With the power that has taken the information technologies, one has developed the study and research about cryptography, and cryptanalysis, in which Latin squares are ideal candidates for being used in cryptographic systems because the Cayley tables of the finite groups are Latin squares. This fact has awakened a new interest in the study of Latin squares by applying them to the study of code theory and error correcting codes. They also play a significant role in the statistical theory of experimental design. In this work, we develop an algorithm for the generation of Latin squares based on the cyclicunion operation defined for effect.
The objective of this dissertation is to study the Riemann zeta function in particular it will examine its analytic continuation, functional equation and applications. We will begin with some historical background, then define of the zeta function and some important tools which lead to the functional equation. We will present four different proofs of the functional equation. In addition, the ζ(s) has generalizations, and one of these the Dirichlet L-function will be presented. Finally, the zeros of ζ(s) will be studied.
A non-linear SHTR mathematical model was used to study the dynamics of drinking epidemic. We discussed the existence and stability of the drinking-free and endemic equilibria. The drinking-free equilibrium was locally asymptotically stable if R0 < 1and unstable if R0 > 1. Global stability of drinking-free and endemic equilibria were also considered in the model, using Lassalle’s invariance principle of Lyapunov functions. Numerical simulations were conducted to confirm our analytic results. Our findings was that, reducing the contact rate between the non-drinkers and heavy drinkers, increasing the number of drinkers that go into treatment and educating drinkers to refrain from drinking can be useful in combating the drinking epidemic.
Numerous plant diseases caused by pathogens like bacteria, viruses, fungi protozoa and pathogenic nematodes are propagated through media such as water, wind and other intermediary carries called vectors, and are therefore referred to as vector borne plant diseases.
Insect vector borne plant diseases are currently a major concern due to abundance of insects in the tropics which impacts negatively on food security, human health and world economies. Elimination or control of which can be achieved through understanding the process of propagation via Mathematical modeling. However existing models are linear and rarely incorporates climate change parameters to improve on their accuracy. Yields of plants can reduce significantly if they are infected by vectors borne diseases whose vectors have very short life span without necessarily inducing death to plants. Despite this, there is no reliable developed mathematical model to describe such dynamics.
This paper formulates and analyzes a dynamical nonlinear plant vector borne dispersion disease model that incorporates insect and plant population at equilibrium and wind as a parameter of climate change, to determine R0 , local and global stability in addition to sensitivity analysis of the basic reproduction number R0.
In this paper we introduce the notion of geodesically complete Lie algebroid. We give a Riemannian distance on the connected base manifold of a Riemannian Lie algebroid. We also prove that the distance is equivalent to natural one if the base manifold was endowed with Riemannian metric. We obtain Hopf Rinow type theorem in the case of transitive Riemannian Lie algebroid, and give a characterization of the connected base manifold of a geodesically complete Lie algebroid.