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Some aspects of mathematical statistics as applied to nonisothermal kinetics

Part III. Unified approach to the analysis of kinetic functions

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

Mathematical analysis has shown that invariant kinetic parameters (IKP) correspond to the real kinetic curve even in the case when the equation prescribing this curve is not used for the calculation of parameters. It has been proved that IKP values coincide with those obtained for isothermal conditions. The theory is verified by calculations using model experimental data. The IKP stability to random experimental errors is studied.

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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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