Applied Mathematics

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.

The combined effects of thermal radiation and viscous dissipation on unsteady, laminar, free convective flow with heat and mass transfer over an incompressible viscous fluid past a non-isothermal vertical cone with variable surface temperature and concentration are considered in this article. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity, temperature and concentration fields have been studied for the effect of Eckert number (Ec), Prandtl number (Pr), radiation parameter (F), Schmidt number (Sc), buoyancy ratio parameter (N), semi vertical cone angle ( ), surface temperature power law exponent (n) and surface concentration power law exponent (m). The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically. It is observed that, when the radiation parameter increases, the velocity decreases close to the cone surface and an increase in Eckert number is observed to increase both velocity and temperature. The present results are compared with the available results in literature and are found to be in good agreement.

A two-dimensional laminar unsteady MHD free convective heat and mass transfer flow past a vertical porous plate immersed in a porous medium has been studied numerically in presence of chemical reaction, heat generation and variable suction. The governing partial differential equations are reduced to a system of self-similar equations using the similarity transformations. The resultant equations are then solved numerically using the Runge-Kutta method along with shooting technique. The effects of governing physical parameters on velocity, temperature and concentration as well as skin-friction coefficient, Nusselt number and Sherwood number are computed and presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement.

The goal objective of this study is to propose a new double ARA transform (DARAT). We employ this transform to prove the convolution, existence and other relevant theorems as well as derivatives properties. Subsequently, this transform is applied to solve some illustrative integral- differential equations. This approach was shown to be a powerful and efficient means to tack integral- differential equations.

Present paper is an important study for constructing magic squares of odd orders. This magic squares have been formed using the properties of Latin squares. Here, reduced Latin square is used and it is formulated by using the cyclic shifting method with the entries (????, ????,...., ????) (????(????- ????),.... ???? power ???? ).This work has been generalized for magic square of order ???? power ????, when ???? is odd and ???? by using the mathematical formula ?????????(???????????? ???? power ????): ????= ????, ????,..., ???? power ????. The method is tested for ????, ???? power ???? and ????.

The magnetic response of transverse wave propagation of double layered nanoplate embedded in an elastic medium is studied employing nonlocal continuum theory. The displacement equation of nanoplate with magnetic and elastic medium is devised with the help of Lorentz force and Winkler elastic foundation. The frequency equations are acquired for nanoplate with simply supported edges. The numerical result reveals that the magnetic strength and elastic medium increases the frequencies of double layered nanoplates. The perfection of the present frequency value is noted by comparing it with the existing literature.

The Line graph L(G) of an undirected graph G is another graph L(G) that represents the find adjacencies between the edges of G. In this paper, we find the Maximum and Minimum of total coloring for a certain Line graphs of a snake graph families and further we established the results on maximum number colors required to total coloring to the graph G is denoted by and similarly we color the vertex of a snake graph and obtained certain results and denoted by X_Max^(G)

Fisher folk form an important community in Kerala, but remain neglected and marginalized in spite of the higher socio-economic progress the state has made as a whole. While we consider fisher folk, they remain isolated from the main stream of development. They remained educationally backward also. It is well known that a rapid growth in educational attainment is the most successful medium for social empowerment of the disadvantaged. The path towards our goal of achieving progress and prosperity of the nation is necessarily through equipping the backward sections through knowledge and skills. They need to be empowered by equipping them with self-sufficiency and existence skills such as Self Confidence, Problem Solving Ability, Logical thinking, Decision Making Power, Computational Speed and Reasoning etc. The present paper throws light on the Supreme power of Vedic Mathematics in enhancing these skills.

We have to make comparison among differential transformation method (DTM) and Variation of Parameter method (VOPM). We provide two examples in order to compare our results and find exact solutions also. The numerical examples show that the DTM is a good method compared to the VOPM since it is effective, uses less time in computation, easy to implement and achieve high accuracy. In addition, DTM has many advantages compared to VOPM since the calculation of Adomian polynomial is tedious. From the numerical results, DTM is suitable to apply for nonlinear problems.

In this paper we presented an analysis of Hamilton formulas. with Three Almost Complex Structures. We have reached important results in differential geometry that can be applied in theoretical physics