水面舰艇编队防空问题的建模研究

数学建模在水面舰艇编队防空系统中起到不可估量的作用.通过实例,分析一枚及多枚来袭导弹穿越护卫舰时的数学关系,得出护卫舰100%发现来袭导弹的最大工作半径为25km;并在此基础上建立100%防御成功条件下防御面积最大化的数学模型.计算得出编队的最佳设计阵型为:四艘护卫舰布置在以指挥舰为中心、半径为59km的圆上,各舰相对于指挥舰的方位角分别为45°、95°、145°和195°.根据各战舰拦截导弹过程的运动关系,求得了最优阵型下舰队拦截来袭导弹的最大批次.     

水面舰艇编队防空和信息化战争评估模型

研究了由一艘驱逐舰和四艘护卫舰组成的水面舰艇编队的防空建模问题,建立了突出信息平衡度的修正兰彻斯特战争模型.对于问题1,利用编队与来袭导弹的时变相对位置速度数据求解模型,得到编队最佳队形.对于问题2,建立了来袭导弹对舰艇编队追击问题的几何模型,从单舰到编队的拦截区域分析了编队最小防御纵深的估算方法.对于问题3,采用问题2中类似的方法,计算出有信息支援条件下可拦截来袭导弹15批,相比问题二提高了37.20%.对于问题4,采用聚类分析方法对已知意图的附件数据进行聚类,将分类后的类别中心作为意图识别的模式,采用基于所提出的意图偏差度判别分析方法对空中可疑目标可能的意图作出了识别.对于问题5,在分析信息优势的特征和信息平衡度的重要作用的基础上,根据交战双方对对方作战信息的掌控能力和实时水平,给出了交战双方之间的信息平衡度计算模型.以海湾战争作为案例,结合两类模型进行了对比计算,对修正模型的有效性作出了初步验证.     

水面舰队建立最佳防空编队的数学模型

防空反导是水面舰艇编队最重要的任务之一,我国南海海域辽阔,水面舰艇执行外围岛礁附近海域巡航任务时,往往超出了空中掩护的作战半径,需要自身的对空防御,这时,水面舰艇的编队阵型至关重要.同时,空中目标意图识别是战场态势分析的一个重要部分.以我海军在南海某开阔海域巡逻的水面舰艇编队为例,探究了最佳编队队形的数学模型,并根据所提供的战场空中目标信息,判断目标可能的意图,为威胁判断、火力分配和抗击来袭目标奠定基础.     

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.     

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].