Weighted Integrals and Bloch Spaces of n-Harmonic Functions on the Polydisc

We study anisotropic mixed norm spaces h(p,q,α) consisting of n-harmonic functions on the unit polydisc of by means of fractional integro-differentiation including small 0 < p < 1 and multi-indices α = (α ₁,...,α _n ) with non-positive α _j  ≤ 0. As an application, two different Bloch spaces of n-harmonic functions are characterized.      

Bergman type operators on mixed norm spaces over the ball in ℂ<Superscript>n</Superscript>

The paper considers Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We prove that there exist values of parameter ß for which these operators are bounded on mixed norm spaces L(p, q, ß) on the unit ball in Cⁿ.     

Littlewood-Paley inequalities in uniformly convex and uniformly smooth Banach spaces

It is proved that the inequality δX(ε)?cεp, p?2, where δX is the modulus of convexity of X, is sufficient and necessary for the inequality

     

The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc

The main results of this note prove that the generalized Libera operator is bounded on the Besov mixed-norm space as well as on the spaces BMOA and VMOA on the unit disk. The compactness of the operator on is also studied.     

Research on unsaturated lactones. 91. Selective oxidation of the bromomethyl group in substituted 2-buten-4-olides

The selective oxidation of the bromomethyl group to a formyl group was realized by the direct action of dimethyl sulfoxide on 2-ethoxycarbonyl-3-bromomethyl-4,4-dialkyl(cycloalkyl)-2-buten-4-olides.See [1] for communication 90.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 6, pp. 740–743, June, 1984.     

Nonlinear quantum theory of interaction of charged particles and monochromatic radiation in a medium

We study the quantum theory of nonlinear interaction of charged particles and a given field of plane-transverse electromagnetic radiation in a medium. Using the exact solution of the generalized Lamé equation, we find the nonlinear solution of the Mathieu equation to which the relativistic quantum equation of particle motion in the field of a monochromatic wave in the medium reduces if one ignores the spin-spin interaction (the Klein-Gordon equation).We study the stability of solutions of the generalized Lamé equation and find a class of bounded solutions corresponding to the wave function of the particle. On the basis of this solution we establish that the particle states in a stimulated Cherenkov process form bands. Depending on the wave intensity and polarization, such a band structure describes both bound particle-wave states (capture) and states in the continuous spectrum. It is obvious that in a plasma there can be no such bands, since bound states of a particle with a transverse wave whose phase velocity v _ph is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the solution of the Mathieu equation. Zh. éksp. Teor. Fiz. 113, 43–57 (January 1998)     

Asymmetric synthesis of β-N-substituted α,β-diamino acidsvia a chiral complex of NiII with a dehydroalanine derivative

Asymmetric synthesis of β-N-substituted (S)-α,β-diamino acids was accomplished by Michael addition of amines to the Ni^II complex of the Schiff base derived from (S)-2-[N-(N′-benzylprolyl)amino]benzophenone (BPB) and dehydroalamine. Diastereoselectivity of the reaction is kinetically and thermodynamically controlled. The chiral auxiliary reagent, BPB, can be recovered and reused. Translated fromIzvestiya Akademii Nauk. Serya Khimicheskaya, No. 3, pp. 504–507, March, 1997.     

Synthesis of 2-Methyl-4-quinolyl Isothiocyanate

A procedure has been developed for the synthesis of substituted 2-methylquinolin-4-ylthiuronium salts by reaction of 2-methyl-4-chloroquinoline with N-substituted thioureas. Alkaline hydrolysis of these salts yields 2-methyl-4-quinolyl isothiocyanate instead of the expected 2-methylquinoline-4-thiol.     

New Quinoline Derivatives on the Basis of (4-Hydroxy-2-methylquinolin-3-yl)acetic Acid

A procedure was developed for the synthesis of (4-hydroxy-2-methylquinolin-3-yl)acetic acid and the corresponding acyl chloride. Reactions of the latter with o-aminobenzenethiol, o-phenylenediamine, o-aminophenol, anthranilic acid, and thiosemicarbazide gave, respectively, 2-(4-hydroxy-2-methylquinolin-3-ylmethyl)-1,3-benzothiazole, -benzoxazole, -benzimidazole, 2-(4-hydroxy-2-methylquinolin-3-ylmethyl)-4H-3,1-benzoxazin-4-one, and 4-hydroxy-2-methyl-3-(5-sulfanyl-1H-1,2,4-triazol-3-ylmethyl)quinoline.