Applied Mathematics

By using Mawhin continuation theorem and comparison theorem, the sufficient conditions ensuring the existence of exponential periodic attractor and exponential convergence of a class of functional differential equation with time varying delays are established. The results are very different from some previously known results [1,19,28]. Finally, applications and an example are given to illustrate the effectiveness of the results.

An attempt has been made to evaluate the effect of surface roughness and deformation on the performance of a magnetic fluid based squeeze film in rough porous circular plates considering porous matrix of variable thickness. The stochastic model of Christensen and Tonder has been adopted to characterize the roughness of the bearing system. With appropriate boundary conditions, the associated Reynolds’ type equation has been solved by invoking the dilog function, to derive the expression for pressure distribution resulting in the calculation of load carrying capacity. It is observed that the adverse effect of transverseroughness gets aggravated due to the bearing deformation. But the situation remains fairly improved in the case of negatively skewed roughness for a large range of bearing deformation with a suitable strength of the magnetic field. Further, it is appealing to note that this positive effect gets augmented with a proper selection of thickness ratio parameter associated withvariable film thickness.

In this article we apply Moore- Penrose generalised inverse method to solve a fully fuzzy linear system. By this method we obtain the solution of fully fuzzy linear system of equations in the case of Trapezoidal fuzzy number matrices. A numerical example is also given.

Let G (V, E) be a graph with vertex set V= V(G) and edge set E= E(G) of order p and size q. 0 –edge magic labeling[4], 1-edge magic labeling[7] and n-edge magic was introduced and extended by [6, 9,10].This article discussed and found generalisation of order and size n- edge magic labeling of special graphs such as caterpillar graph, MÖubius- Kantor graph, Hypercube graph, etc,.

The perturbation method and Runge-kutta shooting method has been carried out to study the influence of the effect of exponential viscosity-temperature relation, exponential thermal conductivity-temperature and the combined effects of the variable viscosity and the variable thermal conductivity on steady free convection flow in a vertical channel filled with porous medium. The Darcy-Brinkman model is used to predict the flow in porous medium. The walls are maintained at constant but different temperatures. Numerical results are presented for a wide range of parameters of variable viscosity parameter, variable thermal conductivity parameter, wall temperature ratio, buoyancy parameter and porous parameter on the velocity and temperature fields. Furthermore, the effect of the governing parameters on skin friction and Nusselt number are tabulated. The solutions obtained by Runge-Kutta shooting method are compared with perturbation method solutions and the results agree very well in the absence of buoyancy parameter.

The problem of generating Trivariate Normal Distributions from univariate ones is drawing the attention of the reliability analyst. Amongst these approaches the characterisation approach and the modelling approach are very appealing. Infact the characterisation approach is of great interest to both theoreticians and applied workers. Here we have used a Trivariate Normal Distribution for application by extending univariate distribution through characterisation approach. In our application part we have considered post-menopausal women. We have concentrated on a 24 hr profile of Melatonin, ACTH, Cortisol, TSH ,Prolactin and GH under the treatment with Placebo and with Progesterone. In this respect we have developed a mathematical model which describes the purpose of the present study. The study investigates in post-menopausal women, the effects of a 24-hr profile of progesterone and placebo administration both on sleep architecture and on multiple hormones profile. The protocol allows us to explore the effects of the placebo and progesterone treatment on combined effects of hormones.

In this paper we have investigated the steady plane poiseuille flow of viscous incompressible fluid between two porous parallel plates in magnetic field. We have studied the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines.

Fully developed laminar mixed convection of permeable couple stress fluid in a vertical channel has been investigated analytically in the presence of heat generation or absorption. Uniform wall temperatures with asymmetric and symmetric heating have been considered. An analytical solution has been developed by using perturbation technique. Results are depicted graphically on the flow for different values of couple stress parameter, porous parameter, mixed convection parameter and heat generation or absorption coefficient. The results show that the flow reversal occurs near the walls of the channel for sufficiently large value of the ratio of Grashof number and Reynolds number.

In this paper we introduced the modified version of the differential transform method, which is called the projected differential transform method (PDTM) .This method can be easily applied to the initial value problems with less computational work. It can also be applied to solve linear and nonlinear partial differential equations. Firstly, we stated the definition of the projected transform method, and some related theorems. Then some illustrative examples are given, the numerical results of these examples compared with those obtained by the Differential transform method are found to be the same.

In this paper we have investigated the steady plane Couette flow of viscous incompressible fluid between two porous parallel plates through porous medium with magnetic field. We have studied the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines.