Results 171 to 180 of about 25,588 (199)
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A MATHEMATICAL THEORY OF DESIGN Representation of Design Artifacts (Part I)
International Journal of General Systems, 1999Abstract This study presents a Formal General Design Theory (FGDT), a mathematical theory of design. The main goal of FGDT is to lay out a domain independent modeling of design artifacts ( ‘Part I’) and the design process ( ‘Part II’ ). We discuss issues such as: the scope of the theory with respect to real design and the guidelines it provides for ...
Oded Maimon, Dan Braha
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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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Formal Representation of Mathematics in a Dependently Typed Set Theory
2007We have formalized material from an introductory real analysis textbook in the proof assistant Scunak. Scunak is a system based on set theory encoded in a dependent type theory. We use the formalized material to illustrate some interesting aspects of the relationship between informal presentations of mathematics and their formal representation.
Feryal Fulya Horozal, Chad E. Brown
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Molecular set theory: A mathematical representation for chemical reaction mechanisms
The Bulletin of Mathematical Biophysics, 1960The present investigation is part of a program aimed at examining the mathematical basis of reaction rate theory (Bartholomay,Bull. Math. Biophys. 20, 1958) from the point of view of individual molecular events. Certain inconsistencies resulting from the classical procedure of using stoichiometric “chemical equations” to represent the ...
Anthony F. Bartholomay +1 more
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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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Linear representation of tree structure - a mathematical theory of parenthesis-free notations
Proceedings of the third annual ACM symposium on Theory of computing - STOC '71, 1971In this paper we present a substantially general theory of parenthesis-free notations for finite plane trees. We obtain stronger one-to-oneness results, including a characterization of one-to-oneness for a large class of notations, and a quite general sufficient condition for one-to-oneness that involves the recursive structure of plane trees in what ...
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