Error bounds for strongly convex programs and (super)linearly convergent iterative schemes for the least 2-norm solution of linear programs

Given an arbitrary point (x, u) inR ⁿ × R ₊ ^m , we give bounds on the Euclidean distance betweenx and the unique solution to a strongly convex program in terms of the violations of the Karush-Kuhn-Tucker conditions by the arbitrary point (x, u). These bounds are then used to derive linearly and superlinearly convergent iterative schemes for obtaining the unique least 2-norm solution of a linear program. These schemes can be used effectively in conjunction with the successive overrelaxation (SOR) methods for solving very large sparse linear programs.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. This material is based on research sponsored by National Science Foundation Grant No. DCR-8420963 and Air Force Office of Scientific Research Grant No. AFOSR-ISSA-85-00080.On leave from CRAI, via Bernini 5, Rende, Cosenza, Italy.     

Homogeneous spaces and invariant tensors

In the present survey a method is presented for the construction of invariant tensors (with respect to a given representation) called the inclusion principle and the possibility of applying the cited method to various problems of algebra, topology, geometry, and analysis.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 18, pp. 105–142, 1986.     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

Linear mode conversion of waves near the maxima or minima of the density in a warm magnetized plasma

Behaviour of the h. f. electrostatic waves near the plasma or upper hybrid resonances was studied in the case that these resonances are situated at the maxima or minima of the plasma density. Supposing the parabolic density profile in these regions we obtained the connection formulae for the WKB solutions. In a weakly inhomogeneous magnetoplasma the effect of the parabolic profile manifests itself only in narrow frequency band centred at the resonance frequency corresponding to the extreme value of the density. The whole process can be then described by only two coefficients, viz. the power conversion and power transmission coefficients.     

Structural and electrical properties of quasicrystalline Al-14 at% Mn alloy

Quasicrystalline Al-14 at. % Mn alloy was prepared by melt-spinning and its structural and electrical properties were studied. This alloy consists of icosahedral grains with sizes from 1 to 4 m and of crystalline aluminium phase. The electrical resistivity was almost temperature independent with a value of about 765 n gWm at 4·2 K.     

Precipitation structure in an Al-2·0 at. % Zn-1·0 at. % Mg alloy within and close to the grain boundaries and its effects on mechanical properties

During ageing the Al-2·0 at. %Zn-1·0 at. % Mg alloy at elevated temperatures the width of the precipitation free zone (PFZ) at both sides of the grain boundaries (GB) is identical with that free of quenched-in dislocation loops (DL). After sufficiently long ageing a band of precipitates is growing inside the former PFZ and the DLs in the midgrain regions act as sites for the heterogeneous nucleation of the-phase. Two precipitation processes significantly affect the mechanical properties. TEM correlates grain boundary precipitate density and morphology with grain boundary misorientation.     

Wave propagation in quasi-one-dimensional quantum plasma in a magnetic field

A cold electron gas fills the lowest Landau level for high enough magnetic fields and for low enough densities. Such a situation is expected to occur for the Malmberg-O'Neil experiment and also for pulsar crusts and atmospheres. Such plasmas behave as a quasi-one-dimensional system and exhibit some peculiarities in their wave structure. We study the dispersion and damping of the low frequencies, i.e., the whistler mode, and the extraordinary mode for zero temperature. The behavior of the whistler mode depends critically on the filling number _Fc=_F/ , where _F is the Fermi energy and is the cyclotron frequency. The one-dimensional character of the system affects the pair excitation spectrum and thus the decay of modes. We find that, in contrast to the three-dimensional situation, the plasma mode and the extraordinary mode remain undamped, while the whistler mode is undamped for all but very highk values.