Nonlinear Free Boundary Problems with Singular Source Terms

We prove the existence of solutions to nonlinear free boundary problem with singularities at given points.     

Some remarks on general commutators theorems

The paper proves some general facts on commutators that refer to Fuglede-Putnam classical theorem in the spectral theory of not necessarily selfadjoint operators.     

Electron microscopic study of chain aggregates of MoO<Subscript>3</Subscript> nanoparticles

Chain aggregates of MoO₃ nanoparticles have been obtained and their polymer-like properties revealed. Chain aggregates of MoO₃ nanoparticles, like polymers, form parallel packings, coils and exhibit coil-helix transition, Brownian motion, and high flexibility.     

Sufficient conditions for regularity of area-preserving deformations

We discuss some basic regularity properties of the area-preserving deformations ${u:\Omega \mapsto \mathbb{R}^2}$ that have minimal elastic energy ${\int \limits_\Omega|\nabla u|^2}$ among a suitable class of admissible vectorfields defined on a smooth, bounded domain ${\Omega\subset \mathbb{R}^2}$ . Although we restrict ourselves to the quadratic stored energy function and 2-space, most of our results extend to three dimensional setting with convex stored energy function.     

The effective action of W 3-gravity

A new method for integrating anomalous Ward identities and finding the effective action is proposed. Two-dimensional supergravity and W ₃-gravity are used as examples to demonstrate its potential. An operator is introduced that associates each physical quantity with a Ward identity, i.e., a quantity that is transformed without anomalous terms and can be nullified in a consistent manner. A covariant form of the action for matter fields interacting with a gravitational and W ₃-gravitational background is proposed. Zh. éksp. Teor. Fiz. 111, 1537–1553 (May 1997)     

On β-uniform Dirichlet algebras

The paper studies the properties of β-uniform Dirichlet algebras and maximal β-uniform algebras. A method is given for construction of a β-uniform Dirichlet algebra and a maximal β-uniform algebra by means of a uniform Dirichlet algebra and amaximal uniform algebra respectively. As a consequence, an analog of the Bishop-Shilov theorem on antisymmetric partition is obtained.     

Nonidentified Kikuchi lines with reverse contrast

Electron diffraction patterns of silicon in transmission with contrast reversal from bright to dark for an unidentified Kikuchi line along its length have been obtained. The contrast reversal of an unidentified line is explained within the elementary mechanism of Kikuchi pattern formation taking into account the Kikuchi electron double diffraction.     

Representations of the Quantum Group SLq(2) in a Space of Functions

We construct representations of the quantum group SL _q(2) in a functional space. We consider the cases of general and exceptional values of the deformation parameter q.