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Some aspects of mathematical statistics as applied to nonisothermal kinetics V

Comparison of the amount of information obtained in traditional and nontraditional approaches

Journal of Thermal Analysis and Calorimetry
Authors: S. V. Vyazovkin and A. I. Lesnikovich

The paper gives a quantitative comparison of two methodological approaches to the solution of the inverse kinetic problem: the traditional approach and the nontraditional approach suggested by the authors. It is shown that the amount of information (in the sense of Shannon) obtained within the scope of the nontraditional approach is always greater than that obtained with the use of the traditional approach.

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This review deals with the choice of a method of solving the inverse kinetic problem (IKP) which would provide the most definite description of the process under conditions of ambiguity. Two fundamentally different methodologies are possible for the IKP solution: one is based on the principle of unambiguous description (discrimination), while the other relies upon the complementarity principle (generalized descriptions). Specific IKP solution methods have been classified, the methodological differences being taken into account. In the first part of this review, general and special limitations in discrimination of formal models have been analysed.

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Some aspects of mathematical statistics as applied to non-isothermal kinetics

Part II. Sensitivity of the kinetic parameter calculation method to the form of the kinetic function

Journal of Thermal Analysis and Calorimetry
Authors: S. V. Vyazovkin and A. I. Lesnikovich

As a numerical characteristic of the sensitivity of the kinetic parameter calculation method to the form of the kinetic function in non-isothermal kinetics, the value of the curvature of the line plotting residual dispersionvs. formal reaction order at the minimum point is suggested. The efficiency of this characteristic is exemplified.

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Journal of Thermal Analysis and Calorimetry
Authors: S. V. Vyazovkin and A. I. Lesnikovich

Restrictions of the simplest use of correlation and regression analysis to obtain a single-valued solution to the inverse kinetic problem are considered. The Coats-Redfern method is suggested as a version of nonlinear regression analysis to increase the unambiguity of the solution.

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Journal of Thermal Analysis and Calorimetry
Authors: S. V. Vyazovkin, I. S. Romanovsky, and A. I. Lesnikovich

A method is suggested for a generalized kinetic description of solid-phase processes on the basis of the complementarity principle. It enables one to obtain spectra as discrete distributions of the probability of describing a process in terms of kinetic functions according to their ordinal numbers. The spectra obtained make it possible to control changes in the behaviour of a solidphase process due to changing process conditions.

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Complementarity methodology as applied for solution of the inverse problem of solid-phase reaction kinetics

Part I. Interpretation of the applicability of the generalized topokinetic equation for describing complex processes

Journal of Thermal Analysis and Calorimetry
Authors: A. I. Lesnikovich, S. V. Vyazovkin, and I. S. Romanovsky

The possibility of describing complex processes by means of the KEKAM equation is demonstrated. The extensive descriptive ability of this equation can be explained within the nontraditional methodology of inverse kinetic problem solving.

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