CONTENTS &
ABSTRACTS

In
English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics

** **

Volume 50 No. 4
December 2001

Looking
back beyond a half century; 187–194

Ivar PIIR

Measurement
of time in nonrelativistic quantum and classical mechanics; 195–213

Piret
KUUSK and Madis KÕIV

Abstract. Possible theoretical frameworks for
measurement of (arrival) time in nonrelativistic quantum mechanics are
reviewed. It is argued that the ambiguity between indirect measurements by a
suitably introduced time operator and direct measurements by a physical clock
particle has a counterpart in the corresponding classical framework of
measurement of the Newtonian time based on the Hamiltonian mechanics.

Key words: time,
measurement, quantum mechanics, Hamiltonian dynamics.

Radiation
field in an atmosphere subjected to cosine varying diffuse radiation; 214–226

Tõnu VIIK and Indrek VURM

Abstract. The radiation field is calculated in an
optically finite or semi-infinite, two-dimensional, plane-parallel,
absorbing–emitting but nonscattering grey atmosphere subjected to diffuse
cosine varying incident boundary radiation. We again approximate the kernel of
the integral equation for the emissive power by a sum of exponents. After this
approximation the integral equation can be solved exactly. The solution can be
written in generalized *x*- and *y*-functions (or *h*- and *g*-functions
in the semi-infinite case) which were introduced for a one-dimensional
atmosphere. Since the radiation field in the case of diffuse incident radiation
can be described as a superposition of solutions for the collimated case, we
can find the accurate values for the source function and the radiative flux at
arbitrary optical depths in the atmosphere. As in the case of collimated incident
radiation, this approximation allowed of finding accurate numerical values for
the source function and the radiative flux.

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

Electron
paramagnetic resonance spectra of human tooth enamel with preferentially
oriented nanocrystals; 227–246

Georg LIIDJA

**Abstract. **Electron paramagnetic
resonance spectra of a selected γ-irradiated human tooth enamel fragment
expressed anisotropy that increased considerably after thermal annealing. By
repeated irradiation, the spectrum of the fragment approached the disoriented
(powder type) spectrum, but repeated thermal treating restored the anisotropy.
The anisotropy is characteristic of an ensemble of hydroxyapatite nanocrystals,
predominantly oriented with the hexagonal axis perpendicular to the outer
surface of the tooth. A Monte Carlo spectral simulation, corresponding to the
bulk arrangement of paramagnetic CO_{2}^{–} radicals possessing
the _{}* *symmetry and normal distribution of *y*-axes (parallel to the O–O direction)
in a space angle of 27° (± 5°) around the surface
normal, gives a satisfactory agreement with the experimental spectra, whereas
the agreement for alternative models with specific surface arrangement of the
radicals is worse.

**Key words: **electron paramagnetic resonance, irradiated tooth
enamel, CO_{2}^{–} radicals, spectral anisotropy, Monte Carlo
simulation.

Contents of volume 50;
247–248