关于等价嵌入于存贮线性有限自动机问题

本文应用模的手段研究域上线性有限自动机等价嵌入于其中存贮类型的问题,分别得到可等价嵌入的一个充分条件与不可等价嵌入的一个充要条件。     

输入存贮线性有限自动机的弱可逆性

应用输入存贮线性有限自动机的结构矩阵讨论了输入存贮线性有限自动机的弱可逆性,得出输入存贮线性有限自动机延迟0步弱可逆的充要条件、延迟τ步弱可逆和严格延迟τ步弱可逆的充分条件,由此条件得出延迟τ步弱可逆和严格延迟τ步弱可逆的输入存贮线性有限自动机的构造方法并且求出延迟0步弱可逆输入存贮线性有限自动机的一个弱逆.     

Separation conditions for conformal iterated function systems

We extend both the weak separation condition and the finite type condition to include finite iterated function systems (IFSs) of injective C ¹ conformal contractions on compact subsets of \mathbbR^d{{\mathbb{R}}^d} . For conformal IFSs satisfying the bounded distortion property, we prove that the finite type condition implies the weak separation condition. By assuming the weak separation condition, we prove that the Hausdorff and box dimensions of the attractor are equal and, if the dimension of the attractor is α, then its α-dimensional Hausdorff measure is positive and finite. We obtain a necessary and sufficient condition for the associated self-conformal measure μ to be singular. By using these we give a first example of a singular invariant measure μ that is associated with a non-linear IFS with overlaps.     

Two-level multiscale finite element methods for the steady navier-stokes problem

In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.     

板-梁组合构件的有限元解法及其误差估计

研究板-梁组合构件的变形和内力分布,是工程上比较关注的课题。目前工程上采用的一般方法,是分别对板及梁采用有限元方法作离散化处理,然后进行适当迭加,得到关于组合构件的有限元解法.这种处理方法,不仅存在有算法问题,更重要的是可靠性问题,也就是由此得到的有限元解是否收敛到真解?正是这一点,人们并不是清楚的。本文将就这个问题,对板-梁组合构件的有限元解法作一些系统的研究。     

TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM

In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.     

Vector transversals

The max-flow min-cut theorem is used to give a necessary and sufficient condition for one or two finite families of finite non-negative vectors to have a (common) vector transversal. The duality theorem of linear programming is then used to prove the polymatroid intersection theorem for any finite number of polymatroids, which in turn is used to give a necessary and sufficient condition for any finite number of finite families of finite sets to have a common vector transversal. (This result was announced without proof in [D. R. Woodall, in “Combinatorics (Proceedings, 4th British Combinatorial Conference)” pp. 195–200, London Mathematical Society Lecture Note Series No. 13, Cambridge Univ. Press, London/New York 1974].) This provides a weak generalization of the well-known conditions of Hall and of Ford and Fulkerson for one and two families of sets, respectively, to have a (common) transversal. It also provides a stronger necessary condition than was previously known for three or more families of sets to have a common transversal.     

拟牛顿流的一种三变量域模型的有限元方法的数值分析

0．引言目前，涉及高温条件下材料蠕变性质的粘弹性流动问题已引起人们广泛的研究兴趣，不少文章讨论了如何对其进行数值求解（见［1］－－［41），首先，人们研究了较简单的仅以速度，压力两个变量来表述此现象的模型问题（如［1，2］）等．鉴于应力变量在材料性质方面的特殊重要性，最近J．Baxanzer等人在［3］中首次对应力满足幂函数规律的蠕变流研究了包含应力、速度和压力三种变量的模型问题的有限元逼近，当粘性的牛顿部分为零时（详见下述）在假定速度与应力、速度与压力有限元空间之间同时满足两种＊＊B条件以后，证明了有限元解…     

Separation conditions for conformal iterated function systems

We extend both the weak separation condition and the finite type condition to include finite iterated function systems (IFSs) of injective C ¹ conformal contractions on compact subsets of . For conformal IFSs satisfying the bounded distortion property, we prove that the finite type condition implies the weak separation condition. By assuming the weak separation condition, we prove that the Hausdorff and box dimensions of the attractor are equal and, if the dimension of the attractor is α, then its α-dimensional Hausdorff measure is positive and finite. We obtain a necessary and sufficient condition for the associated self-conformal measure μ to be singular. By using these we give a first example of a singular invariant measure μ that is associated with a non-linear IFS with overlaps. The authors are supported in part by an HKRGC grant.     

可换幺半群的结构

关于“群”有各种各样的定义 ,本文给出了有限幺半群成为群的一个条件 .并对有限可换幺半群进行了讨论 ,通过对它的商集的研究 ,建立了有限可换幺半群与有限可换幺群之间的联系 ,从而揭示了有限可换幺半群的结构     

Markov跳变系统滚动时域有限记忆控制

针对离散时间Markov跳变系统,提出滚动时域有限记忆控制的方法.在一段有限滤波时域上,利用系统输入与输出变量的线性组合构造一段有限控制时域上的输出反馈控制器.首先,不考虑跳变系统均方可镇定,基于最优控制的方法,获得以迭代计算形式给出的控制器,并使其在无偏条件下能优化二次型性能指标.其次,进一步考虑在成本衰减条件下确定终端加权矩阵,并以它作为边界条件计算得到最优控制律,调节系统均方稳定.为便于求解,成本衰减条件以线性矩阵不等式的形式给出.仿真实例验证了所提方法的可行性和有效性.     

Abel群的一些分解定理的推广(Ⅱ)

本文讨论了2类具体的主理想整环上的拟循环模,研究了A-宽有限的向量空间,刻画了该类向量空间的结构,阐述了A-宽有限的向量空间的A-不变子空间构成的偏序集必满足极小条件,并给出了带有线性变换的向量空间作为F[λ]-模构成拟循环模的一个充要条件.     

The maximum angle condition is not necessary for convergence of the finite element method

We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, finite element approximations may converge even though some dihedral angles of simplicial elements tend to π.     

IBN and Related Properties for Rings

We first tackle certain basic questions concerning the Invariant Basis Number (IBN) property and the universal stably finite factor ring of a direct product of a family of rings. We then consider formal triangular matrix rings and obtain information concerning IBN, rank condition, stable finiteness and strong rank condition of such rings. Finally it is shown that being stably finite is a Morita invariant property.     

A characterization of minimal locally finite varieties

In this paper we describe a one-variable Mal'cev-like condition satisfied by any locally finite minimal variety. We prove that a locally finite variety is minimal if and only if it satisfies this Mal'cev-like condition and it is generated by a strictly simple algebra which is nonabelian or has a trivial subalgebra. Our arguments show that the strictly simple generator of a minimal locally finite variety is unique, it is projective and it embeds into every member of the variety. We give a new proof of the structure theorem for strictly simple abelian algebras that generate minimal varieties.

     

A Berry-Esseen theorem for hypergeometric probabilities under minimal conditions

In this paper, we consider simple random sampling without replacement from a dichotomous finite population and derive a necessary and sufficient condition on the finite population parameters for a valid large sample Normal approximation to Hypergeometric probabilities. We then obtain lower and upper bounds on the difference between the Normal and the Hypergeometric distributions solely under this necessary and sufficient condition.

     

Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions

This paper is concerned with some dynamical property of a reaction-diffusion equation with nonlocal boundary condition. Under some conditions on the kernel in the boundary condition and suitable conditions on the reaction function, the asymptotic behavior of the time-dependent solution is characterized in relation to a finite or an infinite set of constant steady-state solutions. This characterization is determined solely by the initial function and it leads to the stability and instability of the various steady-state solutions. In the case of finite constant steady-state solutions, the time-dependent solution blows up in finite time when the initial function in greater than the largest constant solution. Also discussed is the decay property of the solution when the kernel function in the boundary condition prossesses alternating sign in its domain.     

Finite elements for incompressible flow

We describe in this paper a finite element method for the solution of viscous incompressible flow problems which incorporates an approximate form of the incompressibility condition automatically into the finite element basis. Several examples of such finite elements are presented and applied to a simple test problem.     

有限个广义渐近非扩张映射具误差的复合隐迭代过程

在一致凸Banach空间研究了一个新的有限个广义渐近非扩张映射具误差的复合隐迭代过程.利用空间满足Opial条件和算子满足半紧性条件,我们证明了这个隐迭代过程强、弱收敛于有限个广义渐近非扩张映射的公共不动点.这些结果是目前所得成果的完善和推广.     

Comparing Semigroup and Monoid Presentations for Finite Monoids

 It is known that for any finite group G given by a finite group presentation there exists a finite semigroup presentation for G of the same deficiency, i.e. satisfying . It is also known that the analogous statement does not hold for all finite monoids. In this paper we give a necessary and sufficient condition for a finite monoid M, given by a finite monoid presentation, to have a finite semigroup presentation of the same deficiency.