CONTENTS &
ABSTRACTS

In
English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics

** **

Volume 53 No. 4
December 2004

** **

Riemannian
manifolds of conullity two admitting semiparallel isometric immersions;
203–217

Ülo Lumiste

**Abstract.** A Riemannian manifold _{} is semisymmetric if _{} An isometric
immersion of _{} into a Euclidean
space is semiparallel if _{} holds for the second
fundamental tensor _{} Due to Gauss and
Ricci equations the second condition leads to the first one. Especially _{} holds if _{} is foliated by
codimension two locally Euclidean leaves (equivalently, is of conullity two).
Here the planar, hyperbolic, parabolic, and elliptic types can be specified.
For many cases of these manifolds of conullity two it has been shown already
that their isometric semiparallel immersions into a Euclidean space are
possible only if the manifold is of planar type. Now the same is established
for the rather general manifolds of conullity two; it is claimed that this
holds perhaps for all of them.

**Key words:** semisymmetric Riemannian manifolds, manifolds of conullity
two, planar type, semiparallel immersions.

The
topologization of sequence spaces defined by a matrix of moduli; 218–225

Annemai Mölder

**Abstract.** For a solid double sequence space _{} and a matrix of
moduli F _{} let _{}(F )_{} We characterize the F-seminormability of the sequence space _{}(F ). As
concrete examples we consider the spaces of strongly B-summable
and strongly B-bounded sequences with
respect to F . We also give a correction of the theorem of Esi (*Turkish J.
Math*., 1997, **21**, 61–68) about the topologization of _{}

**Key words:** sequence space, double sequence space, modulus _{}function, F-seminorm, strong summability.

Fowler–Nordheim
tunnelling in TiO_{2} films grown by atomic layer deposition on gold
substrates; 226–236

Indrek Jõgi, Jaan Aarik, Viktor Bichevin, Henn
Käämbre,

Matti Laan, and Väino Sammelselg

**Abstract.** Current–voltage characteristics were measured for Au–TiO_{2}–Ag
structures with TiO_{2} layers of 30–180 nm thickness. In the case
of negative bias on the Au electrode, the conduction currents through TiO_{2}
layers follow over several orders of magnitude the Fowler–Nordheim formula for
the field emission, allowing attribution of the bulk currents to tunnelling,
seemingly through a Schottky barrier at the Au–TiO_{2} junction. In the
case of reversed polarity the currents are also observed, but cannot be
interpreted as tunnelling.

**Key words:** titanium dioxide, thin films, electrical properties,
Fowler–Nordheim plots, tunnelling currents.

New
scintillation materials for scientific, medical, and industrial applications;
237–251

Svetlana Zazubovich

**Abstract. **Information is presented
on the terminated NATO Science for Peace project devoted to the search and
study of some new and/or improved scintillation materials. In the framework of
this project, in 2000–2003 various undoped, Mo^{6+}-, Cr^{3+}-,
Cd^{2+}-, Ba^{2+}-doped and double Mo^{6+}, Y^{3+}-
and Mo^{6+}, Nb^{5+}-doped lead tungstate crystals, undoped and
Ce^{3+}-doped yttrium aluminium and lutetium aluminium perovskite and
garnet crystals, and Ce^{3+}-, Tb^{3+}-, Mn^{2+}-doped
Gd-rich phosphate glasses were studied in the Institute of Physics, University
of Tartu. The most important results of these investigations obtained in
collaboration with the colleagues from Italy and Czech Republic are briefly
reported.

**Key words: **scintillators, lead
tungstates, perovskites, garnets, phosphate glasses.

Antarctic
Circumpolar Current as a density-driven flow; 252–265

Jaak Heinloo and Aleksander Toompuu

**Abstract.** The paper considers the Antarctic Circumpolar Current (ACC) as
a current formed due to the specific density field in the Southern Ocean
characterized by relatively strong frontal zones. Unlike the approach founded
on the geostrophic balance only, the suggested model takes into account
turbulence effects caused by the baroclinic instability. The approach is
grounded on the theory of rotationally anisotropic turbulence (RAT theory).
While classical treatments of the ACC are based on the momentum balance, the
RAT theory is founded on a simultaneous consideration of the momentum and
moment of momentum balance. The equation of the moment of momentum is
introduced due to the rotational anisotropy of turbulence in frontal region(s)
coinciding with the observed ACC occurrence. For the realistic density field,
estimated from the measured and optimally analysed temperature and salinity
long-term data in the Southern Ocean with the density increasing to the south,
the resulting velocity is directed to the east. This velocity is interpreted as
the turbulence-generated ageostrophic constituent of the flow field. In the
regions where turbulence effects are missing, the ageostrophic velocity
constituent vanishes and the model reduces to the classical geostrophic balance
condition. The model predictions are illustrated by velocity profiles
calculated for the case where turbulent effects prevail over the geostrophic
balance.

**Key words:** Southern Ocean, Antarctic Circumpolar
Current, turbulence, zonal flow.

Instructions
to authors; 266–268

Copyright
Transfer Agreement; 269

Contents
of volume 53; 270–271