The graph-theoretic field model— II. application of multi-terminal representations to field problems

This paper is a sequel to a paper entitled “The Graph-Theoretic Field Model—I: Modelling and Formulations” (1). Herein, the Theory of Multi-Terminal Representations is applied to the Graph-Theoretic Field Model to provide mathematical models of finite elements. The element models are obtained solely from the algebraic building blocks of the Graph-Theoretic Field Model, without recourse to any functional mathematics. The theory of Multi-Terminal Representations is developed for both linear and non-linear problems. Examples of the application of the theory to one- and two-dimensional field problems are presented from heat conduction and electrostatics.     

On metrics matched to the discrete memoryless channel

A sequence of metrics {D_N} is said to be additive and matched to a discrete memoryless channel (DMC) if D_N is the sum on its coordinates of N single letter metrics and if the maximum likelihood decoder for sequences of length N is a minimum D_N-distance decoder. Necessary and sufficient conditions on the transition probabilities of a DMC for the existence of a sequence of additive metrics matched to it are given. In the case of the binary channel these are shown to be equivalent to the channel being symmetric. Explicit transition probabilities are given for a large class of ternary DMCs with an associated sequence of additive matched metrics. The problem solved here may be considered a generalization of the problem of finding the DMCs matched to the Lee metric solved by Chiang and Wolf in 1971 (2).     

Research findings and administrative implications for off-campus higher education

While off-campus educational programs grow in number and in importance in American higher education, little systematic research has been conducted concerning their effectiveness and intellectual and developmental impact. The project described here compared students in three categories: those studying abroad; those studying off-campus in this country; and those who remained on their home campus. The implications of the findings of the research suggest that a rethinking of existing programs is appropriate, if off-campus educational programs are to realize their full potential. The authors offer concrete suggestions toward restructuring these programs.

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Zusammenfassung Obwohl Bildungsprogramme ausserhalb der Universität in der amerikanischen Hochschulbildung an Anzahl und Bedeutung zunehmen, wurde deren Fruchtbarkeit und geistige und entwicklungsmässige Auswirkung kaum systematisch untersucht. Das hier geschilderte Projekt vergleicht Studenten dreier Kategorien: im Ausland studierende, im Lande ausserhalb der Universität studierende und solche, die in ihrem heimischen Universitätsbetrieb geblieben sind. Die Ergebnisse der Untersuchung legen die Folgerung nahe, es sei angebracht, bei eingeführten Programmen zu überdenken, ob die Bildungsprogramme ausserhalb der Universität ihre Möglichkeiten voll ausschöpfen sollen. Die Verfasser machen konkrete Vorschläge für eine Neugestaltung dieser Programme.

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Résumé Tandis que l'importance et le nombre des programmes d'éducation en dehors des universités s'accroît dans l'enseignement supérieur aux Etats-Unis, peu de recherche systématique a été effetué en ce qui concerne leur efficacité et leur impact intellectuel et de développement. Le projet décrit ici a comparé des étudiants de trois catégories: ceux qui étudient à l'étranger, ceux qui étudient hors des universités à l'intérieur du pays et ceux qui sont restés dans leurs universités d'origine. Les implications des conclusions de la recherche suggèrent qu'il convient de repenser les programmes existants, si les programmes d'éducation hors des universités doivent réaliser tout leur potentiel. Les auteurs présentent des suggestions concrètes quant à la restructuration de ces programmes.

     

Definition in science teaching

Summary Definitions, I have suggested, have both a function and a form. The function pursued and the form used should depend on the situation and on the term being defined. In the situation described at the outset, Mr. Beta should probably have seen to it that a stipulation of some sort was given-just in order to get on with the task at hand. The stipulation might have been based upon a true reported definition-or it might not-depending on political considerations and the linguistic flexibility of the people concerned. Since no one involved could plausibly have been trying to embody a program in a definition of dough, a programmatic definition was not appropriate in that situation.Several different forms for a definition of dough might reasonably have been used, but in this case the old reliable classification form was probably best, because of its completeness, neatness, and brevity. Two reasonable alternatives are the equivalent-expression form and the range form. The synonym, example-nonexample, and operational forms were probably not appropriate.My main point is that there is not just one way to define. I hope that my delineation of some major possibilities and variations will help those who read this article to be flexible in handling problems of definition when they arise; and they arise more often than most people realize.An ealier draft of this article was presented at a colloquium at the University of Illinois in honor of Professor B. Othanel Smith at his retirement.     

Circular Plate on Multipoint Supports

Formulae are derived for the deflection surface of a symmetrically loaded circular plate having several points supports which are situated at equal distances apart on a single concentric circle. There is no restriction on the diameter of the support circle, which may be as large as the diameter of the plate itself. The results of this paper compare favorably with published experimental results. Numerical deflection coefficients for a uniformly loaded plate are provided, and these could be utilized for optimizing the positions and the number of concentrated supports.