Abstract/Overview In this paper, we examine conservative autonomous dynamic vibration equation, f(x) = sech 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 New mark method are tabulated and then represented graphically. Further the stability of the algorithms employed is also discussed
Abstract/Overview Land use activities along River Nzoia Drainage Basin, Kenya, include cultivation along the river banks, over grazing, deforestation, draining of wetlands for horticulture, harvesting of sand and brick-making. These activities have brought about changes in soil properties in the drainage basin adversely affecting farming output and the ecosystem in general. Consequently, it is important to understand how the different land use activities influence the soil properties in o...
Abstract/Overview Modeling of some physical phenomena and technological processes taking into account dissipation leads to the Sine-Gordon equation with the first time derivative. The (2+1) Sine-Gordon equation with the first time derivative is used in explaining a number of physical phenomena including the propagation of fluxons in Josephson junctions. This study uses Finite Difference Method to solve (2+1) dimensional Sine-Gordon equation with the first time derivative that models dissi...
Abstract/Overview Finite element method is a class of mathematical tool which approximates solutions to initial and boundary value problems. Finite element, basic functions, stiffness matrices, systems of ordinary differential equations and hence approximate solutions of partial differential equations which involves rendering the partial differential equation into system of ordinary differential equations. The ordinary differential equations are then numerically integrated. We present a f...
Abstract/Overview The nonlinear (1+1) Sine-Gordon equation that governs the vibrations of the rigid pendula attached to a stretched wire is solved. The equation is discretized and solved by Finite Difference Method with specific initial and boundary conditions. A Crank Nicolson numerical scheme is developed with concepts of stability of the scheme analysed using matrix method. The resulting systems of linear algebraic equations are solved using Mathematica software. The solutions are pres...
Abstract/Overview In this paper we establish the exact time of death of a murdered person. This leads to an ordinary differential equation whose solution has been analyzed to provide the approximate time of death. Forensic expert will try to estimate this time from body’s current temperature and calculating how long it would have taken to lose heat to reach this point. This provides an accurate approach to establish the approximate time when crime is committed
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 ...