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 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 TiO2 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–TiO2–Ag structures with TiO2 layers of 30–180 nm thickness. In the case of negative bias on the Au electrode, the conduction currents through TiO2 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–TiO2 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, Mo6+-, Cr3+-, Cd2+-, Ba2+-doped and double Mo6+, Y3+- and Mo6+, Nb5+-doped lead tungstate crystals, undoped and Ce3+-doped yttrium aluminium and lutetium aluminium perovskite and garnet crystals, and Ce3+-, Tb3+-, Mn2+-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