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...

Abstract/Overview Jump diffusion processes have been used in modern finance to capture discontinuous behavior in asset pricing. Logistic Brownian motion for asset security prices shows that naturally asset security prices would not usually shoot indefinitely due to the regulating factor that may limit the asset prices. Geometric Brownian motion cannot accurately reflect all behaviors of stock quotation therefore, Merton who was involved in the process of developing the Black-Scholes model...

Abstract Let an operator T belong to an operator ideal J, then for any operators A and B which can be composed with T as BTA then BTA J. Indeed, J contains the class of finite rank Banach Space operators. Now given L(X, Y ). Then J(X, Y ) L(X, Y ) such that J(X Y ) = {T : X Y : T }. Thus an operator ideal is a subclass J of L containing every identity operator acting on a one-dimensional Banach space such that: S + T J(X, Y ) where S, T J(X, Y ). If W,Z,X, Y ,A L(W,X),B L(Y,Z) then BTA J(W,Z...

Abstract The study of finite completely primary rings through the zero divisor graphs, the unit groups and their associated matrices, and the automorphism groups have attracted much attention in the recent past. For the Galois ring R′ and the 2-radical zero finite rings, the mentioned algebraic structures are well understood. Studies on the 3-radical zero finite rings have also been done for the unit groups and the zero divisor graphs Γ(R). However, the characterization of the matrices as...

Abstract In this paper, we investigate the generalizations of the concepts from Heine-Borel Theorem and the Bolzano-Weierstrass Theorem to metric spaces. We show that the metric space X is compact if every open covering has a finite subcovering. This abstracts the Heine-Borel property. Indeed, the Heine-Borel Theorem states that closed bounded subsets of the real line R are compact. In this study, we rephrase compactness in terms of closed bounded subsets of the real line R, that is, the Bol...

Abstract Let n,x,y,z be any given integers. The study of n for which n = x2 +y2 + z2 is a very long-standing problem. Recent survey of sizeable literature shows that many researchers have made some progress to come up with algorithms of decomposing integers into sums of three squares. On the other hand, available results on integer representation as sums of three square is still very minimal. If a,b,c,d,k,m,n,u,v and w are any non-negative integers, this study determines the sum of three-squ...

Abstract The study of completely primary nite rings has generated interest- ing results in the structure theory of nite rings with identity. It has been shown that a nite ring can be classi ed by studying the structures of its group of units. But this group has subgroups which are interesting objects of study. Let R be a completely primary nite ring of character- istic pn and J be its Jacobson radical satisfying the condition Jn = (0) and Jn1 6= (0). In this paper, we characterize the qu...