In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics & Mathematics


Volume 49 No. 2 June 2000


On the approximate calculation of double integrals with weight function; 67–74 (full article in PDF format)

Voldemar ARRO

Abstract. Cubature formulas with the weight function  which are optimal on given sets of functions are obtained for the approximate calculation of a double integral. One type of these formulas consists of the line integrals which may be estimated by optimal quadrature formulas. The optimal cubature formulas include both knots and coefficients of the corresponding values of optimal quadrature formulas. The application of a cubature formula with weight function to the calculation of double integrals over the domain of integration limited by a parabolic curve is shown.

Key words: multivariate singular integral, optimal cubature formula, weight function, approximate formula.


An inverse problem arising in compression of poro-viscoelastic medium; 75–89 (full article in PDF format)


Abstract: An inverse problem for determining a time-and space-dependent memory kernel in a model of compression of poro-viscoelastic medium is considered. The kernel is represented in a form of a finite sum of products of known functions of the local coordinates and of unknown time-dependent functions. An existence and uniqueness theorem is proved.

Key words: integrodifferential equation, inverse problem.


Formal models of DNA computing: a survey; 90–99 (full article in PDF format)


Abstract. DNA computing is a method of solving mathematical problems with the help of biological operations on DNA strands. The paper gives an overview of the existing formal models of DNA computing. The biological and mathematical background is briefly described; splicing systems, insertion–deletion systems, and a model of DNA computing based on equality checking, DNA-EC, are considered more closely.

Key words: DNA computing, splicing systems, H systems, insertion–deletion systems.


One-step memory closed-loop control of linear interconnected subsystems; 100–107 (full article in PDF format)


Abstract. An example of one-step memory control of the linear-quadratic grouped system is presented. It is shown that in the case of unidirectional interconnections between cost functions, one subsystem can indirectly control the behaviour of the whole system and can establish the trajectory it desires only through a properly chosen equivalent representation of its control law in cost functions of other subsystems.

Key words: incentive control, equivalent representation.


Temperature distribution in a finite atmosphere subjected to cosine varying collimated flux; 108–121 (full article in PDF format)


Abstract: The radiation field is calculated in an optically finite, two-dimensional, plane-parallel, absorbing-emitting but nonscattering grey atmosphere subjected to collimated cosine-varying incident boundary radiation. As in the optically semi-infinite case, we approximate the kernel of the integral equation for the emissive power by a sum of exponents. After this approximation the integral equation can again be solved exactly. The solution may be written in x and y functions which were introduced for a one-dimensional atmosphere and which are generalizations of the Chandrasekhar-Ambarzumian X and Y functions. An algorithm to find these functions is given.

This approximation allowed us to find the accurate values for the temperature distribution and the radiative flux at arbitrary optical depths in the atmosphere.

Key words: two-dimensional radiative transfer, X and Y functions, emissive power, radiative flux.


Solar erythemal ultraviolet radiation in Estonia in 1998; 122–132 (full article in PDF format)


Abstract. Regular measurements of solar erythemal ultraviolet irradiance have been carried out at Tõravere, Estonia, since 1 January 1998, using an erythemally weighted sensor Scintec UV SET. The results obtained during 1998 are presented and preliminarily discussed. The maximum daily dose 18.27 MED (here 1 MED = 250 erythemally weighted J/m2 for skin type II) was recorded on 10 June. The yearly mean daily dose was 4.68 MED; the maximum monthly dose was 335.27 MED (June).

Key words: erythemal ultraviolet irradiance, atmospheric column ozone, UV monitoring, UV attenuation by clouds, UV dose, albedo.


Instructions to authors; 133