomon码PPRS_q(F_q~*,k)的一类深洞.实际上,利用有限域F_q上极大距离可分码的生成矩阵,本文证明如下结果成立:如果q≥4,整数k满足2≤k≤q-2,收到的向量u的前q-1个分量的Lagrange插值多项式为u(x)=λx~(q-2)+f≤k-2(x),其中λ∈F_q~*,f≤k-2(x)为F_q上次数不超过k-2的多项式,并且u的第q个分量为0,那么u是本原射影Reed-Solomon码PPRSq(F_q~*,k)的一个深洞.     

多维秩极限定理(Ⅰ)

<正> §1.记号定义 本文中,R_m表示m维向量空间,Z_m(Z_m~+)表示所有分量都是非负(正)整数的m维向量的全体.x∈R_m的第j个分量记作x~(j).对x_1,x_2∈R_m,记号x_1<(≤)x_2表示x_1~(j)<(≤)x_2~(j),j=1,…,m.此外,m元分布函数F(x)的第j_1,…,j_s(1≤j_1<…相似文献   

关于群中乘积元素的阶

讨论群中两个元素a,b的阶不相等时其乘积ab的阶的一类计算问题.设ㄧaㄧ=m,ㄧ bㄧ=n,若(m,n)=1,且存在k∈N使a=bk,则有ㄧabㄧ=mn/d1d2,其中d1=(m,k+1),d2=(n,k+1).若m≠n,ab=ba,且(m,n)ㄧm/(m,n),或(m,n)ㄧn/(m,n),则有ㄧabㄧ=[m,n].     

含有纯净两因子交互作用成分的4m2n设计的某些结果

纯净效应准则是选取最优部分因析设计的重要准则之一,近年来已经成为一个活跃的研究课题.对给定的k,通过构造2n-(n-k)设计,Tang等(2002)得到了分辨度Ⅲ和ⅣV的2n-(n-k)部分因析设计的纯净两因子交互作用最大数的上下界,但是这种方法只局限于对称设计的情形.本文提出和研究了非对称情形的纯净效应问题,改进了Tang等对分辨度Ⅲ的2n-(n-k)设计的构造方法,得到了分辨度Ⅲ和ⅣV的4m2n设计的纯净两因子交互作用成分最大数的上下界,其中下界是通过构造特定的设计得到的.比较表明,本文所得设计的纯净两因子交互作用成分数在很多情形下都达到了最大.这说明在纯净效应准则下,用这些构造方法来构造4m2n设计是令人满意的.     

构造GD设计的组合递推方法

引言 本文给出构造GD设计的一类组合递推方法;当r-λ_1=1时GD设计存在的充要条件(定理9);附表中列出在r≤10范围内新得的设计或与表[3]所列设计不同构的。 以GD[k,λ_1,λ_2,n,m]记GD设计:v=mn个处理分割为大小为n的m个(结合)组;v个处理安排在大小为k的b个区组B_j中(j=1,2,…,b),使同组的两不同处理在λ_1个区组中相遇,不同组的两个处理在λ_2个区组中相遇。这时每个处理恰出现在r个     

（mg＋k,mf—k）—图中正交于r个不相交子图的边不变的（g,f）—因子

设m,k和r为正整数,且使l≤k＜m.设G是一个具有顶点集合V(G)和边集合E(G)的图,并设g和f是定义在V(G)上的使对每个x∈V(G)有r≤g(x)≤f(x)的整数值函数.设H1,H2,…,Hr是G的r个顶点不相交的子图且|E(Hi)|=k,1≤i≤r.本文证明了每个(mg+k,mf-k)-图有k个边不相交的(g,f)-因子正交于Hi,1≤i≤r.     

多维ARMA平稳序列识别的AIC准则

本文是“关于系统识别的 AIC 准则”的续篇.本文整理了赤池教授[1],[2],[3]等文献.整理可能有错,与原文无关.ARMA 序列最本质的描述是其预报空间的维数是有限的.[1]中说,对多维平稳序列也有类似结果.定义1.设 Y(i),i=0,±1,…为一 r 维宽平稳序列(以后略去宽),均值为0,用(?)_n表示 Y(n-i),i=0,1,2,…的分量按均方模张成的希尔伯特空间,E(Y(n+k)|(?)_n)称作 Y(n+k)对(?)的正交投影.E(Y(n+k)|(?))是 r 维随机变量,其第 i 个分量表示为 Y_i(n+k|n),有对1≤i≤(?),Y_i(n+k|n)∈(?).用 Y_i(n+k)表Y(n+k)第 i 个分量,有     

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].