Some exact solutions of the Dirac equation in the Kasner space-time

The exact solutions of the covariant generalization of the Dirac equation are obtained in the Kasner space-time for two types of coordinates, cartesian coordinates and cylindrical ones. The tetrads for both cases are constructed on the basis of a global quasicartesian coordinate systems that allows one to get rid of coordinate effects connected with the rotation of the local frame under transition of the triad from one space-time point to another. The possibility of plane and cylindrical spinor waves in the Kasner space-time is proved.     

Fluctuation forces in a three-layer medium with rough boundaries. IV. Calculations in the second order of perturbation theory (Casimir range)

The perturbation theory developed in the previous paper of the series is used to calculate the correction to the Casimir force due to the surface roughness.Scientific Council on the Problem Complex Kibernetika, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 1, pp. 113–118, July, 1992.     

A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces

In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also K ‐increasing with a K ‐convex K ‐epi‐closed function, where K is a nonempty closed convex cone. These statements prove to be the weakest constraint qualifications given so far under which the formulae for the subdifferential of the mentioned sum of functions are valid. Then we deliver constraint qualifications inspired from them that guarantee some conjugate duality assertions. Two interesting special cases taken from the literature conclude the paper. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simple models of firms emergence

We present a dynamical model of the emergence of firms as opposed to a flat labour market where entrepreneurs would recruit workers for each business opportunity. The model uses a preferential choice of partners based on previous collaborations experience. A sharp transition in the parameter space separates an ordered regime, where preferential links establish, from a disordered regime corresponding to a fast turnover of employees.     

Fluctuation forces in a three-layer medium with rough boundaries. I. Principles of perturbation theory

All-Union Scientific-Research Center for the Study of Surface and Vacuum Properties. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 2, pp. 178–187, February, 1990.     

Submanifolds of generalized Hopf manifolds,type numbers and the first Chern class of the normal bundle

Summary Any orientable real hypersurface M of a complex Hopf manifold (carrying the locally conformal Kaehler (l.c.K.) metric discovered by I.Vaisman [33]) has a natural f-structure P as a generic Cauchy-Riemann submanifold; we show (cf. our § 5) that if P anti-commutes with the Weingarten operator, then the type number of the hypersurface is less equal than 1. Moreover, M carries the natural almost contact metrical structure observed by Y.Tashiro [30]; if its almost contact vector is an eigenvector of the Weingarten operator corresponding to a nowhere vanishing eigenfunction and the holomorphic distribution is involutive, then M is foliated with globally conformai Kaehler manifolds (cf. our § 5), provided that some restrictions on the type number of M are imposed. We derive (cf. our § 6) a «Simons type» formula and apply it to compact orientable hypersurfaces with non-negative sectional curvature (in a complex Hopf manifold) and parallel mean curvature vector. Several examples of submanifolds of l.c.K. manifolds are exhibited in § 3. Our § 7 studies complex submanifolds of generalized Hopf manifolds; for instance, we show that the first Chern class of the normal bundle of a complex submanifold having a flat normal connection is vanishing.     

Analytical performance of an r.f. capacitively coupled plasma for atomic emission with tip-ring electrode geometry

A low to medium power radiofrequency capacitively coupled plasma is characterized as spectral source for atomic emission. The signal to background ratio and the limits of detection were determined for 19 elements as a function of the plasma torch geometry and the observation point.     

Synthesis of hybrid polysiloxane-MO<Subscript>2</Subscript> (M = Si,Ti, Zr) nanoparticles through a sol–gel route

Polysiloxanes in combination with metal oxides show interesting properties as nanocomposites for optical or medical applications. The formation of covalent connections between the metal oxide and the polysiloxane is an important method to overcome phase separation between the two components, but it also can have an influence on the morphology of the final materials. In this contribution we report a method for the synthesis of hybrid materials based on polysiloxanes and various metal oxides in which both components are tightly connected to each other. Alkoxysilane modified polysiloxanes were obtained by hydrosilation reactions between vinyl triethoxysilane and poly(dimethylsiloxane-co-methylhydrosiloxane) (PDMS-co-PMHS). The thus functionalized polymers were used in a sol-gel process applying Stöber conditions and hybrid nanoparticles were obtained. Following the same pathway, different metal alkoxides (M(OR)₄; M = Ti, Zr; R = ethyl, isopropyl) were coordinated to allyl acetoacetate (AAA) and the resulting complexes were applied in a hydrosilation reaction with PDMS-co-PMHS. Metal oxide hybrid nanoparticles were obtained through a sol–gel process.     

Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups

We study equivalence relations and II₁ factors associated with (quotients of) generalized Bernoulli actions of Kazhdan groups. Specific families of these actions are entirely classified up to isomorphism of II₁ factors. This yields explicit computations of outer automorphism and fundamental groups. In particular, every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic II₁ factors.