On Constraint Qualifications in Nonsmooth Optimization

We introduce extensions of the Mangasarian-Fromovitz and Abadie constraint qualifications to nonsmooth optimization problems with feasibility given by means of lower-level sets. We do not assume directional differentiability, but only upper semicontinuity of the defining functions. By deriving and reviewing primal first-order optimality conditions for nonsmooth problems, we motivate the formulations of the constraint qualifications. Then, we study their interrelation, and we show how they are related to the Slater condition for nonsmooth convex problems, to nonsmooth reverse-convex problems, to the stability of parametric feasible set mappings, and to alternative theorems for the derivation of dual first-order optimality conditions.In the literature on general semi-infinite programming problems, a number of formally different extensions of the Mangasarian-Fromovitz constraint qualification have been introduced recently under different structural assumptions. We show that all these extensions are unified by the constraint qualification presented here.     

Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods

The aim of the paper is to present and substantiate a technique to visualize DEA modelling results without any loss of mathematical rigour. The proposed family of parametric optimization methods allows one to construct an intersection of the multidimensional frontier with a two-dimensional plane determined by any pair of given directions. This approach reduces the efficiency analysis of production units to the investigation of well-known functions in economics. We also propose constructive methods to calculate marginal rates of substitution, marginal rates of transformation and so on.     

Ion source with a cold magnetron cathode and magnetic plasma compression

The operating principles, design, and characteristics of an ion source with a cold magnetron cathode and magnetic plasma compression are described. The source is intended for the injector of a linear proton accelerator.     

Relative distance and boundary properties of nonparametric surfaces with finite area

Some boundary properties of nonparametric surfaces with finite area are proved.     

Diffusive behavior of asymmetric zero-range processes

We investigate a new interpretation for the Navier-Stokes corrections to the hydrodynamic equation of asymmetric interacting particle systems. We consider a system that starts from a measure associated with a profile that is constant along the drift direction. We show that under diffusive scaling the macroscopic behavior of the process is described by a nonlinear parabolic equation whose diffusion coefficient coincides with the diffusion coefficient of the hydrodynamic equation of the symmetric version of the process.     

Investigation of thin-film electroluminescent structures on rough subsrates

Results of experimental investigations of the volt-brightness characteristics, frequency dependences of brightness, and the directional radiation pattern of electroluminescent MSDM, MSCM, and MSDCM emitters, where M stands for the first transparent and second nontransparent electrodes, S is a semiconductor, D is a thin-film dielectric, and C is a silicone-based composite liquid dielectric with a powdered segnetoelectric filler, developed on conventional “smooth” and rough glass substrates are presented. It is shown that electroluminescent structures on rough surfaces have a brightness approximately two times higher than that of similar structures developed on a “smooth” substrate. Ul’yanovsk State University, 42, L. Tolstoi St., Ul’yanovsk, 432700, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 4, pp. 507–512, July–August, 1997.     

On asymptotic approximations for slow wave processes in nonlinear dispersive media

We consider the application of asymptotic methods of nonlinear mechanics (the Krylov-Bogolyubov-Mitropol'skii method) and the method of separation of motions in nonlinear systems for the construction of an approximate solution of a nonlinear equation that describes a nonstationary wave process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 357–371, March, 1998.