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 2n reflection vectors of an nth-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.




Annual award of the Estonian Physical Society; 236

Instructions to authors; 237–239

Copyright Transfer Agreement; 240