In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics. Mathematics


Volume 53 No. 1 March 2004


Unary local polynomial functions of K 2-algebras; 3–12

Vladimir Kuchmei

Abstract. The class K2 is a variety of distributive Ockham algebras that includes the varieties of Kleene and Stone algebras. Polynomial functions of algebras K2 were first studied by Haviar (Acta Math. Univ. Comenianae, 1993, 2, 179–190). After hat (local) polynomial functions were described for all proper subvarieties of K2. In this paper we characterize unary (local) polynomial functions of K2-algebras.

Key words: Ockham algebra, compatible function, (local) polynomial Function.

Convergence and l-boundedness of functional series with respect to multiplicative systems; 13–25

Natalia Saealle and Heino Türnpu

Abstract. The series  where  is a product system defined by a multiplicative system, is studied. Some sufficient conditions for p-maximal convergence with speed of this series are found. Also the series  with  and  being a Walsh system is considered. It is proved that this series converges almost everywhere for various product systems. In the last section the   of this series is discussed.

Key words: multiplicative systems, Walsh functions, convergence with speed, convergence almost everywhere,

Nonlinear and scale-invariant analysis of heart rate variability; 26–44

Jaan Kalda, Maksim Säkki, Meelis Vainu, and Mari Laan

Abstract. Human heart rate fluctuates in a complex and nonstationary manner. Elaborating efficient and adequate tools for the analysis of such signals has been a great challenge for the researchers during last decades. Here, an overview of the main research results in this field is given. The following questions are addressed: What are the intrinsic features of the heart rate variability signal? What are the most promising nonlinear measures, bearing in mind clinical diagnostic and prognostic applications?

Key words: heart rate variability, nonlinear time-series, intermittency.

Haar wavelets based technique in evolution problems; 45–63

Carlo Cattani

Abstract. The compression property of wavelets in the analysis of an evolution problem (with unsmooth initial conditions) is investigated. The effectiveness of wavelets both in the reduction of complexity (number of coefficients) and in better approximation is shown. Haar wavelets, having the simplest interpretation of the wavelet coefficients, are used for defining the wavelet solution of an evolution (parabolic-hyperbolic) problem. The approximate solution, at a given fixed scale (resolution), results from the superimposition of (a small set of) fundamental wavelets, thus giving (also) a physical interpretation to wavelets. Since Haar wavelets are not smooth enough, a numerical derivative algorithm, which allows the scale approximation of partial differential evolution operators, is also defined. As application, the heat propagation (of an initial square wave) is explicitly given in terms of wavelets.

Key words: wavelet, Haar, Haar transform, interpolation, differential operator, discrete operator.

Trichotomous noise: applications to stochastic transport; 64–72

Romi Mankin, Ain Ainsaar, and Risto Tammelo

Abstract. A three-level Markovian noise as a model of nonequilibrium fluctuations is presented and the effect of flatness of fluctuations on the noise-driven nonequilibrium dynamics of overdamped Brownian particles in nonlinear systems is considered. Examples of exactly soluble models of stochastic transport are given and the conditions of current reversals in ratchet systems are discussed.

Key words: nonequilibrium fluctuations, stochastic transport, current reversals.