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supercategory of variable molecular sets (Topic)
Definition 0.1   A supercategory of variable molecular sets (or molecular set variables), $\S_{msv}$ is defined as the supercategory whose class of objects is the class of all possible variable molecular sets, $msv$'s, (or molecular set variables), and whose class of morphisms is the class of all molecular transformations, $\eta_t$, of $msv$'s.

Remark All such $msv$–supercategories are semantic interpretations of the ETAS axioms (syntax). This is a mathematical representation of chemical reaction systems in terms of molecular sets that vary with time (or $msv$'s, and their transformations as a result of diffusion, collisions, and chemical reactions.

Bibliography

1
Bartholomay, A. F.: 1960. Molecular Set Theory. A mathematical representation for chemical reaction mechanisms. Bull. Math. Biophys., 22: 285-307.
2
Bartholomay, A. F.: 1965. Molecular Set Theory: II. An aspect of biomathematical theory of sets., Bull. Math. Biophys. 27: 235-251.
3
Bartholomay, A.: 1971. Molecular Set Theory: III. The Wide-Sense Kinetics of Molecular Sets ., Bulletin of Mathematical Biophysics, 33: 355-372.
4
Baianu, I. C.: 1983, Natural Transformation Models in Molecular Biology., in Proceedings of the SIAM Natl. Meet., Denver, CO.; Eprint No. 3675 at cogprints.org/3675/01 as “Naturaltransfmolbionu6.pdf”.
5
I.C. Baianu: 1970, Organismic Supercategories: II. On Multistable Systems. Bulletin of Mathematical Biophysics, 32: 539-561.
6
I.C. Baianu, Brown R., J. F. Glazebrook, and Georgescu G.: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic networks, Axiomathes 16 Nos. 1–2, 65–122.
7
I.C. Baianu: 1980, Natural Transformations of Organismic Structures. Bulletin of Mathematical Biophysics 42: 431-446.
8
I.C. Baianu: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks., FASEB Proceedings 43, 917.



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Also defines:  molecular supercategory, variable molecular sets
Keywords:  molecular supercategory, variable molecular sets, supercategory of variable molecular sets

Cross-references: collisions, systems, representation, ETAS axioms, molecular transformations, morphisms, objects, supercategory, molecular set variables

This is version 1 of supercategory of variable molecular sets, born on 2009-04-05.
Object id is 621, canonical name is SupercategoryOfVariableMolecularSets.
Accessed 545 times total.

Classification:
Physics Classification00. (GENERAL)
 02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )

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