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...
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...
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 ...
Abstract/Overview The matrix models have been applied to evaluate the impacts and management of tree species. Modeling of invasive species using stage based matrix methods has not been exploited to understand the population structure of the invasive species. The study simulated using stage-structured Lefkovitch models to assess the population structure and impacts of invasive population growth within Mount Elgon Ecosystem. The survey data were used to calculate the transition probabilitie...
Abstract/Overview Nonlinear Black-Scholes equations provide more accurate values by taking into account more realistic assumptions, such as transaction costs, illiquid markets, risks from an unprotected portfolio or large investor's preferences, which may have an impact on the stock price, the volatility, the drift and the option price itself. Most modern models are represented by nonlinear variations of the well-known Black-Scholes Equation. On the other hand, asset security prices may n...
Abstract/Overview The purpose of this study was to investigate selected goal-setting as a predictor of mathematics performance among students in public secondary schools in Kisii Central Sub-County, Kenya. The study was guided by the Social Development Theory (1978) by Levi Vygotsky and the Theory of Education Productivity by Walberg (1981). The study employed the Solomon Four pretest-posttest two group design with post-test only control design. The study population included 1665 form 3 s...
Abstract/Overview This paper presents study on the application of multiple discriminant analysis (MDA) to distinguish between languages with a focus on five languages of the Coastal region of Kenya. Chapter one gives an introduction of the paper, chapter two explains the methodology used, chapter three presents the results, chapter four gives a brief discussion of the findings, and lastly chapter five presents the conclusions and recommendations.
Abstract/Overview A probability distribution can be constructed by mixing two distributions. Binomial distribution when compounded with beta distribution as prior forms a binomial mixture that is a continuous distribution. Skellam 1948, mixed a binomial distribution with its parameter being the probability of success considered as a random variable taking beta distribution. Probability distributions with binomial outcome tend to fail to fit empirical data due to over-dispersion. To addres...
Abstract/Overview Various aspects of elementary operators have been characterized by many mathematicians. In this paper, we consider norm-attainability and orthogonality of these operators in Banach spaces. Characterizations and generalizations of norm-attainability and orthogonality are given in details. We first give necessary and sufficient conditions for norm-attainability of Hilbert space operators then we give results on orthogonality of the range and the kernel of elementary operat...
Abstract/Overview Black Scholes formula is crucial in modern applied finance. Since the introduction of Black – Scholes concept model that assumes volatility is constant; several studies have proposed models that address the shortcomings of Black – Scholes model. Heston’s models stands out amongst most volatility models because the process of volatility is positive and is a process that obeys mean reversion and this is what is observed in the real market world. One of the shortcomin...
Abstract/Overview Topological Data Analysis (TDA) is an important aspect in the field of topological data theory since the 21st century’s first decade. Modern TDA utilizes the structural characteristics of Big Data (BD), otherwise known as point cloud data sets. Topology and Geometry are tools used to analyze highly complex and multi-dimensional data by creating a summary of these characteristics to uncover hidden features in these datasets, while preserving feature relationships with...
Abstract/Overview Wave equation is a linear hyperbolic partial differential equation (PDE) which describes the propagation of a variety of waves arising in physical situations. In its simplest form, the one dimension wave equation refers to a scalar function u = u(x, t), which satisfy the PDE utt = C2uxx. When the wave propagates in complex media, form of the governing wave equation changes, so in particular a viscous loss in term µuxxt and the advection term αux are added to the right ...
Abstract/Overview We establish the norm-denseness of the norm-attainable class $NAB(H)$ in the Banach algebra $B(H)$, which consists of all bounded linear operators on a complex Hilbert space $H$. Specifically, for every $O in NAB(H)$ and each $epsilon>0$, there exists $O' in B(H)$ such that $|O - O'| < epsilon$. We achieve this characterization by utilizing the convergence of sequences and the existence of limit points. The properties $A$ and $B$ of Lindenstrauss are sufficient to ensure...
Abstract/Overview The dynamic behavior of a multi-species system that includes a prey refuge and a Holling type III functional response is examined in this work. The pre-requisites for the presence of the equilibrium points, as well as their local and global stabilities, for the suggested system are analyzed and derived. The Routh-Hurwitz criterion and the eigenvalue technique are used to study the local stabilities. On the other hand, the global stabilities have been studied using the Ly...
Abstract/Overview The coexistence of interacting biological species is a vital issue for the management of existing resources and the prediction of the long-term survival of each species. Many species become extinct due to several factors including over-exploitation among others. Suitable measures such as restriction on harvesting, creation of reserved zones among others are key in saving these species. Multi-species models incorporating prey refuge with Holling type I functional response...