拟线性双曲型方程组的大幅度解析中心波

本文考虑拟线性双曲型方程组的大幅度解析中心波解,得到大幅度解析中心波解存在唯一的充要条件.     

拟线性双曲型方程组的大幅度解析中心波

本文考虑拟线性双曲型方程组的大幅度解析中心波解,得到大幅度解析中心波解存在唯一的充要条件。     

时间可逆系统的等时中心问题

若在中心附近的闭轨线都具有相同的周期,则此中心称为等时中心. 时间可逆多项式系统的等时中心问题是一类公开问题. 为了构造性地解决这一难题,讨论一类范围更广的时间可逆解析动力系统, 给出相应横截交换系统的递推公式,此公式可以用于等时中心条件的推导. 在递推公式的基础上,以吴特征集方法为工具,给出一类时间可逆三次系统具有横截交换系统的充要条件.     

集中载荷作用下开顶扁球壳的非线性稳定问题

本文使用修正迭代法研究了具有硬中心的边缘固定的开顶扁球壳在中心集中载荷作用下的轴对称非线性稳定问题,得到了决定上、下临界载荷的二次近似解析公式.     

复合荷载下波纹圆板的非线性分析*

本文按照各向同性和正交各向异性圆板的大挠度理论,研究了具有光滑中心的波纹圆板在均布和中心集中荷载联合作用下的非线性弯曲问题.应用修正迭代法,我们得到了夹紧固定和滑动固定两种边界条件下十分精确的解析解.     

柔性桥梁颤振导数间的相互关系的参数分析(Ⅰ)

在作者先前给出(徐旭,曹志远.柔长结构气固耦合的线性与非线性气动力学理论.应用数学和力学,2001,22(12):1299-1308.)的柔性结构半解析颤振导数的基础上,研究了桥梁颤振导数之间的内在联系和相互关系,并通过两个具体的桥梁颤振导数的测量试验数据,对其进行了分析验证.同时,也对颤振导数随着桥梁断面的气动中心、转速以及角度变化规律作了参数研究.数据分析的结果不仅验证了前文半解析颤振导数表达式的正确性,也进一步验证了半解析颤振导数之间存在一定的必然联系,同时也表明给出的半解析的颤振导数是适用于流线型断面的桥梁的.     

构成单材料裂纹和双材料界面裂纹有限应力集中的一般解析函数

对构成裂纹尖端附近有限应力集中解析函数的方法进行了综述.含裂纹平面问题的应力函数可以用无理函数和指数函数两种型式表示.对单材料裂纹,将裂纹长度作为参数,对无理函数型解析函数采用直接加权积分可以消除裂纹尖端应力的奇异性,构造有限连续的应力函数和尖劈型的张开位移函数.对指数函数型解析函数的间接积分适用于界面裂纹问题,但会使积分区间的应力分布出现正负反转和不合理的张开位移形状;结合选择不同权函数的叠加可以得到满足精度要求的有限应力集中解析函数.给出了中心裂纹和对称边裂纹在面内拉伸、剪切和弯曲等6种受力状态下的基本解.阐述了作为解析函数何以回避裂纹尖端应力奇异性的理由.     

柔性桥梁颤振导数间的相互关系的参数分析(Ⅱ)

在作者先前(徐旭,曹志远.柔长结构气固耦合的线性与非线性气动力学理论.应用数学和力学,2001,22(12):1299-1308.)给出的柔性结构半解析颤振导数的基础上,研究了桥梁颤振导数之间的内在联系和相互关系,并通过两个具体的桥梁颤振导数测量试验数据进行了分析验证.同时,也对颤振导数随着桥梁断面的气动中心、转速以及角度变化规律作了参数研究.数据分析的结果不仅验证了前文半解析颤振导数表达式的正确性,也进一步验证了半解析颤振导数之间存在一定的必然联系,同时也表明其文中给出的半解析的颤振导数是适用于流线型断面的桥梁的.     

关于钱氏摄动法的高阶解的计算机求解和收敛性的研究

本文借助于中心受集中载荷圆板小挠度问题的积分方程,获得了摄动参数为中心挠度的任意n阶摄动解的解析式.于是,任意次摄动解的所有待定系数能用计算机求解.因此,获得了相当高阶的摄动解.在此基础上,讨论了钱氏摄动法的渐近性和适用区.     

均布载荷作用下开顶扁球壳的非线性稳定问题

本文利用修正迭代法研究了具有硬中心的开顶扁球壳在均布载荷作用下的轴对称非线性稳定问题,得到了临界载荷的二次近似解析公式.     

Characterizations of g-frames and g-Riesz bases in Hilbert spaces

In this paper, we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space, which will play a key role in studying g-frames and g-Riesz bases etc. Using the pre-frame operator Q, we give some necessary and sufficient conditions for a g-Bessel sequence, a g-frame, and a g-Riesz basis in a complex Hilbert space, which have properties similar to those of the Bessel sequence, frame, and Riesz basis respectively. We also obtain the relation between a g-frame and a g-Riesz basis, and the relation of bounds between a g-frame and a g-Riesz basis. Lastly, we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.     

On farthest points of sets

For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.     

管状曲面在曲线论中的应用

研究了围绕曲线的管状曲面上的曲率线,渐近线与测地线,给出它们的方程,揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系,采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系．     

二次曲面和平面位置关系的判式

在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离.     

Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation

We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove a continuous dependence result. Then, we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the contact by using a penalized approach and a version of Newton’s method. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of two-dimensional test problems. These simulations provide a numerical validation of our continuous dependence result and illustrate the effects of the conductivity of the foundation, as well.     

A Simple Method for Computing the Observed Information Matrix When Using the EM Algorithm with Categorical Data

Abstract

A simple matrix formula is given for the observed information matrix when the EM algorithm is applied to categorical data with missing values. The formula requires only the design matrices, a matrix linking the complete and incomplete data, and a few simple derivatives. It can be easily programmed using a computer language with operators for matrix multiplication, element-by-element multiplication and division, matrix concatenation, and creation of diagonal and block diagonal arrays. The formula is applicable whenever the incomplete data can be expressed as a linear function of the complete data, such as when the observed counts represent the sum of latent classes, a supplemental margin, or the number censored. In addition, the formula applies to a wide variety of models for categorical data, including those with linear, logistic, and log-linear components. Examples include a linear model for genetics, a log-linear model for two variables and nonignorable nonresponse, the product of a log-linear model for two variables and a logit model for nonignorable nonresponse, a latent class model for the results of two diagnostic tests, and a product of linear models under double sampling.     

Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping.     

An Integrated Inventory-Routing System for Multi-item Joint Replenishment with Limited Vehicle Capacity

In this paper, we develop a mathematical programming approach for coordinating inventory and transportation decisions in an inbound commodity collection system. In particular, we consider a system that consists of a set of geographically dispersed suppliers that manufacture one or more non-identical items, and a central warehouse that stocks these items. The warehouse faces a constant and deterministic demand for the items from outside retailers. The items are collected by a fleet of vehicles that are dispatched from the central warehouse. The vehicles are capacitated, and must also satisfy a frequency constraint. Adopting a policy in which each vehicle always collects the same set of items, we formulate the inventory-routing problem of minimizing the long-run average inventory and transportation costs as a set partitioning problem. We employ a column generation approach to determine a lower bound on the total costs, and develop a branch-and-price algorithm that finds the optimal assignment of items to vehicles. We also propose greedy constructive heuristics, and develop a very large-scale neighborhood (VLSN) search algorithm to find near-optimal solutions for the problem. Computational tests are performed on a set of randomly generated problem instances.The work of this author was supported by a scholarship of the Faculty of Engineering of Ubonratchathani University, Ubonratchathani, Thailand., The work of this author was supported in part by the National Science Foundation under Grant No. DMI-0085682.     

On the (co)girth of a connected matroid

This article studies the girth and cogirth problems for a connected matroid. The problem of finding the cogirth of a graphic matroid has been intensively studied, but studies on the equivalent problem for a vector matroid or a general matroid have been rarely reported. Based on the duality and connectivity of a matroid, we prove properties associated with the girth and cogirth of a matroid whose contraction or restriction is disconnected. Then, we devise algorithms that find the cogirth of a matroid M from the matroids associated with the direct sum components of the restriction of M. As a result, the problem of finding the (co)girth of a matroid can be decomposed into a set of smaller sub-problems, which helps alleviate the computation. Finally, we implement and demonstrate the application of our algorithms to vector matroids.     

Generalized Trajectory Methods for Finding Multiple Extrema and Roots of Functions

Two generalized trajectory methods are combined to provide a novel and powerful numerical procedure for systematically finding multiple local extrema of a multivariable objective function. This procedure can form part of a strategy for global optimization in which the greatest local maximum and least local minimum in the interior of a specified region are compared to the largest and smallest values of the objective function on the boundary of the region. The first trajectory method, a homotopy scheme, provides a globally convergent algorithm to find a stationary point of the objective function. The second trajectory method, a relaxation scheme, starts at one stationary point and systematically connects other stationary points in the specified region by a network of trjectories. It is noted that both generalized trajectory methods actually solve the stationarity conditions, and so they can also be used to find multiple roots of a set of nonlinear equations.