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.     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

Chemical isolation of element 106 from aqueous solutions according to model experiments with short-lived tungsten isotopes

The short-lived isotopes of W and their descendants have been isolated from the products of the bombardment of¹⁴⁴Sm with²⁴Mg by a fast continuous ion-exchange method, using HF solution media. The feasibility of this method for isolation of element 106 is discussed.     

Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Fast and continuous chemical isolation of short-lived isotopes of Hf,Ta and W as homologs of elements 104, 105 and 106

Some short-lived isotopes of Hf, Ta and W, synthesized at the U-400 cyclotron of JINR-Dubna, have been isolated using a previously elaborated fast continuous method of chemical isolation of element 104 from nuclear reaction products. The products were transported by a NaCl aerosol jet, from the irradiated targets to a separation device in which Hf, Ta and W were isolated by using three coupled ion-exchange columns.     

Fluorescence from the second excited singlet state of [18] annulenes

The emission spectra of the second excited singlet state of [18] annulene and of monofluoro [18] annulene (in a 3-methylpentane glass at 4 K) are reported. The large energy gap between the first and second excited singlet states inhibits fast internal conversion and favours the appearance of S₂ → S₀ emission. In addition, fluorescence from the S₁ state can be observed in monofluoro [13] annulene by exciting into the S₂ or directly into the S₁ absorption.     

Anionic polymerization of 1,2-butylene oxide

Anionic polymerizations of 1,2-butylene oxide were carried out in vacuum-sealed dilatometers in the range of 30–60°C. Potassium terbutoxide and dimsyl sodium were used as initiators; dimethyl sulfoxide (DMSO) and mixtures of DMSO with tetrahydrofuran were solvents. The polymer products were analyzed by gel permeation chromatography and infrared spectroscopy. The object of the investigation was to obtain information on the mechanism of the reaction and to elucidate some of its kinetic aspects. It has been shown that the polymerizations occur by two different processes, depending on the choice of experimental conditions. One of the processes involves free ions and ion-pairs, the other, ion-pairs alone. In the first case, where dimethyl sulfoxide is used as solvent, the order of the reaction with respect to the initiator concentration far exceeds unity (～1.8), while in the second case, involving mixed solvents, the order of the reaction, for all practical purposes, is one.     

Natural anti-HIV agents. Part 3: Litseaverticillols A-H, novel sesquiterpenes from Litsea verticillata

Bioassay directed-fractionation led to the identification of litseaverticillols A-H (1-8) from the leaves and twigs of Litsea verticillata Hance. These new sesquiterpenes possess a unique skeleton that was recently designated as ‘litseane’. The structures of these compounds were determined by spectroscopic means including 1D and 2D NMR data. Structural configurations were determined by ROESY experiments. Mosher ester reactions and optical rotation measurements established the sesquiterpenes 1-8 as racemates. Isolates 1-8 inhibited HIV-1 replication in HOG.R5 cells with IC₅₀ values ranging from 2 to 15 μg/ml (8-58 μM) while affecting the growth of HOG.R5 at concentrations 2-3-fold higher. Based on this data, structure-activity relationships can be discerned, suggesting compounds of this class are good candidates for analog production.     

A Perturbation Approach to Vector Optimization Problems: Lagrange and Fenchel–Lagrange Duality

Journal of Optimization Theory and Applications - In this paper, we study a general minimization vector problem which is expressed in terms of a perturbation mapping defined on a product of locally...