CONTENTS &
ABSTRACTS

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 *K*_{2} is a variety of distributive Ockham algebras that includes the
varieties of Kleene and Stone algebras. Polynomial functions of algebras _{}*K*_{2} 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 *K*_{2}. In this paper we characterize unary (local) polynomial functions
of *K*_{2}-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.