The optimality conditions for optimization problems with fuzzy-valued objective functions

The optimality conditions for an optimization problem with fuzzy-valued objective function are derived in this article. The solution concept of this optimization problem will follow the similar solution concept, called nondominated solution, in multiobjective programming problem. In order to consider the differentiation of fuzzy-valued function, we invoke the Hausdorff metric to define the distance between two fuzzy numbers and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the optimality conditions for obtaining the nondominated solutions are elicited naturally by introducing the Lagrange multipliers.     

Optimization of Ethanol Supercritical Fluid Extraction of Medicinal Compounds from St. John's Wort by Central Composite Design

Extraction of medicinal compounds from St John's Wort was performed using supercritical ethanol. The supercritical fluid extraction parameters were optimized via response surface methodology which included a central composite design. The independent variables were extraction temperature (ranging from 300°C to 340°C), extraction times (ranging from 60 to 120 min), and plant concentration (ranging from 8% to 12%). The response was the St John's Wort extract yield. The extraction temperature was the most significant factor which affects St John's Wort yields according to statistical results. The coefficient of determination was estimated to be 0.98 which indicates the effectiveness of the model and its adaptability to the experimental data. The extract of St John's Wort was comprised of a wide array of compounds including phenols, acids, acid esters, and alkanes. The most prominent components of the extract of St. John's Wort in terms of their relative concentrations were linoleic acid ethyl ester, oleic acid ethyl ester, hexadecanoic acid ethyl ester, and nonacosane.     

Determination of Trace Amounts of Copper by Adsorptive Stripping Voltammetry

ABSTRACT

A technique is presented for the determination of trace amounts of copper(II) by adsorptive cathodic stripping voltammetry. The procedure is based on adsorptive accumulation of copper(II)-Alizarin Red S (ARS) complex on a hanging mercury drop electrode, followed by a stripping voltammetric measurement of the reduction current of the adsorbed complex at -0.16 V (vs. Ag/AgCl). The height of the copper -ARS reduction peak is linearly dependent upon the copper(II) concentration between 0.2-15 and 15-500 ng.ml^?1. The detection limit of the technique is 0.05 ng.ml^?1 copper(II) for a collection time of 1 minute. The method is free from most interferences. The procedure has been successfully applied to the determination of trace amounts of copper(II) in some analytical grade salts.     

One Teacher's Quest for Liberation

Abstract

Last year, I was asked to participate in a policy panel on technology co-sponsored by the National Post-secondary Education Cooperative and The George Washington University. The panel was called “Technology and Its Data Systems Ramifications.” I was skeptical at first, fearing the panel would deal largely in dry statistics and technical problems of moving large files of statistical information from one place to another. I was quite wrong. The panel proved to be a forward-thinking, exciting analysis of how colleges and universities may be doing business in the future. Following are some of the interesting outcomes of the panel.