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...
Abstract/Overview We seek to construct a zero coupon yield curve (ZCYC) for Nairobi Securities Exchange (NSE). The objective of this paper is to construct a ZCYC that is differentiable at all points and at the same time, produces continuous and positive forward curve. We will use the classical Nelson-Siegel model, Svensson Model, Rezende-Ferreira model and Svensson extended model. These models have linear and nonlinear guidelines making them have multiple local minima. This condition caus...
Abstract/Overview This study presents a new mathematical model for nutrient exchange across the placenta which include nutrient exchange from foetus to mother to provide a system of equations in the form, Y ሶ ൌ AY rԦሺtሻ and whose solution was analyzed for equilibrium and stability. This model introduces another parameter that takes care of waste elimination from foetus to mother. It was established that the final model is stable compared to the existing models, that is, the e...
Abstract/Overview This descriptive causal comparative study examined the relationship between teacher’s gender and in primary schools pupils’ performance in mathematics in Kenya. The study objective was to investigate the effect of teachers’ gender on primary schools pupils’ mathematics achievement in Vihiga district Kenya. The study was conducted through an ex-post facto research design. A total of 46 mathematics teachers were sampled from 153 schools. Data was collected using a ...
Abstract/Overview This study presents a Mathematical Model Insulin Therapy in Patients with Diabetes Mellitus which includes external rate at which blood glucose, insulin and epinephrine are being increased in the form, Y =AY+r (t) and whose solution was analyzed to provide the systems natural frequency, 0 , which is the basic descriptor of saturation level of the drug. It was established that the resonance period for the final model, that is, T 0 =3.76912 hrs, is in the accepta...
Abstract/Overview A bounded operator with the spectrum lying in a compact set V ⊂ R, has C∞ (V) functional calculus. On the other hand, an operator H acting on a Hilbert space H, admits a C(R) functional calculus if H is self-adjoint. So in a Banach space setting, we really desire a large enough intermediate topological algebra A, with C∞ 0 (R) ⊂ A ⊆ C(R) such that spectral operators or some sort of their restrictions, admit a A functional calculus. In this paper we construct su...
Abstract/Overview It is known that the Hilbert space H is the most rotund space among all Banach spaces. The question whether if a normed space X is a rotund Banach space implies we can obtain other most rotund spaces is still open and represents one of the most interesting and studied problems. In this paper we investigate if there exists other most rotund Banach spaces. It is shown that Frechet spaces are very rotund and also uniformly rotund.
Abstract/Overview The notion of compactness plays an important role in analysis. It has been extensively discussed on both metric and topological spaces. Various properties of compactness have been proved under the underlying spaces. However, if we consider these sets to be from similarity orbits of norm-attainable operators; little has been done to investigate their compactness. In this paper, we introduce the concept of compactness of similarity orbits of norm-attainable operators in as...
Abstract/Overview In this paper we characterize norm-attainable elementary operators, we show that 𝛿 𝑃,𝑄 is norm-attainable if both P and Q are norm-attainable and𝛿𝑃,𝑄 is norm-attainable 𝛿𝑃,𝑄if is normally represented.
Abstract/Overview Let X be a Banach space and T: X→Y be a linear operator, then Tis compact if it maps bounded sequences in X to sequences in Y with convergent subsequences, that is, if xn ∈ X is a bounded sequence, then T xn ∈ Y has a convergent subsequence say, T xnk in Y. The eigenvalue of an operator T, is a scalar λ if there is a nontrivial solution x such that T x=λ x. Such an x is called an eigenvector corresponding to the eigenvalue λ. A vector space is complete if every ...
Abstract/Overview The notion of dense sets has been extensively discussed on both metric and topological spaces. Various properties of the sets have been proved under the underlying spaces. However, if we consider these sets to be from similarity orbits where a topology has been developed on them, little has been done to investigate their denseness. In this paper, we introduce the concept of denseness of similarity orbits of norm-attainable operators in aspect of generalized sets in topol...