This paper analyzes a simple symmetric random walk with finite steps in d-dimensional integer lattice, ℤ and introduces one of its applications. It focuses on the total number of ways in which the walk can be accomplished. The number of ways of accomplishment is used to find the probabilities associated with all possible outcomes as a generalization of the probability associated with return to origin. In addition, the paper discusses on the total number of possible outcomes. (Since the walk is executed in ℤ , all the outcomes are integer points.) It provides an insight into the distribution of the integer lattice, ℤ .
In this chapter we investigate n x n matrix M which is in multiplicative matrix form. This is a quite new concept. A theorem is given to construct an infinite number of matrices M in multiplicative matrix form of different order even if matrix A has only two entries a & b taken alternatively in its first row or first column with examples.
The object of the present paper is to study generalized Sasakian-space-forms satisfying certain curvature conditions on 0 W curvature tensor. In this paper, we study 0 W semisymmetric, W0 flat, 0 W flat, generalized Sasakian-space-forms satisfying A.S = 0, A.R = 0, A.C~ = 0. Also 0 W flat generalized Sasakian-space-form have been studied.
The maximum flow problem was first formulated in 1954 by T.E. Harris and F.S. Ross as a simplified model of soviet Railway traffic flow1. In 1955, Lester R. Ford, Jr. and Delbert R. Fulkerson created the first known algorithm for calculating the maximum flow, the Ford-Fulkerson algorithm2. It was in 1951 when the American mathematician, George Dantzig put forward the network simplex algorithm to solve mininimum cost flow problem. We take a typical example and find the maximum flow and minimum cost. Finally we generalise The Producer’s Problem based on some assumptions and find the maximum flow and minimum cost in it. We observe that the minimum unit cost in The Producer’s Problem increases with the number of items produced increases, in contrast to natural expectation.
In this paper, we investigated the unsteady free convective flow of an incompressible viscous electrically conducting fluid through a porous medium under the action of an inclined magnetic field between two heated vertical plates by keeping one plate is adiabatic. The governing equations of velocity and temperature fields with appropriate boundary conditions are solved by using perturbation technique. The effects of various physical parameters on the velocity and temperature fields are discussed in detail with the help of graphs.
In this paper, an approximate analytical solution is obtained for the unsteady mixed convection flow near the stagnation region of a heated vertical plate. The unsteadiness in the flow field is caused by impulsively creating motion in the free stream and at the same time suddenly raising the surface heat flux above its surroundings. This study gains importance when the buoyancy forces due to the temperature difference between the surface and the free stream become large. The Homotopy Analysis Method (HAM) is applied to solve the coupled system of non linear partial differential equations for analytical solutions. The numerical results of the flow are computed using the Keller-Box Method (KBM). A detailed error analysis is performed to compute the total average squared residual errors for velocity and temperature. It is shown that a more accurate solution can be obtained with least computational effort by the computed approximate analytical series solutionof velocity and temperature.