Abstract/Overview The present paper gives some results on local minimum and orthogonality of normal derivations in Cp-Classes. We employ some techniques for normal derivations due to Mecheri, Hacene, Bounkhel and Anderson. Let CpCp be normal, then the linear map = attains a local minimum at x Cp if and only if z Cp such that ) Also let Cp, and let have the polar decomposition, then the map attains local minimum on Cp at T if and only if. Regarding orthogonality, let SCp and let N(S) have ...
Abstract/Overview Most odour baits designed to attract host-seeking mosquitoes contain carbon dioxide (CO2), which enhances trap catches, given its role as a mosquito fight activator. However, the use of CO2 is expensive and logistically demanding for prolonged area-wide use.
Abstract/Overview Numerical range is useful in studying operators on Hilbert spaces. In particular, the geometrical properties of numerical range often provide useful information about algebraic and analytic properties of an operator. The theory of numerical range played a crucial role in the study of some algebraic structures especially in the non-associative context. The numerical range of an operator depends strongly upon the base field. Motivated by theoretical study and applications,...
Abstract/Overview Whereas phenetics emphasizes the use of maximum characters as practicable, decisions on how observations are translated to characters is of importance in systematics in order to partition objects in to nonoverlapping groups.The acetolysed pollen of selected Indigofera Linn. species were viewed under Mg x100 in Leica light microscope. Pollen characteristics of the following Indigofera species deposited in Maseno University Herbarium have been studied: I.paracapitata, I.as...
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...