PlanetPhysics/Supercategory of Variable Molecular Sets

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A supercategory of variable molecular sets (or \htmladdnormallink{molecular set variables {http://planetphysics.us/encyclopedia/ChemicalTransformations.html})}, §msv is defined as the [[../SuperCategory6/|supercategory]] whose class of [[../TrivialGroupoid/|objects]] is the class of all possible variable molecular sets, msv's, (or molecular set variables), and whose class of [[../TrivialGroupoid/|morphisms]] is the class of all [[../Molecule/|molecular transformations]], ηt , of msv's.

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

All Sources

[1] [2] [3] [4] [5] [6] [7] [8]

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 in Categories, Higher Dimensional Algebra and \L{}ukasiewicz--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. \emph{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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