一类非线性发展方程整体解的存在性、渐近性与解的爆破

研究一类非线性发展方程初边值问题整体弱解的存在性，渐近性和解的爆破问题，证明在关于非线性项的不同条件下，上述初边值问题分别在大初值和小初始能量的情况下存在整体弱解，并且讨论了弱解的渐近性。还证明：在相反的条件下，上述弱解在有限时刻爆破，并且给出了一个实例。     

倒向随机微分方程弱解（英）

引入倒向随机微分方程弱解的概念，应用Girsanov变换，建立了两类倒向随机微分方程（0．1）和（0．2）弱解存在的等价性，由此得到倒向 随机微分方程弱解存在的几个充分条件。     

三维Keller-Segel-Navier-Stokes方程弱解的整体存在性

本文证明具有logistic源的一个3维Keller-Segel-Navier-Stokes方程弱解的整体存在性，并研究了弱解的长时间行为.     

倒向随机微分方程弱解

提出倒向随机微分方程(简称BSDE)弱解的概念, 讨论了两类BSDE弱解存在的等价条件,并得到弱解存在的几个充分条件和减弱BSDE解存在的条件: 漂移系数g关于(y,z)满足Lipschitz 条件.     

具有双障碍的退缩抛物变分不等式解的存在性和唯一性(英)

本文研究具有双障碍的退缩抛物变分不等式．我们利用罚技巧，有限逼近和先验估计方法，得到一类退缩抛物变分不等式弱解的存在性，并在一定条件之下，建立了弱解的唯一性．本文结论对广泛的一类抛物型变分不等式成立．     

三维Keller-Segel-Navier-Stokes方程弱解的整体存在性

本文证明具有logistic源的一个3维Keller-Segel-Navier-Stokes方程弱解的整体存在性,并研究了弱解的长时间行为.     

一类非线性拋物变分不等式解的存在性

本文研究了一类基于非线性抛物算子的变分不等式问题.首先,通过拓展偏微分方程的弱解理论定义了变分不等式的弱解.其次,利用惩罚函数并结合连续方法,证明了变分不等式存在弱解.     

具有双障碍的退缩抛物变分不等式解的存在性和唯一性

本文研究具有双障碍的退缩抛物变分不等式，我们利用罚技巧，有限逼近和先验估计方法，得到一类退缩抛物变分不等式弱解的存在性，并在一定条件下，建立了弱解的唯一性。本文结论对广泛的一类抛物物型变分不等式成立。     

高阶变形的Novikov方程弱解的全局存在性

研究了一类高阶变形的Novikov方程全局弱解的存在性,在初值满足条件u0∈H2,p,p 4时,通过黏性逼近的方法得到了高阶变形Novikov方程全局弱解的存在性.     

一类非线性反应扩散系统弱解的整体不存在性

通过巧妙构造函数,利用试验函数法,根据初值在无穷远处的情况与反应扩散系统弱解的存在性的关系,从一个新的角度给出了其弱解的整体不存在性的一个充分条件.     

Evaluations of Parameters for the Optimization of S.S.O.R. and A.D.I. Preconditioning

The main goal of this paper is to give two ways to estimate the needed parameters in order to obtain the condition number of S.S.O.R. preconditioned matrices, namely, the algebraic matricial formulation of convexity Riesz theorem and the tridiagonal Fourier analysis. The improvement with respect to Axelsson's approach is explicitly given. Estimations of the condition number in the case of A.D.I. preconditioning is also considered.     

Verification of a class of self-timed computational networks

A mathematical model for systolic networks is generalized and applied to a class of VLSI cellular networks which is defined to include both systolic and self-timed networks. The general model is kept simple by assuming that a computation does not deadlock, that is by separating the verification of liveness from the the verification of the results. The main contribution of this paper concerns the study of deadlock in self-timed computational networks. More specifically, an algebra of events is developed and used to prove that the liveness of any self-timed network is determined uniquely by its initial state. Moreover, a method is presented for the verification of liveness in networks preset to given initial states.This work was supported in part under ONR contract N00014-80-C-0455.     

Modeling of superscalar instruction scheduling and analysis of a heuristic scheduling algorithm

The problem of superscalar instruction scheduling is studied and an analysis of a heuristic scheduling algorithm is presented. First, a superscalar architecture is characterized byk, the number of types of functional units employed,m _i , the number of typei functional units,P _ij , thejth functional unit of typei, andz, the maximal number of delay cycles incurred by the execution of instructions. A program trace to be scheduled is modeled by a directed acyclic graph with delay on precedence relations. These two models reflect most of the flavor of the superscalar instruction scheduling problem. A heuristic scheduling algorithm called the ECG-algorithm is designed by compiling two scheduling guidelines. The performance of the ECG-algorithm is evaluated through worst-case analysis. Lettingw _ECG denote the length of an ECG-schedule andw _opt the length of an optimal schedule, we established the boundwv _ECG /w _opt k+1–2/[max{m _i }(z+1)], which is smaller than other known bounds.     

Performance evaluation of shared and separate inverted files

In this paper, two different structures for inverted files are analyzed and compared, when the relational join operation is taken into account. The structures are called shared and separate inverted files. The results are given of some experiments which show that the shared inverted organization is always advantageous when the inverted files are not sorted and is almost always advantageous when the files are sorted.     

一类非拟Newton算法及其收敛性

本文对求解无约束最优化问题提出一类非拟Ｎｅｗｔｏｎ算法，此方法同样具有二次终止性，产生的矩阵序列保持正定对称传递性，并证明了新类中的任何一种算法的全局收敛和超线性收敛性。     

On specifications,subset types and interpretation of proposition in type theory

In this paper we discuss some practical aspects of using type theory as a programming and specification language, where the viewpoint is to use it not only as a basis for program synthesis but also as a programming language with a programming logic allowing us to do ordinary verification.The subset type has been added to type theory in order to avoid irrelevant information in programs. We give an example of a proof which illustrates the problems that may occur if the subset type is used in specifications when we have the standard interpretation of propositions as types. Harrop-formulas and Squash are then discussed as solutions to these problems. It is argued that they are not acceptable from a practical point of view.An extension of the theory to include the two new judgment forms:A is a proposition, andA is true, is then given and explained in terms of the old theory. The logical constants are no longer identified with the corresponding type theoretical constants, but propositions are interpreted as Gödel formulas, which allow us to introduce and justify logical rules similar to rules for classical logic. The interpretation is extended to include predicates defined by using reflections of the ordinary definition of Gödel formulas in a type of small propositions.The programming example is then revisited and stronger elimination rules are discussed.     

On the minimality of polygon triangulation

The problem of triangulating a polygon using the minimum number of triangles is treated. We show that the minimum number of triangles required to partition a simplen-gon is equal ton+2w –d – 2, wherew is the number of holes andd is the maximum number of independent degenerate triangles of then-gon. We also propose an algorithm for constructing the minimum triangulation of a simple hole-freen-gon. The algorithm takesO(nlog² n+DK ²) time, whereD is the maximum number of vertices lying on the same line in then-gon andK is the number of minimally degenerate triangles of then-gon.     

Cubature Formulas of a Nonalgebraic Degree of Precision

We deal with cubature formulas that are exact for polynomials and also for polynomials multiplied by r, where r is the Euclidean distance to the origin. A general lower bound for the number of nodes for a specified degree of precision is given. This bound is improved for centrally symmetric integrals. A set of constraints (consistency conditions) is introduced for the construction of fully symmetric formulas. For one dimension and arbitrary degree, it is shown that the lower bound is sharp for centrally symmetric integrals. For higher dimensions, as an illustration, cubature formulas are only constructed for low degrees. March 6, 2000. Date revised: April 30, 2001. Date accepted: May 31, 2001.     

A systolic generation of combinations

A parallel algorithm for generating all combinations ofm (m fixed) items out of anyn given items in lexicographic order is presented. The computational model is a linear systolic array consisting ofm identical processing elements. This algorithm requires {ie23-1} time-steps for the {ie23-2} combinations, that is, one output at each time-step. Since all processing elements perform the same program, it is suitable for VLSI implementation. Based on mathematical induction, such an algorithm is proved to be correct.     

On the design of reactive systems

The notion of joint actions provides a framework in which the granularity of atomic actions can be refined in the design of concurrent systems. An example of a telephone exchange is elaborated to demonstrate the feasibility of this approach for reactive systems and to illustrate transformations that are justifiable in such a process. Particular problems arise when a refinement would allow new interleavings of semantically relevant events. The meaning of a reactive computation is specified in a way that makes this possible.Dedicated to Peter Naur on the occasion of his 60th birthday