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A comprehensive theory of representation for mathematics education
The Journal of Mathematical Behavior, 1998Representation is a difficult concept. Behaviorists wanted to get rid of it; many researchers prefer other terms like “conception” or “reasoning” or even “encoding;” and many cognitive science resarchers have tried to avoid the problem by reducing thinking to production rules.There are at least two simple and naive reasons for considering ...
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, 2004 To the mathematical theory of representation of information in neural nets
Ukrainian Mathematical Journal, 1995We study irreducible nonorthogonal resolutions of the identity. The results obtained show that, in contrast to traditional requirements of “independent measurements” type, the noncommutative approach gives a more precise description of information systems.
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Mathematical Representation for Wald’s Compartment Theory*
Journal of the Optical Society of America, 1963G. Wald has suggested a compartment theory for the functioning of the rods which corresponds mathematically to that of the Geiger–Muller counter. In this paper a discussion is given as to how the compartment theory fits various models for Geiger–Muller counters. Numerical examples are given to illustrate how the mathematical models can be compared with
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Mathematical representation of articular surfaces using influence surface theory
KSME International Journal, 1998Many mathematical techniques have been developed to determine the geometry of articular joint surfaces, because of its so importance to the study of human joint biomechanics. However, a three-dimensional geometric model of the articular joint, which is essential to solid modelling, contact area measurement, and load bearing analyses, has not been well ...
Haksoo Han, Jungsoo Han
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Knowledge representation for mathematical discovery: Three experiments in graph theory
Applied Intelligence, 1991This paper describes the nature of mathematical discovery (including concept definition and exploration, example generation, and theorem conjecture and proof), and considers how such an intelligent process can be simulated by a machine. Although the material is drawn primarily from graph theory, the results are immediately relevant to research in ...
N. S. Sridharan, Susan L. Epstein
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Comparing the theory of representations and constructive mathematics
2005The paper explores the analogy between reducibility statements of Weihrauch's theory of representations and theorems of constructive mathematics which can be reformulated as inclusions between sets. Kleene's function-realizability is the key to understanding of the analogy, and suggests an alternative way of looking at the theory of reducibilities.
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The mathematical structure of rainfall representations: 2. A review of the theory of point processes
Water Resources Research, 1981Part 2 constitutes the second of three parts devoted to the mathematical structure of rainfall. An expository, yet current, treatment of those features of point process theory which are essential to descriptions of the hydrologic processes is developed. A general overview of this three‐part series is given in part 1.
Vijay K. Gupta, Edward C. Waymire
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Biomedical Engineering: Applications, Basis and Communications, 2002
In this paper, a new technique is developed for representing 3-D articular surface, which is based on an analogy method with application of the thin plate theory in the solid mechanics. The method is suitable to represent the scattered data points. On the other word, it does not involve the surface patches and measuring preparation in experimentally ...
Xishi Wang, Li Qun Zhang
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In this paper, a new technique is developed for representing 3-D articular surface, which is based on an analogy method with application of the thin plate theory in the solid mechanics. The method is suitable to represent the scattered data points. On the other word, it does not involve the surface patches and measuring preparation in experimentally ...
Xishi Wang, Li Qun Zhang
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Knowledge Representation in Mathematics a Case Study in Graph Theory
1983In this dissertation we present our work on representational languages for graph theory. We have shown that a knowledge representation can be structured to provide both expressive and procedural power. Our major research contributions are three. First we have defined representations of infinite sets and recommended that mathematical concepts be ...
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