CONTENTS &
ABSTRACTS

In
English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics

** **

Volume 52 No. 2
June 2003

Determination
of degenerate relaxation functions in three-dimensional viscoelasticity;
171–185

Jaan Janno

**Abstract.** A problem of determination of degenerate relaxation functions
of a three-dimensional isotropic viscoelastic body by means of traction
measurements is studied. The existence, uniqueness, and stability of a solution
to this problem are proved.

**Key words:** identification problems, three-dimensional viscoelasticity,
relaxation functions.

Some
new stability margins for discrete-time systems; 186–197

Ülo
Nurges

**Abstract.** Some new stability margins for discrete-time systems are
proposed in the system characteristic polynomial coefficient space by making
use of the so-called reflection vectors of monic Schur polynomials. Reflection
vector margins give the distance (not minimal) to the stability boundary in
directions of 2*n* reflection vectors of an *n*th-degree polynomial.
The relations between the reflection vectors and the roots of a polynomial on
the unit circle are given.

**Key words:** stability, polynomials, discrete-time systems.

The importance of the Hurst exponent in
describing financial time series; 198–206

Robert Kitt

**Abstract.** Memory in financial time series is a well-known phenomenon.
Long-term self-affine memory leads to fractional Brownian function and is
characterized by the Hurst exponent *H*.
This study aims to clarify the role of the Hurst exponent in describing
financial markets. Hurst exponents were found for time series of Baltic and
international stock exchange indices using the longest available period, from
the beginning of the Baltic markets in 1996 up to August 2002. The Hurst
exponents found varied from market to market. No considerable correlation was
observed between the markets with similar Hurst exponents, but they did have
similarities in economic situation. Therefore, the scaling analysis reveals
hidden similarities between the markets, which open new possibilities in
securities analysis.

**Key words: **fractals,
econophysics, scaling, Hurst exponent.

Emissive
power and flux in an atmosphere subjected to a finite strip of radiation;
207–220

Indrek Vurm and Tõnu Viik

**Abstract.** The emissive power and radiative flux were calculated in a
two-dimensional, absorbing–emitting, finite grey atmosphere subjected to a
strip of collimated incident radiation. In order to find a solution to this
problem, we had to use the solution to the similar problem with collimated
cosine varying incident radiation, which has been found in our previous papers
by approximating the kernel of the integral equation for the emissive power by
a sum of exponents. This allowed us to find all the parameters for both external
and internal radiation fields. The main point of the approach, already used by
Breig and Crosbie (*J. Quant. Spectrosc. Radiat. Transfer*, 1973, **14**,
189–209) for determining only the external radiation field, consists in
expressing the solution for the case in question as a superposition of
solutions to the case of collimated cosine varying incidence. This brought
along infinite integrals which were converted to an alternating series of
finite integrals, while the integration was simplified by separating an integrable
part of the integrand. For speeding up the convergence of these series we used
the Euler transformation.

**Key words:** two-dimensional radiative transfer, emissive power, radiative
flux.

Comparison of ground-level-measured and
satellite-derived erythemal ultraviolet doses in Estonia;
221–235

Kalju Eerme, Uno Veismann, and Rutt Koppel

**Abstract. **A comparison of the ground-level-measured daily erythemal
ultraviolet doses at the Tartu/Tõravere meteorological station (58.3° N,
26.5° E; 70 m a.s.l.) with the doses retrieved by the Earth Probe
satellite instrument Total Ozone Mapping Spectrometer has been provided for the
summer half-years (from vernal equinox to autumnal equinox) of 1998–2001. The
linear correlation between the satellite-retrieved and ground-level-measured
doses was found to be between 0.93 and 0.95 in different years, with the lowest
value registered in extremely cloudy 1998. The mean ratios of the
satellite-retrieved to measured values manifest no systematic difference. The
daily differences reach 200% in the presence of optically thick low cloudiness.
The summer half-year total doses agree within 2%, with the exception of 1998
when the difference reached 6%.

**Key words:** erythemal UV irradiance and dose, relative sunshine duration,
total cloud amount, low cloud amount.

ESTONIAN PHYSICAL SOCIETY

Annual award of the Estonian Physical Society;
236

Instructions to authors; 237–239

Copyright Transfer Agreement; 240