The graph-theoretic field model—I. Modelling and formulations

The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure.This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.     

Ladder realizations of multivariable positive real functions

Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of its transmission zeros either at the origin or at finity. Conditions are also obtained when each of the two-ports is a Fujisawa-type lowpass ladder.     

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.

     

Behavior of narcotics-addicted newborns.

The behavior of narcotics-addicted and nonaddicted newborns on the first 2 days of life was assessed with the Brazelton Neonatal Behavioral Assessment Scale. In addition to classic signs of narcotics abstinence, addicted infants were less able to be maintained in an alert state and less able to orient to auditory and visual stimuli. These deficits were especially pronounced at 48 hours of age. Addicted infants were as capable of self-quieting and responding to soothing intervention as normal neonates, although they were substantially more irritable. These characteristics and addicted infants' greater resistance to cuddling are discussed in terms of their potential impact on early infant-care-giver interaction.     

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.