Abstract/Overview Vector populations fluctuate on a seasonal basis annually. Knowledge on seasonal abundance and distribution of vector species at the local level would improve vector control programmes and contribute to malaria prevention. Despite this, information on malaria vector species distribution and seasonal fluctuations in Baringo County is scarce. This study examined distribution and seasonal abundance of malaria vector species in Baringo. The study area was stratified into fou...
Abstract/Overview Background: Herbal medicines are used widely for primary health care in Kenya among rural populations where modern medicines are not affordable. The flowers, roots, stems and leaves of Senna didymobotrya have both antifungal and antibacterial activity. Decoctions or infusion are used to treat skin diseases, diarrhoea, malaria, venereal diseases and stomach problems. Methods: Plants were collected from farmers' fields in western Kenya. Stem bark, root bark, leaves, flower...
Abstract/Overview In this paper, we examine conservative autonomous dynamic vibration equation, , which is time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Numerical results using Newmark are tabulated. The stability of the algorithm employed is also discussed.
Abstract/Overview Let be an operator on an infinite dimensional Hilbert space . Denote the essential numerical range of the operator by and the Davis-Wielandt shell of the operator by . We review the properties of the essential numerical range and those of the Davis-Wielandt shell. This review is aimed at striking similarities in the properties shared. The results of this study show that some of the properties shared are, for instance, unitary invariance and convexity. However, it is note...
Abstract/Overview Symmetry of a system of differential equations is a transformation that maps any solution to another solution of the system. In Lie’s framework such transformations are groups that depend on continuous parameters and consist of point transformations (point symmetries), acting on the system’s space of independent and dependent variables, or, more generally, contact transformations (contact symmetries), acting on independent and dependent variables as well as on all fi...
Abstract/Overview We study a nonlinear Black-Scholes partial differential equation whose nonlinearity is as a result of a feedback effect. This is an illiquid market effect arising from transaction costs. An analytic solution to the nonlinear Black-Scholes equation via a solitary wave solution is currently unknown. After transforming the equation into a parabolic nonlinear porous medium equation, we find that the assumption of a traveling wave profile to the later equation reduces it to o...
Abstract/Overview Let J be the Jacobson radical of a commutative completely primary finite ring R such that J k 6= (0) and J k+1 = (0). Then R/J ∼= GF(p r ), the finite field of p r elements, and the characteristic of R is p k where k ≥ 2 and p is some prime integer. In this paper, we determine the structures of the quotient groups 1 + J i/1 + J i+1 for every characteristic of R and 1 ≤ i ≤ k − 1.
Abstract/Overview Malaria and persistent childhood diseases are a major threat to child survival in the developing world. In this paper, we develop and analyse a mathematical model for paediatric malaria and pneumonia co-infection. We establish the existence of equilibria points in terms of the basic reproduction numbers Rm and Rp. The analysis shows that the diseasefree equilibrium of the model is globally asymptotically stable whenever the co-infection reproduction number Rmp is less th...
Abstract/Overview Low soil nitrogen (N) is a major constraint for sustainable crop production in smallholder farming systems in Africa. Grain legumes such as bambara groundnuts (Vigna subterraneaL. Verdc). can form N fixing symbiotic association with root nodule bacteria collectively called ‘rhizobia’; in a process that can supply sufficient N for the legume and other crops under intercrop or in rotation. There is currently insufficient information on the diversity of indigenous rhizo...
Abstract/Overview Pneumonia occurs commonly in HIV-infected patients. In this paper, we study a simple mathematical model for the co-infection of HIV/AIDS and Pneumonia. We establish that the model is well presented epidemiologically and mathematically. The disease-free equilibrium point is determined. We establish the basic reproduction number R0 for the model, which is a measure of the course of co-infection.
Abstract/Overview A study has been done using generalized coordinates system with the application of the Lagrangian formalism for n mass units linearly connected to move in space. Lagrangian equations have been developed and used throughout the research to determine the equations of motion for multi-pendula system for several as well as many mass units involved. These equations were solved using various mathematical techniques to determine the zenith angular accelerations for each system....
Abstract/Overview The contribution of appropriate inoculum strains to more efficient nitrogen fixation by legumes has been difficult to assess due to the laborious nature of the assays involved in assessing establishment of inoculum strains in the field. The use of marker genes, in particular the GUS system, changes this, making it possible to assess occupancy by the inoculum strain in large numbers of nodules on whole root systems. Here we used the GUS system to evaluate the competitive ...
Abstract/Overview Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.
Abstract/Overview Rhizobia were isolated from two Kenyan soils with pHs of 4.5 and 6.8 and characterized on the basis of their host ranges for nodulation and nitrogen fixation, colony morphologies, restriction fragment fingerprints, and hybridization with a nifH probe. The populations of rhizobia nodulating Phaseolus vulgaris in the two soils were similar in numbers and in effectiveness of N(inf2) fixation but were markedly different in composition. The population in the Naivasha soil (pH...
Abstract/Overview The transport of solutes through porous media where chemicals undergo adsorption or change process on the surface of the porous materials has been a subject of research over the years. Use of pesticides has resulted in production of diverse quantity and quality for the market. Disposal of excess material has also become an acute problem. The concept of adsorption is essential in determining the movement pattern of pesticides in soil in order to assess the effect of migra...