Some new theorems of Markov Models from the originating Chain measure. New analytical expressions and new techniques in Markov Models: applications in catalysis and in protein dynamics

      Аннотация: Some new theorems of Markov Chains are formulated from Measure-Theoretical aspects; the errors-calculations theorems are analytically spelled.The theorems about the m-states MSM's are descended directly from theMarkov Chain formulations, and, in particular, from the measure of the originating Markov Chain.The new techniques are apt for software implementation in which the numerical simulation are replaced with exact analytical expressions.The opportune representation of the probability matrix is newly chosen. New understanding is provided with in catalysis and protein-dynamics validation.The new theorems and the new techniques are applied to new modelisations of the K-Ras4B evolution and of the pertinent drug preparation: as a further result, the originating Markov Chain of the K-Ras4B protein in catalytic environment is proven to be a finite time-continuous Markov Chain with Hilbert measure (and bounded moments).

Ключевые слова: Markov Chains, Markov models, Measure Theory, catalysis, Protein folding, K-Ras4B protein, Software implementation, Markov errors exact calculations, Anti-cancer drug preparation