Geometric proof of R?dseth’s formula for Frobenius numbers

Using a geometric interpretation of continued fractions, we give a new proof of R?dseth’s formula for Frobenius numbers.     

New class of extremely short electromagnetic solitons

A physical realization is presented for the integrable modified sine-Gordon equation. In this case, this equation describes the propagation of an extremely short vector electromagnetic pulse in the system of asymmetric quantum objects that have permanent dipole moments in the self-energy states. Using soliton solutions for ordinary and extraordinary components, new regimes of the dynamics of the pulse and medium that are specific only to asymmetric media have been found.     

Integrable models of the dynamics of longitudinal-transverse acoustic pulses in a paramagnetic crystal

We study the interaction between longitudinal-transverse acoustic pulses and a system of paramagnetic impurities with the effective spin S = 1 in a statically deformed crystal. We show that the dynamics of a pulse propagating at an arbitrary angle to the static-deformation direction and of the effective spins satisfy the modified reduced Maxwell-Bloch equations and, if the spectrum of the acoustic pulse overlaps the quantum transitions between spin sublevels, the modified sine-Gordon equation. These equations generalize the well-known models in the theory of the inverse scattering method and in the theory of self-induced transparency and also belong to the class of integrable equations. Analyzing soliton solutions shows that the pulse-medium interaction reveals some qualitatively new features in these models compared with the cases of purely transverse or purely longitudinal acoustic fields. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 228–247, May, 2007.     

Almost Chebyshëv subspaces in the spaces of compact operators

Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 4, pp. 917–926, July–August, 1995.     

Long-term stability of long-wavelength (>1.25 µm) quantum-dot lasers fabricated on GaAs substrates

Accelerated degradation testing of long-wavelength (>1.25 µm) quantum-dot lasers made on GaAs substrates is carried out at a fixed current of 1.7 A, initial optical output of about 0.3 W, and a heat sink temperature of 60°C. No signs of degradation are revealed after testing for 450 h. The test bed is not sealed, inert gas purging is not performed, and the laser faces are not passivated.     

Resonant photoluminescence from modulation-doped InAs –GaAs quantum dots

Resonant luminescence studies of InAs quantum dots (QDs) embedded in a GaAs matrix grown by molecular beam epitaxy are presented, showing marked differences for modulation-doped and undoped QDs and indicating that the doping leads to different exciton formation and carrier relaxation mechanisms. The LO-phonon assisted relaxatioin of excitons between sub-levels is identified for the modulation-doped QDs.     

Effect of a steady periodic velocity inhomogeneity on boundary layer stability

Direct numerical simulation is used to investigate laminar-turbulent transition in a boundary layer with a span-periodic inhomogeneity of the velocity profile which is created artificially. It is shown that the presence of the inhomogeneity leads to a slowing down of the growth of unstable perturbations and a delaying of the laminar-turbulent transition.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 45–52, July–August, 1995.     

Numerical Modeling of the Development of a Streaky Structure in a Boundary Layer at a High Freestream Turbulence Level

The disturbances generated by external turbulence in the boundary layer on a flat plate set suddenly in motion are determined. A turbulent flow calculated by direct numerical simulation is taken as the initial conditions. The solution obtained simulates the initial stage of laminar-turbulent transition in the flat-plate boundary layer at a high turbulence level in the oncoming flow. The solution makes it possible to estimate the effects of different factors, such as nonstationarity, nonlinearity, and the parameters of the freestream velocity fluctuation spectrum, on disturbance enhancement in the boundary layer.     

Pulsating regime corresponding to an obstacle in a stationary inhomogeneous flow

The pulsating regime produced by the presence of a cylindrical cavity in a stationary inhomogeneous supersonic flow is simulated mathematically. The system of equations for an inviscid thermally nonconducting gas is solved by a numerical method based on a two-step difference scheme of second order of approximation. This method makes it possible to calculate in each time step the complete flow field at once, which makes it possible to follow the development of the nonstationary flow, which in the present case is a pulsating flow. The flow pattern in the pulsating regime is studied in detail. The pressure pulsations in the cavity are due to the alternating passage through it of shock waves and rarefaction waves, and the pulsations are nonlinear. The influence of the basic parameters on the characteristics of the pulsating flow is studied and some estimates are made.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 64–71, September–October, 1979.     

Stability of a spanwise nonuniform boundary layer flow

The linear stability of a boundary layer flow with a spanwise-periodic nonuniformity in the velocity profile is investigated. This flow can be considered as a model of a streaky structure occurring in the boundary layer at a high freestream turbulence level. It is shown that for a small nonuniformity amplitude symmetric modes similar to Tollmien-Schlichting waves are the most unstable. At higher nonuniformity amplitudes, antisymmetric modes, qualitatively different from Tollmien-Schlichting waves and having a larger phase velocity, are the most amplified. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 54–63, November–December, 1998. The study was carried out with the support of the International Scientific and Technical Center (project No. 199-95) and the Russian Foundation for Basic Research (project No. 95-01-01201a).