Abstract/Overview Sugarcane is the main raw material in the production of sugar in Kenya. The supply of sugarcane affects directly the quantity of sugar supplied in the markets. Low supply of sugarcane leads to a decline in the amount of sugar supplied to the markets and vice versa. This creates the need of determining the quantity of sugarcane supplied by the farmers to the industries to facilitate planning. This study employed Box Jenkins predictive models in forecasting the monthly qua...
Abstract/Overview There is increased use and application of exponential random graphs emanating from use of big data and other techniques. This study sought to establish how sampling bias affects the exponential random graphs. This study was guided by the following objectives: to specify and estimate exponential random graph models with biased sampling, to determine the maximum likelihood estimate for family of exponential random graphs with sampling bias., to determine the suitable sampl...
Abstract/Overview Modeling of invasive species using stage based matrix methods can be exploited to understand population dynamics of plants using stage based Leftkovitch matrix models. This study reviewed and extended the stage based matrix incorporating invasion variables of invasive Cestrum aurantiacum across different forest types, ecological zones and altitudes. The estimation of eigenvalues of the extended stage based Lefkovitch matrix and its corresponding right and left eigenvecto...
Abstract/Overview This research is about a survival analysis on broilers in two poultry farms in Kaloleni sub-county. Chapter one gives an insight into the introduction of the paper, chapter two discusses the methodology used, chapter three gives the results, chapter four discusses the findings briefly and chapter five gives the conclusions arrived at and some recommendations.
Abstract/Overview The Lefkovitch stage specific matrix population models are divided into discrete stage classes defined by a growth variable such as size, height and diameter at breast height for trees. In matrix model, the deterministic matrix projection models are used to estimate growth rate, stable size distribution, reproductive values, and sensitivities of the growth rate to changes in vital rates. This study sampled five forest blocks (Kiptogot, Kimothon, Suam, Saboti and Kitale w...
Abstract/Overview Household water in Kenya is used in agricultural activities, industrial activities and other uses. A lot of water is consumed by indoor appliances. The water management strategy affects the household demand for water. The future demand of water in Kenyan towns has remained uncertain. Therefore this study sought to model household water demand using the non- parametric model in the spectral domain. This study largely relied on the secondary data that was collected from Gu...
Abstract/Overview In queuing theory one deals with the mathematical analysis of the performance of queuing systems. In our daily lives customers encounter queues while seeking services in institutions. The increase in the number of customers has resulted to congestion at revenue collection points in Kenyan towns. There is therefore need to study the queuing systems to identify possible remedies. This study sought to fit a queuing model to bus park revenue collection point as a preliminary...
Abstract/Overview In this paper we describe operator systems and elementary operators via tensor products. We also discuss norms of elementary operators.
Abstract/Overview Determining Equations are linear partial differential equations. The equation to be solved is subjected to extension generator. The coefficient of unconstrained partial derivatives is equated to zero and since the equations are homogeneous their solutions form vector space [1]. The determining equations obtained leads to n-parameter symmetries.
Abstract/Overview The equation F(x, y, y, y, y, y (4)) 0 is a one-space dimension version of wave equation. Its solutions can be classified either as analytic or numerical using finite difference approach, where the convergence of the numerical schemes depends entirely on the initial and boundary values given. In this paper, we have used Lie symmetry analysis approach to solve the wave equation given since the solution does not depend on either boundary or initial va...
Abstract/Overview In this paper, we examine conservative autonomous dynamic vibration equation, x¨ = − tanh2 x, which is time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Numerical results using Wilson-theta method are tabulated and then represented graphically. Further the stability of the algorithms employed are also discussed.
Abstract/Overview A multiple chain pendula system constrained to move in space has been studied within the framework of a generalized coordinate system by using the Lagrangian formalism. Equations of motions for many body pendula systems have been derived .These equations concur very well with known data. We confirm that equations of motion for any values of n and l can be generated from our general equation which presents interesting characteristics. Solutions to these multi-pendula equa...
Abstract/Overview Lie symmetry analysis of Ordinary Differential Equation can be used to obtain exact solution of the equation of the form F (x, y, y’ y’’ y’’’) = 0. In this paper we use Lie Symmetry analysis approach to obtain the nonzero Lie brackets of a nonlinear Ordinary Differential Equation for heat conduction. The Lie Brackets obtained forms Lie solvable algebra that can be used to reduce the equation to lower order.
Abstract/Overview In this study Sum construction method of automorphic symmetric balanced incomplete block designs has been presented in details. Efficiency of a test design used in the Sum construction of automorphic symmetric balanced incomplete block designs has been determined alongside its existence. The process involved the application of sum construction to give new designs of parameters D (v, b, λ1+λ2) and an application of Bruck Ryser Chwola theorem extensively. A test design u...
Abstract/Overview This study analyzes recent data of accidents’ prevalence in Kenya and investigates whether there might be new trends in areas formerly not prone to accidents. Polynomials of order 6 are found best suited for accidents’ prevalence data. The graphs show that seasonal variations explain over 90% of prevalence in Central, Eastern, Nyanza, Rift-Valley and Western Provinces. The highest variation is in Nyanza with 98.54% of the prevalence rate explained by the seasonal var...