X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Determination of mimosine by a sensitive indirect spectrophotometric method

A simple and sensitive indirect spectrophotometric method is described for the determination of mimosine based on its reaction with diazotized sulfanilamide (DZSAM). DZSAM couples with N-(1-naphthyl)ethylenediamine (NEDA) forming a pink colored azodye, absorbing maximally at 540 nm (ε_max=27 mM⁻¹ cm⁻¹). In the present method, mimosine was first reacted with known excess of DZSAM and the unreacted DZSAM was determined by coupling with NEDA. The reaction of mimosine with DZSAM proceeded optimally at neutral pH. The decrease in absorbance of the DZSAM-NEDA-coupled product obeyed Beer’s law in the concentration range of 0.005-0.15 μg ml⁻¹ of mimosine. The present method was applied to estimate mimosine in plant extracts containing lesser than 0.05 μg ml⁻¹ with recovery at 99±0.41%. The method described is superior to other reported methods in terms of ease of adaptability and sensitivity.     

Thermal and photochemical Wallach rearrangement of azoxybenzene in zeolite cages

Acidic zeolites HY and CaY catalyse the Wallach rearrangement of azoxybenzene (I) leading mainly to the formation of para-hydroxyazobenzene (II) and ortho-hydroxyazobenzene (III). In this transformation, increasing the loading level of I results in the formation of a larger amount of para-isomer. As observed in isotropic media, photochemical Wallach rearrangement in the presence of various cation-exchanged faujasites results in the predominant formation of the ortho-isomer from the S₁ state and this rules out any appreciable heavy atom effect.     

Thermodynamic parameters of N-(p-n-alkoxybenzylidene)-p-n-(butyloxyanilines), (nO.O4) liquid crystal compounds — A dilatometric study

Different thermodynamic parameters are estimated from volume expansion coefficient, α for a number of N-(p-n-alkoxybenzylidene)-p-n-butyloxyanilines, nO.O4 compounds in isotropic phase (at T_IN + 5 °C) and in liquid crystalline phases. The variation of different thermodynamic parameters with the alkoxy chain length in nO.O4 series and their variation with the temperature in individual liquid crystal compounds are discussed. The parameters like available volume (V_a), inter molecular free length (L_f) and molecular radius (M_r) are also computed from density, and refractive index for these nO.O4 compounds and the nature of molecular free length and molecular radius are analyzed and discussed.     

Levitin–Polyak well-posedness for constrained quasiconvex vector optimization problems

In this paper, a notion of Levitin–Polyak (LP in short) well-posedness is introduced for a vector optimization problem in terms of minimizing sequences and efficient solutions. Sufficient conditions for the LP well-posedness are studied under the assumptions of compactness of the feasible set, closedness of the set of minimal solutions and continuity of the objective function. The continuity assumption is then weakened to cone lower semicontinuity for vector-valued functions. A notion of LP minimizing sequence of sets is studied to establish another set of sufficient conditions for the LP well-posedness of the vector problem. For a quasiconvex vector optimization problem, sufficient conditions are obtained by weakening the compactness of the feasible set to a certain level-boundedness condition. This in turn leads to the equivalence of LP well-posedness and compactness of the set of efficient solutions. Some characterizations of LP well-posedness are given in terms of the upper Hausdorff convergence of the sequence of sets of approximate efficient solutions and the upper semicontinuity of an approximate efficient map by assuming the compactness of the set of efficient solutions, even when the objective function is not necessarily quasiconvex. Finally, a characterization of LP well-posedness in terms of the closedness of the approximate efficient map is provided by assuming the compactness of the feasible set.     

Stability for Properly Quasiconvex Vector Optimization Problem

The aim of this paper is to study the stability aspects of various types of solution set of a vector optimization problem both in the given space and in its image space by perturbing the objective function and the feasible set. The Kuratowski?CPainlevé set-convergence of the sets of minimal, weak minimal and Henig proper minimal points of the perturbed problems to the corresponding minimal set of the original problem is established assuming the objective functions to be (strictly) properly quasi cone-convex.     

Stability of Parametric Quasivariational Inequality of the Minty Type

In this paper, stability of a parametric quasivariational inequality of the Minty type is studied via various sufficient conditions characterizing upper and lower semicontinuity of the solution sets as well as the approximate solution sets. Sufficient conditions ensuring upper semicontinuity of the approximate solution sets of an optimization problem with quasivariational inequality constraints are also presented.     

Approximate solutions and scalarization in set-valued optimization

Abstract

Certain notions of approximate weak efficient solutions are considered for a set-valued optimization problem based on vector and set criteria approaches. For approximate solutions based on the vector approach, a characterization is provided in terms of an extended Gerstewitz’s function. For the set approach case, two notions of approximate weak efficient solutions are introduced using a lower and an upper quasi order relations for sets and further compactness and stability aspects are discussed for these approximate solutions. Existence and scalarization using a generalized Gerstewitz’s function are also established for approximate solutions, based on the lower set order relation.