Reviews in Mathematics and Mathematical Physics

Reviews in Mathematics and Mathematical Physics

Edited by A.T.Fomenko, Moscow State University, Russia

Reviews in Mathematics and Mathematical Physics publishes review articles in mathematics and mathematical physics from Russia and the former Soviet Union. Topics include soliton theory, the theory of quantum topological models and their applications for algebraic and differential geometry and topology.

Ordering information: Reviews in Mathematics and Mathematical Physics is a journal. Each volume consists of an irregular number of issues, depending on extent. Issues are available individually (see following details) as well as by subscription. For subscription information click on Journals.

Geometry of Singularities of Integrable Systems on Lie Algebras

Pbk 56pp 2006

YU. A.Brailov, Moscow State University, Russia

Integrable systems generated by consistent Poisson brackets on semi-simple Lie Algebras are related to the structure of ground algebra. The most important properties of Liouvilles foliation are expressed in algebraic term. The exact relation is also established between the singularities of momentum mapping and degenerations of the corresponding spectral curve.

1-904868-49-5

Dynamics of DNA and Proton Tunneling

Pbk 100pp 2006

V.L.Golo, Dept of Mathematics and Mechanics, Moscow University, Russia

This review discusses the dynamics of DNA determined by its elasticity and hydrogen bonds between base pairs. The author considers models that take into account the interaction of elastic modes and tunneling of protons inside the hydrogen bonds and also considers possible chaotic regimes of tunneling.

1-904868-53-3

Introduction To The Theory of Representations of Finitely Presented *- Algebra. I. Representations By Bounded Operators

Pb 262pp 1999

V.Ostrovskyi and Yu. Samoilenko

Institute of Mathematics, Kiev, Ukraine

This volume provides the fundamentals of representations of finitely presented *-algebras by bounded operators. The theory is illustrated with numerous examples of *-algebra. The examples, in particular, include *-algebra with two self-adjoint generators that satisfy a quadratic or a more general relation, *-algebra that arise from one- and many-dimensional discrete dynamical systems, Wick *-algebra, various *-wild algebras.

90-5823-042-2

Symplectic and Poisson Geometry on Loop Spaces of Smooth Manifolds and Integrable Equations

Pb 204pp 2001

O.I.Mokhov

L.D.Landau Institute for Theoretical Physics, Moscow, Russia and

University of Paderborn, Germany

This review is devoted to the differential-geometric theory of homogenous forms and other different homogenous structures (mainly Poisson and symplectic structures) on loop spaces of smooth manifolds, their natural generalizations and applications in mathematical physics and field theory.

90-5823-235-2

Analytical Mechanics and its Visualization with Computer Graphics

150pp Pbk 2007

V.L.Golo and Yu.S.Volkov, Moscow State University, Russia

This review comprises two parts and deals with the Hamiltonian formulation of classical mechanics and relies on the concept of Poisson brackets. In contrast to conventional treatises on the subject, the authors focus on obtaining qualitative information essential for numerical simulation; thus computer graphics are an important instrument for studying mechanical problems. The review includes a range of examples, from the simplest: the spherical pendulum, to the more complex: the soft chaos in the spin dynamics of superfluid helium-3. The systematic use of Poisson brackets allows a natural transition to quantum mechanics,. Part II presents a concise description of quantum formalism, mainly within the framework of the Heisenberg approach. Among other physical examples, the authors consider the quantum Kepler problem, and internal symmetries and the related degeneracy of the spectrum. As a conclusion the authors discuss the part played by spatial symmetries in classical and quantum cases, the Einstein, Podolsky and Rosen effect.

1-904868-43-6

Invariant Kahler Structures on the Cotangent Bundle of Symmetric Spaces and Reduction

100pp Pbk 2005

I.V.Mykytyuk, Institute of Applied Problems of Mathematics and Mechanics, Lviv, Ukraine

The main objects of investigation are G-invariant polarizations on domains D in the cotangent bundles T*(G/K).

The book comprises two parts. Part I: Invariant Kahler structures and Part II: Invariant hyperkahler structures.

1-904868-44-4

Basis Properties and Completeness of Certain System of Elementary Functions

2008 112pp Pbk

E. I. Moiseev, A. P. Prudnikov and A. M. SedletskiiA. A. Dorodnitsyn Computational Center, Russian Academy of Sciences, Moscow

The possibility of approximating functions of a sufficiently general form by relatively simple functions and therefore more convenient for analysis and computation is the initial reason for approximation theory. The basic fact of this theory is the Weierstrasse theorem. In the first part of this book the authors consider the problem of description of complete power systems. In the second part, the authors study the problem on bases in Sobolev spaces, in their subspaces and also in weighted spaces and finally consider continuous analogs of basis expansions (the generalized sine and cosine Fourier transforms).

1-904868-58-3