Applied Mathematics

In this article an interesting and famous realistic problem harmonic oscillators is discussed using the single-term Haar wavelet series (STHW) method. The results (approximate solutions) obtained very accurate using classical Runge-Kutta (RK) method, single-term Walsh Series (STWS) and STHW methods are compared with the ODE45 in Matlab. It is found that the solution obtained using STHW is closer to the ODE45 in Matlab. The high accuracy and the wide applicability of STHW approach will be demonstrated with numerical example. Solution graphs for discrete exact solutions are presented in a graphical form to show the efficiency of the STHW. The results obtained show that STHW is more useful for solving harmonic oscillators and the solution can be obtained for any length of time.

The present study focused on the numerical solution of boundary layer flow of a radiating dusty fluid over a stretching porous surface. The governing boundary layer equations of the problem are formulated and transformed into ordinary differential equation by using similarity transformation. The resulting equations are then solved numerically using Runge Kutta fourth order scheme along with shooting technique. It has been observed that the temperature of the particle phase increases with the increase of radiation parameter but the radiation parameter has no significant effect on fluid phase temperature.

In this paper we have explored the problem for generalized temperature functions considered over positive and negative time. We have established representation theorems and their applications.

Field equations of Saffman’s dusty gas with pressure-dependent viscosity and variable number density through isotropic porous media of variable porosity are developed in this work. The porous microstructure, the Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the intrinsic volume averaging process.

In the present paper, unsteady MHD flow past an impulsively started vertical plate with constant wall temperature and variable mass diffusion in the presence of Hall current is studied. The fluid considered is an electrically conducting, absorbing-emitting radiation but a non-scattering medium. The Laplace transform technique has been used to find the solutions for the velocity profile and skin friction. The velocity profile and skin friction have been studied for different parameters like Schmidt number, Hall parameter, magnetic parameter, mass Grashof number, thermal Grashof number, Prandtl number, and time. The effect of parameters are shown graphically and the value of the skin-friction for different parameters has been tabulated.

This paper is concerned with the global asymptotic stability analysis problem for a general class of uncertain stochastic neural networks with mixed time-delays. The mixed time-delays under consideration comprise both the discrete time-varying delays and unbounded distributed delays. The main purpose of this paper is by using Lyapunov-Krasovskii functional, the well-known Leibniz-Newton formula and the linear matrix inequality (LMI) approach, and then to establish easy to test sufficient stability conditions under which the addressed neural network is globally, robustly, asymptotically stable in the mean square for all admissible parameter uncertainties. The proposed criteria can be checked effectively by the Matlab LMI toolbox. Finally a simple example is provided to demonstrate the effectiveness of the proposed criteria.

A three dimensional eco-epidemiological model consisting of prey, susceptible predator, infected predator species, is proposed and analyzed in the present work. From infected predator, the disease is transmitted to the susceptible predator species. Differential predation rate is considered due to disease in predator as the infection reduces the predation ability of infected predator. The recovery of infected predator from disease is incorporated; therefore, an SIS model is taken for predator species. The dynamics of the system is analyzed mathematically and conditions for existence and stability of disease free equilibrium point has been found out. Also conditions for disease to be endemic in predator species are obtained. Numerical simulations have been carried out to justify the results obtained.

There are many examples for co-orbital motion in the Solar system, including temporary co-orbital companions of the Earth, raising many interesting questions. The problem of co-orbital motion is formulated in the Hamiltonian form when the larger primary is an oblate body. Different forms of the disturbing function are outlined; the relevant form is developed in terms of Laplace’s coefficients. The Hamiltonian of the problem is formed in Delaunay-like canonical elements. The ratio of the primaries’masses is considered as a small parameter of the first order while the leading oblateness term of the first primary is considered of second order. Finally, the short-period terms are eliminated from the Hamiltonian using the procedure based on Lie series and Lie transform, leaving the Hamiltonian as a function of only the secular and critical (resonant) terms.

Decisions are complex in nature. Decisions may include uncertainty to some extent. Some decisions may be sequential in nature. Decisions are made within a decision environment. It is defined as the collection of information, alternatives, values, and preferences available at the time of decision. A sequential decision problem consists of n sequential states which are independent or interdependent. Therefore, action must be taken at each state and hence a sequence of actions must be taken to arrive at a solution. A decision made at one state due to an action is passed on to next state and the overall decision depends on the decisions made at each state. Probabilistic Transition System (PTS) is an extension of Labeled Transition System where each transition depends on a probability. PTS constitutes a framework for the description and comparison of processes with stochastic behaviour. Stochastic Finite Automata are suitable for the construction of mathematical models of complex systems having stochastic behavior in a finite way. In the study, PTS is extended by adding a component so as to represent a Transition System for Sequential Decision Problem under Uncertainty. The study is an attempt to exhibit Stochastic Finite Automata as a Mathematical Model for Sequential Decision Making under Uncertainty.

The definition of the Drazin inverse of a square matrix with complex elements is extended to Con-s-k-EP matrices by showing that for any B and W, n by n respectively, there exists a unique matrix, X, such that for some positive integer k, , and . Various expressions satisfied by B,W,X and related matrices are developed.