The E.E.C. and the development of O.R.

The growth of the E.E.C. has brought about a change in the scale of many organizational problems and a change in the ways that they can be tackled. Accordingly it is plausible that the techniques of O.R. should develop in response to these changes. This paper examines some desirable developments and suggests ways in which they might be achieved by adapting methods devised in other fields for similar problems.     

On the generalization of the D. H. Lehmer problem

Let n ≥ 2 be a fixed positive integer, q ≥ 3 and c be two integers with （n, q） = （c, q） = 1. We denote by rn（51, 52, C; q） （δ 〈 δ1,δ2≤ 1） the number of all pairs of integers a, b satisfying ab ≡ c（mod q）, 1 〈 a ≤δ1q, 1 ≤ b≤δ2q, （a,q） = （b,q） = 1 and nt（a＋b）. The main purpose of this paper is to study the asymptotic properties of rn （δ1, δ2, c; q）, and give a sharp asymptotic formula for it.     

On the r.e. predecessors of d.r.e. degrees

Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets) and R[d] be the class of less than d r.e. degrees in whichd is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d R[d] is not empty. We show that the r.e. degree defined by Lachlan for a d.r.e.set d is just the minimum degree in which D is r.e. Then we study for a given d.r.e. degree d class R[d] and show that there exists a d.r.e.d such that R d] has a minimum element 0. The most striking result of the paper is the existence of d.r.e. degrees for which R[d] consists of one element. Finally we prove that for some d.r.e. d R[d] can be the interval [a,b] for some r.e. degrees a,b, a b d. Received: 17 January 1996     

On the fundamental solutions of the operators of S. Timoshenko and R. D. Mindlin

Our recent paper about some new fundamental solutions is complemented by a representation of the fundamental solution of certain evolution operators of fourth order in terms of a family of fundamental solutions of operators of second order. By applying this to the operators of vibrating beams and plates we deduce representations of their fundamental solutions as simple definite integrals over tabulated functions.     

Construction of the functional model of B. S.-Nagy-C. Foias

Methodological paper: quick and simple construction of the Nagy—Foias functional model, using only elementary information about Hilbert spaces and operators on them. A formula is derived for a characteristic function. The account is based on an idea of B. S. Pavlov (Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 1, 123–148 (1975)) on symmetrization of the notation for a model space.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 16–23, 1977.     

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.     

多元统计方法与体育人才选择

本文应用系统聚类法从多项基本体质测试成绩中对研究对象按其素质好坏进行分类。用主成分分析方法给出研究对象素质好坏的综合评价。为选拔培养体育人才提供数量分析依据。