On a construction of B.P. Zwahlen

In this paper a construction of B. P. Zwahlen is completed. The construction is of a three-dimensional space for which the dimensions of its intersections with a given set of nine subspaces satisfy a certain set of inequalities. This space is needed in the study of the linear inequalities satisfied by matrix sums. It is also shown how a device of A. Hoffman can be adapted to construct such spaces.     

On a construction of B.P. Zwahlen

In this paper a construction of B. P. Zwahlen is completed. The construction is of a three-dimensional space for which the dimensions of its intersections with a given set of nine subspaces satisfy a certain set of inequalities. This space is needed in the study of the linear inequalities satisfied by matrix sums. It is also shown how a device of A. Hoffman can be adapted to construct such spaces.     

Distribution theory on P.C.F. fractals

We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure theorem showing that distributions are locally-finite sums of powers of the Laplacian applied to continuous functions, and an analysis of the distributions with point support. Possible future applications to the study of hypoelliptic partial differential operators are suggested.     

Note on an eta identity presented by B. C. Berndt and W. B. Hart

An eta identity in two independent variables, presented by Berndtand Hart, can be deduced in a few lines from Jacobi's identityfor ³.     

一类微分方程边值问题解的唯一性

研究一个来源于研究退化抛物方程组的渐近性而产生的常微分方程组，证明了具紧支集解的唯一性。     

Investigations of an early Sumerian division problem,c. 2500 B.C.

Two Sumerian school tablets from c. 2500 B.C. —containing respectively a correct and an erroneous solution of the same problem of dividing a very large amount of grain into rations of 7 sila each—are analyzed. It is suggested that the error committed cannot reasonably be explained by two earlier conjectures on the method of solution (normal “long division,” and multiplication by the reciprocal), but only by conversion to an intermediary unit and calculation in two steps analogous to the principle of “long division.” Also discussed are some possible implications of this result for contemporary Sumerian arithmetical abilities and general techniques.     

Normalizing constants for branching processes in random environments (B.P.R.E.)

Normalizing constants are obtained for B.P.R.E. such that the limiting random variable is finite almost everywhere and is zero only on the extinction set of the process w.p.1. Furthermore, the normalizing constants can be chosen so that they grow exponentially fast, and so that the ratio of successive constants converges in distribution. The method of proof used is to prove the result for increasing branching processes, and then, to transfer the result to general B.P.R.E. by employing the relationships between B.P.R.E., the associated B.P.R.E., and the reduced branching process.     

Two Simple Derivations of Universal Bounds for the C.B.S. Inequality Constant

Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.     

Recent Applications of the Maximal Covering Location Planning (M.C.L.P.) Model

To enhance the research and application of mathematical programming and any other O.R. methodologies, it is desirable to investigate some ‘general’ models. This is particulary important in the development of decision support systems, where models play a significant role in management support. This study examines several applications of the maximal covering location planning (M.C.L.P.) model. They include data abstraction, statistical classification, cognitive process modelling, etc. In addition to demonstrating the wide applicability of the model, we also address some implementation issues associated with the applications of the M.C.L.P. model.     

灰色工序时间的统筹方法及其应用

用传统的统筹方法解决实际问题时 ,有些工序时间难以确定 .根据灰色系统的思想确定工序时间 ,使统筹方法的应用更简单、更方便 .本文给出了一个实际例子 .