Greedy Approximation with Regard to Bases and General Minimal Systems

*This research was supported by the National Science Foundation Grant DMS 0200187 and by ONR Grant N00014-96-1-1003

The Doitchinov Completion of a Regular Paratopological Group

In memory of Professor D. Doitchinov ∗ This paper was written while the first author was supported by the Swiss National Science Foundation under grants 21–30585.91 and 2000-041745.94/1 and by the Spanish Ministry of Education and Sciences under DGES grant SAB94-0120. The second author was supported under DGES grant PB95-0737. During her stay at the University of Berne the third author was supported by the first author’s grant 2000-041745.94/1 from the Swiss National Science Foundation.

A functional representation of almost isometries

For each quasi-metric space X we consider the convex lattice SLip(1)(X) of all semi-Lipschitz functions on X with semi-Lipschitz constant not greater than 1. If X and Y are two complete quasi-metric spaces, we prove that every convex lattice isomorphism T from SLip(1)(Y) onto SLip(1)(X) can be written in the form Tf = c . (f o tau) + phi, where tau is an isometry, c > 0 and phi is an element of SLip(1)(X). As a consequence, we obtain that two complete quasi-metric spaces are almost isometric if, and only if, there exists an almost-unital convex lattice isomorphism between SLip(1)(X) and SLip(1) (Y).

Investigations on Bi2CuO4: a quasi-one-dimensional oxide system

The potential of Bi2CuO4 as the first oxide system to show a linear-chain magnetic behaviour is examined. Electron diffraction studies do not resolve the previously reported ambiguity regarding its space group. The magnetic susceptibility data at high temperatures are best fitted to a uniform antiferromagnetic spin-1/2 Heisenberg chain. At low temperatures, however, neither the uniform nor the alternating Heisenberg antiferromagnetic model fits the data. Magnetic susceptibility data over the entire temperature range can be fitted if one assumes dimeric units with a nearly degenerate second singlet state close to the ground state, these states being separated from an excited triplet state by an energy gap. A simple heuristic model of a dimer that gives such an energy level spectrum is examined.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

New space-time trellis codes for two-antenna quasi-static channels

New space-time trellis codes with four- and eight-level phase-shift keying (PSK) and 16-phase quadrature amplitude modulation (QAM) for two transmit antennas in slow-fading channels are presented in this paper. Unlike most of the codes that are reported in the literature, the proposed codes are specifically designed to minimize the frame error probability from a union-bound perspective. The performance of the proposed codes with various memory orders and receive antennas is evaluated by simulation. It is shown that the proposed codes outperform previously known codes in all studied cases.

STUDIES ON SCATTERING AND QUASI-NORMAL MODES IN BLACK HOLE SPACE-TIMES

The question of stability of black hole was first studied by Regge and Wheeler who investigated linear perturbations of the exterior Schwarzschild spacetime. Further work on this problem led to the study of quasi-normal modes which is believed as a characteristic sound of black holes. Quasi-normal modes (QNMs) describe the damped oscillations under perturbations in the surrounding geometry of a black hole with frequencies and damping times of oscillations entirely fixed by the black hole parameters.In the present work we study the influence of cosmic string on the QNMs of various black hole background spacetimes which are perturbed by a massless Dirac field.

Quasi Monte Carlo approach with uniform separation for solving of the rendering equation, ICNAAM 2007

This paper is directed to the advanced parallel Quasi Monte Carlo (QMC) methods for realistic image synthesis. We propose and consider a new QMC approach for solving the rendering equation with uniform separation. First, we apply the symmetry property for uniform separation of the hemispherical integration domain into 24 equal sub-domains of solid angles, subtended by orthogonal spherical triangles with fixed vertices and computable parameters. Uniform separation allows to apply parallel sampling scheme for numerical integration. Finally, we apply the stratified QMC integration method for solving the rendering equation. The superiority our QMC approach is proved.

Signal detection for distributed space-time block coding: 4 relay nodes under quasi-synchronisation

Most research on Distributed Space-Time Block Coding (D-STBC) has so far focused on the case of 2 relay nodes and assumed that the relay nodes are perfectly synchronised at the symbol level. This paper applies STBC to 4-relaynode systems under quasi-synchronisation and derives a new detector based on parallel interference cancellation, which proves to be very effective in suppressing the impact of imperfect synchronisation.

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.