Applied Mathematics

In this paper, the application of homotopy perturbation method (HPM) is applied to solve nonlinear fuzzy volterra integral classes equation. Comparison are made between the exact solution and solution of homotopy perturbation method, also we proved the convergence of the solution for the nonlinear fuzzy volterra integral classes equation with high computational and complexity to find the solution by using analytical method, so we describable this solution by using Homotopy perturbation method , in Banach fixed point theory for existence and uniqueness. Numerical examples are given to represent the efficiency and the accuracy of the method and all of the results reveal that the homotopy perturbation method is very effective and simple to solve our problem . Finally using the MAPLE program version (18).

Assignment problem is an important subject discussed in real physical world. We endeavor in this paper introduce by using Min Max Zero Suffix Method (MMZS) is Symmetric.This method o?ers signi?cant advantages over similar methods, in the process, ?rst we de?ne the assignment matrix, apply the transpose for original assignment problem then by using determinant representation we obtain a reduced matrix which has at least one zero in each row and columns. Then by using Min Max Zero Suffix Method (MMZS), we obtain an optimal solution for assignment problem by assigning zeros to each row and each column. The Min Max Zero Suffix Method (MMZS) is based on creating some zeros in the assignment matrix and then try to ?nd a complete assignment to their Zeros.The proposed method is a systematic procedure, easy to apply and can be utilized for all types of assignment problem with maximize or minimize objective functions

The problem of generating bivariate life distributions from univariate ones is drawing the attention of the reliability analysts for quite long. Several approaches have been developed for generalizing univariate laws. Amongst those approaches, the characterization approach and the modeling approach are very appealing. Here Bivariate Inverse Exponential Distribution is used in the application part. This study aims to test the hypothesis that moderate exercise training combined with caloric restriction would produce significant menstrual disturbances and alterations in ovarian steroids in premenopausal women. Sedentary premenopausal women (25 –40 years; body mass index: 23.6±0.6 kg/m2 ) assigned to either a light conditioning (LC, n = 9) or an exercise combined with caloric restriction group (EX + CR, n = 24) were studied for one screening, one baseline and four intervention periods equivalent to the length of subjects’ menstrual cycles. In conclusion, the results of this study suggest that a moderate aerobic exercise training program combined with modest weight loss in accordance with recommended guidelines produces significant reductions in ovarian steroid exposure without disrupting menstrual cyclicity in premenopausal women of advanced gynecological age.

This research introduces a new set of 32 in-equivalent Hadamard matrices of order 404 of Goethals Seidel type. To apply the Goethals Seidel method, four Turyn type sequences of lengths 34 are found by a computer search. These sequences are used to construct base sequences of lengths 67 and are used to generate a set of four T-sequences of length 101. There were 16 possible ways of the linear combinations of these T- sequences and 1820 possible ways of choosing four sequences. Among them only 32 possible choices gave the new set of in-equivalent Hadamard matrices of order 404.

An analysis is presented for the problem of the fully developed natural convection magnetohydrodynamics micropolar fluid flow of heat and mass transfer in a vertical channel. Asymmetric temperature and convection boundary conditions are applied to the walls of the channel. The cases of double diffusion and Soret-induced connections are both considered. Solutions of the coupled non-linear governing equations are obtained for different values of the buoyancy ratio and various material parameters of the micropolar fluid and magnetic parameters. The resulting non dimensional boundary value problem is solved by the Galerken Finite element method using MATLAB Software. Influence of the governing parameters on the fluid flow as well as heat and solute transfers is demonstrated to be significant.

Fourier-Mellin transform has many properties such as linearity, scaling, shifting, differentiation property etc. Mainly linearity and shifting property is used for image registration in medical field. Due to such properties transform has many applications like visual odometry, detection of human face, the comparison of plant leaves which is based on Fourier-Mellin transform.In present work we discussed about linearity, scaling, shifting, differentiation, first shifting property of two-dimensional fractional Fourier-Mellin Transform.

The -expansion method is predominant and useful mathematical tool for constructing exact traveling wave solutions to nonlinear evolution equations interweaved in mathematical physics, engineering, and physical sciences. In this article, we investigate solutions to the Korteweg-de Vries (KdV) equation and the (2+1)-dimensional Zakharov-Kuznetsov (ZK) equations through the -expansion method. Abundant exact traveling wave solutions with arbitrary parameters have successfully been obtained by this method which are articulated in terms of trigonometric, hyperbolic, and rational functions.

This paper mainly deals with the solution of Optimal Power Flow (OPF) problem which can be formulated as a Quadratic Programming (QP) model and then decomposed by Lagrangian Relaxation (LR) method.The objective of this model is to minimize the total cost of real power generation. Many researchers have discussed the solution for OPF by using different methodologies like Newton Raphson (NR) method, Particle Swarm Optimization (PSO) method, Genetic Algorithm (GA), Artificial Intelligence (AI) method, Interior Point (IP) method, Differential Evolution (DE) algorithm. In this paper the proposed methodology is compared with the other methods like Particle Swarm Optimization method, Genetic Algorithm and Differential Evolution algorithm. These methods have been tested through the results of IEEE 30 bus system. The optimum generation cost is minimized for OPF using Lagrangian Relaxation method.

Stock control is an important functional branch of any manufacturing/service organization. Stock control has been discussed using the dynamic programming model approach. The distribution of goods to warehouses is a multistage process which the dynamic programming is adapted to providing solution to and also guarantees optimal feasible solution. The stock in warehouses is used as a partition of the firms main store. An equation ensues from the stock record which is shown to be piecewise continuous. The Laplace transform is used to test the existence of the function. The step function that derives from the supply to the warehouses is transformed to a piecewise linear function which can be approximated as continuous function. The step function is then applied on the function to obtain the returns from the respective allocations if the function exists. The allocation with the highest return is the optimum. Some relevant theorem have been stated and proved and illustrative examples included.

Heat and mass transfer effects on the unsteady flow of micropolar fluids embedded in a porous medium are studied by taking into the account of viscous dissipation with a homogeneous chemical reaction of the first order. Using the Galerkin finite element method the expressions for the velocity, microrotation, temperature and concentrations are obtained. The effect of material parameters such as Prandtl number Pr, Grashof number G, Modified Grashof number Gm, Schmidth number Sc, Eckert number Ec, the spin-gradient viscosity ?, the dimensionless viscosity ratio ?, the coefficient of gyro-viscosity or vortex viscosity ?, permeability of the porous medium K, Chemical reaction parameter , and time t. Further the results of Skin friction coefficient, the rate of heat transfer and mass transfer at the wall are presented with various values of fluid properties and flow conditions on the velocities, temperature and concentration are plotted in the graph and discussed. In the present analysis we study the effect of viscous dissipation on unsteady free convection flow of a laminar incompressible micropolar fluid with heat and mass transfer past a vertical porous plate embedded in a porous medium with chemical reaction.