Open Access Original Research Article

A Tutorial Exposition of Various Methods for Analyzing Capacitated Networks

Ali Muhammad Ali Rushdi, Omar Mutab Alsalami

Journal of Advances in Mathematics and Computer Science, Page 1-23
DOI: 10.9734/jamcs/2020/v35i630288

In order to assess the performance indexes of some practical systems having fixed channel capacities, such as telecommunication networks, power transmission systems or commodity pipeline systems, we propose various types of techniques for analyzing a capacitated network. These include Karnaugh maps, capacity-preserving network reduction rules associated with delta-star transformations, and a generalization of the max-flow min-cut theorem. All methods rely on recognizing the network capacity function as a random pseudo-Boolean function of link successes; a fact that allows the expected value of this function to be easily obtainable from its sum-of-products expression. This network capacity has certain advantages for representation of nonbinary discrete random functions, mostly employed in the analysis of flow networks. Five tutorial examples demonstrate the afore-mentioned methods and illustrate their computational advantages over the exhaustive state enumeration method.

Open Access Original Research Article

Oblateness Effects on Solar Sail in the Restricted Three–body Problem

Fatma M. Elmalky, M. N. Ismail, Ghada F. Mohamedien

Journal of Advances in Mathematics and Computer Science, Page 24-34
DOI: 10.9734/jamcs/2020/v35i630289

In the present work, the equations of motion of the solar sail are derived in the restricted three–body system. The dimensionless coordinates are used to obtain the solution of the problem. The Laplace transformations are used to solve these systems of equations to obtain the components of the solar sail acceleration. The motion about L2, L4 and its stability are studied under obalteness effects. The results obtained are in good agreement with previous results in this field. It is remarked that this model has special importance in space-dynamics to enabling spacecraft to do some maneuvers depends on the solar sail acceleration.

Open Access Original Research Article

An SEIQR Mathematical Model for The Spread of COVID-19

Samuel B. Apima, Jacinta M. Mutwiwa

Journal of Advances in Mathematics and Computer Science, Page 35-41
DOI: 10.9734/jamcs/2020/v35i630290

COVID-19, a novel coronavirus, is a respiratory infection which is spread between humans through small droplets expelled when a person with COVID-19 sneezes, coughs, or speaks. An SEIQR model to investigate the spread of COVID-19 was formulated and analysed. The disease free equilibrium point for formulated model was shown to be globally asymptotically stable. The endemic states were shown to exist provided that the basic reproduction number is greater than unity. By use of Routh-Hurwitz criterion and suitable Lyapunov functions, the endemic states are shown to be locally and globally asymptotically stable respectively. This means that any perturbation of the model by the introduction of infectives the model solutions will converge to the endemic states whenever reproduction number is greater than one, thus the disease transmission levels can be kept quite low or manageable with minimal deaths at the peak times of the re-occurrence.

Open Access Original Research Article

Odd Lindley-Kumaraswamy Distribution: Model, Properties and Application

Kuje Samson, Abubakar, Mohammad Auwal, Asongo, Iorkaa Abraham, Alhaji, Ismaila Sulaiman

Journal of Advances in Mathematics and Computer Science, Page 42-58
DOI: 10.9734/jamcs/2020/v35i630291

This article uses the odd Lindley-G family of distributions to propose and study a new compound distribution called “odd Lindley-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lindley-Kumaraswamy distribution are defined and studied by deriving and discussing many properties of the distribution such as the ordinary moments, moment generating function, characteristics function, quantile function, reliability functions, order statistics and other useful measures. The unknown model parameters are also estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real life datasets. The results show that the proposed distribution outperforms the other fitted compound models selected for this study and hence it is a flexible generalization of the Kumaraswamy distribution.

Open Access Original Research Article

Open Access Original Research Article

The Eigenvectors of the Transition Matrix as Predictors of the Dynamics of a Synchronous Boolean Network

Ali Muhammad Ali Rushdi, Adnan Ahmad Alsogati

Journal of Advances in Mathematics and Computer Science, Page 80-99
DOI: 10.9734/jamcs/2020/v35i630293

The synchronous Boolean network model is a simple and powerful tool in describing, analyzing and simulating cellular biological networks. This paper seeks a complete understanding of the dynamics of such a model by utilizing conventional matrix methods, rather than scalar methods, or matrix methods employing the non-conventional semi-tensor products (STP) of matrices. The paper starts by relating the network transition matrix to its function matrix via a self-inverse (involutary) state matrix, which has a simple recursive expression, provided a recursive ordering is employed for the underlying basis vector. Once the network transition matrix is obtained, it can be used to generate a wealth of information including its powers, characteristic equation, minimal equation, 1-eigenvectors, and 0-eigenvectors. These might be used to correctly predict both the transient behavior and (more importantly) the cyclic behavior of the network. In a short-cut partial variant of the proposed approach, the step of computing the transition matrix might be by-passed. The reason for this is that the transition matrix and the function matrix are similar matrices that share the same characteristic equation and hence the function matrix might suffice when only the partial information supplied by the characteristic equation is all that is needed. We demonstrate the conceptual simplicity and practical utility of our approach via two illustrative examples. The first example illustrates the computation of 1-eigenvectors (that can be used to identify loops or attractors), while the second example deals with the evaluation of 0-eigenvectors (that can be used to explore transient chains). Since attractors are the main concern in the underlying model, then analysis of the Boolean network might be confined to the determination of 1-eigenvectors only.

Open Access Original Research Article

The Reciprocal Generalized Inverse Gaussian Frailty with Application in Life Annuity Business

Walter Onchere, Richard Tinega, Patrick Weke, Jam Otieno

Journal of Advances in Mathematics and Computer Science, Page 112-131
DOI: 10.9734/jamcs/2020/v35i630295

Aims: As shown in literature, several authors have adopted various individual frailty mixing distributions as a way of dealing with possible heterogeneity due to unobserved covariates in a group of insurers. This research contribution is to generalize the frailty mixing distribution to nest other classes of frailty distributions not in literature and apply the proposed distributions in valuation of life annuity business.

Methodology: A simulation study is done to assess the performance of the aforementioned models. The baseline parameters is estimated using Bayesian Inference and a better model is suggested for valuation of life annuity business.

Results: As a result of generalizing the frailty some new classes of frailty distributions are constructed such as; the Reciprocal Inverse Gaussian Frailty, the Inverse Gamma Frailty, the Harmonic Frailty and the Positive Hyperbolic Frailty.

From the simulation study, the proposed new frailty models shows that ignoring frailty leads to an underestimation of future residual lifetime since the survival curve shifts to the right when heterogeneity is accounted for. This is consistent with frailty literature.

The Reciprocal Inverse Gaussian model closely represents the Association of Kenya Insurers graduated rates with a slight increase in survival due to longevity risk.

Conclusion: The proposed new frailty models show an increase in the insurers expected liability when unobserved heterogeneity is accounted for. This is consistent with frailty literature and thus can be applied to avoid underestimating the insurer’s liability in the context of life annuity business.

The RIG model as proposed in estimating future liability by directly adjusting the AKI mortality rates shows an increase in longevity risk. The extent of heterogeneity of the insured group determines the level of risk. The RIG frailties should be considered for multivariate cases where the insureds are clustered in groups.

Open Access Original Research Article

On gω-Open Sets in Grill Topological Spaces

Amin Saif, Mohammed Al-Hawmi, Basheer Al-Refaei

Journal of Advances in Mathematics and Computer Science, Page 132-143
DOI: 10.9734/jamcs/2020/v35i630296

The propose of this paper is to introduce and investigate a weak form of ω-open set in grill topological spaces. We introduce the notion of 113.png-open set as a form stronger than βω-open set and weaker than ω-open set and Untitled1.png-open set. By using this form, we study the generalization property, the interior operator, closure operator and θ-cluster operator.

Open Access Original Research Article

Some Topological and Algebraic Features of Symmetric Spaces

Um Salama, Ahmed Abd Alla, A. Elemam

Journal of Advances in Mathematics and Computer Science, Page 144-155
DOI: 10.9734/jamcs/2020/v35i630297

In this study, we introduce some approaches, geometrical and algebraic, which help to give further understanding of symmetric spaces. Symmetric space is a very important field for understanding abstract and applied features of spaces. We have introduced Riemannian Manifold, Lie groups and Lie algebras, and some of their topological and algebraic properties, with some concentration on Lie algebras and root systems , which help classification and many applications of symmetric spaces. The paper is an attempt to explain some algebraic features of symmetric spaces and how to get some of their properties using algebraic approach, concluded with some results.

Open Access Review Article

Regional Boundary Exact Controllability of the Wave Equation by Strategic Actuators on a Polygonal Domain with Cracks

Cheikh Seck, Ousmane Sène, Teuw Niane

Journal of Advances in Mathematics and Computer Science, Page 100-111
DOI: 10.9734/jamcs/2020/v35i630294

In this work we prove the exact controllability of the wave equation by acting on a strategic zone of the border of a non-convex polygonal domain with crack. Indeed, by combining two methods: that of Grisvard on the exact controllability on domains with corners and that of EL. Jai on the boundary strategic actutors, this exact controllability result has been proven.