Fuzzy delay differential equations

In this paper, we prove a local existence and uniqueness result for fuzzy delay differential equations driven by Liu process. We also establish continuous dependence of solution with respect to initial data.     

Fixed point, approximate fixed point and Kantorovich-Rubinstein maximum principle in convex metric spaces

We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and asymptotically nonexpansive maps defined on a closed bounded convex subset of a uniformly convex complete metric space and study the structure of the set of fixed points. We construct Mann type iterative sequences in convex metric space and study its convergence. As a consequence of fixed point results, we prove best approximation results. We also prove Kantorovich-Rubinstein maximum principle in convex metric spaces.     

Spectrophotometric and spectrofluorimetric investigation of different equilibria of a recently synthesized Schiff base with the aid of chemometric methods

In this study ground and excited states acidic dissociation constants of a recently synthesized Schiff base was obtained in a DMF:water mixture of 30:70 (v/v) using absorption and fluorescent spectra of the Schiff base in different pH values with the aid of chemometric methods. In addition, the fluorescent of the two kinds of tautomers of this Schiff base was investigated and the rate of tautomerization was obtained using rank annihilation factor analysis (RAFA). The effect of different kinds of surfactants such as sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB) and Triton X-100 on fluorescence spectrum of the Schiff base in a DMF:water mixture of 2:98 (v/v) was investigated. CTAB increased the fluorescence intensity of the Schiff base while SDS and Triton X-100 had no significant effect on it. β-Cyclodextrin increased the fluorescence intensity of the Schiff base. Also the sensing behavior of this Schiff base toward metal ions was studied in DMF and ethanol by fluorescence spectroscopy. The Schiff base showed prominent fluorescent signal in the presence of Zn²⁺, whereas other metal ions failed to induce response and ground-state dissociation constant of the complex was determined by direct fluorimetric titration as a function of Zn²⁺ concentration.     

Pexider type operators and their norms in <Emphasis Type="Italic">X</Emphasis><Subscript><Emphasis Type="Italic">λ</Emphasis></Subscript> spaces

In this paper, we introduce Pexiderized generalized operators on certain special spaces introduced by Bielecki-Czerwik and investigate their norms.     

Complete analysis of photonic crystal fibers by full-vectorial 2D-FDTD method

In this paper, an extended finite difference time domain (FDTD) algorithm for the full-vectorial analysis of photonic crystal fibers has been derived. For achieving a good convergence and high accuracy, a kind of modified conformal FDTD method has been applied. An anisotropic perfectly matched layer for truncation of boundary conditions has been introduced. Material and chromatic dispersions are numerically investigated for the photonic crystal fibers with different dimensions and geometrical parameters and different dispersion behaviors are exhibited.     

Channel flow of a Maxwell fluid with chemical reaction

This work is concerned with the two-dimensional boundary layer flow of an upper-convected Maxwell (UCM) fluid in a channel with chemical reaction. The walls of the channel are porous. Employing similarity transformations the governing non-linear partial differential equations are reduced into non-linear ordinary differential equations. The resulting ordinary differential equations are solved analytically using homotopy analysis method (HAM). Expressions for series solutions are derived. The convergence of the obtained series solutions are shown explicitly. The effects of Reynold’s number Re, Deborah number De, Schmidt number Sc and chemical reaction parameter γ on the velocity and the concentration fields are shown through graphs and discussed.     

Common fixed point results for noncommuting mappings without continuity in cone metric spaces

The existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions, without appealing to continuity, in a cone metric space is established. These results generalize several well-known comparable results in the literature.