Cylindrical multidimensional surfaces in Lobachevsky space

We study complete, strongly parabolic metrics with constant relative index of nullity _c=k and complete, strongly parabolic surfaces with constant index of relative nullityv=k in a constant curvature space Rⁿ(c) under the assumption that there exists a surface orthogonal to the fibers of total geodesity, and if c<0, under the additional condition that the orthogonal surface be totally umbilical. For c>0 we have _c=l;v=l, for c=0 the Riemannian manifold is a metric product of the metric of R^l–k and the Euclidean space E^k while the surface is a cylinder in Euclidean space. For c<0 the metric has a special form and the surface is a cylindrical surface in Lobachevsky space.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 18–27, 1990.     

The isometric immersion of strongly parabolic metrics in the class of strongly parabolic surfaces

It is known that a k-strongly parabolic surface in Euclidean space (index of relative nullity is at least k) inherits a k-strongly parabolic metric (index of nullity is at least k). For the definitions of the index of relative nullity (x) and the index of nullity (x) see Sh. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience Publishers, New York (1969), Vol. II, pp. 347–348. The converse is not true. In particular, there exists an analytic, three-dimensional, 1-strongly parabolic metric that does not admit a local isometric immersion into Euclidean space of any dimension in the class of three-dimensional 1-strongly parabolic surfaces. The proof is carried out with the help of the method of exterior Cartan forms.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 27–37, 1990.     

Isoperimetric inequality for curves with curvature bounded below

For embedded closed curves with curvature bounded below, we prove an isoperimetric inequality estimating the minimal area bounded by such curves for a fixed perimeter.     

Stability of the single-domain state in single crystals of triglycine sulphate

The stability of the single-domain state in single crystals of triglycine sulfate is investigated using the Barkhausen effect. Barkhausen jumps are detected upon invariable macroscopic polarization. The parameters of the observed Barkhausen jumps are estimated and compared.     

Numerical simulation of resistive switching in heterostructures based on anisotropic oxide compounds

Numerical simulation is used to study the effect anisotropic electrical conductivity and anisotropic oxygen diffusion have on the bipolar resistive switching effect in oxide compounds.     

Element-Substituted Acylphosphines

Abstract

Element-substituted acylphosphines are stable in form 2 R¹P(ER_n)COR² (A), when E=Ge, Sn, Sb, P, T1 and in form R¹ P=C(OER_n)R² by NMR data. The reaction     

C- and N-Substituted Phosphorus(III) Derivatives of Azomethines

Abstract

The reactions of halogenides of P(III) acids with lithium derivatives of azomethines depending on the substituents at the phosphorus atom, the structure of azomethines and conditions of the reaction were studied. A method for synthesizing tile C- and N-phorphorus(III) substituted azomethines was proposed: