一类复杂循环排队系统的计算机模拟及其在进程调度中的应用

讨论了顾客到达时间和服务时间与等待队列队长有关的排队系统模拟,顾客服务次数不止1次即出现循环的复杂排队系统,引入到达因子、服务台因子和循环因子,在串并联多服务台情形下建立了4类计算机模拟模型,给出该复杂循环排队系统在进程调度中的应用并进行了计算机模拟.     

基于函数值的线性有理插值样条的区域控制

将插值曲线约束于给定的区域之内是插值与逼近的一个重要内容.本文讨论了一种带形状参数的线性有理插值样条的区域控制问题.给出将插值曲线约束于给定的折线及抛物线之上、之下或之间的条件.数值实例表明本文给出的条件在曲线设计中是有效的.     

Moduli of convexity and smoothness of reflexive subspaces of L

We show that for any probability measure μ there exists an equivalent norm on the space L¹(μ) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This renorming provides also an estimate for the corresponding modulus of smoothness of such subspaces.     

Well-posedness and stability of the repairable system with N failure modes and one standby unit

The well-posedness and stability of the repairable system with N failure modes and one standby unit were discussed by applying the c₀ semigroups theory of function analysis. Firstly, the integro-differential equations described the system were transformed into some abstract Cauchy problem of Banach space. Secondly, the system operator generates positive contractive c₀ semigroups T(t) and so the well-posedness of the system was obtained. Finally, the spectral distribution of the system operator was analyzed. It was proven that 0 is strictly dominant eigenvalue of the system operator and the dynamic solution of the system converges to the steady-state solution. The steady-state solution was shown to be the eigenvector of the system operator corresponding to the eigenvalue 0. At the same time the dynamic solution exponentially converges to the steady-state solution.     

Decay estimates of functions through singular extensions of vector-valued Laplace transforms

Let X be a Banach space and let f∈L^∞(R⁺;X) whose Laplace transform extends analytically to some region containing iR?{0}, possibly having a pole at the origin. In this paper, we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its Laplace transform along the imaginary axis. This technique is applied to obtain decay estimates of smooth orbits of bounded C₀-semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum. These results are close to those given recently by C.J.K. Batty and T. Duyckaerts.     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Divergence points of self-similar measures satisfying the OSC

Recently, Barreira and Schmeling (2000) [1] and Chen and Xiong (1999) [2] have shown, that for self-similar measures satisfying the SSC the set of divergence points typically has the same Hausdorff dimension as the support K. It is natural to ask whether we obtain a similar result for self-similar measures satisfying the OSC. However, with only the OSC satisfied, we cannot do most of the work on a symbolic space and then transfer the results to the subsets of Rd, which makes things more difficult. In this paper, by the box-counting principle we show that the set of divergence points has still the same Hausdorff dimension as the support K for self-similar measures satisfying the OSC.     

Riesz means associated with certain product type convex domain

In this paper we study the maximal operators and the convolution operators Tδ associated with multipliers of the form

     

Some generalizations of locally and weakly locally uniformly convex space

In this paper, we prove that strongly convex space and almost locally uniformly rotund space, very convex space and weakly almost locally uniformly rotund space are respectively equivalent. We also investigate a few properties of k-strongly convex space and k-very convex space, and discuss the applications of strongly convex space and very convex space in approximation theory.     

Ekeland’s variational principle for vectorial multivalued mappings in a uniform space

In this paper, we establish Ekeland’s variational principle and an equilibrium version of Ekeland’s variational principle for vectorial multivalued mappings in the setting of separated, sequentially complete uniform spaces. Our approaches and results are different from those in Chen et al. (2008), Hamel (2005), and Lin and Chuang (2010) [13], [14] and [15]. As applications of our results, we study vectorial Caristi’s fixed point theorems and Takahashi’s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated, sequentially complete uniform space. We also apply our results to study maximal element theorems, which are unified methods of several variational inclusion problems. Our results contain many known results in the literature Fang (1996) [21], and will have many applications in nonlinear analysis.