Use of the additivity principle in the calculation of the free energy of activation of radical reactions

The free energy of activation of bimolecular radical substitution reactions can be calculated from the increment values of the transition state. The latter are calculated, starting from the general principle of the additivity of thermodynamic functions in the transition state. The values of the reaction rate constants calculated from them are in satisfactory agreement with experimental data. The values of the free energy of activation can be used as characteristics of the relative activity of the radicals and molecules in bimolecular substitution reactions.     

Dynamics of detonation waves in an annular layer of a round pipe

The dynamics of axisymmetric detonation waves in a round pipe containing an annular near-wall bubble layer with a combustible gaseous mixture are studied. The situations in which within the annular layer there are a pure liquid or a bubbly mixture with an inert (unexplosive) gas are considered.     

The grothendieck property in the spacel ∞ (E) and the weak Banach-Saks property inc 0 (E)

We prove the following: 1) if E is a B-convex Banach lattice, the space l(E) is a Grothendieck space; 2) if the space E has the p-Banach-Saks property for some p>1, the space c₀(E) also has this property. It is shown by examples that these conditions are close to being necessary. These results are applied to study the geometric structure of limits of symmetric spaces.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 39–44.     

Weak variations of Lipschitz graphs and stability of phase boundaries

In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity.