The F. and M. Riesz theorem revisited

A result (Lemma 1) is obtained concerning the absolute continuity properties of operators implementing the unitary equivalence of two self-adjoint operators having a positive difference. A proof of the F. and M. Riesz theorem is given as a consequence.This work was supported by a National Science Foundation research grant.     

Two Multidimensional Analogs of the F. and M.~Riesz Theorem

A new collection of Riesz sets for and is exhibited. The results are new even in the one-dimensional case. The asymptotic estimate of Fourier multipliers on finite measures in the space used in the proof is interesting in itself. Bibliography: 3 titles.     

An F. and M. Riesz theorem for planar vector fields

We prove that solutions of the homogeneous equation Lu=0, where L is a locally integrable vector field with smooth coefficients in two variables possess the F. and M. Riesz property. That is, if is an open subset of the plane with smooth boundary, satisfiesLu=0 on , has tempered growth at the boundary, and its weak boundary value is a measure , then is absolutely continuous with respect to Lebesgue measure on the noncharacteristic portion of . Received March 10, 2000 / Published online April 12, 2001     

An F. and M. Riesz Theorem on the Complex Sphere

Let μ be a measure on the complex sphere. Denote by μ_pq the projection of μ on H(p, q), the space of complex spherical harmonics. Assume that μ_pq = 0 if (p − 1)q ≠ 0, and ∥μ_1q∥_∞ → 0 as q → ∞. Then μ is absolutely continuous with respect to Lebesgue measure on the sphere.     

F.E.M. implementation for the asymptotic partial decomposition

We consider a Finite Element Method (F.E.M.) implementation for the asymptotic partial decomposition. The advantage of this approach is an important reduction of the number of nodes. The convergence is proved for some model problems. Finally the relation with the “mixed formulation” is discussed.     

弹、粘性体动力学变分原理的Laplace变换形式、有限元构式及数值方法

作者在[1]文中提出了弹、粘动力学变分原理的谱分解形式,本文将其推广到Laplace变换形式,具体写出了薄壳动力学的混合变分原理以及弹-粘-孔隙介质力学的变分原理,并对后者作出了有限元构式. Laplace变换形式的变分原理具有简洁形式,为便于有限元法计算,当已知Laplace变换式的有限个值时,需求原时间函数的有限个值,对此当前尚无成熟方法,本文提供了求原函数的数值方法.从例题可见,这种数值方法是有效的. 结合以上两种理论:从变分原理进行有限元构式以及求Laplace反变换的数值方法,可以使相当广的一类固体动力学问题能够用电子计算机进行求解.     

Cyclic scheduling for F.M.S.: Modelling and evolutionary solving approach

This paper concerns the domain of flexible manufacturing systems (FMS) and focuses on the scheduling problems encountered in these systems. We have chosen the cyclic behaviour to study this problem, to reduce its complexity. This cyclic scheduling problem, whose complexity is NP-hard in the general case, aims to minimise the work in process (WIP) to satisfy economic constraints. We first recall and discuss the best known cyclic scheduling heuristics. Then, we present a two-step resolution approach. In the first step, a performance analysis is carried out; it is based on the Petri net modelling of the production process. This analysis resolves some indeterminism due to the system’s flexibility and allows a lower bound of the WIP to be obtained. In the second step, after a formal model of the scheduling problem has been given, we describe a genetic algorithm approach to find a schedule which can reach the optimal production speed while minimizing the WIP. Finally, our genetic approach is validated and compared with known heuristics on a set of test problems.     

A knowledge-based approach to scheduling in an F.M.S.

This paper reports the development of a computer-based system for production scheduling in a dedicated FMS. The system is based on the state-operator framework commonly used in artificial intelligence. Such a system consists of three components: (i) a knowledge base of states, which describes both the current task domain situation and the goal to be achieved; (ii) a set of operators that are used to manipulate the knowledge base; and (iii) a control strategy to decide which operators to apply next and to resolve conflicts. Some of the interesting features of the scheduling system include: (i) the ability to detect resource conflicts; (ii) the ability to determine alternate routes for a given part in the event of a resource conflict; and (iii) the ability to amend plans if an alternate route is found. These features allow the system to take advantage of the flexible routing for parts that an FMS allows. The system has been implemented using the XLISP programming language. Implementation considerations are discussed. A small but comprehensive example is presented. Further research directions are suggested.     

线性对流占优Sobolev方程的流线扩散有限元方法

Abastract. In this paper,a streamline-diffusion F. E. M. for linear Sobolev equations with con-vection-dominated term is given. According to the range of space-time F. E mesh parameter h,two choices for artifical diffusion parameter are presented,and for the corresponding computa-tion schemes the stability and error estimates in suitable norms are estabilished.     

An F. and M. Riesz theorem for a system of vector fields

This work extends the classical F. and M. Riesz theorem for holomorphic functions to the continuous solutions of real analytic involutive structures. Mathematics Subject Classification (1991) 35F15, 35B30, 42B30, 42A38, 30E25     

不可压混流驱动问题的最小二乘混合元方法

1引言考虑多孔介质中两相不可压缩可混溶渗流驱动问题,它是由一组非线性耦合的椭园型压力方程和抛物型浓度方程组成：dVV。—一山人V什）gVV却）一q,VEn,（．1）＆,,。＿．、。。—一。x）＿＋u·grade－dlv（D（u）grade）一（1－c）q－,xEn,tEJ,（1．2）＆”－－’”””‘”－”””——－’——,、—’一其中a（）一a（x,c）一是（x）／卢（c）,J一［0,Ti,DcyR‘为水平油藏区域．方程式（1．l）一（1．2）中各物理量的意义如下：广为流体压力,c为流体的浓度,u为流体的Darer速度,叶为源汇项,／一—。x（q,O）,…