This research aims to solve a comprehensive one-dimensional model of drug release from cardiovascular stents in which the drug binding is saturable and reversible. We used the Lagrange collocation method for space dimension and the modified Euler method for time discretization. The existence and uniqueness of the solution, are provided. The consistency, stability, and convergence analysis of the proposed scheme are provided, to show that numerical simulations are valid. Numerical results accurate enough and efficient just by using fewer mesh.
{"title":"An Explicit spectral collocation method for the drug Release coronary Stents","authors":"Somayeh Fakhri, S. H. Momeni-Masuleh","doi":"10.3846/mma.2022.15066","DOIUrl":"https://doi.org/10.3846/mma.2022.15066","url":null,"abstract":"This research aims to solve a comprehensive one-dimensional model of drug release from cardiovascular stents in which the drug binding is saturable and reversible. We used the Lagrange collocation method for space dimension and the modified Euler method for time discretization. The existence and uniqueness of the solution, are provided. The consistency, stability, and convergence analysis of the proposed scheme are provided, to show that numerical simulations are valid. Numerical results accurate enough and efficient just by using fewer mesh.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75337979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. González‐Olivares, Adolfo Mosquera-Aguilar, Paulo C. Tintinago-Ruiz, A. Rojas‐Palma
A Leslie-Gower type predator-prey model including group defense formation is analyzed. This phenomenon, described by a non-monotonic function originates interesting dynamics; positiveness, boundedness, permanence of solutions, and existence of up to three positive equilibria are established. The solutions are highly sensitive to initial conditions since there exists a separatrix curve dividing their behavior. Two near trajectories can have far omega-limit sets. The weakness of a singularity is established showing two limit cycles can exist. Numerical simulations endorse the analytical outcomes.
{"title":"Bifurcations in a Leslie-Gower Type predator-prey Model with a rational non-Monotonic Functional response","authors":"E. González‐Olivares, Adolfo Mosquera-Aguilar, Paulo C. Tintinago-Ruiz, A. Rojas‐Palma","doi":"10.3846/mma.2022.15528","DOIUrl":"https://doi.org/10.3846/mma.2022.15528","url":null,"abstract":"A Leslie-Gower type predator-prey model including group defense formation is analyzed. This phenomenon, described by a non-monotonic function originates interesting dynamics; positiveness, boundedness, permanence of solutions, and existence of up to three positive equilibria are established. The solutions are highly sensitive to initial conditions since there exists a separatrix curve dividing their behavior. Two near trajectories can have far omega-limit sets. The weakness of a singularity is established showing two limit cycles can exist. Numerical simulations endorse the analytical outcomes.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88804152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes an efficient method for active unsupervised texture segmentation. A new descriptor for texture features extractions based on Gaussian and mean curvature is constructed. Then the optimization of a functional who uses the R´enyi divergence measure and our descriptor is proposed in order to design an active contour model for texture segmentation. To get a global solution and efficient, fast algorithm, the optimization problem is redefined. The algorithm associated with this last optimization problem avoids local minimums and the run-time consuming compared to the level-set representation of our active contour model. In order to illustrate the performance of the technique, some results are presented showing the effectiveness and robustness of our approach.
{"title":"An Active Contour Model for texture Image Segmentation using RéNyi Divergence Measure","authors":"Sidi Yassine Idrissi","doi":"10.3846/mma.2022.14060","DOIUrl":"https://doi.org/10.3846/mma.2022.14060","url":null,"abstract":"This paper proposes an efficient method for active unsupervised texture segmentation. A new descriptor for texture features extractions based on Gaussian and mean curvature is constructed. Then the optimization of a functional who uses the R´enyi divergence measure and our descriptor is proposed in order to design an active contour model for texture segmentation. To get a global solution and efficient, fast algorithm, the optimization problem is redefined. The algorithm associated with this last optimization problem avoids local minimums and the run-time consuming compared to the level-set representation of our active contour model. In order to illustrate the performance of the technique, some results are presented showing the effectiveness and robustness of our approach.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72367836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Somia Ayad, Ali Laksaci, Saâdia Rahmani, R. Rouane
The focus of functional data analysis has been mostly on independent functional observations. It is therefore hoped that the present contribution will provide an informative account of a useful approach that merges the ideas of the ergodic theory and the functional data analysis by using the local linear approach. More precisely, we aim, in this paper, to estimate the conditional distribution function (CDF) of a scalar response variable given a random variable taking values in a semimetric space. Under the ergodicity assumption, we study the uniform almost complete convergence (with a rate), as well as the asymptotic normality of the constructed estimator. The relevance of the proposed estimator is verified through a simulation study.
{"title":"Local linear modelling of the Conditional Distribution function for Functional Ergodic Data","authors":"Somia Ayad, Ali Laksaci, Saâdia Rahmani, R. Rouane","doi":"10.3846/mma.2022.14909","DOIUrl":"https://doi.org/10.3846/mma.2022.14909","url":null,"abstract":"The focus of functional data analysis has been mostly on independent functional observations. It is therefore hoped that the present contribution will provide an informative account of a useful approach that merges the ideas of the ergodic theory and the functional data analysis by using the local linear approach. More precisely, we aim, in this paper, to estimate the conditional distribution function (CDF) of a scalar response variable given a random variable taking values in a semimetric space. Under the ergodicity assumption, we study the uniform almost complete convergence (with a rate), as well as the asymptotic normality of the constructed estimator. The relevance of the proposed estimator is verified through a simulation study.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74093442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Potato virus Y (PVY) is an aphid-borne plant virus that causes substantial yield losses in potato production. Control measures of the viral infection are both limited and expensive. A proper use of mixed-cropping strategy can reduce the spread of PVY. In this paper, we formulate and analyze a mathematical model of PVY spread in a mixed-cropping system. Then, we extend the model to an optimal control problem by considering use of mineral oil, insecticide and farmer’s level of field inspection for infected plants. The analytic results show that the basic reproduction number ℜ0, a threshold parameter that decides properties of the dynamics. The disease free equilibrium is stable if ℜ0 < 1 and unstable when ℜ0 > 1. It is found that ℜ0, and hence, the disease dynamics is highly sensitive to the representative parameters of density the non-host plant and its quality in attracting vectors. The model exhibits forward bifurcation at ℜ0 = 1. The study of optimal control problem suggests that mixed-cropping combined with either mineral oil or insecticide is the best to control the disease. Furthermore, simulation results show that mixed-cropping can be used as an alternative strategy and can reduce the need of mineral oil or insecticide.
{"title":"Mathematical Model of Potato virus y disease spread with Optimal control","authors":"Shambel Tadesse Degefa, O. Makinde, T. T. Dufera","doi":"10.3846/mma.2022.15077","DOIUrl":"https://doi.org/10.3846/mma.2022.15077","url":null,"abstract":"Potato virus Y (PVY) is an aphid-borne plant virus that causes substantial yield losses in potato production. Control measures of the viral infection are both limited and expensive. A proper use of mixed-cropping strategy can reduce the spread of PVY. In this paper, we formulate and analyze a mathematical model of PVY spread in a mixed-cropping system. Then, we extend the model to an optimal control problem by considering use of mineral oil, insecticide and farmer’s level of field inspection for infected plants. The analytic results show that the basic reproduction number ℜ0, a threshold parameter that decides properties of the dynamics. The disease free equilibrium is stable if ℜ0 < 1 and unstable when ℜ0 > 1. It is found that ℜ0, and hence, the disease dynamics is highly sensitive to the representative parameters of density the non-host plant and its quality in attracting vectors. The model exhibits forward bifurcation at ℜ0 = 1. The study of optimal control problem suggests that mixed-cropping combined with either mineral oil or insecticide is the best to control the disease. Furthermore, simulation results show that mixed-cropping can be used as an alternative strategy and can reduce the need of mineral oil or insecticide.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85440558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mudasir Younis, Deepak Singh, Lili Chen, M. Metwali
In the commenced work, we establish some novel results concerning graph contractions in a more generalized setting. Furthermore, we deliver some examples to elaborate and explain the usability of the attained results. By virtue of nontrivial examples, we show our results improve, extend, generalize, and unify several noteworthy results in the existing state-of-art. We adopt computer simulation validating our results. To arouse further interest in the subject and to show its efficacy, we devote this work to recent applications which emphasize primarily the applications for the existence of the solution of various models related to engineering problems viz. fourth-order two-point boundary value problems describing deformations of an elastic beam, ascending motion of a rocket, and a class of integral equations. This approach is entirely new and will open up some new directions in the underlying graph structure.
{"title":"A Study on the solutions of Notable Engineering Models","authors":"Mudasir Younis, Deepak Singh, Lili Chen, M. Metwali","doi":"10.3846/mma.2022.15276","DOIUrl":"https://doi.org/10.3846/mma.2022.15276","url":null,"abstract":"In the commenced work, we establish some novel results concerning graph contractions in a more generalized setting. Furthermore, we deliver some examples to elaborate and explain the usability of the attained results. By virtue of nontrivial examples, we show our results improve, extend, generalize, and unify several noteworthy results in the existing state-of-art. We adopt computer simulation validating our results. To arouse further interest in the subject and to show its efficacy, we devote this work to recent applications which emphasize primarily the applications for the existence of the solution of various models related to engineering problems viz. fourth-order two-point boundary value problems describing deformations of an elastic beam, ascending motion of a rocket, and a class of integral equations. This approach is entirely new and will open up some new directions in the underlying graph structure.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89629186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a multi-parameter projection method for solving a variational inequality problem, and establish its strong convergence in a Hilbert space under appropriate conditions. The method involves two projectionsteps with different variable stepsizes where one of them is computed explicitly on a specifically structural half-space. The proof of strong convergence of the method is based on the regularization solutions depending on parameters of the original problem. It turns out that the solution obtained by the method is the solution of a bilevel variational inequality problem whose constraint is the solution set of our considered problem. In order to support the obtained theoretical results, we perform some experiments on transportation equilibrium and optimal control problems, and also involve comparisons. Numerical results show the computational effectiveness and the fast convergence of the new method over some existing ones.
{"title":"Strong convergence of Multi-parameter Projection Methods for variational inequality Problems","authors":"D. Hieu, L. Muu, Pham Kim Quy","doi":"10.3846/mma.2022.14479","DOIUrl":"https://doi.org/10.3846/mma.2022.14479","url":null,"abstract":"In this paper, we introduce a multi-parameter projection method for solving a variational inequality problem, and establish its strong convergence in a Hilbert space under appropriate conditions. The method involves two projectionsteps with different variable stepsizes where one of them is computed explicitly on a specifically structural half-space. The proof of strong convergence of the method is based on the regularization solutions depending on parameters of the original problem. It turns out that the solution obtained by the method is the solution of a bilevel variational inequality problem whose constraint is the solution set of our considered problem. In order to support the obtained theoretical results, we perform some experiments on transportation equilibrium and optimal control problems, and also involve comparisons. Numerical results show the computational effectiveness and the fast convergence of the new method over some existing ones.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87684086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a class of non-linear SIRS epidemic model, we analyse some useful conditions on the model parameters to determine a safety set for the containment of an epidemic. In addition, once that set is determined, we find control actions so that the epidemic remains within the security set with infection rates below an allowed amount. More specifically, for every initial state in a certain safety set of the state space there exists an adequate control policy maintaining the state of the system in such safety set. Sufficient conditions for the existence of a solution under a feedback are derived in terms of linear inequalities on the input vectors at the vertices of a polytope.
{"title":"On a Safety Set for an epidemic Model with a Bounded Population","authors":"C. Coll, S. Romero-Vivó, E. Sánchez","doi":"10.3846/mma.2022.14586","DOIUrl":"https://doi.org/10.3846/mma.2022.14586","url":null,"abstract":"Given a class of non-linear SIRS epidemic model, we analyse some useful conditions on the model parameters to determine a safety set for the containment of an epidemic. In addition, once that set is determined, we find control actions so that the epidemic remains within the security set with infection rates below an allowed amount. More specifically, for every initial state in a certain safety set of the state space there exists an adequate control policy maintaining the state of the system in such safety set. Sufficient conditions for the existence of a solution under a feedback are derived in terms of linear inequalities on the input vectors at the vertices of a polytope.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76396926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a simple scheme is constructed for finding approximate solution of the nonlinear Fredholm integral equation of the second kind. To this end, the Lagrange interpolation polynomials together with the Gauss-Legendre quadrature rule are used to transform the source problem to a system of nonlinear algebraic equations. Afterwards, the resulting system can be solved by the Newton method. The basic idea is to choose the Lagrange interpolation points to be the same as the points for the Gauss-Legendre integration. This facilitates the evaluation of the integral part of the equation. We prove that the approximate solution converges uniformly to the exact solution. Also, stability of the approximate solution is investigated. The advantages of the method are simplicity, fastness and accuracy which enhance its applicability in practical situations. Finally, we provide some test examples.
{"title":"An Effective and Simple Scheme for solving nonlinear Fredholm integral equations","authors":"A. Shahsavaran, F. Fotros","doi":"10.3846/mma.2022.14194","DOIUrl":"https://doi.org/10.3846/mma.2022.14194","url":null,"abstract":"In this paper, a simple scheme is constructed for finding approximate solution of the nonlinear Fredholm integral equation of the second kind. To this end, the Lagrange interpolation polynomials together with the Gauss-Legendre quadrature rule are used to transform the source problem to a system of nonlinear algebraic equations. Afterwards, the resulting system can be solved by the Newton method. The basic idea is to choose the Lagrange interpolation points to be the same as the points for the Gauss-Legendre integration. This facilitates the evaluation of the integral part of the equation. We prove that the approximate solution converges uniformly to the exact solution. Also, stability of the approximate solution is investigated. The advantages of the method are simplicity, fastness and accuracy which enhance its applicability in practical situations. Finally, we provide some test examples.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87342425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we show the existence result of the following fractional p-Laplacian system (−∆)spu = f(x,u) in Ω, u = 0 in RnΩ, for a given datum f. The existence of weak solutions is obtained by using the theory of Young measures.
{"title":"Existence Results for fractional P-Laplacian Systems via Young Measures","authors":"Farah Balaadich, E. Azroul","doi":"10.3846/mma.2022.14452","DOIUrl":"https://doi.org/10.3846/mma.2022.14452","url":null,"abstract":"In this paper, we show the existence result of the following fractional p-Laplacian system (−∆)spu = f(x,u) in Ω, u = 0 in RnΩ, for a given datum f. The existence of weak solutions is obtained by using the theory of Young measures.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91096731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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