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We consider the equations uyy=uyuxx−(ux+u)uxy+uxuy,uyy=(ux+uy)uxy−(uxx+2)uy that arise as reductions of the universal hierarchy and rdDym equations, respectively, and describe the Lie algebras of nonlocal symmetries in the infinite-dimensional coverings naturally associated to these equations. [ABSTRACT FROM AUTHOR]

The famous Kissinger's kinetic evaluation method (Anal. Chem. 1957) is examined with respect to: a) the relation between the DTA signal θ ( t) and the reaction rate r( t) ≡ dα/d t; b) the requirements on reaction mechanism model f(α); and c) the relation of starting kinetic equation to the equilibrium behavior of sample under study. Distorting effect of heat inertia and difference between the temperature T of extreme DTA deviation and the temperature T at which the reaction rate is maximal are revealed. The kinetic equations respecting the influence of equilibrium temperature T, especially fusion temperature T, are tested as bases for a modified Kissinger-like evaluation of kinetics. [ABSTRACT FROM AUTHOR]

The equations for heat capacity measured under isodynamical conditions (fixed activity of a single component) are derived for partly open systems exchanging one component with the surroundings while keeping the contents of all other components constant. Compared to conventional isobaric (and isoplethal) heat capacity of a strictly stoichiometric phase, the isodynamical heat capacity of a nonstoichiometric phase is found to involve two additional terms-the saturation contribution due to incorporation (or release) of the free component and the contribution due to deviation from stoichiometry reflecting a different number of the involved phonon modes (due to different free component content) and in some cases a variation of free component incorporation mechanism. [ABSTRACT FROM AUTHOR]