Operator Approach to the Master Equation for the One-Step Process

Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows to write down the master equation based on the type of of the kinetic equations and assumptions about the nature of the process. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. Leaving in the expansion terms up to the second order we can get the Fokker-Planck equation, and thus the Langevin equation. It should be clearly understood that these equations are approximate recording of the master equation. However, this does not eliminate the need for the study of the master equation. Moreover, the power series produced during the master equation decomposition may be divergent (for example, in spatial models). This makes it impossible to apply the classical perturbation theory. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. As an example the Verhulst model is used because of its simplicity and clarity (the first order equation is independent of the spatial variables, however, contains non-linearity). We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation.Comment: in Russian; in Englis

Hybrid multicyclophanes based on thiacalix[4]arene and pillar[5]arene: Synthesis and influence on the formation of polyaniline

© 2018 the Partner Organisations. For the first time, fragments of a pillar[5]arene were spatially preorganized with a thiacalix[4]arene core in a single multimacrocyclic structure. It was shown that the synthesized hybrid multicyclophanes bind aniline and do not interact with p-toluenesulfonic acid. Supramolecular assistance of the synthesized multicyclophanes in oxidative polymerization of aniline in aqueous p-toluenesulfonic acid solutions was studied. It was found that the use of the multicyclophane template in the reaction of the oxidative polymerization of aniline led to the formation of emeraldine with a higher molecular weight and a similar conductivity (1-2 mSm cm-1), which formed more stable emeraldine dispersions in acetone in comparison with traditionally obtained polyaniline

DEVELOPMENT OF A MODEL OF ASSEMBLY-DESIGN PROTECTION AGAINST IONIZING RADIATION

В работе представлено конструктивное решение модели сборной биологической защиты от ионизирующего излучения, относящейся к ядерной технике и служащей для защиты персонала объектов атомной энергетики от ионизирующего (гамма) излучения, а именно к устройствам наблюдения и ремонта с защитой оператора при ремонте оборудования в условиях повышенного уровня ионизирующего излучения.The paper presents a constructive solution of the model of an assembly-design biological protection against ionizing radiation related to nuclear engineering and serving to protect personnel of nuclear power facilities from ionizing (gamma) radiation, namely, monitoring and repair devices with operator protection when repairing equipment in conditions of an increased level of ionizing radiation

Kinetics of casein hydrolysis by peptidase from Bacillus thuringiensis var. israelensis

The kinetics of enzyme reaction is generally studied using the Michaelis-Menten equation and various methods of its linearization. Each method has its advantages and drawbacks, so their comparison for determining the kinetics of new enzymes action is topical. The aim of this work was to study the kinetics of casein hydrolysis catalyzed by new peptidase from Bacillus thuringiensis var. israelensis IMB B-7465 using several methods of enzyme activity assessment and Michaelis-Menten equation linearization. The satisfactory agreement between kinetic constants values obtained by the methods of Lineweaver-Burk, Hanes, Eadie-Hofstee, Cornish-Bowden-Eisenthal was established. The Lineweaver-Burk method was shown to be optimal for determining Km and Vmax of casein hydrolysis. Estimation of caseinolytic activity with the use of ortho-phthalic dialdehyde allowed more accurate Vmax determination compared to the use of Anson and Kunitz methods