Abstract/Overview Fiber quality and yield improvement are crucial for cotton domestication and breeding. With the transformation in spinning techniques and multiplicity needs, the development of cotton fiber quality and yield is of great importance. A genetic map of 5178 Single Nucleotide Polymorphism (SNP) markers were generated using 277 F2:3 population, from an intra-specific cross between two upland cotton accessions, CCRI35 a high fiber quality as female and Nan Dan Ba Di Da Hua (NH)...
Abstract/Overview Phytochemical and biological evaluation of the stem bark of Alysicarpus ovalifolius led to the isolation of three carbazole alkaloids identified as mohanimbine (1), koenimbine (2) and koenidine (3) along with quercetin 3-O-glucoside (4), kaempferol 7-O-glucoside (5), orientin (6), apigenin (7), quercetin (8), plumbagin (9) and stigmasterol (10). The structures of these compounds were elucidated using physical and spectroscopic methods as well as comparison with the liter...
Abstract/Overview Modernisation of statistics teaching is a continual problem the world over. The advances in statistical methods and tools along with the growing demand of applied practitioners creates a dual need of people with the theoretical knowledge to take the subject further and those with the practical knowledge and skills for the many current problems requiring statistical support. The universities in Kenya are largely still teaching theory as was done 40 years ago. Change is po...
Abstract/Overview We consider certain properties of operators. A lot of studies have been done on reflexivity, compactness and numerical radius attainability on Hilbert space operators [1-12] and the reference therein.
Abstract/Overview A closed densely defined operator H, on a Banach space X, whose spectrum is contained in R and satisfies (z −H)−1 ≤ c hziα |=z|β ∀ z 6∈ R (0.1) for some α , β ≥ 0; c > 0, is said to be of (α, β)−type R . If instead of (0.1) we have (z −H)−1 ≤ c |z|α |=z|β ∀ z 6∈ R, (0.2) then H is of (α, β)0−type R . Examples of such operators include self-adjoint operators, Laplacian on L1(R), Schro¨dinger operators on Lp(Rn) and operators H whose ...
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.