Coloured Permutations Containing and Avoiding Certain Patterns

Let be the set of all coloured permutations on the symbols 1, 2, . . . , n with colours 1, 2, . . . , r, which is the analogous of the symmetric group when r = 1, and the hyperoctahedral group when r = 2. Let be a subset of d colours; we define to be the set of all coloured permutations . We prove that the number of -avoiding coloured permutations in . We then prove that for any , the number of coloured permutations in which avoid all patterns in except for and contain exactly once equals . Finally, for any , this number equals . These results generalize recent results due to Mansour, Mansour and West, and Simion.AMS Subject Classification: 05A05, 05A15.     

Definability of Completely Decomposable Torsion-Free Abelian Groups by Groups of Homomorphisms

Let C be an Abelian group. An Abelian group A in some class of Abelian groups is said to be _C H-definable in the class if, for any group B\in , it follows from the existence of an isomorphism Hom(C,A) Hom(C,B) that there is an isomorphism A B. If every group in is _C H-definable in , then the class is called an _C H-class. In the paper, conditions are studied under which a class of completely decomposable torsion-free Abelian groups is a _C H-class, where C is a completely decomposable torsion-free Abelian group.     

Combinatorial analysis of Tetris-like games

We study some combinatorial properties of Tetris-like games by using Schützenberger methodology and probability generating functions. We prove that every Tetris-like game is equivalent to a finite state automaton and propose a straight foward algorithm to transform a Tetris-like game into its corresponding automaton. In this way, we can study the average number of pieces inserted during a game and the average score as a function of the player's ability and the pieces extrusion.     

Generalized Waiting Time Problems Associated with Pattern in Polya's Urn Scheme

Let X ₁, X ₂, ... be a sequence obtained by Polya's urn scheme. We consider a waiting time problem for the first occurrence of a pattern in the sequence X ₁, X ₂, ... , which is generalized by a notion score. The main part of our results is derived by the method of generalized probability generating functions. In Polya's urn scheme, the system of equations is composed of the infinite conditional probability generating functions, which can not be solved. Then, we present a new methodology to obtain the truncated probability generating function in a series up to an arbitrary order from the system of infinite equations. Numerical examples are also given in order to illustrate the feasibility of our results. Our results in this paper are not only new but also a first attempt to treat the system of infinite equations.     

Properties of Restricted NCP Functions for Nonlinear Complementarity Problems

In this paper, we study restricted NCP functions which may be used to reformulate the nonlinear complementarity problem as a constrained minimization problem. In particular, we consider three classes of restricted NCP functions, two of them introduced by Solodov and the other proposed in this paper. We give conditions under which a minimization problem based on a restricted NCP function enjoys favorable properties, such as equivalence between a stationary point of the minimization problem and the nonlinear complementarity problem, strict complementarity at a solution of the minimization problem, and boundedness of the level sets of the objective function. We examine these properties for three restricted NCP functions and show that the merit function based on the restricted NCP function proposed in this paper enjoys favorable properties compared with those based on the other restricted NCP functions.     

Continuous Selectors of Fixed Point Sets of Multifunctions with Decomposable Values

Existence theorems of continuous selectors whose values are fixed points of multivalued contractions are proved. As an application, the existence of continuous selectors to generalized solution sets of partial differential inclusions, depending on a parameter, is obtained.     

限制性卖空的均值-方差投资组合优化

本文提出了限制性卖空的均值-方差投资组合模型,通过变量替换将该模型转变为一般二次规划问题,从而运用不等式组的旋转算法进行求解.文章还以一个具体例子验证该算法的有效性,并证明在一定变化范围内,借入资产的资金与总资金的比例越大越有助于拓展投资机会空间.     

状态右端受限的滞后控制系统的最优控制

本文对非线性滞后控制系统就其状态右端x（t1）在的限制条件下，给出最大值原理．作为特例，还将给出在部分状态变量右端完全固定的情况下的最大值原理．最后举例说明主要结果的应用．     

���k-out-of-nϵͳ����Լ���²����Ĺ��ƺ��㷨

In this paper we focus on the sequential k-out-of-n model with covariates. We assume that the lifetime distribution given covariates belongs to the exponential family, and deal with log-linear model of the scale parameter of the exponential distribution. The maximum likelihood estimators (MLEs) of the model parameters with order restrictions are derived and some properties of the MLEs are discussed, and we give the algorithm of MLES and the result of simulation.     

行和列和为常量的(0,1)-矩阵的计数

Let fs,t(m,n) be the number of (0,1) - matrices of size m x n such that each row has exactly s ones and each column has exactly t ones (sm = nt). How to determine fs,t(m,n)? As R. P. Stanley has observed (Enumerative CombinatoricsⅠ(1997), Example 1.1.3), the determination of fs,t(m, n) is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2(n,n), f3,2(m,n), f4,2(m,n) are given. And recursion formulas and generating functions are discussed.     

Cores of games with restricted cooperation

Games with restricted cooperation are cooperativeN-person games with sidepayments, where the collection of feasible coalitions need not comprise all subsets of players and thus is restricted. We study balanced and completely balanced games in this context and derive the corresponding core theorems from a sandwich theorem for set functions within the setting of linear programming. In particular, we discuss general convex games, which Edmonds and Giles (1977) have shown to be of particular importance also in combinatorial optimization.

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Zusammenfassung Spiele mit beschränkter Kooperation sind kooperativeN-Personenspiele mit Nebenzahlungen, wobei nicht jede Teilmenge von Spielern zulässig zu sein braucht. In diesem Sinn sind die Kooperationsmöglichkeiten beschränkt. Balancierte und vollständig balancierte Spiele werden in diesem Zusammenhang untersucht. Die entsprechenden Sätze über die Existenz von Kernen werden von einem Sandwichsatz über Mengenfunktionen im Rahmen der linearen Programmierung abgeleitet. Insbesondere werden allgemeine konvexe Spiele diskutiert, deren Bedeutung auch für die kombinatorische Optimierung Edmonds and Giles (1977) aufgezeigt haben.

     

Polynomial Dehn Functions and the Length of Asynchronously Automatic Structures

We extend the range of observed behaviour among length functionsof optimal asynchronously automatic structures. We do so bymeans of a construction that yields asynchronously automaticgroups with finite aspherical presentations where the Dehn functionof the group is polynomial of arbitrary degree. Many of thesegroups can be embedded in the automorphism group of a free group.Moreover, the fact that the groups have aspherical presentationsmakes them useful tools in the search to determine the spectrumof exponents for second order Dehn functions. We contributeto this search by giving the first exact calculations of groupswith quadratic and superquadratic exponents. 2000 Mathematical Subject Classification: 20F06, 20F65, 20F69.     

A Class of Rational Arithmetical Functions with Combinatorial Meanings

ＡＣｌａｓｏｆＲａｔｉｏｎａｌＡｒｉｔｈｍｅｔｉｃａｌＦｕｎｃｔｉｏｎｓｗｉｔｈＣｏｍｂｉｎａｔｏｒｉａｌＭｅａｎｉｎｇｓＰｅｎｔｉＨａｕｋｋａｎｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｓｃｉｓ．，Ｕｎｉｖ．ｏｆＴａｍｐｅｒｅ，Ｐ．Ｏ．Ｂｏｘ６０７，ＦＩＮ－...     

一类有理算术函数及其组合意义（英）

An arithmetical function f is said to be a rational arithmetical function of order (s,r) if there existcompletely multiplicative functions f₁,f₂,…,f_s and g₁,g₂,…,g_r such thatf=f₁*f₂*… *f_s*(g₁)^-1*(g₂)^-1*… *(g_r) -1 ,where * is the Dirichlet convolution. Recently, L.C. Hsu and Wang Jun studied combinatorial meanings of rational arithmetical functions of order (1,r) . We study these meanings in the setting of Narkiewicz's regular convolution.     

A Monotonicity of Moments Concerned with Order Restricted Statistical Inference

In the order restricted statistical inference problem, moments of the distance between a true parameter and the least square estimate are non-decreasing when the true parameter moves along a half line from an initial point in the null space. This follows from stochastically larger property of the distance.     

Collapsing Construction with Nilpotent Structures

A fundamental result concerning collapsed manifolds with bounded sectional curvature is the existence of compatible local nilpotent symmetry structures whose orbits capture all collapsed directions of the local geometry [CFG]. The underlying topological structure is called an N-structure of positive rank. We show that if a manifold M admits such an N-structure , then M admits a one-parameter family of metrics g _∈ with curvature bounded in absolute value while injectivity radii and the diameters of -orbits away from the singular set of uniformly converge to zero as . Moreover, g _∈ is -invariant away from the singular set. This result extends collapsing results in [CG1], [Fu3] and [G]. Q.C. supported partially by a Jingshi research fund from Beijing Normal University. X.R. supported partially by NSF Grant DMS 0504534 and by a Jingshi research fund from Beijing Normal University.     

Global and Superlinear Convergence of a Restricted Class of Self-Scaling Methods with Inexact Line Searches, for Convex Functions

This paper studies the convergence properties of algorithms belonging to the class of self-scaling (SS) quasi-Newton methods for unconstrained optimization. This class depends on two parameters, say _k and _k , for which the choice _k =1 gives the Broyden family of unscaled methods, where _k =1 corresponds to the well known DFP method. We propose simple conditions on these parameters that give rise to global convergence with inexact line searches, for convex objective functions. The q-superlinear convergence is achieved if further restrictions on the scaling parameter are introduced. These convergence results are an extension of the known results for the unscaled methods. Because the scaling parameter is heavily restricted, we consider a subclass of SS methods which satisfies the required conditions. Although convergence for the unscaled methods with _k 1 is still an open question, we show that the global and superlinear convergence for SS methods is possible and present, in particular, a new SS-DFP method.     

壁面结构对三维可压缩气泡群影响的数值模拟研究

基于流体体积(VOF)法追踪自由液面,研究了壁面结构对三维可压缩气泡群流动的影响.通过在待测壁面上设置不同形状的壁面结构(长方体、椭球体和圆锥体)并改变它们各自的几何参数(位置和长度),来研究壁面结构对壁面附近的气泡群流动的影响,该影响表现为气泡群对壁面的空间平均压力.研究发现,壁面结构对气泡群的拓扑结构的影响会造成壁...     

Design and Fabrication of Composite Smart Structures with High Electric and Mechanical Performances for Future Mobile Communication

In this paper, we have developed a load-bearing outer skin for antennas, which is termed a composite smart structure (CSS). The CSS is a multilayer composite sandwich structure in which antenna layers are inserted. A direct-feed stacked patch antenna is considered. A design procedure including the structure design, material selection, and design of antenna elements in order to obtain high electric and mechanical performances is presented. An optimized honeycomb thickness is selected for efficient radiation and impedance characteristics. High gain conditions can be obtained by placing the outer facesheet in the resonance position, which is at about a half wavelength distance from the ground plane. The measured electrical performances show that the CSS has a great bandwidth (over 10%) and a higher gain than an antenna without a facesheet and has excellent mechanical performances, owing to the composite laminates and honeycomb cores. The CSS concept can be extended to give a useful guide for manufacturers of structural body panels and for antenna designers.     

Pin c and Lipschitz Structures on Products of Manifolds

The topological condition for the existence of a pin ^c structure on the product of two Riemannian manifoldsis derived and applied to construct examples of manifolds havingthe weaker Lipschitz structure, but no pin ^c structure.An example of a five-dimensional manifold with this property is given;it is pointed out that there are no manifolds of lower dimension withthis property.