Gear's method in vibrational kinetics

Gear's predictor-corrector multistep method is applied to a rigid system of nonlinear ordinary differential equations, describing vibrational kinetic processes in molecular (diatomic) gas. The applicability of Naidis's formulas, for the linear problem is studied. The evolution of the starting Boltzmann distribution to the quasiequilibrium Trinor distribution is studied. The vibrational relaxation curves are calculated taking into account VV and VT processes and the possibilities of a more complicated starting physical model are examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 57–62, March, 1985.     

Two-phonon hyper-Raman scattering and polariton spectra in rutile crystal

The first observation of both two-phonon and polariton hyper-Raman scattering in rutile crystal is reported. The effect of two-phonon states on A_u-polariton dispersion has been found.     

Yb3+-doped YVO4 crystal for efficient Kerr-lens mode locking in solid-state lasers

We report the first demonstration, to our knowledge, of soft-aperture Kerr-lens mode locking in a diode-pumped femtosecond Yb3+:YVO4 laser. Near-transform-limited pulses as short as 61 fs are generated around a center wavelength of 1050 nm with an output power of 54 mW and a pulse repetition frequency of 104.5 MHz. This is, to our knowledge, the shortest pulse generated directly from an Yb laser having a crystalline host material. The femtosecond operation has a mode-locking threshold at an absorbed pump power of 190 mW. The nonlinear refractive indexes of the Yb3+:YVO4 crystal have been measured to be 19 x 10(-16) cm2/W and 15 x 10(-16) cm2/W for the sigma and pi polarizations, respectively, at 1080 nm.     

An existence theorem for an inverse problem for a semilinear hyperbolic system

In the present paper, we consider a semilinear hyperbolic system with coefficients depending on different solution components. We study the inverse problem of finding one of the coefficients on the basis of additional information on the solution. The proof of the existence theorem for the inverse problem is based on the reduction of the latter to a nonlinear operator equation, which is a nonlinear integro-differential equation for the unknown coefficient. This approach was used in [1] to prove the existence of a solution of the inverse problem for a quasilinear hyperbolic equation. Inverse problems for quasilinear hyperbolic equations and systems were also considered in [2–6] and other papers.Translated from Differentsialnye Uravneniya, Vol. 40, No. 9, 2004, pp. 1155–1165.Original Russian Text Copyright © 2004 by Denisov.     

High-gain wide-band gyrotron traveling wave amplifier with a helically corrugated waveguide

First bandwidth measurements of a novel gyrotron amplifier are presented. The coupling between the second harmonic cyclotron mode of a gyrating electron beam and the radiation field occurred in the region of near infinite phase velocity over a broad bandwidth by using a cylindrical waveguide with a helical corrugation on its internal surface. With a beam energy of 185 keV, the amplifier achieved a maximum output power of 1.1 MW, saturated gain of 37 dB, linear gain of 47 dB, saturated bandwidth of 8.4 to 10.4 GHz ( 21% relative bandwidth), and an efficiency of 29%, in good agreement with theory.     

Shell corrections,magic numbers,and mean field

It is shown that the positions of deep local minima of shell corrections associated with magic numbers in the region of superheavy nuclei depend on the parameters of the central and spin-orbit mean-field potentials. The accuracy of nuclear-mass predictions made within various models for superheavy nuclei is analyzed.     

Schrödinger operators and associated hyperbolic pencils

For a large class of Schrödinger operators, we introduce the hyperbolic quadratic pencils by making the coupling constant dependent on the energy in the very special way. For these pencils, many problems of scattering theory are significantly easier to study. Then, we give some applications to the original Schrödinger operators including one-dimensional Schrödinger operators with L²-operator-valued potentials, multidimensional Schrödinger operators with slowly decaying potentials.