Common coupled fixed point theorems in cone metric spaces for w-compatible mappings

In this paper we introduce the concept of a w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non-empty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well known comparable results in the literature. Results are supported by three examples.     

Bending of thick functionally graded plates resting on Winkler–Pasternak elastic foundations

The static response of simply supported functionally graded plates (FGP) subjected to a transverse uniform load (UL) or a sinusoidally distributed load (SL) and resting on an elastic foundation is examined by using a new hyperbolic displacement model. The present theory exactly satisfies the stress boundary conditions on the top and bottom surfaces of the plate. No transverse shear correction factors are needed, because a correct representation of the transverse shear strain is given. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second parameter is zero. The equilibrium equations of a functionally graded plate are given based on the hyperbolic shear deformation theory of plates presented. The effects of stiffness and gradient index of the foundation on the mechanical responses of the plates are discussed. It is established that the elastic foundations significantly affect the mechanical behavior of thick functionally graded plates. The numerical results presented in the paper can serve as benchmarks for future analyses of thick functionally graded plates on elastic foundations.     

Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order

In this paper we investigate the existence of solutions for a class of initial value problems for impulsive partial hyperbolic differential equations involving the Caputo fractional derivative by using the lower and upper solutions method combined with Schauder’s fixed point theorem.     

Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field

Based on nonlocal theory of thermal elasticity mechanics, an elastic multiple column model is developed for column buckling of MWNTs with large aspect ratios under axial compression coupling with temperature change. The present model treats each of the nested tubes as an individual column interacting with adjacent nanotubes through the intertube van der Waals forces. The thermal effect is incorporated in the formulation. In particular, an explicit expression is derived for the critical axial strain of a double-walled carbon nanotube which clearly demonstrates that small scale effects contribute significantly to the thermo-mechanical behavior of multiwalled carbon nanotubes and cannot be ignored.     

A linear programming approach to test efficiency in multi-objective linear fractional programming problems

In a multi-objective linear fractional programming problem (MOLFPP), it is often useful to check the efficiency of a given feasible solution, and if the solution is efficient, it is useful to check strong or weak efficiency. In this paper, by applying a geometrical interpretation, a linear programming approach is achieved to test weak efficiency. Also, in order to test strong efficiency for a given weakly efficient point, a linear programming approach is constructed.     

Multiproduct single-machine production system with stochastic scrapped production rate, partial backordering and service level constraint

In this paper, a multiproduct single-machine production system under economic production quantity (EPQ) model is studied in which the existence of only one machine causes a limited production capacity for the common cycle length of all products, the production defective rates are random variables, shortages are allowed and take a combination of backorder and lost sale, and there is a service rate constraint for the company. The aim of this research is to determine the optimal production quantity, the allowable shortage level, and the period length of each product such that the expected total cost, including holding, shortage, production, setup and defective items costs, is minimized. The mathematical model of the problem is derived for which the objective function is proved to be convex. Then, a derivative approach is utilized to obtain the optimal solution. Finally, two numerical examples in each of which a sensitivity analysis is performed on the model parameters, are provided to illustrate the practical usage of the proposed methodology.     

A new one-step iterative scheme for approximating common fixed points of two multivalued nonexpansive mappings

In this paper, we introduce a new one-step iterative process to approximate the common fixed points of two multivalued nonexpansive mappings. We will also prove a strong convergence theorem in a uniformly convex Banach space under the multivalued version of so-called Condition (A′).     

A numerical study of micropolar flow inside a lid-driven triangular enclosure

A study is carried out to analyze the mixed convection flow and heat transfer inside a lid-driven triangular conduit under the effects of micro-gyration boundary conditions. The micropolar constitutive equation characterizes the fluid inside the cavity. The lower boundary is at a uniform temperature and sliding in its plane with constant velocity u₀, while the inclined walls are cold. Dual cases are considered here, namely the intense concentration (d) and the weak concentration of microelements (\(m = 0.5\)). The governing nonlinear equations are simulated employing the Galerkin finite element method, where the pressure term is handled via the Penalty approach. Using the numerical data, graphical results are produced to illustrate the effects of physical parameters. Specifically, this refers to the effects of the Grashof number (Gr), Prandtl number (Pr), Reynolds number (Re) and vortex viscosity parameter (K) on the streamlines, mid-section velocity profiles, temperature contours, and local and average Nusselt numbers on the cold and heated boundaries of the conduit. Particular emphasis is given on the identification of the set of parameters for which simultaneous symmetry in streamlines and isotherms prevails. The grid independence test is also performed by comparing the average Nusselt numbers (on the hot and cold boundaries of the conduit) for various mesh sizes, and the optimal solution is found. Moreover, the results are also benchmarked with the previously published data.     

Electrochemical Sensing of Ascorbic Acid,Hydrogen Peroxide and Glucose by Bimetallic (Fe,Ni)−CNTs Composite Modified Electrode

In this research, bimetallic supported CNT modified electrode ( Fe,Ni/CNTs/GCE) has been developed for sensitive, stable and highly elctroactive sensing of glucose, ascorbic acid and hydrogen peroxide. Transition metals such as Iron (Fe) and Nickel (Ni) offer high electrical and thermal conductance, high active surface‐to‐volume ratio and presence of d‐band electrons gives enhanced electrocatalytic behavior. While, CNTs provide high surface area, stability and excellent conductivity. Synthesized material is characterized by SEM, EDS, XRD and FTIR to access morphology, elemental composition and structure. This unique combination is employed for the electrochemical sensing of ascorbic acid, glucose and hydrogen peroxide and different experimental parameters are optimized. Fe,Ni/CNTs/GCE shows good sensing efficiency at pH 7.4 which is ideally suitable for variety of analytes. The modified electrode also show good reproducibility and sensitivity under optimized conditions and can be reused upto 30 cycles without compromising the efficiency. With good linearity, reproducibility and limit of detection, this material possess significant potential as non‐enzymatic biosensor for variety of analytes.