Interaction of cavity solitons in degenerate optical parametric oscillators

Numerical studies, together with asymptotic and spectral analysis, establish regimes in which soliton pairs in degenerate optical parametric oscillators fuse, repel, or form bound states. A novel bound state that is stabilized by coupled internal oscillations is predicted.     

Drop deposition of thin nanostructured coatings of lead telluride

The current-voltage relationships of deposited structures are measured for cluster structures consisting of nanoparticles of lead telluride. Variation in the value of the tunnel current is shown. Optimum conditions for the possible emergence of quantum-hopping conductivity due to carrier tunneling (the characteristic sizes of the nanoclusters and the distances between them) are determined.     

Studying the structure and electrical conductivity of thin granulated bimetallic films

The surface resistance of bimetallic granular films prepared by means of laser-induced deposition is studied. The possibility of modeling their conductivity is demonstrated, depending on their morphological properties.     

Flatness of Noetherian Hopf algebras over coideal subalgebras

It is proved in the paper that a Noetherian residually finite-dimensional Hopf algebra H is a flat module over any right Noetherian right coideal subalgebra A. In the case when A is a Hopf subalgebra we get faithful flatness. These results are obtained by verifying the existence of classical quotient rings of A and H. It is also proved that the antipode of either right or left Noetherian residually finite-dimensional Hopf algebra is bijective. As a consequence, such a Hopf algebra is right and left Noetherian simultaneously.

     

Metamagnetic phase transition in Nd1−x TbxCo2 compounds

The electric resistivity and neutron diffraction measurements of the intermetallic compounds Nd_1?x Tb_xCo₂ (x = 0, 0.2, 0.3, 0.5, 0.7, or 1) have been performed. All compounds have a cubic structure at room temperature and a rhombohedral structure at 4.2 K. The magnetic structure of these compounds is described by the wave vector k = 0. The magnetizations of the rare earth and cobalt sublattices increase with increasing x. The concentration dependence of the cobalt sublattice magnetization is explained on the basis of the model of metamagnetic band subsystem in compounds of the RCo₂ type.     

Projectivity and freeness over comodule algebras

Let be a Hopf algebra and an -simple right -comodule algebra. It is shown that under certain hypotheses every -Hopf module is either projective or free as an -module and is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras, and the latter are Frobenius algebras. Similar results are obtained for -simple -module algebras.

     

Structure of <Emphasis Type=Italic>H</Emphasis>-Semiprime Artinian Algebras

Let H be a Hopf algebra over a field. It is proved that every H-semiprime right artinian left H-module algebra A is quasi-Frobenius and H-semisimple. If H grows slower than exponentially, then all H-equivariant A-modules are shown to be A-projective. With the additional assumption that H is cosemisimple it is proved that the Jacobson radical of any right artinian left H-module algebra is stable under the action of H.