Abstract This study investigates the impact of debt on economic performance in Kenya, focusing on both internal and external debt. Using regression analysis and correlation techniques, data from 2000 to 2021 was analyzed to understand the relationship between debt levels and economic growth indicators such as GDP. The findings reveal a nuanced relationship: while internal debt shows a positive association with economic growth, external debt demonstrates a negative association. Effective debt...

Abstract This study was to investigates the dynamics of inflation in Kenya through the application of advanced time series modeling techniques, specifically Autoregressive Integrated Moving Average (ARIMA) analysis. Inflation is a critical economic indicator that directly influences monetary policy, investment decisions, and overall economic stability. Given the dynamic of inflation in emerging economies such as Kenya, a fine understanding of its patterns and the ability to make accurate for...

Abstract The relationship between government revenue and economic growth is a debate that has existed for a long time in the living history.Government revenue impacts economic growth differently within different regions. Some researchers argue that government revenue positively affects economic growth while others argue that the relationship is negative. However, minimal literature exists exploring the relationship between the two variables at country specific level. The objective of this st...

Abstract Rainfall patterns play a critical role in shaping various aspects of our lives. Understanding the patterns, trends and predictability of rainfall is essential for effective planning and decision making in various aspects including agriculture, water resource management, disaster preparedness and social economic planning. In agricultural activities crops require specific amount of water at the right time for growth. By understanding the rainfall patterns, farmers can adapt their farm...

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...