求有限集合覆盖的构造方法

在近似算法领域,集合覆盖问题是研究的比较早和比较透彻的问题之一.文中解决与经典SCP不同的另一问题,针对有限集合覆盖的构造,提出一种构造有限集合上的集合覆盖的算法,并且给出了该算法的完备性证明.该算法简单有效,是一种用于构造集合覆盖的规范方法.     

A New Duality Approach to Solving Concave Vector Maximization Problems

We introduce a special class of monotonic functions with the help of support functions and polar sets, and use it to construct a scalarized problem and its dual for a vector optimization problem. The dual construction allows us to develop a new method for generating weak efficient solutions of a concave vector maximization problem and establish its convergence. Some numerical examples are given to illustrate the applicability of the method.     

A Finite Algorithm for Almost Linear Complementarity Problems

We present an algorithm for solving a class of nonlinear complementarity problems called the almost linear complementarity problem (ALCP), which can be used to simulate free boundary problems. The algorithm makes use of a procedure for identifying an active index subset of an ALCP by bounding its solution with an interval vector. It is shown that an acceptable solution of the given ALCP can be obtained by solving at most n systems of equations. Numerical results are reported to illustrate the efficiency of the algorithm for large-scale problems.     

Central Sets Theorem on noncommutative semigroups

Let $D$ be a directed set without maximal element, $S$ be an infinite semigroup and ${}^{D}S$ be the collection of all functions from $D$ into $S$. It is shown that for a commutative semigroup $S$, $A?S$ is a $C$-set with respect to ${}^{\mathbb{N}}S$ if and only if $A$ is a $C$-set with respect to ${}^{D}S$. We investigate the Central Sets Theorem for arbitrary semigroups. In fact the Central Sets Theorem is stated with respect to ${}^{S}S$ for arbitrary semigroups.     

On Non-commuting Sets in a Finite p-group with Derived Subgroup of Prime Order

Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If |X| ≥ |Y| for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.     

A Homological Bridge Between Finite and Infinite-Dimensional Representations of Algebras

Given a finite-dimensional algebra , we show that a frequently satisfied finiteness condition for the category -mod) of all finitely generated (left) -modules of finite projective dimension,namely contravariant finiteness of (-mod) in -mod, forces arbitrary modules of finite projective dimension to be direct limits of objects in (-mod). Among numerous applications, this yields an encompassing sufficient condition for the validity of the first finitistic dimensionconjecture, that is, for the little finitistic dimension of to coincide with the big (this is well known to fail overfinite-dimensional algebras in general).     

Two Generalized Constructions of Relative Difference Sets

We give two generalizations of some known constructions of relative difference sets. The first one is a generalization of a construction of RDS by Chen, Ray-Chaudhuri and Xiang using the Galois ring GR(4, m). The second one generalizes a construction of RDS by Ma and Schmidt from the setting of chain rings to a setting of more general rings.     

Two Remarks on Independent Sets

In the first part we generalize the notion of strongly independent sets, introduced in [10] for polynomial ideals, to submodules of free modules and explain their computational relevance. We discuss also two algorithms to compute strongly independent sets that rest on the primary decomposition of squarefree monomial ideals.Usually the initial ideal in(I) of a polynomial ideal I is worse than I. In [9] the authors observed that nevertheless in(I) is not as bad as one should expect, showing that in(I) is connected in codimension one if I is prime.In the second part of the paper we add more evidence to that observation. We show that in(I) inherits (radically) unmixedness, connectedness in codimension one and connectedness outside a finite set of points from I and prove the same results also for initial submodules of free modules. The proofs use a deformation from I to in(I ).     

求解奇异摄动问题混合有限元的最优一致收敛的统一方法

给出了在些Shiskin型网格[21,23,19,18]上,利用一个任意次的混合有限元方法在L2一模下得到奇异摄动问题解的最优一致收敛阶的一个统一方法,通过研究一个四阶问题,定常和不定常问题,我们显示了这个方法的一般性,结果显示非传统Shiskin型网格上的误差估计比传统Shiskin型网格上的误差估计更容易得到,但两种网格给出的误差估计是相容的,它们证明了Roos的猜想[21]是合理的。     

从树型集上最优停止问题到一般偏序集上最优停止问题

本文讨论了树型集上与偏序集上最优停止问题两者间的关系，证明了最优策略与最优控制变量的一一对应关系，从而导出最优策略．可在最优控制变量中取到．     

分支问题的有限决定性和万有开折

本文给出了分支问题有限决定的一些充分必要条件，并用横切性条件刻划了分支问题的万有开折，证明了分支问题的万有开折与无穷小稳定是等价的     

Grasping Infinity by Finite Sets

We show that the existence of an infinite set can be reduced to the existence of finite sets “as big as we will”, provided that a multivalued extension of the relation of equipotence is admitted. In accordance, we modelize the notion of infinite set by a fuzzy subset representing the class of (finite) wide sets.     

A Family of Semi-Regular Divisible Difference Sets

We give a construction of semi-regular divisible difference sets with parametersm = p2a(r–1)+2b (pr – 1)/(p – 1), n = pr, k = p(2a+1)(r–1)+2b (pr – 1)/(p – 1)1 = p(2a+1)(r–1)+2b (pr–1 – 1)/(p-1), 2 = p2(a+1)(r–1)–r+2b (pr – 1)/(p – 1)where p is a prime and r a + 1.     

清晰集构造模糊集的简易方法及其在模糊评判中的应用

运用清晰集合的交、并运算、模糊集的分解定理,本文提出了一个用多个清晰集合构造一个模糊集合的简易方法,并将这个方法应用于模糊综合评判.本方法能将模糊综合评判中取值范围不同的指标的取值范围归一化为区间(0,1).实例表明,本方法在模糊综合评判领域是有效的、且易于操作,可以广泛应用于工程、社科等领域.     

Unbounded Components in the Solution Sets of Strictly Quasiconcave Vector Maximization Problems

Let (P) denote the vector maximization problem

波动方程反演问题的一种新的逼近方法

本文给出了一种求解波动方程反演问题的“多目标函数法”.这种方法简单、有效,并具有明确的物理意义.对于三维问题的程序化它有很强的优越性.     

A White Noise Approach to Stochastic Neumann Boundary-Value Problems

We illustrate the use of white noise analysis in the solution of stochastic partial differential equations by explicitly solving the stochastic Neumann boundary-value problem LU(x)–c(x)U(x)=0, xDR ^d ,(x)U(x)=–W(x), xD, where L is a uniformly elliptic linear partial differential operator and W(x), xR ^d , is d-parameter white noise.     

Rectifiability of Sets of Finite Perimeter in Carnot Groups: Existence of a Tangent Hyperplane

We consider sets of locally finite perimeter in Carnot groups. We show that if E is a set of locally finite perimeter in a Carnot group G then, for almost every x∈G with respect to the perimeter measure of E, some tangent of E at x is a vertical halfspace. This is a partial extension of a theorem of Franchi-Serapioni-Serra Cassano in step 2 Carnot groups: they show in Math. Ann. 321, 479–531, 2001 and J. Geom. Anal. 13, 421–466, 2003 that, for almost every x, E has a unique tangent at x, and this tangent is a vertical halfspace. The second author was partially supported by NSF grant DMS-0701515.