Non-cooperative monopolistic games and monopolistic market games

A class of non-cooperative games is discussed in which one player (“the monopolist”) by choosing his strategy restricts the other players to subsets of their strategy sets. Examples of such games in various fields are given. In particular it is shown that some very important economic situations fall within this class of games. A solution concept is defined and sufficient conditions for its existence are derived. The question of the advantages a player derives from being a monopolist is raised and conditions are derived for him to benefit from being a monopolist.     

A TEMPO-like nitroxide combined with an alkyl-substituted pyridine: An efficient catalytic system for the selective oxidation of alcohols with iodine

An efficient method for the oxidation of alcohols to aldehydes or ketones in a two-phase CH₂Cl₂/NaHCO₃ (aq.) system, using iodine and catalytic amounts of 4-acetylamino-2,2,6,6-tetramethylpiperidine-1-oxyl and 2,4,6-trimethylpyridine, was developed. The performance of the method was demonstrated by the selective oxidation of 37 variously substituted alcohols in ≥90% yield, including the gram-scale synthesis of the important chemical 2,5-diformylfuran from biomass-derived 5-hydroxylmethylfurfural.     

On the nature of the de Branges Hamiltonian

We prove the theorem announced by the author in 1995 in the paper “A criterion for the discreteness of the spectrum of a singular canonical system” (Funkts. Anal. Prilozhen., 29, No. 3).In developing the theory of Hilbert spaces of entire functions (we call them Krein-de Branges spaces), de Branges arrived at a certain class of canonical equations of phase dimension 2. He showed that, for any given Krein-de Branges space, there exists a canonical equation of the class indicated that restores a chain of Krein-de Branges spaces imbedded one into another. The Hamiltonians of such canonical equations are called de Branges Hamiltonians. The following question arises: Under what conditions will the Hamiltonian of a certain canonical equation be a de Branges Hamiltonian? The main theorem of the present work, together with Theorem 1 of the paper cited above, gives an answer to this question.     

Left-handed interfaces for electromagnetic surface waves

We show that surface electromagnetic waves (SEMWs) propagating along two-dimensional (2D) interfaces separating different metamaterials can behave analogously to 3D electromagnetic waves in either usual or left-handed media, depending on the permeabilities and/or permittivities of the two materials forming the interface. We derive the conditions when SEMWs carry energy opposite to the phase velocity. In analogy to three-dimensional (3D) left-handed media, we derive both an anomalous Cherenkov emission and a reversed Doppler effect. We also predict a negative refraction at the boundary between two different interfaces, which can be useful for perfect 2D lensing.