Applied Mathematics

In this work a new integral transform, namely Tarig transform was applied to solve linear system of partial differential equations with constant coefficients. We derive the formulate for Tarig transform of partial derivatives and apply them to solve initial value problems. Our purpose here is to show the applicability of this interesting new transform and its effecting to solve such problems.

Minimum weight spanning tree is a well known graph optimization problem, which has a wide range of applications in telecommunications and routing problems. The problem considered in this paper is to find the second minimum weight spanning tree for a given network. A new algorithm is proposed and its computational complexity is discussed with numerical illustrations.

The numerical solution of the transport equation was utilized to study the transport phenomena. The currents and transport coefficients such as, the diffusivity, the electrical conductivity, the thermal conductivity and Wiedemmann-Franz Law in addition of investigating the Einstein relation which calculated from the equations (23-25) and (27-37) respectively at 300oK for values E/N=(0.5,1,2,3,4,5)×10-16 V.cm2 and (1,2,4,6,8,10)×10-18 V.cm2 for nitrogen and argon gases respectively. The results reveals to the agreement with the publisher lectures.

In this article, wave propagation in non-homogenous transversely isotropic electro-magneto-elastic plate of polygonal cross-section is studied using the Fourier expansion collocation method. The frequency equations are obtained from the polygonal cross-sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary along the surface of the plate directly. Hence, the Fourier expansion collocation method is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method applicable for complex roots. The computed non-dimensional frequencies are plotted in the form of dispersion curves and their characteristics are discussed. This problem may be extended to any kinds of cross-sections using the proper geometrical relations.

In practical problems involving flow past a porous lining, it is necessary to involve directly the thickness of the porous lining to have an increase in the mass flow rate. The peristaltic pumping of a Newtonian fluid in an inclined channel lined with porous material is investigated under long wavelength and low Reynolds number assumptions. The velocity distribution, the volume flow rate, the pressure rise and the frictional force are obtained. The effect of thickness of porous lining on the peristaltic pumping is discussed.

This paper deals with an analysis of rotation effects on unsteady free convective flow past an impulsively started vertical plate with variable mass diffusion in the presence of transversely applied uniform magnetic field. The problem is solved analytically using the Laplace Transform technique. A selected set of graphical results illustrating the effects of various parameters involved in the problem are presented and discussed. The numerical values of skin-friction have been tabulated.

This paper analyzes the vibration of non-homogeneous transversely isotropic electro-magneto-elastic plate of arbitrary cross-section using the Fourier expansion collocation method. The frequency equations are derived for the arbitrary cross-sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary along the surface of the plate directly. Hence, the Fourier expansion collocation method is applied along the boundary to satisfy the boundary conditions. The secant method is applied to determine the roots of the frequency equation. The non-dimensional frequencies are computed numerically and are plotted in the form of dispersion curves and further their characteristics are discussed. This problem may be extended to any kinds of cross-sections using the proper geometrical relations.

Correlation measure is an important tool in the field of fuzzy, rough and neutrosophic environments. The main aim of this paper is to introduce the correlation measure for rough neutrosophic refined sets. This concept is the extension of correlation measure of neutrosophic sets and intuitionistic fuzzy multi sets. Finally, using the correlation of rough neutrosophic refined set measure, the application of medical diagnosis and pattern recognition are presented.

The solid transportation problem (STP) arises when bounds are given on three item properties. The fuzzy solid transportation problem (FSTP) appears when the nature of the data problem is fuzzy. This paper deals with the robust fuzzy solid transportation problem based on extension principle under uncertain demands. The fuzzy solid transportation problem is transformed into a pair of mathematical programs that is employed to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level . In this paper, we are interested in a robust version of location fuzzy transportation problem with an uncertain demand using a 2-stage formulation: one with inequality constraints and the other with equality constraints.

The aim of this paper is to establish a fixed point theorem for non-self mappings by using the Meir and Keeler (£, delta) type contraction condition. Our result generalizes completely or partially the result due to Meir and Keeler [5], Rhoades [10] and others.