supercategory of variable molecular sets

Definition 0.1.

A supercategory of variable molecular sets (or molecular set variables), $\\S_{msv}$ is definedas the supercategory whose class of objects is the class of all possible variable molecular sets, $m s v$ ’s, (or molecular set variables), and whose class of morphisms is the class of all molecular transformations, $\\eta_{t}$ , of $m s v$ ’s.

RemarkAll such $m s v$ –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 $m s v$ ’s, and their transformations as a result of diffusion, collisions, and chemical reactions.

References

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 inCategories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations ofNeuronal, Genetic and Neoplastic networks, Axiomathes 16 Nos. 1–2, 65–122.
7 I.C. Baianu: 1980, Natural Transformations of Organismic Structures. Bulletin of MathematicalBiophysics 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.

单词	SupercategoryOfVariableMolecularSets
释义	supercategory of variable molecular sets Definition 0.1. A supercategory of variable molecular sets (or molecular set variables), $\\S_{msv}$ is definedas the supercategory whose class of objects is the class of all possible variable molecular sets, $m s v$ ’s, (or molecular set variables), and whose class of morphisms is the class of all molecular transformations, $\\eta_{t}$ , of $m s v$ ’s. RemarkAll such $m s v$ –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 $m s v$ ’s, and their transformations as a result of diffusion, collisions, and chemical reactions. References 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 inCategories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations ofNeuronal, Genetic and Neoplastic networks, Axiomathes 16 Nos. 1–2, 65–122. 7 I.C. Baianu: 1980, Natural Transformations of Organismic Structures. Bulletin of MathematicalBiophysics 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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