Natural & Applied Sciences

Natural & Applied Sciences Research Papers/Topics

Mathematical model for nutrient exchange across the placenta

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...

Teachers` gender and primary school pupils` achievement in mathematics in Kenya

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 ...

Mathematical modeling of insulin therapy in patients with diabetes mellitus

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...

The algebra of smooth functions of rapid descent

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...

On Characterization of Very Rotund Banach Spaces

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.

On Compactness of Similarity Orbits of Norm-Attainable Operators

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...

Characterization of Norm-Attainable Operators

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.

On Compact Operators Whose Norms Are Eigenvalues and Completeness

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 ...

On denseness of similarity orbits of norm-attainable operators

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...

Prokaryotic diversity and potentially pathogenic bacteria in vended foods and environmental samples

Abstract Purpose: Ready-to-eat fast food vending outlets provide a cheap and readily available food. Foodborne diseases have been previously reported in Embu, Kenya, but data on the prokaryotic metagenome in vended foods is scanty. This study aimed to determine the prokaryotic diversity in fruits, vegetable salad, African sausage, chips (potato fries), fried fish, roasted beef (meat), smokies, samosa, soil, and water collected from food vendors and the surrounding environment in Embu Town an...

Probability of Default Estimation for Commercial Lenders in Developing Economies: Creditworthiness of Consumer Borrower

Abstract/Overview The Business of advancing credits is gradually becoming a major target for many banks, as a result there is high competition among the financial institutions leading to default of most credits. In order to raise the quality of advancing credits and reducing the risk involved thereafter, CSM’s have been developed to improve the process of assessing credit worthiness during the credit evaluation process. Previous repayments, demographic characteristics and statistical te...

Optimal Allocation in Double Sampling for Stratification in the Presence of Nonresponse and Measurement Errors

Abstract/Overview The present study addresses the problem of minimum cost and precision in the estimation of the population mean in the presence of nonresponse and measurement errors. It is assumed that both the survey variable and the auxiliary variable suffer from nonresponse and measurement errors in the second phase sample. A ratio, exponential ratio-ratio type, and exponential product-ratio type estimators of the population mean are proposed using the information on a single auxiliar...

Choi Matrices of 2-positive Maps on Positive Semidefinite Matrices

Abstract/Overview Several investigations have been done on positive maps on their algebraic structures with more emphasis on completely positive maps. In this study we have described the structure of the Choi matrices for 2−positive maps on positive semidefinite matrices and the conditions for complete positivity of positive linear maps fromMntoMn+1. The motivation behind these objectives is work done by Majewski and Marciniak on the structure of positive mapsφfromMntoMn+1(2≥2) betwe...

Logistic Black-Scholes-Merton Partial Differential Equation: A Case of Stochastic Volatility

Abstract/Overview Real world systems have been created using differential equations, this has made it possible to predict future trends and behaviour. Specifically, stochastic differential equations have been fundamental in describing and understanding random phenomena. So far the Black-Scholes-Merton partial differential equation used in deriving the famous Black-Scholes-Merton model has been one of the greatest breakthroughs in finance as far as prediction of asset prices in the stock m...

Metacognitive Monitoring as Predictor of Mathematics Achievement among Students in Public Secondary Schools in Kenya

Abstract/Overview This study investigated metacognitive monitoring as a predictor of mathematics achievement among students in public secondary schools in Kisii Central Sub County, Kenya. The study was guided by the Social Development Theory (1978) by Lev Vygotsky and the Theory of Education Productivity by Walberg (1981). The study employed the Solomon Four pretest-posttest two group design with posttest only control design. The study population included 1665 form 3 students and 41 form ...


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