CONTENTS & ABSTRACTS

In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics

Volume 51 No. 4 December 2002

On sampling series based on some combinations of sinc functions; 203–220

Andi Kivinukk and Gert Tamberg

Abstract. The generalized sampling series given in Jahresber. Deutsch. Math.-Verein., 1988, 90, 1–70 are studied. We introduce some new generalized sampling series which are defined by certain combinations of the sinc functions and find the order of approximation by those series. Sampling series of this kind are motivated by some summation methods of trigonometric Fourier series. Our discussion is based on the Rogosinski-type sampling series.

Key words: generalized sampling series, Rogosinski-type sampling series, sinc function, operator norms, order of approximation.

Quadratic spline collocation method for weakly singular integral equations on graded grids; 221–237

Rene Pallav

Abstract. The spline collocation method for weakly singular Fredholm integral equations of the second kind is studied. Using smooth quadratic splines, we derive the rate of uniform convergence of this method on graded grids.

Key words: weakly singular integral equation, collocation method, quadratic splines, graded grids.

Removing or lowering the orders of input shifts in discrete-time generalized state-space systems with Mathematica; 238–254

Ülle Kotta and Maris Tõnso

Abstract. The problem of lowering the orders of input forward shifts in generalized~state-space systems by generalized state transformations is studied using the language of differential forms. Necessary and sufficient conditions are given for the local existence of such transformations. These conditions are formulated in terms of the integrability of certain subspaces of one-forms classified according to their relative degree. The sufficiency part of the proof gives a constructive procedure (up to finding the integrating factors and integration of the set of one-forms) for finding these generalized state transformations. In a particular case, these conditions show when it is possible to transform a generalized state-space representation into the classical state equations. A set of functions developed in Mathematica 4.0 is described, allowing us to test if the generalized state equation is transformable into the classical state-space form, and also to find the transformation for simple examples. The application of the developed functions is demonstrated on four examples obtained via identification.

Key words: nonlinear systems, discrete-time systems, generalized dynamics, generalized state transformations, linear algebraic approach, symbolic computation, Mathematica.

A technique to study the mechanisms of pressure broadening of spectral holes; 255–268

Kristjan Leiger and Jaak Kikas

Abstract. An experimental procedure to distinguish between the two possible mechanisms (dispersive and diffusive) of pressure broadening of spectral holes in nonisobaric experiments is proposed. The method makes use of nonlinear saturation properties of the hole burning process. The proposed four-step procedure consists of burning a hole, applying hydrostatic pressure to the system, additional burning at the hole minimum at this second pressure, and then applying more pressure. By model calculations it is demonstrated that, under certain conditions, the dispersive mechanism yields a double-minimum hole, while the diffusive mechanism does not. Experimental observability of such an effect is discussed.

Key words: hole burning, pressure tuning, inhomogeneous broadening.

CHRONICLE

Harald Keres 90; 269

Contents of volume 51; 270–271