In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics


Volume 51 No. 2 June 2002


Semiparallelity, semisymmetricity, and Ric-semisymmetricity for normally flat submanifolds in Euclidean space; 67–85

Ülo Lumiste

Abstract. The long-standing P. J. Ryan’s problem asks if the Ric-semisymmetric (RSS) hypersurfaces in a Euclidean space are semisymmetric (SS). It is proved now that all known results about this problem are covered by recent V. A. Mirzoyan's theorem classifying all RSS hypersurfaces. The problem is extended to normally flat submanifolds and solution is given for one particular case. On the other hand, it is established that there exist SS normally flat codimension two submanifolds which are not semiparallel (SP). This gives additional support to the conjecture that among Riemannian manifolds of conullity two (they are all SS) only those of planar type can be immersed isometrically as SP submanifolds.

Key words: semiparallel submanifolds, semisymmetric submanifolds, Ric-semisymmetric submanifolds, Ryan’s problem, manifolds of conullity two.

Non-axisymmetric buckling of elastic-plastic annular plates; 86–104

Ülo Lepik

Abstract. The elastic-plastic stability of an annular plate under uniform radial loads applied at its edges is considered. Emphasis is laid on the non-axisymmetric buckling forms since the assumption of symmetric buckling does not necessarily lead to the lowest critical load. As a constitutive law elastic-plastic relations with linear strain hardening and the Tresca yield condition are adopted. The buckling equation is integrated by the Runge–Kutta method. Numerical results for three types of loading and two versions of the boundary conditions are presented.

Key words: annular plates, non-axisymmetric buckling, elastic-plastic material, Tresca yield condition.

Analysis of large deformations of curved surfaces in holographic interferometry with remarks concerning nonspherical gravitational fields and rotating bodies; 105–121

Walter Schumann

Abstract. The principles of analysis of large deformations in holographic interferometry are briefly outlined. Modifications at the reconstruction are necessary to recover the previously invisible fringes. The spacing and contrast are characterized by the fringe and visibility vectors. The relevant first derivative of the path difference involves the polar decomposition of the deformation gradient and affine connections. By the modification the image aberration must be considered together with changes in geodesic curvatures and surface curvatures. This leads to similar aspects for hypersurfaces, and in particular to an interpretation of the Schwarzschild-solution by virtual deformations. Remarks concerning nonspherical gravitational fields and a tentative approach to the Kerr-solution for rotating bodies are added.

Key words: deformation analysis, holographic interferometry, curved surfaces.




Privacy of experiments in the absence of local reality; 122–123

Karl K. Rebane

Key words: local reality, entanglement, privacy of experiment.




Annual award of the Estonian Physical Society; 124


Instructions to authors; 125–127

Copyright Transfer Agreement; 128