<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-Versions of One Conformally Invariant Inequality

We obtain L_p-versions of theorems proved by J. L. Fernández and J. M. Rodríguez in the paper “The Exponent of Convergence of Riemann Surfaces, Bass Riemann Surfaces”, Ann. Acad. Sci. Fenn. Ser.A. I.Mathematica 15, 165–182 (1990). An important role in the proof of our results is due to the approach of V. M. Miklyukov and M. K. Vuorinen. In particular, we use the isoperimetric profile of hyperbolic domains.     

Theoretical Study of Nonradiative Energy Transfer from Exciplex to Perovskites

Russian Physics Journal - The results of theoretical studies of energy transfer from the exciplex of TCTA and Bphen molecules to CaZrO3, SrZrO3, and BaZrO3 perovskites are presented. As a result,...     

Metallocene catalysis in the complex-radical polymerization of methyl methacrylate

The initiation stage of methyl methacrylate polymerization in the presence of benzoyl peroxide-metallocene (MC) systems is considered, with MC = Cp₂Fe, (C₅Me₅)₂Fe, (AcC₅H₄)(C₅H₅)Fe, Cp₂TiCl₂, Cp₂ZrCl₂, and (C₅Me₅)₂ZrCl₂. The decomposition of benzoyl peroxide in the presence of a metallocene proceeds via the formation of its complex with the metallocene. The catalytic effect of the metallocenes on the initiation of methyl methacrylate polymerization is due to the formation of a metallocene-benzoyl peroxide complex and its decomposition yielding primary radicals. The chain propagation stage is metallocene-dependent, which is explained by the formation of complex sites. Their formation pathway and structures are analyzed using quantum-chemical calculations.     

Hardy and Rellich type inequalities with remainders

Czechoslovak Mathematical Journal - Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain...     

Generalizations of hardy-type inequalities in the form of Dubinskii

Hardy-type inequalities with power and logarithmic singularities are considered. New one-dimensional inequalities and their multidimensional analogs are proved.     

Initiation of complex-radical polymerization of methyl methacrylate in the presence of metallocenes

The initiation of radical polymerization of methyl methacrylate in the presence of benzoyl peroxide-metallocene (Cp₂Fe, Cp₂ZrCl₂, and Cp₂TiCl₂; (C₅Me₅)₂Fe, (C₅Me₅)₂ZrC_l2, and (AcC₅H₄)(C₅H₅)Fe) systems is studied. It is shown that a metallocene affects the rate of initiation and the initial rate of polymerization. On the basis of quantum-chemical calculations, a new mechanism of the initiation reaction may be advanced: Namely, the decomposition of benzoyl peroxide proceeds via the stage of complexation with a metallocene, while the nature of a metallocene determines the probability of complexation and decomposition.     

Hardy-type inequalities with power and logarithmic weights in domains of the Euclidean space

We consider Hardy-type inequalities in domains of the Euclidean space for the case when the weight depends on the distance function to the domain boundary and has power and logarithmic singularities. We prove several new inequalities with sharp constants.     

Becker type univalence conditions for harmonic mappings

We obtain Becker type univalence conditions for locally univalent harmonic mappings defined in one of the following domains: the unit disc, a halfplane, the exterior of the unit disc and prove a generalization of John’s univalence condition.     

Hardy-type inequalities in arbitrary domains with finite inner radius

We prove Hardy-type inequalities in spatial domains with finite inner radius, in particular, one-dimensional L ^p -inequalities and their multidimensional analogs. The powers of the distance to the boundary of a set occur in the weight functions of spatial inequalities. It is demonstrated that the constant is sharp of the L ¹-inequalities in one-dimensional and multidimensional cases for convex domains.