**CONTENTS &
ABSTRACTS**

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)

Jaan JANNO

**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)

Tiina ZINGEL

**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)

Ingmar RANDVEE

**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)

Tõnu VIIK

**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)

Uno VEISMANN, Kalju EERME, and Rutt KOPPEL

**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/m^{2 }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