Volume 15 – Issue 1

In this study we present the analysis of Adomian Decomposition Method using He’s Polynomials for nonlinear WhithamBroer-Kaup equations dealing with propagation of shallow water waves with different dispersion relations. The exact solutions of two variants of WhithamBroer-Kaup equations are studied. The suggested method is used without discretization, linearization or restrictive assumptions. Numerical results show that the proposed method was efficient and capable to obtain the exact solution of this set of wave equations. The obtained solutions of these equations could straightforwardly show some facts of the described process deeply such as the propagation. It is clear that this method can be easily extended to other nonlinear wave equations arising in mathematical physics.

In this paper we show that the two sided estimate of 𝑒𝑥 − (1 + 𝑥⁄𝑡)𝑡, stated in [1, Theorem 1], must be reversed for 𝑡 > 0 and 0 < 𝑥 < 1. This modification of Theorem 1 in [1] led us to revisit the short proof given in [1] and improve the condition (𝑡 > (1 − 𝑥)⁄2) for an inequality bounding 𝑒𝑥 − (1 + 𝑥⁄𝑡)𝑡 , established in [2].

In this paper, we use cubic polynomial, Viet’s theorem and equation transformations to achieve some new identities and inequalities on triangles. To fix notations, suppose we are given a triangle ABC with sidelengh a, b, c. Denote the center and radius of the circumcircle by O, R, the center and radius of incircle by I, r, the area of triange ABC by S, the semiperimeter as P, the radii of the excircles as r_1, r_2, r_3, and the altitudes from sides a, b, c respectively, as ha, hb, hc and l_a, l_b, l_c are the lengths of bisector of triangle ABC; m-a, m_b, m_c are the lengths of median line of triangle ABC.

In this paper, a new mathematical technique Differential Transform Method (DTM) is presented for solving variants of nonlinear Klein-Gordon equation. The Differential Transform Method (DTM) provides an effective tool to solve analytically partial differential equations. The method is demonstrated by several examples. The obtained results indicate that this method to be very effective and simple. The method can easily be applied to many problems and is capable of reducing the size of computational work

In this study, we determine criteria of being integral curve for the geodesic spray of the natural lift curves of the spherical indicatrices of a given spacelike curve on the tangent bundle and in Minkowski 4-space.

The main objective of this paper is to study the continuous fractional generalized Hankel-Clifford transformation and continuous fractional generalized HankelClifford wavelet transformation and some of their basic properties. Graphical representations for continuous fractional generalized Hankel-Clifford transformations have been demonstrated for some values. Applications to the continuous fractional generalized HankelClifford transformation in solving generalized nth order linear non-homogeneous ordinary differential equations are given. The continuous fractional generalized Hankel-Clifford transformation wavelet transformation, its inversion formula and Parseval’s are also studied.

The phenomenon of aging and overaging of Pb-Cd-Bi-Sn alloys is characterized by a discontinuous processing and a continuous reaction, it’s hardening and softening. The presence of tin slows kinetics of hardening transformation and increases the hardness. Our study is devoted to determine precipitation type, nature and phase morphology of precipitates and the intensity of hardening in the quaternary alloys Pb-Cd-Bi-Sn. The return to equilibrium of supersaturated alloys Pb-Cd-Sn-Bi has been studied by different techniques: hardness, optical microscopy and X-ray diffraction. Two structural states were considered: raw casting alloy and rehomogenized alloy. The studied alloys are: Pb2% Cd1% Bi, Pb 2% Cd2% Bi, Pb 2% Cd3% Bi with different percentages of tin 0.25% Sn, 0.5% Sn, 1.25% Sn and 2% Sn. Experimental temperatures are 20 °C and 80 °C. Bismuth accelerates the hardening reaction, while tin has a retarding effect on the hardening process.

The objective of this study is to find numerical solution of unsteady magnetohydrodynamic free convective flow of viscous incompressible and electrically conducting fluids past an infinite vertical porous plate in the presence of constant suction and heat source/sink has been made. The problem is governed by coupled non – linear partial differential equations. Dimensionless equations of the problem have been solved numerically by finite element method. The effects of flow parameters, viz. thermal Grashof number, Hartmann number, Prandtl number, Heat source/sink parameter and Eckert number on velocity and temperature fields are investigated through graphs. Skin – friction and Rate of heat transfer coefficients are derived, discussed numerically and presented in tabular forms

In this research paper, the numerical solutions are carried out for the combined effects of Soret and Dufour on unsteady hydromagnetic free convective flow of a Newtonian, viscous, electrically conducting fluid on a continuously vertical permeable surface in the presence of heat source, a first – order homogeneous chemical reaction and the mass flux are reported. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this investigation are solved numerically by finite difference method using symbolic software MATLAB. Graphical results for velocity, temperature and concentration profiles of both phases based on the numerical solutions are presented and discussed.