Applied Mathematics

In this paper we have investigated the steady plane poiseuille flow of viscous incompressible fluid between two porous parallel plates through porous medium. We have investigated the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines.

Strategic planning has always been used as an important management tool in organizations across the world. The use of strategic planning necessitates decisions to be made in order to achieve the intended objectives and ensure continuity and relevance. Organizations may have good strategic planning practices, but the extent to which they are successfully implemented influence service delivery. The aim of the study was to establish the influence of strategic planning practice on service delivery by Trans Nzoia County government. The study was guided by Survival-Based Theory which explains how organizations can come up with ways to ensure that they achieve their objectives. The target population included management staff, employees and citizens of Trans Nzoia County. Semi structured questionnaires and Interview guides were used for data collection. The instruments were checked for both reliability and validity by use of Cronbach’s alpha and construct validity index respectively. Descriptive, quantitative and qualitative designs were used to find out the relationship between the variables. Multiple Linear Regression model was used to explain how strategic planning practice influences service delivery of Trans Nzoia County government. With the values of the beta coefficients for the model = 3.648 and = 0.412 respectively. Setting of vision and mission statement had the most influence on service delivery and identification of objectives had the least influence. The findings are crucial especially to the management of the County government of Trans Nzoia and can also be emulated by other Counties.

By using Mawhin continuation theorem and comparison theorem, the sufficient conditions ensuring the existence of exponential periodic attractor and exponential convergence of a class of functional differential equation with time varying delays are established. The results are very different from some previously known results [1,19,28]. Finally, applications and an example are given to illustrate the effectiveness of the results.

An attempt has been made to evaluate the effect of surface roughness and deformation on the performance of a magnetic fluid based squeeze film in rough porous circular plates considering porous matrix of variable thickness. The stochastic model of Christensen and Tonder has been adopted to characterize the roughness of the bearing system. With appropriate boundary conditions, the associated Reynolds’ type equation has been solved by invoking the dilog function, to derive the expression for pressure distribution resulting in the calculation of load carrying capacity. It is observed that the adverse effect of transverseroughness gets aggravated due to the bearing deformation. But the situation remains fairly improved in the case of negatively skewed roughness for a large range of bearing deformation with a suitable strength of the magnetic field. Further, it is appealing to note that this positive effect gets augmented with a proper selection of thickness ratio parameter associated withvariable film thickness.

Let G (V, E) be a graph with vertex set V= V(G) and edge set E= E(G) of order p and size q. 0 –edge magic labeling[4], 1-edge magic labeling[7] and n-edge magic was introduced and extended by [6, 9,10].This article discussed and found generalisation of order and size n- edge magic labeling of special graphs such as caterpillar graph, MÖubius- Kantor graph, Hypercube graph, etc,.

The perturbation method and Runge-kutta shooting method has been carried out to study the influence of the effect of exponential viscosity-temperature relation, exponential thermal conductivity-temperature and the combined effects of the variable viscosity and the variable thermal conductivity on steady free convection flow in a vertical channel filled with porous medium. The Darcy-Brinkman model is used to predict the flow in porous medium. The walls are maintained at constant but different temperatures. Numerical results are presented for a wide range of parameters of variable viscosity parameter, variable thermal conductivity parameter, wall temperature ratio, buoyancy parameter and porous parameter on the velocity and temperature fields. Furthermore, the effect of the governing parameters on skin friction and Nusselt number are tabulated. The solutions obtained by Runge-Kutta shooting method are compared with perturbation method solutions and the results agree very well in the absence of buoyancy parameter.

The problem of generating Trivariate Normal Distributions from univariate ones is drawing the attention of the reliability analyst. Amongst these approaches the characterisation approach and the modelling approach are very appealing. Infact the characterisation approach is of great interest to both theoreticians and applied workers. Here we have used a Trivariate Normal Distribution for application by extending univariate distribution through characterisation approach. In our application part we have considered post-menopausal women. We have concentrated on a 24 hr profile of Melatonin, ACTH, Cortisol, TSH ,Prolactin and GH under the treatment with Placebo and with Progesterone. In this respect we have developed a mathematical model which describes the purpose of the present study. The study investigates in post-menopausal women, the effects of a 24-hr profile of progesterone and placebo administration both on sleep architecture and on multiple hormones profile. The protocol allows us to explore the effects of the placebo and progesterone treatment on combined effects of hormones.

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, A survey on the use of the Haar wavelet method to solve linear and nonlinear integral equations (Volterra, Fredholm, integro-differential equations) is presented. Also, the investigation of Haar wavelet method for solving singular integral equations is presented. Review shows that the Haar wavelet method is efficient and powerful in solving wide class of linear and nonlinear integral equations.

In this paper we have investigated the steady plane poiseuille flow of viscous incompressible fluid between two porous parallel plates in magnetic field. We have studied the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines.

In this paper, we study some of the properties of (Q, L)-fuzzy ideal of a ring and prove some results on these.