Polynomial approximation on the boundary and strictly inside

We investigate the possibility of approximating a function on a compact setK of the complex plane in such a way that the rate of approximation is almost optimal onK, and the rate inside the interior ofK is faster than on the whole ofK. We show that ifK has an external angle smaller than π at some point z_o∈δK, then geometric convergence insideK is possible only for functions that are analytic at z_o. We also consider the possibility of approximation rates of the form exp(?cn ^β), for approximation insideK, where β is related to the largest external angle ofK. It is also shown that no matter how slowly the sequence {γ _n } tends to zero, there is aK and a Lip β, β<1, functionf such that approximation insideK cannot have order {γ _n }.     

Gain saturation in quantum-well heterostructures

The effect of radiation gain saturation in quantum-well heretostructures was investigated in the system GaAs—AlGaAs with regard to the spectral line broadening and the type of radiation polarization. Belarusian State University, 4, F. Skorina Ave., Minsk, 220050, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 797–800, November–December, 1997.     

Electronic structure of the antiferromagnetic phase of NiMn

We present for the first time a self-consistent calculation of the electronic energy band structure of NiMn in the antiferromagnetic tetragonal phase. The electronic energy spectrum is calculated, along with the full and partial electronic density of states, the Fermi surface, the electronic specific heat coefficient, and the magnetic moments on each type of atom. We have studied the influence of structural distortions and antiferromagnetic ordering on the electronic structure of NiMn. Satisfactory agreement is found with the existing experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 18–23, August, 1991.The authors express their appreciation to N. I. Kulikov and A. F. Tatarchenko for assistance in the computer calculations and for useful discussion of the work.     

Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.     

Integrated Superconducting Submillimeter-Wave Receivers

We overview recent achievements in the field of cryogenic submillimeter-wave receivers based on superconductor–insulator–superconductor (SIS) tunnel junctions. The main attention is paid to the novel superconducting integrated receivers (SIRs) with an on-chip superconducting local oscillator. The single-chip microcircuit of the receiver, which integrates a quantum mixer based on the nonlinearity of a quasi-particle current in the SIS junction, a planar superconducting receiving antenna, and a cryogenic local oscillator, is described. Being dc-powered only by batteries, such a microcircuit operates as a submillimeter-wave superheterodyne receiver without any additional microwave equipment. Such receivers are very attractive for radioastronomical research, space communication systems, and monitoring of the environment from satellites, balloons, and special aircraft. A breadboard of a superconducting spectrometer with a phase-locked flux-flow oscillator (FFO) has been developed and tested. A frequency resolution better than 10 kHz was reached at a frequency of 365 GHz. We describe a balloon-borne 500-650 GHz integrated spectrometer for oblique atmospheric sounding, developed for the international Terahertz Limb Sounder (TELIS) project. The first flight is scheduled for 2005.     

A characterization of certain irreducible symplectic 4-folds

 We give a characterization of irreducible symplectic fourfolds which are given as Hilbert scheme of points on a K3 surface. Received: 26 June 2002 / Revised version: 9 September 2002 Published online: 14 February 2003 Mathematics Subject Classification (2000): Primary 14J32, Secondary 32Q20     

A symmetry-adapted force-constant lattice-dynamical model for single-walled carbon nanotubes

We develop a lattice-dynamical model based on the screw symmetry of single-walled carbon nanotubes that allows for reducing the size of the dynamical matrix to six, for all tube chiralities. The model uses force constants derived from fitting to the phonon dispersion of 2D graphite. We present the calculation procedure in a clear and transparent way, making the model easier to follow. We calculate the phonon dispersions of a number of nanotubes of different chiralities. The splitting of two highest Raman active modes and the radial breathing mode frequency are studied by changing the tube diameter and chirality.     

Ray expansions for the solution of dynamic problems of linear viscoelasticity

Voronezh' Civil-Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 89–95, January, 1991.     

Approximation by polynomials with small coefficients

Translated from Matematicheskie Zametki, Vol. 57, No. 1, pp. 150–153, January, 1995.