Applied Mathematics

In this paper we present a new class of interval valued vague sets and interval valued vague volterra space. We obtain several properties and some of their characterizations concerning volterra space.

In this paper, we propose a different approach for efficiently conserving energy in wireless sensor networks. Our approach towards energy consuming in sensor networks is fully distributed to consume very low energy for finding the path along with data transmission. We use two protocols LEACH and ELEACH-M to find the route for data transmission and make its performance by comparing the route discovery of those two protocols. Bayesian inference is used to inference the missing data from the nodes that were not active during each sensing. Game theory offers mode for distributed allocation of energy resources and thus provides a way of expecting the characteristics of wireless sensor networks. We make game approach to obtain the optimal probabilities of sleep and wake up states that were used for energy conservation.

The effects of chemical reactions on free convection MHD flow of an incompressible, viscous, electrically conducting fluid past an exponentially accelerated infinite vertical plate through a porous medium with variable temperature and mass diffusion is discussed. The plate temperature and the concentration level near the plate increase linearly with time. The magnetic lines of force are assumed to be fixed relative to the plate. The Laplace transform method has been used to find the solutions for the velocity, temperature and concentration profiles. The effects of the various parameters such as Prandtl number, Schmidt number, time, magnetic parameter, permeability parameter, thermal Grashof number, mass Grashof number, accelerating parameter and chemical reaction parameter for velocity, temperature, and concentration and skin-friction profiles have been discussed in detail with the help of graphical representation. The numerical values of skin-friction, Nusselt number and Sherwood number have been tabulated.

In this short search, we will prove the mathematical fact that all the even integers are equals that equal to zero. And all the odd integers are equals that equal to One, Through simple numerical proof as we shall see below.

In this paper, a mathematical model is proposed to study the effect of the depleting dissolved oxygen on the existence of interacting planktonic population. The mathematical model is formulated using the system of nonlinear ordinary differential equations. The model includes four state variables viz., nutrient concentration, density of algae, and density of the zooplankton population and concentration of dissolved oxygen. All the feasible equilibria of the system are obtained and the conditions for the existence of the interior equilibrium are determined. The local stability analyses of all the feasible equilibrium points are obtained. The non-linear stability analysis of the non trivial equilibrium point has been carried out and the criteria for the survival or extinction of the species have been obtained with numerical simulation.

A graph with n vetices is said to have a prime labeling if the vertices can be labeled with first n positive integers such that each pair of adjacent vertices are relatively prime. The present work in prime labeling focuses on finite simple undirected graphs, in particular on complete bipartite graphs. Our results are analogous to those stated by A. H. Berlineer et al., where they considered prime and coprime labeling of complete bipartite graphs while ours are for prime labeling of complete tripartite graphs. In our work, we have proved prime labeling for the general case K_(1,m,n), where m,n are positive integers. Further, some non-existing cases have been proved.

In this paper, we consider a deterministic mathematical model for the transmission dynamics of an infectious disease in a community. Although, the equilibria of the model could not be expressed analytically, their existence and the threshold conditions for their stability are theoretically and numerically investigated. We analyzed the stability of the model using the linearization techniques via the Jacobian matrix approach and the Routh-Hurwitz stability criteria to determine the equilibria for the model. The basic reproductive number of the model was determined using the next generation matrix operator. Their numerical results were shown in graphical forms using some hypothetical values for the parameters used in the model. It was shown graphically that the mathematical model produced asymptotically stable population when the parameter values are perturbed to a certain degree.

The aim of the present paper is to find some exact solutions of steady two dimensional finitely conducting incompressible non-Newtonian fluid flow under the presence of transverse magnetic field using transformation of variables. We have considered, vorticity distribution proportional to the stream function perturbed by a quadratic stream. Moreover, the results are shown by various graphs.

In the present paper, chemical reaction effect on MHD flow in porous media past an impulsively started oscillating vertical plate with variable mass diffusion and constant wall temperature in the presence of Hall current is studied here. The fluid considered is an electrically conducting. The Laplace transform technique has been used to find the solutions for the velocity, Sherwood number and skin friction. The velocity profile, heat transfer and mass diffusion have been studied for different parameters like Schmidt number, Hall parameter, magnetic parameter, chemical reaction parameter, mass Grashof number, thermal Grashof number, Prandtl number, and time. The effect of various parameters are shown graphically and the value of the skin-friction and Sherwood number for different parameters has been tabulated.

The present paper is concerned the second-order differential equation ,(*) with Neumann boundary conditions. By using the asymptotic solutions we find the distribution of eigenvalues of (*) in two turning points.