On nonlinear programming with support functions

Optimality conditions are derived for a nonliear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various dualityresults are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semidefinite quadratic form or anLp norm. It is pointed out that these special cases can easily be generated from our results.     

Extractive spectrophotometric determination of nitrite in polluted waters

Nitrite is diazotised with p-nitroaniline in hydrochloric acid and coupled with 8-quinolinol in alkaline medium to give a purple azo dye (λ_max = 550 nm, ? = 3.88 × 10⁴ l mol^-1 cm^-1). Extraction of the dye into 3-methyl-1-butanol shifts the absorption maximum to 570 nm and improves the apparent molar absorptivity to 5.852 × 10⁴ l mol^-1 cm^-1. Beer's law is obeyed for 0.01–0.06 ppm nitrite. The Sandell sensitivity is 0.00078 μg cm^-2. The method is applicable to polluted waters.     

Quantitative Relationships Between Molecular Descriptors,Chromatographic Retention Behavior,and In Vitro Antituberculosis Activity of Phytol Derivatives

JPC – Journal of Planar Chromatography – Modern TLC - The lipophilic character of phytol derivatives has been studied using reverse-phase planar chromatographic procedures....     

More Efficient Palladium Catalyst for Hydrogenolysis of Benzyl Groups

Organic halides absorbed without solvent onto sodium phenylsulfinate on alumina (1) gave phenylsulfones (2) under microwave or ultrasound activation.     

Thermodynamic investigations of uranium-rich binary and ternary alloys

Uranium–zirconium, uranium niobium, and uranium–zirconium–niobium alloys were synthesized by the arc melting technique and their phase transition temperatures were determined using a high temperature calorimeter. Heat capacities of U–7 wt%Zr, U–7 wt%Nb, U–5 wt%Zr–2 wt%Nb, U–3.5 wt%Nb–3.5 wt%Zr, and U–2 wt%Zr–5 wt%Nb were measured using a differential scanning calorimeter in the temperature range 303–921 K. A set of self-consistent thermodynamic functions such as entropy, enthalpy, and Gibbs energy function data for these binary and ternary alloys were reported for the first time using heat capacity data obtained in this study and required literature data.     

Influence of magnetic quantization on the effective electron mass in Kane-type semiconductors

Summary We study the effective electron mass at the Fermi level in Kane-type semiconductors on the basis of fourth order in effective mass theory and taking into account the interactions of the conduction electrons, heavy holes, light holes and split-off holes, respectively. The results obtained are then compared to those derived on the basis of the well-known three-band Kane model. It is found, takingn-Hg_1−x Cd _x Te as an example, that the effective electron mass at the Fermi level in accordance with fourth-order model depends on the Fermi energy, magnetic quantum number and the electron spin respectively due to the influence of band nonparabolicity only. The dependence of effective mass on electron spin is due to spin-orbit splitting parameter of the valence band in three-band Kane model and the Fermi energy due to band nonparabolicity in two-band Kane model. The same mass exhibits an oscillatory magnetic-field dependence for all the band models as expected since the origin of oscillations in the effective mass in nonparabolic compounds is the same as that of the Shubnikov-de Hass oscillations. In addition, the corresponding results for parabolic energy bands have been obtained from the generalized expressions under certain limiting conditions.     

Numerical solution of a system of coupled non-linear integro-differential equations of Fredholm type

A method, based on a generalization of Runge-Kutta's method, is applied to a system of coupled integro-differenital equations of Fredholm type. It is shown that, under certain conditions, the related integral, containing an unknown variable, in each integro-differential equation can be approximated by a contraction operator, converging in the respective space concerned. Therefore they may be found by the method of iteration, starting from arbitrary values, and hence the given system may be solved, with a high degree of accuracy.     

Separation of lignosulfonate from its aqueous solution using supported liquid membrane

This paper presents an experimental and theoretical study on facilitated transport of lignosulfonate (LS) through a flat sheet supported liquid membrane using trioctylamine (TOA) as carrier and dichloroethane as diluent. The studies were carried out with various support materials and operating conditions (viz. carrier concentration, strip phase concentration, salt concentration, etc.) and their effects on the transport of LS. The results were analyzed to identify a suitable combination of support and operating condition that would yield best performance of the supported liquid membrane (SLM) in terms of fast and efficient transport of LS. The stability of the SLM was assessed in terms of loss of liquid from the pores of membrane support. The SLM is found to be stable till 10 h. Co-transport mechanism has been adopted in this work by using NaOH as the strip phase. It was observed that extraction of LS is increased with increase in concentration of NaOH up to a limiting value of 0.5 M NaOH. Difference of salt concentration between feed and strip phase considerably affect the separation process. The diffusional resistances of organic membrane (Δorg) and aqueous solution (Δaq) calculated from the permeation model, which is again a combination of three unique mechanisms viz., diffusion through a feed aqueous layer, a fast interfacial chemical reaction, and diffusion of carrier–complex through the organic membrane, are found to be 609.9 and 176.6 s cm⁻¹, respectively. The values of the diffusion coefficient in the membrane (D_org) and in the bulk organic phase (D_complex) are 1.67×10⁻⁹ and 6.68 × 10⁻⁸ m²s⁻¹, respectively. The extraction of LS is about 90%. Nearly 43% of LS can be recovered at optimum condition.