Lie-algebraic structure of integrable nonlinear dynamical systems on extended functional manifolds

We consider the general Lie-algebraic scheme of construction of integrable nonlinear dynamical systems on extended functional manifolds. We obtain an explicit expression for consistent Poisson structures and write explicitly nonlinear equations generated by the spectrum of a periodic problem for an operator of Lax-type representation.     

Investigation of invariant sets with random perturbations with the use of the Lyapunov function

We consider invariant sets of the form V(t, x) = 0, where V(t, x) is the Lyapunov function of the corresponding deterministic system. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 309–312, February, 1998. This work was partially financially supported by the Ministry of Ukraine for Science and Technology.     

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps. Received: 10 June 1996 / In revised form: 9 August 1996     

Nonequilibrium Vibrational Kinetics during Hypersonic Flow of a Solid Body in Nitrogen and Its Influence on the Surface Heat Flux

Plasma Chemistry and Plasma Processing - Nonequilibrium nitrogen dissociation-recombination kinetics in the boundary layer and on the surface of a solid body during hypersonic flow. the subsequent...     

On the conjugate boundary value problem

We study the conjugate boundary-value problem with boundary conditions whose orders can be as large as the order of the differential equation or larger. We construct the Green's function of the problem over the entire space when the separating surface is a hyperplane, and we describe its properties. Bibliography: 6 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 20–24.     

Barium ferrite particulates prepared by a salt-melt method

Barium ferrite particulates have been prepared by coprecipitation and calcination in a flux of NaCl-KCl. It was found that a flux containing more than 30 wt% KCl tends to seriously deteriorate the magnetic properties of resultant perticulates. The flux with 10 wt% KCl or less showed promising results. A Ba(CoZr)_0.75Fe_10.5O₁₉ particulate showed the best properties, i.e., a saturation magnetization of 68.5, a squareness ratio of 0.49, and a coercivity of 1280 Oe, when calcined in NaCl at 900°C for 4 h.     

The anomalous 3-boson couplings as an implication of the Higgs sector

We discuss the possible new electroweak interactions which may be generated by the Higgs sector at the scale of theZ mass. For this purpose, we give a set ofSU(2)×U(1) gauge invariant operators constructed in terms ofW, Z, γ and Higgs fields which in the unitary gauge describe all possible γWW andZWW anomalous couplings. The dimension of these operators varies from 6 to 12. This fact allows us to consider various scenaria for the manifestations of the New Physics. We conclude that the underlying dynamics induced by the Higgs sector can be tested through a model-independent amplitude analysis of gauge boson pair production at LEP2 and future colliders.     

Variations of constants and red-shift in 6D cosmology

On the basis of the general class of solutions of 6D vacuum Einstein equations and using well-known results of the 6D geometric model of electroweak and gravitational interactions, the variations of fundamental physical constants and their influence on the observed red-shift of galaxies are investigated. By considering the interpretation of extra components of the 6D metric as reproducing the properties of matter in the 4D curved space-time, the effective quantities of matter are obtained. In particular, the states of dust and radiation are shown. The corresponding 5D models were also investigated.