Physicochemical investigations of anionic–nonionic mixed surfactant microemulsions in nonaqueous polar solvents: I. Phase behavior

Phase behaviors of AOT/heptane (Hp)/formamide (FA), ethylene glycol (EG), propylene glycol (PG), triethylene glycol (TEG) and glycerol (GLY) have been investigated in the absence and presence of a nonionic surfactant, polyoxyethylene(2) cetyl ether (Brij-52) at 303 K. The phase characteristics of (AOT+Brij-52)/Hp/(EG or PG or TEG) have been found to be different from that of AOT/Hp/FA systems in respect of both the area of monophasic domain and the appearance of other mesophases. The area of monophasic domain of (AOT+Brij-52)/Hp/EG depends on the content of Brij-52 (X _Brij-52) and shows a maximum at X _Brij-52=0.4. A negligible effect on the area of the monophasic domain has been shown by more hydrophobic surfactants, polyoxyethylene(2) stearyl ether (Brij-72) and polyoxyethylene(2) oleyl ether (Brij-92). The effect of oils (dodecane and hexadecane) on the mixed systems stabilized by (AOT+Brij-52) in EG has been investigated. The area of monophasic domain has been found to be dependent on the type of nonaqueous solvents and follows the order GLY>EG>PG>TG. A systematic investigation on the measurement of phase volumes of mixed surfactant systems [AOT+nonionic surfactant(s)] stabilized in oils of different chain lengths (heptane, dodecane and hexadecane) and polar solvent (EG) has been carried out at different compositions of the ingredients to identify the phase transitions of these systems as a function of X _Brij-52. The threshold point of phase transition (both W I→W IV and W IV→W II transitions) has been found to be a function of the configuration of added nonionic surfactant, nature of the polar solvent and oil. The conversion of the initial oil/EG droplets into EG/oil droplets with increasing X _nonionic has been facilitated for hydrophobic surfactants polyoxyethylene(4) lauryl ether (Brij-30), Brij-52, and Brij-72 in comparison to the hydrophilic surfactants polyoxyethylene(10) cetyl ether (Brij-56) and polyoxyethylene(20) cetyl ether (Brij-58).     

An algorithm for constructing a basis for -spline modules over polynomial rings

Let be a polyhedral complex embedded in the euclidean space and , , denote the set of all -splines on . Then is an -module where is the ring of polynomials in several variables. In this paper we state and prove the existence of an algorithm to write down a free basis for the above -module in terms of obvious linear forms defining common faces of members of . This is done for the case when consists of a finite number of parallelopipeds properly joined amongst themselves along the above linear forms.

     

Determination and correlation of heavy atom positions in the derivatives used in the X-ray analysis of ribonuclease A at 2.5 Å resolution

The analysis of four heavy atom derivatives of ribonuclease A is described leading to isomorphous phasing at 2.5 resolution. Differences in the characteristics of the derivatives are discussed with respect to the determination of their heavy atom parameters and the correlation of sites between derivatives to produce a self consistent set. The criteria used to ensure consistency are described. In the final phase analysis using refined heavy atom parameters the least squaresR factors of the derivatives were .124, .143, .101, and .067 respectively, and the mean figure of merit for the 3444 observed reflexions was 0.66.In recognition of C. H. Carlisle's pioneering work in this field.     

Exact energy eigenvalues for the doubly anharmonic oscillator

The exact energy eigenvalues for the potentialV(r) = 1/2 ² r ² + 1/4r⁴ +1/6 r⁶ and the conditions for their occurrence have been determined.     

Oligopoly models for market price of electricity under demand uncertainty and unit reliability

Several oligopoly models have been proposed for representing strategic behavior in electricity markets, which include Bertrand, Cournot, and Supply Function Equilibrium (SFE). For the most part, these models are deterministic, with the exception of the SFE originally developed by Klemperer and Meyer. However, their model does not include supply side uncertainties. In this paper, we consider both load and supply side uncertainties (resulting from generator availabilities). We obtain Nash equilibrium solutions for Cournot and SFE models, in which asymmetric firms (whose generating units have different costs and capacities) submit their bids so that each firm’s expected profit is maximized.     

Efimov Effect in 2-Neutron Halo Nuclei

We provide a brief overview of our theoretical investigations, carried out in recent years, to study Efimov effect in 2-n halo nuclei. The calculations provide the evidence for the occurrence of at least two Efimov states in ²⁰C. These states disappear one by one as the two-body binding energy is increased and show up as asymmetric resonances in the elastic scattering cross section of n–¹⁹C system. The asymmetric nature of the resonances is explained by invoking the mechanism of Fano resonance.