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...
Abstract Fungi are eukaryotic microorganisms that have simple multicellular or unicellular cell structures. They are distributed in terrestrial soils, forests, aquatic habitats and in extreme environments with high ambient salts, temperature, pH and pressure. Fungi from extreme environments are potential sources of novel biocatalysts for example antimicrobial agents that can help solve the rising cases of drug resistance. However, the diversity of fungi recovered and described from less stud...
Abstract/Overview Background: Metagenomics approaches are increasingly being utilized as “dipstick” for microbial carriage. In this study, 16S rRNA metagenomics was used to probe for microbial community that resides in the ticks, those they pick from the environment, wildlife and livestock and to identify potential tick borne zoonoses. Methods: Tick DNA from 463 tick pools collected from domestic animals between 2007 and 2008 were amplified with primers that target the 16S rRNA V3-V4 ...
Abstract/Overview Several construction methods have been introduced to build the elements of BIBDs’ for specific parameters, with different techniques suggested for testing their existence, still no general technique to determine the efficiencies of these designs has been realized. In this study the efficiencies and relative efficiencies of Sum constructed automorphic symmetric balanced incomplete block designs with respect to parent designs has been presented. The process involved the ...
Abstract Acacia trees are among the most dominant tree species found in semi arid ecosystems with a vast geographical distribution throughout the savanna habitats. The trees are leguminous and have remarkable ability to fix nitrogen in the soil, thereby, improving fertility. About all parts of an Acacia tree are edible to different types of animals and their leaves provide the only greenery in the dry season, so are bound to be eaten. As such, they support enormous pyramids of biomass in com...
Abstract Genus Eucalyptus belongs to the family Myrtaceae and consists of more than 900 species, various hybrids and varieties. The major species that are grown in Kenya are Eucalyptus grandis, E. globulus, E. saligna and E. camaldulensis. Most Eucalyptus species are highly dependent on rainfall and this is challenged by climatic changes owing to global warming making it difficult to effectively match the availability of mature trees and the market demand especially for use as power transmi...
Abstract Pigeon pea is a versatile pulse crop grown in semi-arid regions of Kenya; however, its production is affected by plant-parasitic nematodes. The current study was undertaken to investigate the diversity of nematodes and the influence of soil properties on their diversity in monocrop pigeon pea fields in Mbeere North, Embu County, Kenya. Soil samples were collected from Gatunguru B, Gwakaithi, Itururi, Kambungu, Kanyueri, Karigiri, Mbangua and Njarange regions. From each field, soil s...