Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

On simultaneous linear extensions of partial (pseudo)metrics

We consider the question of simultaneous extension of (pseudo) metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to Künzi and Shapiro for the case of extension operators of partial continuous functions and includes, as a special case, Banakh's theorem on linear regular operators extending (pseudo)metrics.

     

Noncommutative differential geometry related to the Young-Baxter equation

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf is considered in which local solutions of the Young-Baxter quantum equation are defined but there is no global section. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 51–70. Translated by I. A. Izergina.     

Theory of electromagnetic stirring by AC fields

Electromagnetic fields are often used industrially to controlthe flow of liquid metal, and in particular this review is concernedwth applications of alternating fields. An alternating fieldinduces eddy currents in liquid metal which interact with thefield to give a Lorentz body force which is generally rotationaland which must therefore drive fluid motion. We derive generalexpressions for the Lorentz force, showing that it consistsof both steady and oscillatory components. The flow in a circularcylinder due to a rotating field is discussed in detail, sincethis problem is simple to analyse and illustrates several importantgeneral principles. In the high-frequency limit, the field isconfined to a narrow layer on the surface of the conductor,and we derive approximate methods for calculating the surfacemagnetic pressure andthe induced flow. We also examine the otherextreme of slowly alternating fields. As each problem is studied,we discuss practical applications.     

Measurement of Hartmann-Hahn cross-polarization dynamics with quenching of proton T1ρ relaxation dependence

A simple modification of the standard cross-polarization method designed for quenching the proton T_1ρ dependence when studying polarization transfer is presented. It is demonstrated that by using this simple procedure, new and subtle details of cross-polarization dynamics, previously hidden by the T_1ρ(¹H) effect, can be observed in dipolar-coupled spin systems.     

Future contributions toJournal of Crystallographic and Spectroscopic Research

Future contributions toJournal of Crystallographic and Spectroscopic Research     

Spectral Theory of Perturbative Decays

We propose a complex approach to evaluating afunction sum of two noncommuting non-Hermitianoperators. We propose an explicit expansion of theevolution operator in the case of the neutral K-mesonsystem influenced by an external interaction. Theimportance is pointed out of considering the algebraicexpansion of the time evolution operator whenever thedynamics decouples the internal transitions andcenter-of-mass motion.     

Theory of mixed-polarization propagation in anisotropic cubic media

Polarization dynamics are considered in the presence of an anisotropic Kerr non-linearity in the most common semiconductor waveguide geometry. The equations of motion are formulated in terms of Stokes polarization parameters and their Hamiltonian form is derived. Stationary solutions and their stability are found for plane-wave propagation. It is found that the non-integrable problem of mixed-polarization spatial soliton dynamics can be largely explained in terms of the equivalent plane-wave solutions.