Počet záznamů: 1

Projective Geometry and the Law of Mass Action

  1. 1.
    0335097 - UPT-D 2010 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
    Gottvald, Aleš
    Projective Geometry and the Law of Mass Action.
    Mendel 2009 - 15th International Conference on Soft Computing. Brno: Brno University of Technology, 2009, s. 259-268. ISBN 978-80-214-3884-2.
    [Mendel 2009 - International Conference on Soft Computing /15./. Brno (CZ), 24.06.2009-26.06.2009]
    Výzkumný záměr: CEZ:AV0Z20650511
    Klíčová slova: projective geometry * chemical equilibrium * law of mass action * cross-ratio * incidence structure * Ceva's theorem * Menelaus' theorem * Routh's theorem * Camot's theorem * cyclic products * Riccati's equation
    Kód oboru RIV: BA - Obecná matematika

    A new law of nature asserts that chemical equilibria and chemical kinetics are governed by fundamental principles of projective geometry. The equilibrium constans of chemical reactions are the invariants of projective geometry in disguise. Chemical reactions may geometrically be represented by incidence structures, which are preserved under projective transformations. Theorems of Ceva, Menelaus, and Carnot for triangles and n-gons represent the chemical equilibria, while Routh's theorem represents non-equilibria. Intrinsically projective Riccati's differential equation, being also generic to many other equations of mathematical physics, governs parametric dependence of the equilibrium constants. The theory offers tangible geometrizations and generalizations to the Law of Mass Action, including a new projective-geometric approach to soft computing of very complex problems.
    Trvalý link: http://hdl.handle.net/11104/0179666