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Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.
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Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets
The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of -soft semi- and -soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi- and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a -soft semiregular space and demonstrate that it guarantees the equivalence of -soft semi-. Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.
Extended Gumbel Type-2 Distribution: Properties and Applications
In this paper, we proposed a new four-parameter Extended Gumbel type-2 distribution which can further be split into the Lehman type I and type II Gumbel type-2 distribution by using a generalized exponentiated distribution. The distributional properties of the proposed distribution have been studied. We derive the th moment; thus, we generalize some results in the literature. Expressions for the density, moment-generating function, and th moment of the order statistics are also obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix of the developed distribution. Two life data, which consist of data on cancer remission times and survival times of pigs, were used to show the applicability of the Extended Gumbel type-2 distribution in modelling real life data, and we found out that the new model is more flexible than its submodels.
Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep
In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if . We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if . Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep (). Thus, the effective controlling strategies are associated with this parameter.
Some Common Fixed Point Theorems in Partially Ordered Sets
The purpose of this paper is to prove some new fixed point theorem and common fixed point theorems of a commuting family of order-preserving mappings defined on an ordered set, which unify and generalize some relevant fixed point theorems.
Water Quality Analysis for the Depletion of Dissolved Oxygen due to Exponentially Increasing Form of Pollution Sources
Analyzing and improving mathematical models for water quality investigation are imperative for water quality issues around the world. This study is aimed at presenting the 1D unsteady state regarding analytical and numerical solutions of dissolved oxygen (DO) concentration in a river, in which the increase of pollution from a source is considered as an exponential term. Laplace transformation was utilized to obtain analytical solutions, while the finite difference technique was selected for numerical solutions. The results show that the rate of pollutant addition along the river () and the arbitrary constants of an exponentially increasing pollution source term () affected inversely, while the initial concentration affected directly, DO in the river. These solutions and simulations can be enabled for testing in various scenarios in terms of the behavior of oxygen depletion in polluted rivers.
Mathematical Model to Estimate and Predict the COVID-19 Infections in Morocco: Optimal Control Strategy
In this paper, we aim to estimate and predict the situation of the new coronavirus pandemic (COVID-19) in countries under quarantine measures. First, we present a new discrete-time mathematical model describing the evolution of the COVID-19 in a population under quarantine. We are motivated by the growing numbers of infections and deaths in countries under quarantine to investigate potential causes. We consider two new classes of people, those who respect the quarantine and stay at home, and those who do not respect the quarantine and leave their homes for one or another reason. Second, we use real published data to estimate the parameters of the model, and then, we estimate these populations in Morocco. We investigate the impact of people who underestimate the quarantine by considering an optimal control strategy to reduce this category and then reducing the number of the population at risk in Morocco. We provide several simulations to support our findings.