The bipolar decomposition

It is shown that every nonsingular square complex matrix Z   can be factored as Z=e^Le^iTe^iKe^S$Z=e^L{e}^{iT}{e}^{iK}{e}^S$, where S and T are real symmetric matrices, and K and L are real skew-symmetric matrices. New proofs are given for some related decomposition theorems for unitary and positive definite matrices.     

Higher-order cone-pseudoconvex, quasiconvex and other related functions in vector optimization

Recently Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010) introduced higher-order cone-convex functions and used them to obtain higher-order sufficient optimality conditions and duality results for a vector optimization problem over cones. The concepts of higher-order (strongly) cone-pseudoconvex and cone-quasiconvex functions were also defined by Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010). In this paper we introduce the notions of higher-order naturally cone-pseudoconvex, strictly cone-pseudoconvex and weakly cone-quasiconvex functions and study various interrelations between the above mentioned functions. Higher-order sufficient optimality conditions have been established by using these functions. Generalized Mond–Weir type higher-order dual is formulated and various duality results have been established under the conditions of higher-order strongly cone-pseudoconvexity and higher-order cone quasiconvexity.     

Optimality via generalized approximate convexity and quasiefficiency

In this article, we look beyond convexity and introduce the four new classes of functions, namely, approximate pseudoconvex functions of type I and type II and approximate quasiconvex functions of type I and type II. Suitable examples illustrating the non emptiness of the newly defined classes and distinguishing them from the existing classical notions of pseudoconvexity and quasiconvexity are provided. These newly defined concepts are then employed to establish sufficient optimality conditions for the quasi efficient solutions of a vector optimization problem.     

Diversified Synthetic Strategies for Pyrroloindoles: An Overview

In current scenario, heterocyclic compounds' role in medicinal chemistry has been tremendously increased as they possess wide number of pharmacological activities. One of the common heterocycles include indole skeleton with well‐established biological significance in field of medicinal chemistry. Fusion of indole nucleus with pyrrole heterocycle constitutes pyrroloindole scaffold, which further modifies the existing properties of indole alone. Pyrroloindole is a privileged scaffold found in various types of bioactive entities including natural compounds and exhibits wide variety of pharmacological activities like muscle relaxant, antifungal, antitumor, and antibiotic. Therefore, it is considered as attractive template for drug discovery. From several years, numbers of synthetic strategies have been reported for the synthesis of pyrroloindole and its derivatives, including also natural compounds such as amauromine, yuremamine, and chimonanthines. Here, in this review, we have tried to compile various synthetic strategies of pyrroloindole and its derivatives.     

X-ray crystal and molecular structure of cis-dichlorobis[1,2-ethanebis(diphenylphosphineoxide)] iron(III)tetrachloroferrate(III), [FeCl2(L-L)2] [FeCl4]

Reaction of iron(III) chloride with 1,2-ethanebis(diphenylphosphine oxide) in an ethanol/chloroform mixture formed a 11 adduct of stoichiometry FeCl₃(L-L) which has been characterized by X-ray crystallography as [FeCl₂(L-L)₂] [FeCl₄]. The structure was solved by the heavy atom method, using MoK diffractometer data and refined by full-matrix least squares toR=0.044 for 8506 observed reflections. The coordination is slightly distorted octahedral for the cation with acis-arrangement of the chlorine atoms and a seven-membered chelate ring formation by Ph₂P(O)CH₂CH₂P(O)Ph₂ with the donor O atoms also in acis arrangement. The Fe-Cl distances are equal at 2.306(1) Å but the Fe-O distances differ significantly in each of the two ligands, (avg. 2.076(2) Å; avg. 1.975(3) Å).     

Structure and photoelectric behavior of amorphous semiconductors in the system PbSGeSGeS2

A study of the PbS-based vitreous semiconductors: (PbS)_x(GeS)_0.7?x(GeS)_0.3 has been made. The presence of Pb atoms is found to induce structural changes in the network. These semiconductors display chemical ordering which depends upon the relative concentration of the constituent atoms. This property influences the electronic behavior of the semiconductors. For x = 0.23 the composition exhibits different features in its electrical conductivity and photoconductivity, as compared with the other compositions.     

Higher order duality in multiobjective fractional programming with support functions

In this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond-Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases.     

Effect of counterion substitution on the viscosity anomaly in AOT microemulsions

AOT-based water-in-oil microemulsions display an anomalous maximum in the viscosity with X, the water to surfactant ratio. Several explanations for this phenomenon have been offered. In this work, we investigate viscosity and droplet interactions in Ca(AOT)(2)/water/n-decane and KAOT/water/n-decane microemulsions and compare our results with the commonly studied NaAOT/water/oil system. The Ca(AOT)(2) system demonstrates a maximum in relative viscosity and droplet attraction near X=15, similar to the NaAOT system, although the maximum occurs at a higher value of X in the Ca(AOT)(2) system. By contrast, the viscosity and interparticle interactions in the KAOT system do not strongly depend on the amount of water in the system. We attribute the differences in behavior between the two systems to different hydration characteristics of the counterion, and we believe that our results are consistent with a previously proposed model that attributes interdroplet attractions to charge fluctuations and surfactant exchange. Our findings support the connection between the viscosity anomaly and interparticle interactions.     

Nanoparticle-reinforced associative network hydrogels

ABA triblock copolymers in solvents selective for the midblock are known to form associative micellar gels. We have modified the structure and rheology of ABA triblock copolymer gels comprising poly(lactide)-poly(ethylene oxide)-poly(lactide) (PLA-PEO-PLA) through addition of a clay nanoparticle, laponite. Addition of laponite particles resulted in additional junction points in the gel via adsorption of the PEO corona chains onto the clay surfaces. Rheological measurements showed that this strategy led to a significant enhancement of the gel elastic modulus with small amounts of nanoparticles. Further characterization using small-angle X-ray scattering and dynamic light scattering confirmed that nanoparticles increase the intermicellar attraction and result in aggregation of PLA-PEO-PLA micelles.     

Effect of pharmaceuticals on thermoreversible gelation of PEO-PPO-PEO copolymers

Pluronic F127, a triblock copolymer of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO), has generated considerable interest as a drug delivery vehicle due to its ability to gel at physiological temperatures. This work examines the gelation behavior of Pluronic F127 in the presence of a series of hydrophobic pharmaceuticals, to determine whether there is any correlation between gelation and physicochemical parameters of drug solutes. The study includes the local anesthetics dibucaine, lidocaine, and tetracaine; the pharmaceutical additives methyl paraben, ethyl paraben, and propyl paraben; the anti-cancer agents paclitaxel and baccatin III; and the anti-inflammatory agent sulindac. The results indicate that the presence of local anesthetics and pharmaceutical additives allows F127 solutions to form gels at lower copolymer concentrations; local anesthetics and pharmaceutical additives also shift gelation down to a lower gelation temperature. This behavior is strongly dependent on drug solubility; poorly soluble drugs (paclitaxel, baccatin III, sulindac) do not change the lower gelation temperature or minimum F127 concentration for gelation. An equation relating the decrease in gelation temperature to drug solubility is presented, and the equation fits the data well. The results have significant positive implications on the toxicity and economic issues related to use of Pluronic F127 in drug delivery.