supercategory of variable molecular sets


Definition 0.1.

A supercategory of variable molecular sets (or molecular set variables), §m⁢s⁢v is defined as the supercategoryPlanetmathPlanetmath 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 morphismsMathworldPlanetmathPlanetmath is the class of all molecular transformations, ηt, of m⁢s⁢v’s.

Remark All such m⁢s⁢v–supercategories are semantic interpretationsMathworldPlanetmathPlanetmath 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 transformationsPlanetmathPlanetmath 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 SupercategoriesPlanetmathPlanetmath: 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 AlgebraPlanetmathPlanetmath 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.
Title supercategory of variable molecular sets
Canonical name SupercategoryOfVariableMolecularSets
Date of creation 2013-03-22 18:30:08
Last modified on 2013-03-22 18:30:08
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 5
Author bci1 (20947)
Entry type Definition
Classification msc 81-00
Classification msc 92B05
Classification msc 18-00
Synonym supercategory of molecular set variables
Synonym m⁢s⁢v-supercategory
Related topic CategoryOfMolecularSets
Related topic ETAS
Related topic MolecularSetVariable
Related topic MolecularSetTheory
Related topic SupercategoriesOfComplexSystems
Related topic ComplexSystemsBiology
Related topic AbstractRelationalBiology
Defines m⁢s⁢v-supercategory
Defines classes of molecular set variables and their chemical transformations with time