Abstract The characterization of the group of units of any commutative ring has not been done in general, and previous studies have restricted the classes of rings or groups under consideration. In this work, we determine the structures of the groups of units of commutative completely primary finite rings R of characteristic pn for some prime integer p and positive integer n.
Abstract Let R be a completely primary finite ring and J be its Jacobson radical. A class of such rings in which J4 = (0), J3 = (0) has been constructed. Moreover, the structures of their groups of units have been determined for all the characteristics of R. Mathematcs Subject Classification: Primary 13M05, 16P10, 16U60; Secondary 13E10, 16N20
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...
Abstract In this paper, an application of the updated vector autoregresive model incorporating new information or measurements is considered. We consider secondary data obtained from the Kenya National Bureau of statistics, Statistical Abstract reports from 2000-2021 which is on monetary value marketed at current prices from crops, horticulture, livestock and related products, fisheries and forestry. A VAR(1) model is fitted to the data and then the model updated to incorporate the measureme...
Abstract Over the last decade major global efforts mounted to address the HIV epidemic has realized notable successes in combating the pandemic. Sub Saharan Africa (SSA) still remains a global epicenter of the disease, accounting for more than 70% of the global burden of infections. Despite wide spread use of various intervention strategies that act as mediation factors in Human Immunodeficiency Virus (HIV) prevention, HIV prevalence still remains a challenge especially in some geographic ar...
Abstract In this paper, a mathematical model based on a system of nonlinear parabolic partial differential equations is developed to investigate the effect of human mobility on the dynamics of coronavirus 2019 (COVID-19) disease. Positivity and boundedness of the model solutions are shown. The existence of the disease-free, the endemic equilibria, and the travelling wave solutions of the model are shown. From the numerical analysis, it is shown that human mobility plays a crucial role in the...
Abstract In this paper, a mathematical model based on a system of ordinary differential equations is developed with vaccination as an intervention for the transmission dynamics of coronavirus 2019 (COVID-19). The model solutions are shown to be well posed. The vaccine reproduction number is computed by using the next-generation matrix approach. The sensitivity analysis carried out on this model showed that the vaccination rate and vaccine efficacy are among the most sensitive parameters of t...
Abstract ABSTRACT: Radicalization is the process by which people come to adopt in- creasingly extreme political, social or religious ideologies. When radicalization leads to violence, radical thinking becomes a threat to national and international security. Prevention programs are part of an effort to combat violent extremism and terrorism. This type of initiative seek to prevent radicalization process from occurring and tak- ing hold in the first place. In this paper we introduce a simple c...
Abstract In this paper, we use the idealization procedure for finite rings to construct a class of quasi-3 prime Near-Rings N with a Jordan ideal J(N) and admitting a Frobenius derivation. The structural characterization of N; J(N) and commutation of N via the Frobenius derivations have been explicitly determined.
Abstract Infant mortality is an important marker of the overall society health. The 3rd goal of the Sustainable Development Goals aims at reducing infant deaths that occur due to preventable causes by 2030. Due to increased infant mortality the Kenyan government introduced Free Maternal Health Care as an intervention towards reducing infant mortality through elimination of the cost burden of accessing medical care by the mother and the infant. The study examines the impact of Free Maternal H...
Abstract In the present paper, we formulate a new mathematical model for the dynamics of moral corruption with comprehensive age-appropriate sexual information and provision of guidance and counselling. The population is subdivided into three (3) different compartments according to their level of information on sexual matters. The model is proved to be both epidemiologically and mathematically well posed. The existence of unique morally corrupt-free and endemic equilibrium points is investig...