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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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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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Determining the level of cognitive demand in school tasks is a significant challenge, marked by the lack of consensus among evaluators when assigning cognitive complexity in different areas of knowledge. In view of this problem, we propose a methodology based on the Theory of Registers of Semiotic Representation to guide the assignment of cognitive ...
Eduardo Puraivan +6 more
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Eduardo Puraivan +6 more
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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 ...
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Application of Mathematics in the Representation of Images: From Geometry to Set Theory
2016Mathematics has long been applied to images, especially in a number of ways that rely on categorizing visible properties not just geometrically, that is, spatially, but also algebraically or quantitatively. In Part 1 I have discussed how fuzzy set theory has been applied to the empirical (Zadeh) and conceptual (Smith) understanding of linguistic ...
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2013
This thesis assembles two papers in mathematics and two papers in mathematics education. In the mathematics part, representation theory is practised. Two Clebsch-Gordan type problems are addressed. The original problem concerns the decomposition of the tensor product of two finite dimensional, irreducible highest way representations of $GL_{\mathbb{C}}(
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This thesis assembles two papers in mathematics and two papers in mathematics education. In the mathematics part, representation theory is practised. Two Clebsch-Gordan type problems are addressed. The original problem concerns the decomposition of the tensor product of two finite dimensional, irreducible highest way representations of $GL_{\mathbb{C}}(
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Working Hypotheses, Mathematical Representation, and the Logic of Theory-Mediation
2023Zvi Biener, Mary Domski
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