Levi Harmonic Maps of Contact Riemannian Manifolds

We study Levi harmonic maps, i.e., C ^∞ solutions f:M→M′ to \(\tau_{\mathcal{H}} (f) \equiv \operatorname{trace}_{g} ( \varPi_{\mathcal{H}}\beta_{f} ) = 0\) , where (M,η,g) is an (almost) contact (semi) Riemannian manifold, M′ is a (semi) Riemannian manifold, β _f is the second fundamental form of f, and \(\varPi_{\mathcal{H}} \beta_{f}\) is the restriction of β _f to the Levi distribution \({\mathcal{H}} = \operatorname{Ker}(\eta)\) . Many examples are exhibited, e.g., the Hopf vector field on the unit sphere S ²ⁿ⁺¹, immersions of Brieskorn spheres, and the geodesic flow of the tangent sphere bundle over a Riemannian manifold of constant curvature 1 are Levi harmonic maps. A CR map f of contact (semi) Riemannian manifolds (with spacelike Reeb fields) is pseudoharmonic if and only if f is Levi harmonic. We give a variational interpretation of Levi harmonicity. Any Levi harmonic morphism is shown to be a Levi harmonic map.     

Exergetic Analysis of a Cryogenic Air Separation Unit

This case study analyzes a cryogenic air separation unit (ASU) with a production of V˙O2=58,300 [m3Nh] of gaseous oxygen with a concentration greater than 98.5%, operating in Romania on a steel plant platform. The goal of the paper is to provide an extensive model of exergetic analysis that could be used in an optimization procedure when decisional parameters are changed or structural design modifications are implemented. For each key part of the Air Separation Unit, an exergetic product and fuel were defined and, based on their definition, the coefficient of performance of each functional zone was calculated. The information about the magnitude of the exergetic losses offers solutions for their future recovery. The analysis of the exergy destructions suggests when it is worth making a larger investment. The exergetic analysis of the compression area of the ASU points out an exergy destruction and loss of 37% from the total plant’s electrical energy input. The exergy loss with the heat transferred to the cooling system of compressors can be recovered; for the exergy destruction portion, the challenge between investment and operating costs should be considered. The exergy destruction of the air separation columns found the High Pressure Column (HPC) to be more destructive than the Low Pressure Column. The share of the exergy destruction in the total plant’s electrical energy input is 8.3% for the HPC. The local COP of the HPC, calculated depending on the total exergy of the local product and fuel, is 62.66%. The calculus of the air separation column is performed with the ChemSep simulator.     

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.