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.     

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.     

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.     

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.

     

Mn site substitution of La0.67Ca0.33MnO3 with closed shell ions: Effect on magnetic transition temperature

Mn site is substituted with closed shell ions (Al, Ga, Ti, Zr and a certain combination of Zr and Al) and also with Fe and Ru ions carrying the magnetic moment (S=5/2 and 2 respectively) at a fixed concentration of 5 at %. Substitution did not change either the crystal symmetry or the oxygen stoichiometry. All substituents were found to suppress both the metal-insulator and ferromagnetic transition temperatures (T _p(ρ) and T _C, respectively) to varied extents. Two main contributions identified for the suppression are the lattice disorder arising due to difference in the ionic radii between the substituent (r _M) and the Mn³⁺ ion (r _Mn ³⁺) and in the case of the substituents carrying a magnetic moment, the type of magnetic coupling between the substituent and that of the neighboring Mn ion.