Higher‐order generalized invexity in variational problems

We introduce higher‐order duality (Mangasarian type and Mond–Wier type) of variational problems. Under higher‐order generalized invexity assumptions on functions that compose the primal problem, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for this pair of problems. Also, we establish many examples and counter‐examples to support our investigation. Copyright © 2012 John Wiley & Sons, Ltd.     

Tunable magnetic interaction at the atomic scale in oxide heterostructures

We report on a systematic study of a number of structurally identical but chemically distinct transition metal oxides in order to determine how the material-specific properties such as the composition and the strain affect the properties at the interface of heterostructures. Our study considers a series of structures containing two layers of ferromagnetic SrRuO?, with antiferromagnetic insulating manganites sandwiched in between. The results demonstrate how to control the strength and relative orientation of interfacial ferromagnetism in correlated electron materials by means of valence state variation and substrate-induced strain, respectively.     

Third order duality in nonlinear programming problems

Third order dual of a primal nonlinear programming problem is established which involves the third order derivatives of the functions constituting the primal problem. Desired duality theorems are provided for the pair of primal and the corresponding third order dual problem. Numerical examples are illustrated to justify the efficiency of the proposed method. It is also observed that some of the existing results are obtained as special cases.     

Anisotropic pinned/biased magnetization in SrRuO3/SrMnO3 superlattices

The exchange coupling at the interfaces of magnetic superlattices consisting of ferromagnetic SrRuO3 and antiferromagnetic SrMnO3 grown on (001) oriented SrTiO3 is studied with in-plane and out-of-plane orientations of the cooling magnetic field, with respect to the substrate plane. The magnetization of the in-plane, field cooled hysteresis loop is lower than the corresponding in-plane zero-field-cooled hysteresis loop. The out-of-plane field cooled hysteresis loop is shifted, from the origin, along the graphical magnetization axis. We attribute this irreversible rotation of the moment to the pinning/biasing of spin in the SrRuO3 layer in the vicinity of interfaces by the antiferromagnetic SrMnO3 layer.     

Effect of temperature on pseudoternary system Tween-80-butanol-hexane-water

Novel periodic mesostructured organometallic silicas of MCM-41 type bearing homogeneously distributed bis(8-quinolinolato)dioxomolybdenum(VI) inside the channel walls (denoted as MoO(2)Q(2)@PMO-x) are synthesized via a convenient one-pot method and examined as catalysts in the epoxidation of cyclooctene. The ordered mesoporous structures as well as the organometallic groups incorporated into the framework are fully determined by comprehensive characterization techniques such as XRD, TEM, N(2) adsorption/desorption, SEM, FT-IR, UV-vis spectroscopy, solid-state NMR, ICP-AES, XPS and TG/DSC. MoO(2)Q(2)@PMO-6% catalyst exhibits higher activity for the epoxidation of cyclooctene with tert-butyl hydroperoxide than other MoO(2)Q(2)@PMO materials and its homogeneous or randomly grafted analogue.     

Temperature-induced phase separation in pseudoternary mixtures of Triton X-100–butanol–kerosene–water

The transparent Winsor IV domain in the phase diagram of the mixtures of emulsifier (Triton X-100 and butanol), oil (kerosene), and water is found to be 34% of the total phase diagram in presence of emulsifier with surfactant:cosurfactant::1:1, and is water dominant. Increase in cosurfactant/surfactant ratio inverts the Winsor IV domain to become oil rich. The plot of conductance of the microemulsions prepared by substituting water by brine against water content depicts the existence of three distinct phases like oil-in-water, bicontinuous, and water-in-oil microemulsion in the phase diagram. The phase contrast micrographs of the mixtures of different compositions in these three different phases reveal the existence of microdroplets of oil dispersed in water and water dispersed in oil. Further, the dynamic light scattering studies of these solutions reveal an inhomogeneity in the size distribution of the droplets. A temperature-induced clouding in the microemulsion domain leading to phase separation has been observed. Additives like glucose, sucrose, and sodium chloride decrease the cloud point (CP), while addition of ammonium thiocyanate increases it. A quantitative relationship of the clouding temperature with the composition of the microemulsion has been established. With increase in oil and emulsifier, the cloud point of the microemulsion increases. The separated phases after the clouding have been used for preconcentration of water-soluble metal ions as well as oil-soluble dyes. The turbid systems on heating led to separation into three isotropic phases which are found to be stable at ambient temperature. The stability of these phases is ascribed to the formation of stable microemulsions by mass transfer from one phase to other.