Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

Core-shell structure in fullerene-containing molecular complexes

A shell model that describes the formation of molecular complexes around a C₆₀ molecule upon the solid-phase interaction of the powders is considered. From the absorption spectra, it follows that a reacting particle is a fullerene dimer.     

Prefiltration technique via aggregation for constructing low‐density high‐quality factorized sparse approximate inverse preconditionings

This paper considers a new approach to a priori sparsification of the sparsity pattern of the factorized approximate inverses (FSAI) preconditioner using the so‐called vector aggregation technique. The suggested approach consists in construction of the FSAI preconditioner to the aggregated matrix with a prescribed sparsity pattern. Then small entries of the computed ‘aggregated’ FSAI preconditioning matrix are dropped, and the resulting pointwise sparsity pattern is used to construct the low‐density block sparsity pattern of the FSAI preconditioning matrix to the original matrix. This approach allows to minimize (sometimes significantly) the construction costs of low‐density high‐quality FSAI preconditioners. Numerical results with sample matrices from structural mechanics and thin shell problems are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

A Theorem on Multiplicators in Nonhomogeneous Hölder Spaces and Some of Its Applications

In Sec. 2, sufficient conditions of the boundedness of convolution operators with kernel m in a nonhomogeneous Hölder space are given in terms of the Fourier-image of m. After that, the results of Sec. 2 are used to prove the solvability in a Hölder space of the Cauchy problem for linear systems of the hydrodynamic type. Bibliography: 6 titles.     

Changes in the Laser-Induced Fluorescence Spectrum of Myocardium Tissue with Decrease in Its Viability

We investigated the laser-induced fluorescence spectra (LIF) of porcine cardiac tissues with different degrees of viability. The data obtained are compared with the results of routine histological investigations and also with the experiments performed with the use of fluorescent probes. It has been found with a high degree of reliability that the loss of the viability of the myocardium tissue leads to the alteration of its LIF spectra. This can be used for low-invasive rapid control of transplant viability in the process of its preparation and during surgery.     

The stable forking conjecture and generic structures

 We prove that for any simple theory which is constructed via Fr?issé-Hrushovski method, if the forking independence is the same as the d-independence then the stable forking property holds. Received: 22 January 2001 / Published online: 19 December 2002 This article is part of the author's D-Phil thesis, written at the University of Oxford and supported by the Ministry of Higher Education of Iran. The author would like to thank the Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran, for its financial support whilst working on this article. Mathematics Subject Classification (2000): 03C45 Key words or phrases: Generic structures – Fr?issé-Hrushovski method – Predimension – Simple theories – Stable theories – Stable forking conjecture     

Relaxor properties of Fe-doped TlInS<Subscript>2</Subscript>

The relaxor properties of Fe-doped TlInS₂ crystals are investigated. It is shown that Fe-doped TlInS₂ compounds exhibit all features inherent in relaxor ferroelectric materials. The temperature range of existence of the microdomain (relaxor) state and the temperature of the transition from this state to a macro-domain state are determined.