Isometric Isomorphisms Between Banach Algebras Related to a Certain Class of Clifford Topological Semigroups

In the present paper it is shown that if S₁ and S₂ are two Clifford topological semigroups satisfying certain conditions and T is an isometric isomorphism of LUC(S₁*) onto LUC(S₂*), then T maps S₁ topologically isomorphically onto S₂. Furthermore, T maps M ^l _n(S₁) (M(S₁), respectively) isometrically isomorphically onto M ^l _n(S₂) (M(S₂), respectively). Indeed, we have obtained a generalization of a well-known result of Ghahramani, Lau and Losert for locally compact groups to a more general setting of Clifford topological semigroups.     

Nonlinear wave processes in media containing cracks partially filled with a viscous liquid

A nonlinear (in the cubic approximation) relaxation equation of state is derived for a rod containing cracks partially filled with an incompressible viscous liquid. The nonlinear effects of the self-action and interaction of low-and high-frequency longitudinal elastic waves propagating in such a rod are studied for the cases of identical and size-varied cracks. Linear and nonlinear acoustic parameters characterizing the self-action and interaction of elastic waves in a cracked rod are determined.     

Dynamics and spectra of excited states of water-micellar suspensions of single-walled carbon nanotubes

The dynamics of the photoinduced differential absorption and excited-state bleaching spectra of single-walled carbon nanotubes suspended in a micellar solution were studied in the spectral range from 40 to 1000 nm within a time interval from 70 fs to 150 ps under excitation by 50-fs pulses with photon energies 2 and 4 eV. The bleaching and absorption bands were observed in the spectra; the positions of the bleaching peaks were independent of the photon energy of the exciting femtosecond pulse in the range 2–4 eV. It was established that, for delay times shorter than 1 ps, the shape of the differential spectrum of excited nanotubes coincided with the shape of the second derivative of the absorption spectrum of unexcited nanotubes in the frequency range of exciting pulse above 18000 cm^?1 (the range of absorption bands of metallic nanotubes). In the frequency range below 16000 cm^?1 (the range of absorption peaks of semiconducting nanotubes), the bleaching peaks in the differential spectrum of excited nanotubes undergo a high-frequency shift of 200–300 cm^?1 with respect to the second-derivative spectrum of unexcited nanotubes. The excited-state relaxation rate constants were measured. They are well approximated by the exponential dependences and depend on the probe-pulse wavelength. An assumption was made about the nature of the observed spectra of excited nanotubes and about the excitation relaxation.     

Selective photorefractive scattering in LiNbO<Subscript>3</Subscript>:Rh crystals

Photorefractive scattering occurs in rhodium-doped lithium niobate crystals irradiated by coherent light. The photorefractive scattering has both wide-angle and selective components. The results of experimental investigation of selective photorefractive scattering in LiNbO₃:Rh crystals and calculation of the spatial structure of scattering are reported. The selective scattering is regarded as a kind of a frequency-degenerate fourwave vector interaction.     

Influence of seeded impurities on the fusion reactor operation

In order to study the influence of seeded impurities on ITER like reactor operation the COREDIV code has been extended to include the transport of several sputtered and/or injected impurities. In the COREDIV code the core plasma is treated in the frame of 1D radial transport model whereas in the edge the 2D multifluid code EPIT is used. The EPIT code solves in the slab geometry the MHD equations for densities and velocities for all ions species as well as for electron and ion temperatures. The iteration scheme in the code leads to steady state solution of coupled core and SOL system. The numerical results for Carbon and Nickel plate and seeded impurities Silicon and Neon are presented.     

On one-port characterization of noise sources in ducts by using external loads

Equivalent acoustic source characterization of duct-borne fluid machinery noise is often undertaken by interpolating the results of two-microphone pressure measurements with different external acoustic loads over a linear one-port source model. If the source is time-invariant, the one-port source characteristics can be determined by using only two external loads. This is well known as the two-load method. An extension of the two-load method for time-variant sources is also available and known as the multiple-load method. In these methods the source is treated as a ‘black-box’. This paper addresses the problem of one-port source characterization when the linear operations inherent in the ‘black-box’ are known explicitly. The equations governing the explicit one-port source models are derived and the source characteristics are shown to be measurable using only few acoustic loads. It is not the purpose of this paper to discuss the application of these models to any specific fluid machinery; however, of particular interest are the explicit source models that require only two loads. Numerical results are presented to show some features of such time-invariant and time-variant explicit one-port source models.     

Pressure Stabilization Method for Steady Viscous Flows in a System of Pipes

This paper deals with a singular perturbation of the stationary Stokes and Navier-Stokes systems. The term ε²Δp is added to the continuity equation, where ε is a small parameter. For a domain with cylindrical outlets to infinity and exponentially decaying data, existence and uniqueness of solutions under flux conditions at infinity are established for the linear problem and also for the nonlinear problem in the case of small data. Asymptotically exact estimates are proved for ε tending to zero. For sufficiently regular data, these estimates imply the convergence in H _loc ^5/2−δ for the velocity parts and in H _loc ^3/2−δ for the pressure parts, respectively. Bibliography: 17 titles.Dedicated to V. A. Solonnikov on the occasion of his 70th birthday__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 107–133.