Effect of rotation in generalized thermoelastic solid under the influence of gravity with an overlying infinite thermoelastic fluid

The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress,and temperature distribution are first obtained in Laplace and Fourier domains by applying integral transforms,and then obtained in the physical domain by applying a numerical inversion method.Some particular cases are also discussed in the context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.

DYNAMICAL BEHAVIOR OF AN INNOVATION DIFFUSION MODEL WITH INTRA-SPECIFIC COMPETITION BETWEEN COMPETING ADOPTERS

In this paper,we proposed an innovation diffusion model with three compartments to investigate the diffusion of an innovation(product)in a particular region.The model exhibits two equilibria,namely,the adopter-free and an interior equilibrium.The existence and local stability of the adopter-free and interior equilibria are explored in terms of the effective Basic Influence Number(BIN)R_(A).It is investigated that the adopter free steady-state is stable if R_(A)<1.By consideringτ(the adoption experience of the adopters)as the bifurcation parameter,we have been able to obtain the critical value ofτresponsible for the periodic solutions due to Hopf bifurcation.The direction and stability analysis of bifurcating periodic solutions has been performed by using the arguments of normal form theory and the center manifold theorem.Exhaustive numerical simulations in the support of analytical results have been presented.

STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL

In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period （time delay, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.

Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients

In this paper, the variable-coefficient diffusion-advection （DA） equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended （Gl/G）-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.

Group Action on Fuzzy Modules

In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of a fuzzy prime submodule, fuzzy prime G-submodule, fuzzy semi prime submodule, fuzzy G-semi prime submodule, G-invariant fuzzy submodule and G-invariant fuzzy prime submodule of M are introduced and their properties are described. The homomorphic image and pre-image of fuzzy G-submodules, G-invariant fuzzy submodules and G-invariant fuzzy prime submodules of M are also established.

Modified(G'/G)-expansion method for finding traveling wave solutions of the coupled Benjamin-Bona-Mahony-KdV equation

Using the Lie symmetry approach,the author has examined traveling wave solutions of coupled Benjamin-Bona-Mahony-KdV equation.The coupled Benjamin-Bona-Mahony-KdV equation is reduced to nonlinear ordinary differential equations for all optimal subalgebras by using Lie classical symmetries and various solutions are obtained by the modified(G'/G)-expansion method.Further,with the aid of solutions of the nonlinear ordinary differential equations,more explicit traveling wave solutions of the coupled Benjamin-Bona-Mahony-KdV equation are found out.The traveling wave solutions are expressed by rational function.

Optimal Eighth Order Convergent Iteration Scheme Based on Lagrange Interpolation

In this paper, based on fourth order Ostrowski method, we derive an optimal eighth order iteration scheme for obtaining simple roots of nonlinear equations using Lagrange interpolation and suitable weight functions. The scheme requires three evaluations of the function and one evaluation of the first derivative per iteration. Numerical examples are included to confirm the theoretical results and to show the competitive performance of the proposed iteration scheme.