Boundary-value problem for the nonlinear Schrödinger equation

A mixed boundary-value problem for the nonlinear Schrödinger equation and its generalization is studied by the method used for the inverse scattering problem. A connection is established between conservation laws and boundary conditions in integrable boundary-value problems for higher nonlinear Schrödinger equations. It is shown that the generalized boundary-value problem requires a joint consideration of regular and singular solutions for the nonlinear Schrödinger equation with repulsion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 151–165, 1988.     

A New Distribution Function for Risk Analysis

This paper presents an alternative to the beta continuous probability distribution for risk analysis. Particular attention has been given to two major applications of distributions, namely project management risk and critical path analysis (PERT). In conjunction with the beta, the triangular and normal distributions are frequently employed in order to give sufficient robustness to risk analysis. The beta distribution, as used in PERT, has a major theoretical implementation flaw. The new distribution was developed to give a possible alternative method of assessing risk. It is shown that the requirement to estimate the most pessimistic variate may be replaced by the probability to exceed the mode. Proposals for other simplifications in risk analysis are discussed. Practical means to validate the most appropriate distributions for risk analysis are outlined, and a cost-data case study is included.     

On decomposition of continuity

Summary The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain a decomposition of continuity.     

Electrochemical Recovery of Silver from Lead Alloys in Chloride Melts

Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry.     

Electroactive conducting polymers for corrosion control

There is an intensive effort underway to develop new corrosion control coatings for structural metals. In part, this effort has been motivated by the desire to replace chromium(VI)-containing coatings currently used for corrosion control of iron and aluminum alloys. Cr(VI) has been shown to be hazardous to the environmental and to human health, and its use in many countries will be sharply curtailed in the coming years. Electroactive conducting polymers (ECPs) represent a class of interesting materials currently being explored for use in corrosion control coating systems, possibly as a replacement for Cr(VI)-based coatings. The electroactivity and the electronic conductivity (or semiconductivity) of ECPs set them apart from traditional organic coatings. As with chromate, interesting and potentially beneficial interactions of ECPs with active metal alloys such as steel and aluminum are anticipated, with concomitant alteration of their corrosion behavior. A review of this active research area will be presented in two parts. Here in Part 1, a general introduction to the topic of corrosion control by ECPs will be presented, including an overview of corrosion and its control by traditional methods, an introduction to ECPs and their properties, and a discussion of the processing issues surrounding the use of ECPs as coatings. Part 1 also includes a review of the literature on the use of ECPs as coatings (or components of coatings) on non-ferrous active metals, principally aluminum and aluminum alloys, although some work on zinc, copper, silver, titanium and silicon will also be described. In Part 2 of this review (to be published in the next issue of this journal), the rather extensive literature on the use of ECPs for the corrosion control of ferrous alloys (steels) will be reviewed. Electronic Publication     

Multicriteria decision making under uncertainty

Formalization for problems of multicriteria decision making under uncertainty is constructed in terms of guaranteed and weak estimates. A relevant definition of the vector maximinimax value is given. Parameterization and approximation of maximum, minimax, and maximinimax values based on the inverse logical convolution are suggested. An application for multicommodity networks is considered. Received: December 13, 2000 / Accepted: August 21, 2001?Published online May 8, 2002     

On the problem of calculating the optical film parameters from the measured transmission spectra

The procedure for calculating the dispersion of the refractive and absorption indices and thickness of an optical film, based on measurements of spectral dependence of the transmittance, is described. The film parameters are calculated using a solution of the approximation problem. The effect of the film model on the calculated values of the refractive and absorption indices is analyzed.