β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

群的融合自由积的几种广义Fratttini子群

M.K.Azarian将C.Y.Tang的一个引理推广到了下拟Frattini子群的情况,并且还提出了两个公开问题.为了回答这两个问题,进一步研究了群的融合自由积的一些广义Frattini子群,并且得到了一些结果.     

具有超抛物型极限方程的非线性奇摄动反应扩散问题

讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.     

一类具有跳跃层的非线性反应扩散系统的渐近行为

讨论了一类具有跳跃层的反应扩散系统.首先,求出了问题的外部解.其次,引入伸长变量,构造了跳跃层校正项.最后,利用微分不等式理论,得到了原问题解的一致有效的渐近展开式.从而研究了相应问题的解的渐近性态.     

多维布朗运动的几个极限定理

本文研究了d(≥3)维布朗运动离开起点a.s.趋向无穷远的速度问题,获得了精密的结果.作为推论,给出了一个有趣的重对数律.同时,我们也给出了布朗运动靠近起点的相应性质.     

关于z.Ditzian定理

1987年Z.Ditzian提出了反映Bernstein算子收敛阶与所逼近函数光滑模之间关系的一个定理,并在α+β≤2情形下给出了这个定理的证明.对于α+β》2情形,Z.Ditzian给出了猜想.1992年周定轩证明了Z.Ditzian的猜想,完成了Z.Ditzian定理的证明.本文对于Z.Ditzian定理给出了一个新的直接证明,这个证明不需要讨论α,β的情况,而且还将Z.Ditzian定理拓广到Bernstein算子线性组合上.     

不对称柔性壁管道内幂律流体蠕动传输的精确解

在不对称管道内,研究了壁面柔曲性对非Newton流体蠕动流的影响.流变学性质由幂律流体本构方程表征.在数学表达中,采用了长波和低Reynolds数近似.得到了流函数和速度的精确解.给出了流线图及其俘获现象.对所讨论的流动,陈列了关键参数的显著特征,并最后给出了主要结论.     

空中加油问题的递推模型与调度策略

首先对空中加油问题进行了分析,提取了相关性质,在此基础上建立了问题的递推模型.根据该模型,提出了一种启发式搜索算法.该算法计算复杂度低,适用性好.对应于辅机是否可以多次起飞,该算法分为两子算法.对这两种不同情况下的具体问题,设计了相关的优化函数.所有算法都在计算机中运行,并得到了相应结果.值得指出的是,提出的启发式搜索算法十分高效.对于问题1和问题2,该算法所得解是约束条件下的最优调度策略.对于问题3,问题4,问题5,该算法所得解逼近最优调度策略.     

关于局部对称空间中极小子流形的n个整体拼挤定理

研究局部对称δ-拼挤黎曼流形中紧致的极小子流形,给出了若干个整体的拼挤定理,推广了S.S.Chern,M.do Carm o,S.K obayash i及S.T.Y au相应的结果.     

Maxwell流体在有限长管道中作不稳定的蠕动传输:食道吞咽进程分析

解析地研究了有限长管道中Maxwell流体的不稳定蠕动传输.管壁受到不超过静止边界的收缩波作用.对无量纲形式的方程,应用长波长近似进行分析.导出了轴向速度和径向速度的表达式,评估了沿波长和管道长度方向的压力.讨论了回流现象,确定了回流极限区域.对食道中咀嚼食物(如面包、蛋白等)传输的数学公式给出了物理上的解释.可以看出,与Newton流体相比,Maxwell流体有利于在食道中的流动.与Takahashi等[Rheology,1999,27:169-172]的实验结果相符合.进一步揭示了松弛时间既不影响剪应力,也不影响回流极限.发现了压力的峰值,对整数值波列是相同的,而对非整数值波列是不同的.     

Extensional wave motion in homogenous isotropic thermoelastic plate by using asymptotic method

The present investigation is concerned with the study of extensional wave motion in an infinite homogenous isotropic, thermoelastic plate by using asymptotic method. The governing equation for the extensional wave motions have been derived from the system of three-dimensional dynamical equations of linear coupled theory of thermoelasticity. All coefficients of the differential operator are expressed as explicit functions of the material parameters. The velocity dispersion equation for the extensional wave motion is deduced from the three-dimensional analog of Rayleigh–Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity are also derived. The thermoelastic Rayleigh–Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established to that of asymptotic method. The dispersion curves for phase velocity and attenuation coefficient are shown graphically for extensional wave motion of the plates.     

Trigonometric polynomial or exponential fitting approach?

The application of a trigonometric polynomial and an exponential fitting approach is compared for a three-point formula for second-order derivatives, for Simpson’s quadrature rule and for Numerov’s scheme for second-order differential equations. The expressions for the occurring parameters are constructed in both the approaches and the behaviour of these parameters with respect to the introduced frequency is studied. The errors for specific problems obtained in both the approaches as a function of the frequency are compared.     

A Note on the Stability of the Integral-Differential Equation of the Hyperbolic Type in a Hilbert Space

In this paper, the initial-value problem for integral-differential equation of the hyperbolic type in a Hilbert space H is considered. The unique solvability of this problem is established. The stability estimates for the solution of this problem are obtained. The difference scheme approximately solving this problem is presented. The stability estimates for the solution of this difference scheme are obtained. In applications, the stability estimates for the solutions of the nonlocal boundary problem for one-dimensional integral-differential equation of the hyperbolic type with two dependent limits and of the local boundary problem for multidimensional integral-differential equation of the hyperbolic type with two dependent limits are obtained. The difference schemes for solving these two problems are presented. The stability estimates for the solutions of these difference schemes are obtained.     

Optimal control for systems described by hyperbolic equations with strong nonlinearity

An optimization control problem for a hyperbolic equation is considered. The system is nonlinear with respect to the state derivative. The regularization technique for the state equation is applied. The necessary conditions of optimality for the regularized control problem are proved. It uses the extended differentiability of the control-state mapping for the regularized equation. The convergence of the regularization method is proved. Thus the optimal control for the regularized problem with a small enough regularization parameter can be chosen as an approximate solution of the initial optimization problem.     

Existence results for dynamic adhesive contact of a rod

The existence and uniqueness of the weak solution to the model for the dynamics of a viscoelastic rod which is in adhesive contact with an obstacle is established. The model consists of a hyperbolic equation for the vibrations of the rod coupled with a nonlinear ordinary differential equation (ODE) for the evolution of the bonding function. The model allows for failure, i.e., complete debonding, in finite time. The existence of the weak solution is established by using an existence result for ODEs and the Schauder fixed-point theorem. The limit of an elastic rod when the viscosity vanishes is studied, too.     

The hyperbolic–elliptic equation with the nonlocal condition

The nonlocal boundary value problem for a hyperbolic–elliptic equation in a Hilbert space is considered. The stability estimate for the solution of the given problem is obtained. The first and second orders of difference schemes approximately solving this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established. The theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces

The well-posedness of the nonlocal boundary-value problem for abstract parabolic differential equations in Bochner spaces is established. The first and second order of accuracy difference schemes for the approximate solutions of this problem are considered. The coercive inequalities for the solutions of these difference schemes are established. In applications, the almost coercive stability and coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary-value problem for parabolic equation are obtained.     

Heuristics with guaranteed performance bounds for a manufacturing system with product recovery

We consider a manufacturing system with product recovery. The system manufactures a new product as well as remanufactures the product from old, returned items. The items remanufactured with the returned products are as good as new and satisfy the same demand as the new item. The demand rate for the new item and the return rate for the old item are deterministic and constant. The relevant costs are the holding costs for the new item and the returned item, and the fixed setup costs for both manufacturing and remanufacturing. The objective is to determine the lot sizes and production schedule for manufacturing and remanufacturing so as to minimize the long-run average cost per unit time. We first develop a lower bound among all classes of policies for the problem. We then show that the optimal integer ratio policy for the problem obtains a solution whose cost is at most 1.5% more than the lower bound.     

重建极性连续统理论的基本定律和原理(Ⅺ)——兼容性问题

对现有连续统场论中存在若干有关兼容性问题进行了简略的评论．根据重建的极性的连续统基本定律阐述三类兼容性问题．第一类是讨论各基本定律间的兼容性问题．第二类是讨论微极连续统基本定律兼容一般连续统基本定律的问题．第三类是讨论微极连续统基本定律兼容刚体动力学基本方程的问题．推导出的结果有助于深刻理解各种连续统理论的基本定律体系的结构和它们之间的联系．明确地指出,在传统的连续统场论的基本均衡定律的框架下,相容性问题是不可能自然地得到解决．     

Mathematical modelling of flow control in a tundish using electro-magnetic forces

The control of flow in a tundish is important for improving the quality of the steel. Dams, Wiers and Pouring chamber are some of the devices used for controlling the flow in the tundish. The investigation about the role of electromagnetic forces as a replacement for these devices is an objective for the present work. Thus, 3-D MHD simulation was performed to study the effect of electromagnetic forces on flow behaviour in the tundish. The MHD model developed for carrying out the simulation was validated with the analytical solution of the Hartman problem. The results obtained shows improvement in the desired characteristics for inclusion flotataion with magnetic flow modifier of optimum strength of magnetic field.