Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints

2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.In this paper, we establish necessary optimality conditions and sufficient optimality conditions for D.C. vector optimization problems under D.C. constraints. Under additional conditions, some results of [9] and [15] are also recovered

Calculus of Tangent Sets and Derivatives of Set Valued Maps under Metric Subregularity Conditions

In this paper we intend to give some calculus rules for tangent sets in the sense of Bouligand and Ursescu, as well as for corresponding derivatives of set-valued maps. Both first and second order objects are envisaged and the assumptions we impose in order to get the calculus are in terms of metric subregularity of the assembly of the initial data. This approach is different from those used in alternative recent papers in literature and allows us to avoid compactness conditions. A special attention is paid for the case of perturbation set-valued maps which appear naturally in optimization problems.Comment: 17 page

Mg-modified Zn-Co-Fe-La nano ferrites: a study of structural, morphological, vibrational, electro-optical, dielectric and magnetic evolution

The series of Zn0.4Co0.6−xMgxFe1.9La0.1O4 (x = 0.0, 0.15, 0.30, 0.45, 0.6) nanoferrites prepared via co-precipitation technique. Scherrer and Williamson-Hall (W-H) methods were used to find the crystallite size (29.6–39.2 nm and 31.6–36.3 nm, respectively) and lattice constant was calculated (8.406–8.395 Å). Moreover, Fourier transform infrared (FTIR) spectroscopy revealed the existence of absorption bands along with functional groups. The vibrations of O2- ions at the tetrahedral and octahedral sites were shown by the Raman five active modes. DC resistivity reduced in the range of 5.2961 × 108 Ω cm to 9.6453 × 107 Ω cm for x = 0.0 to x = 0.6, respectively. The maximum DC resistivity and activation energy (0.1035 eV) were obtained at the parent sample (Zn0.4Co0.6Fe1.9La0.1O4). The optical bandgaps reduced from 2.61 to 1.47 eV, as the Mg2+ contents increased. With increasing frequency the dielectric loss and the dielectric constant decrease. The magnetic parameters such as saturation magnetization (Ms = 60.82–25.94 emu/g), remnant magnetization (Mr = 47.82–18.64 emu/g), and coercivity (Hc = 1334–511 Oe) demonstrated reducing trends with the increase of Mg2+ doping. The best magnetic behavior of the as-prepared samples suitable in microwave devices was observed for Zn0.4Co0.6Fe1.9La0.1O4 sample

Necessary optimality conditions for a set valued fractional programming problem in terms of contingent epiderivatives

In this paper, we are concerned with a multi-objective fractional extremal programming problem. Using the concept of subdifferential of cone-convex set valued mappings, introduced by Baier and Jahn (1999), together with the convex separation principle, we give necessary optimality conditions. An example illustrating the usefulness of our results is also provided

SUFFICIENT SECOND ORDER OPTIMALITY CONDITIONS FOR C 1 MULTIOBJECTIVE OPTIMIZATION PROBLEMS

Abstract. In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C 1, but not necessarily of class C 1.1

Combined photocatalytic degradation of pollutants and inactivation of waterborne pathogens using solar light active α/β-Bi2O3

A solar light active composite of α/β-Bi2O3 was synthesized using a chemical-free solid-state reduction method. The obtained composite was characterized by X-ray diffraction, UV–vis spectroscopy, field emission scanning electron microscopy, and zeta potential. Initially, to validate the photocatalytic effectiveness, the obtained α/β-Bi2O3 composite was used to degrade indigo carmine dye. Then, the inactivation of E. coli and S. aureus waterborne pathogens was performed on solid and in liquid media. On solid agar media, a significant inhibition zone was observed for both bacterial strains. Similarly, in liquid culture, these strains E. coli and S. aureus were reduced from 1 × 106 CFU/mL to a few CFU/mL, after 240 min of photocatalytic exposure. Furthermore, mixed wastewater of indigo carmine and E. coli/S. aureus were tested to study the combined photocatalytic mechanism against the organic dye and microorganisms. Overall, the obtained results suggested the efficacy of α/β-Bi2O3 towards visible light inactivation of bacteria even in combination with other pollutants, highlighting the great potential of the advanced photocatalytic process for combined treatment of organic pollutants and pathogens