Signature Characters for A_2 and B_2

The signatures of the inner product matrices on a Lie algebra's highest weight representation are encoded in the representation's signature character. We show that the signature characters of a finite-dimensional Lie algebra's highest weight representations obey simple difference equations that have a unique solution once appropriate boundary conditions are imposed. We use these results to derive the signature characters of all $A_2$ and $B_2$ highest weight representations. Our results extend, and explain, signature patterns analogous to those observed by Friedan, Qiu and Shenker in the Virasoro algebra's representation theory.Comment: 22 p

Combined reactive‐separation process epoxidation of natural rubber production waste

Предложена  схема  совмещенного  реакционно‐разделительного  про‐ цесса эпоксидирования скрапа натурального каучука в cреде вода‐ксилол. Дана коли‐ чественная и качественная оценка результатов химической модификации.  The A scheme of combined reactive separation process epoxidation of natu- ral rubber scrap in water‐xylene medium was proposed. A quantitative and qualitative as‐ sessment of the results of chemical modification was given.

Kazakhstani material testing Tokamak KTM. project status

Creation of cost-efficient and safe fusion reactor will require the development of special structural materials for first wall, blanket, reactor components, which will be operated under conditions of the high heat fluxes, superconducting magnets, plasma heating systems and other elements. The existing tokamaks and other fusion facilities do not currently allow for conduction of specialized researches of plasma-facing structural materials. Kazakhstani Material Testing Tokamak (hereinafter - KTM) provides for a unique opportunity to conduct materials research and testing of separate units and components of fusion reactors..

Kazakhstani material testing Tokamak KTM. project status

Creation of cost-efficient and safe fusion reactor will require the development of special structural materials for first wall, blanket, reactor components, which will be operated under conditions of the high heat fluxes, superconducting magnets, plasma heating systems and other elements. The existing tokamaks and other fusion facilities do not currently allow for conduction of specialized researches of plasma-facing structural materials. Kazakhstani Material Testing Tokamak (hereinafter - KTM) provides for a unique opportunity to conduct materials research and testing of separate units and components of fusion reactors..

Anisotropic porous metals production by melt processing

The collapse of the Soviet Union has left many of its scientific institutes and technical universities without their traditional backbone of financial support. In an effort to stem the export of science to nations advocating nuclear proliferation, and to acquire potentially useful technology, several US government-sponsored programs have arise to mine the best of former USSR scientific advances. In the field of metallurgy, the earliest institutes to be investigated by Sandia National Laboratories are located in Ukraine. In particular, scientists at the State Metallurgical Academy have developed unique porous metals, resembling what could be described as gas-solid ``eutectic``. While porous metals are available in the US and other western countries, none have the remarkable structure and properties of these materials. Sandia began a collaborative program with the Ukrainian scientists to bring this technology to the US, verify the claims regarding these materials, and begin production of the so-called Gasars. This paper will describe the casting process technology and metallurgy associated with the production of Gasars, and will review the progress of the collaborative project

The evolution operator of the Hartree-type equation with a quadratic potential

Based on the ideology of the Maslov's complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.Comment: 23 pege

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 13 pages, no figure

Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Hartree type equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 15 pages, no figure

On the existence of the second Dirac operator in Riemannian space

We describe a Riemannian space class where the second Dirac operator arises and prove that the operator is always equivalent to a standard Dirac one. The particle state in this gravitational field is degenerate to some extent and we introduce an additional value in order to describe a particle state completely. Some supersymmetry constructions are also discussed. As an example we study all Riemannian spaces with a five-dimentional motion group and find all metrics for which the second Dirac operator exists. On the basis of our discussed examples we hypothesize about the number of second Dirac operators in Riemannian space.Comment: LaTex, 10 pages, no figure