Dual Characterizations of Set Containments with Strict Convex Inequalities

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key roles in solving large scale knowledge-based data classification problems where they are used to describe the containments as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments.     

Selective oxidation of sulfides to sulfoxides and sulfones at room temperature using H2O2 and a Mo(VI) salt as catalyst

Selective oxidation of sulfides to sulfoxides and sulfones is achieved by H₂O₂ using MoO₂Cl₂ as the catalyst. Various substituted sulfides having functional groups such as methyl, methoxy, bromo, nitro, alkene, alkyne, alcohol, ester, aldehyde and remarkably an oxime are successfully and selectively oxidized without affecting the sensitive functionalities.     

Generalizations of Slater's constraint qualification for infinite convex programs

In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g ₁,g ₂) andS = S ₁ ×S ₂,S _i are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg _i are, respectively, convex andS _i -convex,i = 1, 2. In particular, we consider the special case whenS ₂ is in afinite dimensional space,g ₂ is affine andS ₂ is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g ₂ is affine andS = S ₂ is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong ₂ and the finite dimensionality assumption onS ₂, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones.     

Determination of trace concentrations of thorium in uranium oxide matrix by epithermal instrumental neutron activation analysis

An epithermal instrumental neutron activation analysis (EINAA) method using cadmium filter was standardized to determine trace concentrations of thorium in four samples of uranium oxide (U₃O₈) samples. Samples and thorium standards, wrapped with cadmium foil, were irradiated at a reactor neutron flux of about 10¹² cm^?2 s^?1. Radioactive assay was carried out using a Compton suppressed anticoincidence gamma ray spectrometer consisting of HPGe-BGO detectors coupled to MCA. Concentrations of thorium in these samples were found to be in the range of 15–72 mg kg^?1. EINAA results were validated by determining thorium concentrations in uranium matrix by standard addition method. EINAA results were compared with those obtained by two wet chemical methods namely ion chromatography (IC) and inductively coupled plasma atomic emission spectrometry (ICP-AES). The results obtained by the three methods were found to be in good agreement, indicating further validity of the proposed EINAA method.     

Determination of calcium and iron in silicon and uranium silicide using ion chromatography

Two separate ion chromatography methods were developed for the determination of calcium and iron in silicon and uranium silicide. A cation exchange separation with conductivity detection was developed for Ca. A reversed phase column modified with 50 mM camphor-10-sulphonic acid was used for separating Fe. Iron was detected photometrically. Linear calibrations for Ca (0.1–10 ppm) and Fe (0.5–25 ppm) were performed. Limits of detections for Ca and Fe are 0.03 and 0.2 ppm, respectively. The precision of the methods are better than 2 % for Ca at 0.2 ppm and Fe at 2 ppm.     

Convex composite multi-objective nonsmooth programming

This paper examines nonsmooth constrained multi-objective optimization problems where the objective function and the constraints are compositions of convex functions, and locally Lipschitz and Gâteaux differentiable functions. Lagrangian necessary conditions, and new sufficient optimality conditions for efficient and properly efficient solutions are presented. Multi-objective duality results are given for convex composite problems which are not necessarily convex programming problems. Applications of the results to new and some special classes of nonlinear programming problems are discussed. A scalarization result and a characterization of the set of all properly efficient solutions for convex composite problems are also discussed under appropriate conditions.This research was partially supported by the Australian Research Council grant A68930162.This author wishes to acknowledge the financial support of the Australian Research Council.     

Cyclic voltammetric measurements of growth of Aspergillus terreus.

A detailed study using the cyclic voltammogram was done on the live cells of Aspergillus terreus. The peak current values were obtained for different days of growth and plotted against time. The response of cyclic voltammogram showed the phases of the growth of the fungus. The growth curve obtained matched well with the conventional methodology, which assesses the increase of dry weight of the organisms against time. The electrochemical method is more advantageous because it is easy to assess and consumes less time. Further the electrochemical method clearly shows the decline phase which is generally not very defined in the conventional method of assessment of the growth curve. It was confirmed by further experiments that the metabolites were responsible for the anodic peak and not the biomass. Further work is in progress in order to analyze the metabolite(s) that is/are responsible for the anodic peak.     

A note on sufficient global optimality conditions for fixed charge quadratic programs

In this work we establish conditions for a feasible point to be a global minimizer of a fixed charge quadratic model program. This program has a wide variety of classic applications, for instance, in facility location, scheduling and portfolio selection. However, the existence of the fixed charges in its objective function has hindered the development of extensive theory for its global solutions. We derive sufficient conditions for global optimality by way of underestimating the Lagrangian using a weighted sum of squares. We present a numerical example to illustrate our optimality conditions.