MATHEMATICAL SCIENCES
Year:2011 | Volume:5 | Issue:2|Papers Count:8

Mathematical modeling of Tornado paved the way in understanding the cause [1], basic structure [2], and the dynamical behavior aspect [3] of the Tornado in the present model. Modeling in Tornado have been basically focused onto estimating the flow parameters such as velocity [radial, Azimuthal, and axial] and pressure across the rotational axis so that, one can estimate the speed with which Tornado is moving and amount of pressure it can induce onto the structure. Studies from mathematical aspects have been incorporated to include nonlinear aspect of the flow phenomena in the Tornado and studying rotational velocity and radial velocity aspect [4].

In this paper an analytical solution is presented to solve Darcy-Brinkman equation for fully developed forced convection in a porous channel surrounded by two isoflux parallel plates, using homotopy perturbation method (HPM). The results show an excellent agreement between HPM and exact solution of the equation in various values of key parameters.

The present investigation is concerned with two problems. (i) Reflection and transmission of thermoelastic waves between two thermoelastic half-spaces with two temperature at an imperfect interface; and (ii) Propagation of Rayleigh waves at the free surface of thermoelastic solid with two temperature. In problem (i) the amplitude ratios for reflection and transmission coefficients are obtained and deduced for normal force stiffness, transverse force stiffness, thermal contact con-ductance and perfect bonding. The numerical results obtained have been illustrated graphically to understand the behavior of amplitude ratios versus angle of incidence of longitudinal wave (P-wave), thermal wave (T-wave) and SV-wave. It is found that the amplitude ratios of various reflected and transmitted waves are affected by the sti ness and two temperature effects. In problem (ii) the phase velocity and attenuation coefficient are obtained and presented graphically to depict the effect of two temperatures. Some special cases of interest have been deduced from the two problems also.

The collocation methods based on cubic B-spline, are developed to approximate solution of the second and first kind Fredholm integral equations. First we collocate the solution by B-spline and the Newton-Cotes formula is used to approximate integral. Convergence analysis has been investigated and proved that the quadratur rule is fourth order convergent. The presented methods are tested to the problem, and the absolute error in the solution are compared with existing methods [1, 2, 7, 10] to verify the accuracy and convergent nature of proposed methods.

According to the main result of W. Feit and G. M. Seitz (see, Illinois J. Math.33 (1), 103-131, 1988), the sporadic Mathieu M11, M12, Mc Laughlin (MC L) and Higman-Sims (HS) groups are unmatured. In this paper, all the dominant classes and Q- conjugacy characters for the above groups are derived.

In this paper, an application of homotopy perturbation method is applied to finding the solutions of a generalized fifth order KdV (gfKdV) equation. Then we obtain the exact solitary-wave solutions and numerical solutions of the gfKdV equation for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the gfKdV equation.

In this article, a class of solitary wave solutions of the coupled KdV equations by using the homotopy analysis method (HAM). The results obtained by this method have a good agreement with the exact ones. Numerical simulations indicate that the HAM is still valid and effective for solving the nonlinear coupled differential equations.

In this paper I will determine all of the JS - maximal soluble subgroups of the groups GL (18; pk), GL (20; pk), and GL (21; pk). It turns out that the number of types of the JS - maximal soluble subgroups in the groups GL (18; pk), GL (20; pk), and GL (21; pk) are 21, 20 and 10 respectively. Furthermore, we find the structure of these subgroups.