On the possible connection between renormalization-groups and nonlinear semi-groups

Some algebraic properties of the renormalization-group (RNG) are studied using the nonlinear semi-group theory. The RNG is defined in an axiomatic manner as a bounded nonlinear semi-group on an abstract Banach space. Perturbations of the fixed point of RNG and the problem of marginality are investigated using a hierarchy of nonlinear semi-groups.     

s-wave bound and scattering state wave functions for a velocity-dependent Kisslinger potential

A relation linking the normalized s-wave scattering and the corresponding bound state wave functions at bound state poles is derived. This is done in the case of a non-local, velocity-dependent Kisslinger potential. Using formal scattering theory, we present two analytical proofs of the validity of the theorem. The first tackles the non-local potential directly, while the other transforms the potential to an equivalent local but energy-dependent one. The theorem is tested both analytically and numerically by solving the Schr?dinger equation exactly for the scattering and bound state wave functions when the Kisslinger potential has the form of a square well. A first order approximation to the deviation from the theorem away from bound state poles is obtained analytically. Furthermore, a proof of the analyticity of the Jost solutions in the presence of a non-local potential term is also given. Received: 3 March 2001 / Accepted: 9 June 2001     

Monopoles in an antiferromagnetic Bose-Einstein condensate

We show that even in three dimensions an antiferromagnetic spin-1 Bose-Einstein condensate, which can, for instance, be created with (23)Na atoms in an optical trap, has not only singular linelike vortex excitations, but also allows for singular pointlike topological excitations, i.e., monopoles similar to the 't Hooft-Polyakov monopoles. We discuss the static and dynamic properties of these monopoles.     

Investigation of Physical Processes in the Gas Discharge Region Between Liquid Electrodes

Electrophysical, hydro-gas-dynamic, and thermal characteristics of a discharge arising between liquid electrodes are considered. Spatial visualization of flow patterns in the gas discharge region is performed by using the schlieren technique.     

Simple Interpretation of Kinetics of Fast Solid-State Reactions

A simple model of fast solid-state reaction of two substances on the phase boundary is proposed. It is assumed that the reaction is controlled by the formation of new surface. The dependence of a change in the surface on the value of shear deformation is calculated. Thus, the relation between the product yield and shear deformation independently of time is explained.     

Photoconductivity,Antioxidant, and Antimicrobial Activities of Some Acenaphthenequinone Derivatives

Russian Journal of General Chemistry - Photoconductive acenaphthenequinone derivatives have been synthesized by a one-pot process of acenaphthenequinone with different aromatic hydrazides...     

Electrical Conductivity in a Laser Beam Channel

Russian Physics Journal - Electrical conductivity in a laser beam channel has been investigated. Oscillations of the conductivity caused by the oscillation motion of electrons in laser-induced...     

Energy Characteristics of Non-Resonator Generation in Nanodispersed Active Media Irradiated with Femtosecond Laser Pulses

Russian Physics Journal - Results of experimental measurements of the energy characteristics of stimulated emission in coumarin-30 and rhodamine 6G dyes with nanoparticles under irradiation with...     

Joint bounds for the Perron roots of nonnegative matrices with applications

Given a finite set {A_x}_{x ∈ X} of nonnegative matrices, we derive joint upper and lower bounds for the row sums of the matrices D⁻¹ A^(x) D, x ∈ X, where D is a specially chosen nonsingular diagonal matrix. These bounds, depending only on the sparsity patterns of the matrices A^(x) and their row sums, are used to obtain joint two-sided bounds for the Perron roots of given nonnegative matrices, joint upper bounds for the spectral radii of given complex matrices, bounds for the joint and lower spectral radii of a matrix set, and conditions sufficient for all convex combinations of given matrices to be Schur stable. Bibliography: 20 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 30–56.