Mathematical and Computational Applications Latest open access articles published in Math. Comput. Appl. at http://www.mdpi.com/journal/mca http://www.mdpi.com/journal/mca MDPI en Creative Commons Attribution (CC-BY) MDPI support@mdpi.com MCA, Vol. 24, Pages 32: Global Sensitivity Analysis to Study the Impacts of Bed-Nets, Drug Treatment, and Their Efficacies on a Two-Strain Malaria Model http://www.mdpi.com/2297-8747/24/1/32 Malaria is a deadly infectious disease, which is transmitted to humans via the bites of infected female mosquitoes. Antimalarial drug resistance has been identified as one of the characteristics of malaria that complicates control efforts. Typically, the use of insecticide-treated bed-nets (ITNs) and drug treatment are some of the recommended control strategies against malaria. Here, the use of ITNs, drug treatment, and their efficacies and evolution of antimalarial drug resistance are considered to be the major driving forces in the dynamics of malaria transmissions. We formulate a mathematical model of two-strain malaria to assess the impacts of ITNs, drug treatment, and their efficacies on the transmission dynamics of the disease in a human population. We propose a simple mosquito biting rate function that depends on both the proportion of ITN usage and its efficacy. We show that both disease-free and co-existence equilibrium points are globally-asymptotically stable where they exist. The global uncertainty and sensitivity analysis conducted show that if about 95% of malaria cases can be treated with fewer than 5% treatment failure in a population with 95% ITN usage that remains 95% effective, malaria can be controlled. We find that the order in which numerous intervention measures are taken is important. MCA, Vol. 24, Pages 32: Global Sensitivity Analysis to Study the Impacts of Bed-Nets, Drug Treatment, and Their Efficacies on a Two-Strain Malaria Model

Mathematical and Computational Applications doi: 10.3390/mca24010032

Authors: Saminu Bala Bello Gimba

Malaria is a deadly infectious disease, which is transmitted to humans via the bites of infected female mosquitoes. Antimalarial drug resistance has been identified as one of the characteristics of malaria that complicates control efforts. Typically, the use of insecticide-treated bed-nets (ITNs) and drug treatment are some of the recommended control strategies against malaria. Here, the use of ITNs, drug treatment, and their efficacies and evolution of antimalarial drug resistance are considered to be the major driving forces in the dynamics of malaria transmissions. We formulate a mathematical model of two-strain malaria to assess the impacts of ITNs, drug treatment, and their efficacies on the transmission dynamics of the disease in a human population. We propose a simple mosquito biting rate function that depends on both the proportion of ITN usage and its efficacy. We show that both disease-free and co-existence equilibrium points are globally-asymptotically stable where they exist. The global uncertainty and sensitivity analysis conducted show that if about 95% of malaria cases can be treated with fewer than 5% treatment failure in a population with 95% ITN usage that remains 95% effective, malaria can be controlled. We find that the order in which numerous intervention measures are taken is important.

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Global Sensitivity Analysis to Study the Impacts of Bed-Nets, Drug Treatment, and Their Efficacies on a Two-Strain Malaria Model Saminu Bala Bello Gimba doi: 10.3390/mca24010032 Mathematical and Computational Applications 2019-03-12 Mathematical and Computational Applications 2019-03-12 24 1 Article 32 10.3390/mca24010032 http://www.mdpi.com/2297-8747/24/1/32
MCA, Vol. 24, Pages 31: An Analytical Study of Adversely Affecting Radiation and Temperature Parameters on a Magnetohydrodynamic Elasto-viscous Fluid http://www.mdpi.com/2297-8747/24/1/31 An investigation of how the velocity of elasto-viscous fluid past an infinite plate, with slip and variable temperature, is influenced by combined thermal-radiative diffusion effects has been carried out. The study of dynamics of a flow model leads to the generation of characteristic fluid parameters ( G r , G m , M, F, S c and P r ). The interaction of these parameters with elasto-viscous parameter K &amp;prime; is probed to describe how certain parametric range and conditions could be pre-decided to enhance the flow speed past a channel. In particular, the flow dynamics&amp;rsquo; alteration in correspondence to the slip parameter&amp;rsquo;s choice, along with temperature provision to the boundary in temporal pattern, is determined through uniquely calculated exact expressions of velocity, temperature and mass concentration of the fluid. The complex multi-parametric model has been analytically solved using the Laplace and Inverse Laplace transform. Through study of calculated exact expressions, an identification of variables, adversely (M, F, S c and P r ) and favourably ( G r and G m ) affecting the flow speed and temperature has been made. The accuracy of our results have also been tested by computing matching numerical solutions and by graphical reasoning. The verification of existing results of Newtonian fluid with varying boundary condition of velocity and temperature has also been completed, affirming the veracity of present results. MCA, Vol. 24, Pages 31: An Analytical Study of Adversely Affecting Radiation and Temperature Parameters on a Magnetohydrodynamic Elasto-viscous Fluid

Mathematical and Computational Applications doi: 10.3390/mca24010031

Authors: Nazish Shahid

An investigation of how the velocity of elasto-viscous fluid past an infinite plate, with slip and variable temperature, is influenced by combined thermal-radiative diffusion effects has been carried out. The study of dynamics of a flow model leads to the generation of characteristic fluid parameters ( G r , G m , M, F, S c and P r ). The interaction of these parameters with elasto-viscous parameter K &amp;prime; is probed to describe how certain parametric range and conditions could be pre-decided to enhance the flow speed past a channel. In particular, the flow dynamics&amp;rsquo; alteration in correspondence to the slip parameter&amp;rsquo;s choice, along with temperature provision to the boundary in temporal pattern, is determined through uniquely calculated exact expressions of velocity, temperature and mass concentration of the fluid. The complex multi-parametric model has been analytically solved using the Laplace and Inverse Laplace transform. Through study of calculated exact expressions, an identification of variables, adversely (M, F, S c and P r ) and favourably ( G r and G m ) affecting the flow speed and temperature has been made. The accuracy of our results have also been tested by computing matching numerical solutions and by graphical reasoning. The verification of existing results of Newtonian fluid with varying boundary condition of velocity and temperature has also been completed, affirming the veracity of present results.

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An Analytical Study of Adversely Affecting Radiation and Temperature Parameters on a Magnetohydrodynamic Elasto-viscous Fluid Nazish Shahid doi: 10.3390/mca24010031 Mathematical and Computational Applications 2019-03-12 Mathematical and Computational Applications 2019-03-12 24 1 Article 31 10.3390/mca24010031 http://www.mdpi.com/2297-8747/24/1/31
MCA, Vol. 24, Pages 30: Toward Optimality of Proper Generalised Decomposition Bases http://www.mdpi.com/2297-8747/24/1/30 The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the ROB, i.e., the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of a Proper Generalized Decomposition (PGD) basis using a randomised Singular Value Decomposition (SVD) algorithm. Comparing to conventional approaches such as Gram&amp;ndash;Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the ROB. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method. MCA, Vol. 24, Pages 30: Toward Optimality of Proper Generalised Decomposition Bases

Mathematical and Computational Applications doi: 10.3390/mca24010030

Authors: Shadi Alameddin Amélie Fau David Néron Pierre Ladevèze Udo Nackenhorst

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the ROB, i.e., the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of a Proper Generalized Decomposition (PGD) basis using a randomised Singular Value Decomposition (SVD) algorithm. Comparing to conventional approaches such as Gram&amp;ndash;Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the ROB. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

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Toward Optimality of Proper Generalised Decomposition Bases Shadi Alameddin Amélie Fau David Néron Pierre Ladevèze Udo Nackenhorst doi: 10.3390/mca24010030 Mathematical and Computational Applications 2019-03-05 Mathematical and Computational Applications 2019-03-05 24 1 Article 30 10.3390/mca24010030 http://www.mdpi.com/2297-8747/24/1/30
MCA, Vol. 24, Pages 29: A Mathematical Model for Intimate Partner Violence http://www.mdpi.com/2297-8747/24/1/29 In the context of mathematical models applied to social sciences, we present and analyze a model based on differential equations for the intimate partner violence (IPV). Such a model describes the dynamics of a heterosexual romantic couple in which the man perpetrates violence against the woman. We focus on incorporating different key factors reported in the literature as causal or motivational factors to perpetrate IPV. Among the main factors included are the failures in self-regulation, the man&amp;rsquo;s need to control the woman, the social pressure on the woman to remain married, and empowerment programs. Another aspect that we include is periodic alcohol consumption for the man. The discussion of the model includes a stability analysis of its equilibrium points and the asymptotic behavior of its solutions. Also, the interpretation of results is presented in terms of IPV phenomenon. Finally, a brief review is given on different scales to quantify human behavioral traits and numerical simulations for some IPV scenarios. MCA, Vol. 24, Pages 29: A Mathematical Model for Intimate Partner Violence

Mathematical and Computational Applications doi: 10.3390/mca24010029

Authors: Sandra Delgadillo-Aleman Roberto Ku-Carrillo Brenda Perez-Amezcua Benito Chen-Charpentier

In the context of mathematical models applied to social sciences, we present and analyze a model based on differential equations for the intimate partner violence (IPV). Such a model describes the dynamics of a heterosexual romantic couple in which the man perpetrates violence against the woman. We focus on incorporating different key factors reported in the literature as causal or motivational factors to perpetrate IPV. Among the main factors included are the failures in self-regulation, the man&amp;rsquo;s need to control the woman, the social pressure on the woman to remain married, and empowerment programs. Another aspect that we include is periodic alcohol consumption for the man. The discussion of the model includes a stability analysis of its equilibrium points and the asymptotic behavior of its solutions. Also, the interpretation of results is presented in terms of IPV phenomenon. Finally, a brief review is given on different scales to quantify human behavioral traits and numerical simulations for some IPV scenarios.

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A Mathematical Model for Intimate Partner Violence Sandra Delgadillo-Aleman Roberto Ku-Carrillo Brenda Perez-Amezcua Benito Chen-Charpentier doi: 10.3390/mca24010029 Mathematical and Computational Applications 2019-03-02 Mathematical and Computational Applications 2019-03-02 24 1 Article 29 10.3390/mca24010029 http://www.mdpi.com/2297-8747/24/1/29
MCA, Vol. 24, Pages 28: Spectral Element Method Modeling of Eddy Current Losses in High-Frequency Transformers http://www.mdpi.com/2297-8747/24/1/28 This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre&amp;ndash;Gauss&amp;ndash;Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem. MCA, Vol. 24, Pages 28: Spectral Element Method Modeling of Eddy Current Losses in High-Frequency Transformers

Mathematical and Computational Applications doi: 10.3390/mca24010028

Authors: Koen Bastiaens Mitrofan Curti Dave C. J. Krop Sultan Jumayev Elena A. Lomonova

This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre&amp;ndash;Gauss&amp;ndash;Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem.

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Spectral Element Method Modeling of Eddy Current Losses in High-Frequency Transformers Koen Bastiaens Mitrofan Curti Dave C. J. Krop Sultan Jumayev Elena A. Lomonova doi: 10.3390/mca24010028 Mathematical and Computational Applications 2019-02-21 Mathematical and Computational Applications 2019-02-21 24 1 Article 28 10.3390/mca24010028 http://www.mdpi.com/2297-8747/24/1/28
MCA, Vol. 24, Pages 27: Trustworthiness in Modeling Unreinforced and Reinforced T-Joints with Finite Elements http://www.mdpi.com/2297-8747/24/1/27 As required by regulations, Finite Element Analyses (FEA) can be used to investigate the behavior of joints which might be complex to design due to the presence of geometrical and material discontinuities. The static behavior of such problems is mesh dependent, thus these results must be calibrated by using laboratory tests or reference data. Once the Finite Element (FE) model is correctly setup, the same settings can be used to study joints for which no reference is available. The present work analyzes the static strength of reinforced T-joints and sheds light on the following aspects: shell elements are a valid alternative to solid modeling; the best combination of element type and mesh density for several configurations is shown; the ultimate static strength of joints can be predicted, as well as when mechanical properties are roughly introduced for some FE topologies. The increase in strength of 12 unreinforced and reinforced (with collar or doubler plate) T-joints subjected to axial brace loading is studied. The present studies are compared with the literature and practical remarks are given in the conclusion section. MCA, Vol. 24, Pages 27: Trustworthiness in Modeling Unreinforced and Reinforced T-Joints with Finite Elements

Mathematical and Computational Applications doi: 10.3390/mca24010027

Authors: Slimane Ouakka Nicholas Fantuzzi

As required by regulations, Finite Element Analyses (FEA) can be used to investigate the behavior of joints which might be complex to design due to the presence of geometrical and material discontinuities. The static behavior of such problems is mesh dependent, thus these results must be calibrated by using laboratory tests or reference data. Once the Finite Element (FE) model is correctly setup, the same settings can be used to study joints for which no reference is available. The present work analyzes the static strength of reinforced T-joints and sheds light on the following aspects: shell elements are a valid alternative to solid modeling; the best combination of element type and mesh density for several configurations is shown; the ultimate static strength of joints can be predicted, as well as when mechanical properties are roughly introduced for some FE topologies. The increase in strength of 12 unreinforced and reinforced (with collar or doubler plate) T-joints subjected to axial brace loading is studied. The present studies are compared with the literature and practical remarks are given in the conclusion section.

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Trustworthiness in Modeling Unreinforced and Reinforced T-Joints with Finite Elements Slimane Ouakka Nicholas Fantuzzi doi: 10.3390/mca24010027 Mathematical and Computational Applications 2019-02-20 Mathematical and Computational Applications 2019-02-20 24 1 Article 27 10.3390/mca24010027 http://www.mdpi.com/2297-8747/24/1/27
MCA, Vol. 24, Pages 26: Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations http://www.mdpi.com/2297-8747/24/1/26 This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green&amp;rsquo;s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green&amp;rsquo;s functions. The obtained Green&amp;rsquo;s functions was analyzed. Test calculations were performed on the examples of some technological processes. MCA, Vol. 24, Pages 26: Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

Mathematical and Computational Applications doi: 10.3390/mca24010026

Authors: Sergey A. Davydov Andrei V. Zemskov Elena R. Akhmetova

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green&amp;rsquo;s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green&amp;rsquo;s functions. The obtained Green&amp;rsquo;s functions was analyzed. Test calculations were performed on the examples of some technological processes.

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Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations Sergey A. Davydov Andrei V. Zemskov Elena R. Akhmetova doi: 10.3390/mca24010026 Mathematical and Computational Applications 2019-02-19 Mathematical and Computational Applications 2019-02-19 24 1 Article 26 10.3390/mca24010026 http://www.mdpi.com/2297-8747/24/1/26
MCA, Vol. 24, Pages 25: On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces http://www.mdpi.com/2297-8747/24/1/25 We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet&amp;ndash;Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight | x | a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions. MCA, Vol. 24, Pages 25: On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces

Mathematical and Computational Applications doi: 10.3390/mca24010025

Authors: Hovik Matevossian

We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet&amp;ndash;Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight | x | a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions.

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On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces Hovik Matevossian doi: 10.3390/mca24010025 Mathematical and Computational Applications 2019-02-18 Mathematical and Computational Applications 2019-02-18 24 1 Article 25 10.3390/mca24010025 http://www.mdpi.com/2297-8747/24/1/25
MCA, Vol. 24, Pages 24: Exact Two-Dimensional Analytical Calculations for Magnetic Field, Electromagnetic Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface Inset Permanent Magnet Machines http://www.mdpi.com/2297-8747/24/1/24 This paper presents a two-dimensional analytical model of outer rotor permanent magnet machines equipped with surface inset permanent magnets. To obtain the analytical model, the whole model is divided into the sub-domains, according to the magnetic properties and geometries. Maxwell equations in each sub-domain are expressed and analytically solved. By using the boundary/interface conditions between adjacent sub-regions, integral coefficients in the general solutions are obtained. At the end, the analytically calculated results of the air-gap magnetic flux density, electromagnetic torque, unbalanced magnetic force (UMF), back-electromotive force (EMF) and inductances are verified by comparing them with those obtained from finite element method (FEM). One of the merits of this method in comparison with the numerical model is the capability of rapid calculation with the highest precision, which made it suitable for optimization problems. MCA, Vol. 24, Pages 24: Exact Two-Dimensional Analytical Calculations for Magnetic Field, Electromagnetic Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface Inset Permanent Magnet Machines

Mathematical and Computational Applications doi: 10.3390/mca24010024

Authors: AmirAbbas Vahaj Akbar Rahideh Hossein Moayed-Jahromi AliReza Ghaffari

This paper presents a two-dimensional analytical model of outer rotor permanent magnet machines equipped with surface inset permanent magnets. To obtain the analytical model, the whole model is divided into the sub-domains, according to the magnetic properties and geometries. Maxwell equations in each sub-domain are expressed and analytically solved. By using the boundary/interface conditions between adjacent sub-regions, integral coefficients in the general solutions are obtained. At the end, the analytically calculated results of the air-gap magnetic flux density, electromagnetic torque, unbalanced magnetic force (UMF), back-electromotive force (EMF) and inductances are verified by comparing them with those obtained from finite element method (FEM). One of the merits of this method in comparison with the numerical model is the capability of rapid calculation with the highest precision, which made it suitable for optimization problems.

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Exact Two-Dimensional Analytical Calculations for Magnetic Field, Electromagnetic Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface Inset Permanent Magnet Machines AmirAbbas Vahaj Akbar Rahideh Hossein Moayed-Jahromi AliReza Ghaffari doi: 10.3390/mca24010024 Mathematical and Computational Applications 2019-02-17 Mathematical and Computational Applications 2019-02-17 24 1 Article 24 10.3390/mca24010024 http://www.mdpi.com/2297-8747/24/1/24
MCA, Vol. 24, Pages 23: An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation http://www.mdpi.com/2297-8747/24/1/23 This article considers an unsteady elastic diffusion model of Euler&amp;ndash;Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum to formulate the problem. A model of unsteady bending for the elastic diffusive Euler&amp;ndash;Bernoulli beam was obtained using Hamilton&amp;rsquo;s variational principle. The Laplace transform on time and the Fourier series expansion by the spatial coordinate were used to solve the obtained problem. MCA, Vol. 24, Pages 23: An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation

Mathematical and Computational Applications doi: 10.3390/mca24010023

Authors: Dmitry Tarlakovskii Andrei Zemskov

This article considers an unsteady elastic diffusion model of Euler&amp;ndash;Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum to formulate the problem. A model of unsteady bending for the elastic diffusive Euler&amp;ndash;Bernoulli beam was obtained using Hamilton&amp;rsquo;s variational principle. The Laplace transform on time and the Fourier series expansion by the spatial coordinate were used to solve the obtained problem.

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An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation Dmitry Tarlakovskii Andrei Zemskov doi: 10.3390/mca24010023 Mathematical and Computational Applications 2019-02-06 Mathematical and Computational Applications 2019-02-06 24 1 Article 23 10.3390/mca24010023 http://www.mdpi.com/2297-8747/24/1/23
MCA, Vol. 24, Pages 22: Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach http://www.mdpi.com/2297-8747/24/1/22 In this paper, stochastic analysis of a diseased prey&amp;ndash;predator system involving adaptive back-stepping control is studied. The system was investigated for its dynamical behaviours, such as boundedness and local stability analysis. The global stability of the system was derived using the Lyapunov function. The uniform persistence condition for the system is obtained. The proposed system was studied with adaptive back-stepping control, and it is proved that the system stabilizes to its steady state in nonlinear feedback control. The value of the system is described mostly by the environmental stochasticity in the form of Gaussian white noise. We also established some conditions for oscillations of all positive solutions of the delayed system. Numerical simulations are illustrated, and sustained our analytical findings. We concluded that controlled harvesting on the susceptible and infected prey is able to control prey infection. MCA, Vol. 24, Pages 22: Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach

Mathematical and Computational Applications doi: 10.3390/mca24010022

Authors: Kalyan Das M. N. Srinivas V. Madhusudanan Sandra Pinelas

In this paper, stochastic analysis of a diseased prey&amp;ndash;predator system involving adaptive back-stepping control is studied. The system was investigated for its dynamical behaviours, such as boundedness and local stability analysis. The global stability of the system was derived using the Lyapunov function. The uniform persistence condition for the system is obtained. The proposed system was studied with adaptive back-stepping control, and it is proved that the system stabilizes to its steady state in nonlinear feedback control. The value of the system is described mostly by the environmental stochasticity in the form of Gaussian white noise. We also established some conditions for oscillations of all positive solutions of the delayed system. Numerical simulations are illustrated, and sustained our analytical findings. We concluded that controlled harvesting on the susceptible and infected prey is able to control prey infection.

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Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach Kalyan Das M. N. Srinivas V. Madhusudanan Sandra Pinelas doi: 10.3390/mca24010022 Mathematical and Computational Applications 2019-02-05 Mathematical and Computational Applications 2019-02-05 24 1 Article 22 10.3390/mca24010022 http://www.mdpi.com/2297-8747/24/1/22
MCA, Vol. 24, Pages 21: Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments http://www.mdpi.com/2297-8747/24/1/21 In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard a Black&amp;ndash;Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton&amp;ndash;Jacobi&amp;ndash;Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed individual claim amount distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price. MCA, Vol. 24, Pages 21: Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

Mathematical and Computational Applications doi: 10.3390/mca24010021

Authors: Christian Kasumo

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard a Black&amp;ndash;Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton&amp;ndash;Jacobi&amp;ndash;Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed individual claim amount distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

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Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments Christian Kasumo doi: 10.3390/mca24010021 Mathematical and Computational Applications 2019-02-02 Mathematical and Computational Applications 2019-02-02 24 1 Article 21 10.3390/mca24010021 http://www.mdpi.com/2297-8747/24/1/21
MCA, Vol. 24, Pages 20: Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods http://www.mdpi.com/2297-8747/24/1/20 The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE 2 method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss&amp;ndash;Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE 2 framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies. MCA, Vol. 24, Pages 20: Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

Mathematical and Computational Applications doi: 10.3390/mca24010020

Authors: Benjamin Brands Denis Davydov Julia Mergheim Paul Steinmann

The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE 2 method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss&amp;ndash;Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE 2 framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies.

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Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods Benjamin Brands Denis Davydov Julia Mergheim Paul Steinmann doi: 10.3390/mca24010020 Mathematical and Computational Applications 2019-02-01 Mathematical and Computational Applications 2019-02-01 24 1 Article 20 10.3390/mca24010020 http://www.mdpi.com/2297-8747/24/1/20
MCA, Vol. 24, Pages 19: High-Order Methods Applied to Nonlinear Magnetostatic Problems http://www.mdpi.com/2297-8747/24/1/19 This paper presents a comparison between two high-order modeling methods for solving magnetostatic problems under magnetic saturation, focused on the extraction of machine parameters. Two formulations are compared, the first is based on the Newton-Raphson approach, and the second successively iterates the local remanent magnetization and the incremental reluctivity of the nonlinear soft-magnetic material. The latter approach is more robust than the Newton-Raphson method, and uncovers useful properties for the fast and accurate calculation of incremental inductance. A novel estimate for the incremental inductance relying on a single additional computation is proposed to avoid multiple nonlinear simulations which are traditionally operated with finite difference linearization or spline interpolation techniques. Fast convergence and high accuracy of the presented methods are demonstrated for the force calculation, which demonstrates their applicability for the design and analysis of electromagnetic devices. MCA, Vol. 24, Pages 19: High-Order Methods Applied to Nonlinear Magnetostatic Problems

Mathematical and Computational Applications doi: 10.3390/mca24010019

Authors: Léo A. J. Friedrich Mitrofan Curti Bart L. J. Gysen Elena A. Lomonova

This paper presents a comparison between two high-order modeling methods for solving magnetostatic problems under magnetic saturation, focused on the extraction of machine parameters. Two formulations are compared, the first is based on the Newton-Raphson approach, and the second successively iterates the local remanent magnetization and the incremental reluctivity of the nonlinear soft-magnetic material. The latter approach is more robust than the Newton-Raphson method, and uncovers useful properties for the fast and accurate calculation of incremental inductance. A novel estimate for the incremental inductance relying on a single additional computation is proposed to avoid multiple nonlinear simulations which are traditionally operated with finite difference linearization or spline interpolation techniques. Fast convergence and high accuracy of the presented methods are demonstrated for the force calculation, which demonstrates their applicability for the design and analysis of electromagnetic devices.

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High-Order Methods Applied to Nonlinear Magnetostatic Problems Léo A. J. Friedrich Mitrofan Curti Bart L. J. Gysen Elena A. Lomonova doi: 10.3390/mca24010019 Mathematical and Computational Applications 2019-01-29 Mathematical and Computational Applications 2019-01-29 24 1 Article 19 10.3390/mca24010019 http://www.mdpi.com/2297-8747/24/1/19
MCA, Vol. 24, Pages 18: Data Pruning of Tomographic Data for the Calibration of Strain Localization Models http://www.mdpi.com/2297-8747/24/1/18 The development and generalization of Digital Volume Correlation (DVC) on X-ray computed tomography data highlight the issue of long-term storage. The present paper proposes a new model-free method for pruning experimental data related to DVC, while preserving the ability to identify constitutive equations (i.e., closure equations in solid mechanics) reflecting strain localizations. The size of the remaining sampled data can be user-defined, depending on the needs concerning storage space. The proposed data pruning procedure is deeply linked to hyper-reduction techniques. The DVC data of a resin-bonded sand tested in uniaxial compression is used as an illustrating example. The relevance of the pruned data was tested afterwards for model calibration. A Finite Element Model Updating (FEMU) technique coupled with an hybrid hyper-reduction method aws used to successfully calibrate a constitutive model of the resin bonded sand with the pruned data only. MCA, Vol. 24, Pages 18: Data Pruning of Tomographic Data for the Calibration of Strain Localization Models

Mathematical and Computational Applications doi: 10.3390/mca24010018

Authors: William Hilth David Ryckelynck Claire Menet

The development and generalization of Digital Volume Correlation (DVC) on X-ray computed tomography data highlight the issue of long-term storage. The present paper proposes a new model-free method for pruning experimental data related to DVC, while preserving the ability to identify constitutive equations (i.e., closure equations in solid mechanics) reflecting strain localizations. The size of the remaining sampled data can be user-defined, depending on the needs concerning storage space. The proposed data pruning procedure is deeply linked to hyper-reduction techniques. The DVC data of a resin-bonded sand tested in uniaxial compression is used as an illustrating example. The relevance of the pruned data was tested afterwards for model calibration. A Finite Element Model Updating (FEMU) technique coupled with an hybrid hyper-reduction method aws used to successfully calibrate a constitutive model of the resin bonded sand with the pruned data only.

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Data Pruning of Tomographic Data for the Calibration of Strain Localization Models William Hilth David Ryckelynck Claire Menet doi: 10.3390/mca24010018 Mathematical and Computational Applications 2019-01-28 Mathematical and Computational Applications 2019-01-28 24 1 Article 18 10.3390/mca24010018 http://www.mdpi.com/2297-8747/24/1/18
MCA, Vol. 24, Pages 17: Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity http://www.mdpi.com/2297-8747/24/1/17 This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients. MCA, Vol. 24, Pages 17: Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

Mathematical and Computational Applications doi: 10.3390/mca24010017

Authors: Clément Olivier David Ryckelynck Julien Cortial

This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

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Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity Clément Olivier David Ryckelynck Julien Cortial doi: 10.3390/mca24010017 Mathematical and Computational Applications 2019-01-28 Mathematical and Computational Applications 2019-01-28 24 1 Article 17 10.3390/mca24010017 http://www.mdpi.com/2297-8747/24/1/17
MCA, Vol. 24, Pages 16: On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity http://www.mdpi.com/2297-8747/24/1/16 The re-quantization method&amp;mdash;one of the resurgent analysis methods of current importance&amp;mdash;is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse Laplace&amp;ndash;Borel transform is solved for a particular type of functions with holomorphic coefficients that exponentially grow at zero. Two examples of constructing the uniform asymptotics at infinity for the second- and forth-order differential equations with the help of the re-quantization method and the result obtained in this study are considered. MCA, Vol. 24, Pages 16: On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity

Mathematical and Computational Applications doi: 10.3390/mca24010016

Authors: Maria Korovina Ilya Smirnov Vladimir Smirnov

The re-quantization method&amp;mdash;one of the resurgent analysis methods of current importance&amp;mdash;is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse Laplace&amp;ndash;Borel transform is solved for a particular type of functions with holomorphic coefficients that exponentially grow at zero. Two examples of constructing the uniform asymptotics at infinity for the second- and forth-order differential equations with the help of the re-quantization method and the result obtained in this study are considered.

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On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity Maria Korovina Ilya Smirnov Vladimir Smirnov doi: 10.3390/mca24010016 Mathematical and Computational Applications 2019-01-28 Mathematical and Computational Applications 2019-01-28 24 1 Article 16 10.3390/mca24010016 http://www.mdpi.com/2297-8747/24/1/16
MCA, Vol. 24, Pages 15: A Novel Air Quality Monitoring Unit Using Cloudino and FIWARE Technologies http://www.mdpi.com/2297-8747/24/1/15 Smart City applications aim to improve the quality of life of citizens. Applying technologies of the Internet of Things (IoT) to urban environments is considered as a key of the development of smart cities. In this context, air pollution is one of the most important factors affecting the quality of life and the health of the increasing urban population of industrial societies. For this reason, it is essential to develop applications that allow citizens monitoring the concentration of pollutants and avoid places with high levels of pollution. Due to the increasing use of IoT in different areas, there are arising platforms which deal with the challenges IoT implies, such as FIWARE, which provides technologies to facilitate the development of IoT applications. In this paper, an Air Quality Monitoring Unit using Cloudino and Arduino devices and FIWARE technologies is presented. Through Cloudino and Arduino, the monitoring unit gather data from various sensors and transforms the data in a FIWARE data model. Then, the measurements are sent to the Orion Context Broker (OCB), which is a software component provided by FIWARE. The Orion Context Broker allows to manage and publish the data to be consumed by users and applications. MCA, Vol. 24, Pages 15: A Novel Air Quality Monitoring Unit Using Cloudino and FIWARE Technologies

Mathematical and Computational Applications doi: 10.3390/mca24010015

Authors: Yolanda Baca Gómez Hugo Estrada Esquivel Alicia Martínez Rebollar Daniel Villanueva Vásquez

Smart City applications aim to improve the quality of life of citizens. Applying technologies of the Internet of Things (IoT) to urban environments is considered as a key of the development of smart cities. In this context, air pollution is one of the most important factors affecting the quality of life and the health of the increasing urban population of industrial societies. For this reason, it is essential to develop applications that allow citizens monitoring the concentration of pollutants and avoid places with high levels of pollution. Due to the increasing use of IoT in different areas, there are arising platforms which deal with the challenges IoT implies, such as FIWARE, which provides technologies to facilitate the development of IoT applications. In this paper, an Air Quality Monitoring Unit using Cloudino and Arduino devices and FIWARE technologies is presented. Through Cloudino and Arduino, the monitoring unit gather data from various sensors and transforms the data in a FIWARE data model. Then, the measurements are sent to the Orion Context Broker (OCB), which is a software component provided by FIWARE. The Orion Context Broker allows to manage and publish the data to be consumed by users and applications.

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A Novel Air Quality Monitoring Unit Using Cloudino and FIWARE Technologies Yolanda Baca Gómez Hugo Estrada Esquivel Alicia Martínez Rebollar Daniel Villanueva Vásquez doi: 10.3390/mca24010015 Mathematical and Computational Applications 2019-01-24 Mathematical and Computational Applications 2019-01-24 24 1 Article 15 10.3390/mca24010015 http://www.mdpi.com/2297-8747/24/1/15
MCA, Vol. 24, Pages 14: A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript http://www.mdpi.com/2297-8747/24/1/14 Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze the underlying structure of an ancient and complex manuscript, known as the Voynich manuscript, which remains undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscripts, we train the network by means of the &amp;alpha; and &amp;beta; -pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices to compare with known languages concerning the frequency of consonant andvowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript. MCA, Vol. 24, Pages 14: A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript

Mathematical and Computational Applications doi: 10.3390/mca24010014

Authors: Luis Acedo

Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze the underlying structure of an ancient and complex manuscript, known as the Voynich manuscript, which remains undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscripts, we train the network by means of the &amp;alpha; and &amp;beta; -pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices to compare with known languages concerning the frequency of consonant andvowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.

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A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript Luis Acedo doi: 10.3390/mca24010014 Mathematical and Computational Applications 2019-01-23 Mathematical and Computational Applications 2019-01-23 24 1 Article 14 10.3390/mca24010014 http://www.mdpi.com/2297-8747/24/1/14
MCA, Vol. 24, Pages 13: Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems http://www.mdpi.com/2297-8747/24/1/13 In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, from which we show the intricate and complex dynamical behavior of their orbits. MCA, Vol. 24, Pages 13: Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems

Mathematical and Computational Applications doi: 10.3390/mca24010013

Authors: Francisco Solis

In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, from which we show the intricate and complex dynamical behavior of their orbits.

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Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems Francisco Solis doi: 10.3390/mca24010013 Mathematical and Computational Applications 2019-01-18 Mathematical and Computational Applications 2019-01-18 24 1 Article 13 10.3390/mca24010013 http://www.mdpi.com/2297-8747/24/1/13
MCA, Vol. 24, Pages 12: Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process http://www.mdpi.com/2297-8747/24/1/12 A new mathematical model is presented to study the effects of macrophages on the bone fracture healing process. The model consists of a system of nonlinear ordinary differential equations that represents the interactions among classically and alternatively activated macrophages, mesenchymal stem cells, osteoblasts, and pro- and anti-inflammatory cytokines. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. Numerical simulations are also presented to support the theoretical results, and to monitor the evolution of a broken bone for different types of fractures under various medical interventions. The model can be used to guide clinical experiments and to explore possible medical treatments that accelerate the bone fracture healing process, either by surgical interventions or drug administrations. MCA, Vol. 24, Pages 12: Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process

Mathematical and Computational Applications doi: 10.3390/mca24010012

Authors: Imelda Trejo Hristo Kojouharov Benito Chen-Charpentier

A new mathematical model is presented to study the effects of macrophages on the bone fracture healing process. The model consists of a system of nonlinear ordinary differential equations that represents the interactions among classically and alternatively activated macrophages, mesenchymal stem cells, osteoblasts, and pro- and anti-inflammatory cytokines. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. Numerical simulations are also presented to support the theoretical results, and to monitor the evolution of a broken bone for different types of fractures under various medical interventions. The model can be used to guide clinical experiments and to explore possible medical treatments that accelerate the bone fracture healing process, either by surgical interventions or drug administrations.

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Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process Imelda Trejo Hristo Kojouharov Benito Chen-Charpentier doi: 10.3390/mca24010012 Mathematical and Computational Applications 2019-01-17 Mathematical and Computational Applications 2019-01-17 24 1 Article 12 10.3390/mca24010012 http://www.mdpi.com/2297-8747/24/1/12
MCA, Vol. 24, Pages 11: Acknowledgement to Reviewers of MCA in 2018 http://www.mdpi.com/2297-8747/24/1/11 Rigorous peer-review is the corner-stone of high-quality academic publishing [...] MCA, Vol. 24, Pages 11: Acknowledgement to Reviewers of MCA in 2018

Mathematical and Computational Applications doi: 10.3390/mca24010011

Authors: MCA Editorial Office

Rigorous peer-review is the corner-stone of high-quality academic publishing [...]

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Acknowledgement to Reviewers of MCA in 2018 MCA Editorial Office doi: 10.3390/mca24010011 Mathematical and Computational Applications 2019-01-16 Mathematical and Computational Applications 2019-01-16 24 1 Editorial 11 10.3390/mca24010011 http://www.mdpi.com/2297-8747/24/1/11
MCA, Vol. 24, Pages 10: Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation http://www.mdpi.com/2297-8747/24/1/10 This paper studies the nonlinear fractional undamped Duffing equation. The Duffing equation is one of the fundamental equations in engineering. The geographical areas of this model represent chaos, relativistic energy-momentum, electrodynamics, and electromagnetic interactions. These properties have many benefits in different science fields. The equation depicts the energy of a point mass, which is well thought out as a periodically-forced oscillator. We employed twelve different techniques to the nonlinear fractional Duffing equation to find explicit solutions and approximate solutions. The stability of the solutions was also examined to show the ability of our obtained solutions in the application. The main goals here were to apply a novel computational method (modified auxiliary equation method) and compare the novel method with other methods via the solutions that were obtained by each of these methods. MCA, Vol. 24, Pages 10: Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

Mathematical and Computational Applications doi: 10.3390/mca24010010

Authors: Raghda A. M. Attia Dianchen Lu Mostafa M. A. Khater

This paper studies the nonlinear fractional undamped Duffing equation. The Duffing equation is one of the fundamental equations in engineering. The geographical areas of this model represent chaos, relativistic energy-momentum, electrodynamics, and electromagnetic interactions. These properties have many benefits in different science fields. The equation depicts the energy of a point mass, which is well thought out as a periodically-forced oscillator. We employed twelve different techniques to the nonlinear fractional Duffing equation to find explicit solutions and approximate solutions. The stability of the solutions was also examined to show the ability of our obtained solutions in the application. The main goals here were to apply a novel computational method (modified auxiliary equation method) and compare the novel method with other methods via the solutions that were obtained by each of these methods.

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Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation Raghda A. M. Attia Dianchen Lu Mostafa M. A. Khater doi: 10.3390/mca24010010 Mathematical and Computational Applications 2019-01-16 Mathematical and Computational Applications 2019-01-16 24 1 Article 10 10.3390/mca24010010 http://www.mdpi.com/2297-8747/24/1/10
MCA, Vol. 24, Pages 9: Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation http://www.mdpi.com/2297-8747/24/1/9 In nuclear engineering, the &amp;lambda; -modes associated with the neutron diffusion equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied. MCA, Vol. 24, Pages 9: Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation

Mathematical and Computational Applications doi: 10.3390/mca24010009

Authors: Amanda Carreño Luca Bergamaschi Angeles Martinez Antoni Vidal-Ferrándiz Damian Ginestar Gumersindo Verdú

In nuclear engineering, the &amp;lambda; -modes associated with the neutron diffusion equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied.

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Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation Amanda Carreño Luca Bergamaschi Angeles Martinez Antoni Vidal-Ferrándiz Damian Ginestar Gumersindo Verdú doi: 10.3390/mca24010009 Mathematical and Computational Applications 2019-01-15 Mathematical and Computational Applications 2019-01-15 24 1 Article 9 10.3390/mca24010009 http://www.mdpi.com/2297-8747/24/1/9
MCA, Vol. 24, Pages 8: An Efficient Semi-Analytical Solution of a One-Dimensional Curvature Equation that Describes the Human Corneal Shape http://www.mdpi.com/2297-8747/24/1/8 In this paper, a numerical approach is proposed to find a semi analytical solution for a prescribed anisotropic mean curvature equation modeling the human corneal shape. The method is based on an integral operator that is constructed in terms of Green&amp;rsquo;s function coupled with the implementation of Picard&amp;rsquo;s or Mann&amp;rsquo;s fixed point iteration schemes. Using the contraction principle, it will be shown that the method is convergent for both fixed point iteration schemes. Numerical examples will be presented to demonstrate the applicability, efficiency, and high accuracy of the proposed method. MCA, Vol. 24, Pages 8: An Efficient Semi-Analytical Solution of a One-Dimensional Curvature Equation that Describes the Human Corneal Shape

Mathematical and Computational Applications doi: 10.3390/mca24010008

Authors: Marwan Abukhaled Suheil Khuri

In this paper, a numerical approach is proposed to find a semi analytical solution for a prescribed anisotropic mean curvature equation modeling the human corneal shape. The method is based on an integral operator that is constructed in terms of Green&amp;rsquo;s function coupled with the implementation of Picard&amp;rsquo;s or Mann&amp;rsquo;s fixed point iteration schemes. Using the contraction principle, it will be shown that the method is convergent for both fixed point iteration schemes. Numerical examples will be presented to demonstrate the applicability, efficiency, and high accuracy of the proposed method.

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An Efficient Semi-Analytical Solution of a One-Dimensional Curvature Equation that Describes the Human Corneal Shape Marwan Abukhaled Suheil Khuri doi: 10.3390/mca24010008 Mathematical and Computational Applications 2019-01-10 Mathematical and Computational Applications 2019-01-10 24 1 Article 8 10.3390/mca24010008 http://www.mdpi.com/2297-8747/24/1/8
MCA, Vol. 24, Pages 7: Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method http://www.mdpi.com/2297-8747/24/1/7 The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature. MCA, Vol. 24, Pages 7: Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

Mathematical and Computational Applications doi: 10.3390/mca24010007

Authors: Abdelhalim Ebaid Asmaa Al-Enazi Bassam Z. Albalawi Mona D. Aljoufi

The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature.

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Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method Abdelhalim Ebaid Asmaa Al-Enazi Bassam Z. Albalawi Mona D. Aljoufi doi: 10.3390/mca24010007 Mathematical and Computational Applications 2019-01-09 Mathematical and Computational Applications 2019-01-09 24 1 Article 7 10.3390/mca24010007 http://www.mdpi.com/2297-8747/24/1/7
MCA, Vol. 24, Pages 6: Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia http://www.mdpi.com/2297-8747/24/1/6 The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters&amp;rsquo; identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia. MCA, Vol. 24, Pages 6: Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia

Mathematical and Computational Applications doi: 10.3390/mca24010006

Authors: Gilberto C. González-Parra Diego F. Aranda Benito Chen-Charpentier Miguel Díaz-Rodríguez Jaime E. Castellanos

The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters&amp;rsquo; identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia.

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Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia Gilberto C. González-Parra Diego F. Aranda Benito Chen-Charpentier Miguel Díaz-Rodríguez Jaime E. Castellanos doi: 10.3390/mca24010006 Mathematical and Computational Applications 2019-01-03 Mathematical and Computational Applications 2019-01-03 24 1 Article 6 10.3390/mca24010006 http://www.mdpi.com/2297-8747/24/1/6
MCA, Vol. 24, Pages 5: An Approach for Integrating Uncertainty When Selecting an Anti-Torpedo Decoy in Brand New Warships http://www.mdpi.com/2297-8747/24/1/5 The Spanish Navy has planned that the F-80 frigates will be replaced by the brand new F-110 frigates in 2022. The F-110 program is in the conceptual design phase and one of the objectives is to provide the new F-110 frigate with a salient anti-submarine capability. Therefore, it is necessary to choose what anti-torpedo decoy should be installed in the warship. The Joint Chiefs of Navy Staff (EMA) established some guidelines and, considering the Navy guidance&amp;rsquo;s, the Analytic Hierarchy Process (AHP) method was applied. After applying the AHP method, none of the decoys obtained a better score to the other one to make a decision. This paper addresses the problem of the selection of the best anti-torpedo decoy to be installed in the new frigates. This allowed implementing a new approach, the Graphic Method of Measurement of Uncertainty Beyond Objectivity (GMUBO). This approach considers different scenarios from the AHP, quantifies the uncertainty, and evaluates which is the best alternative. The method integrates the uncertainty in the AHP and allows measuring the robustness of the selected alternative, also providing a useful graphical tool. Furthermore, GMUBO has a great ease of use and it is helpful to make decisions under uncertainty conditions. MCA, Vol. 24, Pages 5: An Approach for Integrating Uncertainty When Selecting an Anti-Torpedo Decoy in Brand New Warships

Mathematical and Computational Applications doi: 10.3390/mca24010005

Authors: Rafael M. Carreño Javier Martínez José Benito Bouza

The Spanish Navy has planned that the F-80 frigates will be replaced by the brand new F-110 frigates in 2022. The F-110 program is in the conceptual design phase and one of the objectives is to provide the new F-110 frigate with a salient anti-submarine capability. Therefore, it is necessary to choose what anti-torpedo decoy should be installed in the warship. The Joint Chiefs of Navy Staff (EMA) established some guidelines and, considering the Navy guidance&amp;rsquo;s, the Analytic Hierarchy Process (AHP) method was applied. After applying the AHP method, none of the decoys obtained a better score to the other one to make a decision. This paper addresses the problem of the selection of the best anti-torpedo decoy to be installed in the new frigates. This allowed implementing a new approach, the Graphic Method of Measurement of Uncertainty Beyond Objectivity (GMUBO). This approach considers different scenarios from the AHP, quantifies the uncertainty, and evaluates which is the best alternative. The method integrates the uncertainty in the AHP and allows measuring the robustness of the selected alternative, also providing a useful graphical tool. Furthermore, GMUBO has a great ease of use and it is helpful to make decisions under uncertainty conditions.

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An Approach for Integrating Uncertainty When Selecting an Anti-Torpedo Decoy in Brand New Warships Rafael M. Carreño Javier Martínez José Benito Bouza doi: 10.3390/mca24010005 Mathematical and Computational Applications 2019-01-03 Mathematical and Computational Applications 2019-01-03 24 1 Article 5 10.3390/mca24010005 http://www.mdpi.com/2297-8747/24/1/5
MCA, Vol. 24, Pages 4: Construction of Regular Developable Bézier Patches http://www.mdpi.com/2297-8747/24/1/4 The modeling of developable surfaces is considered a very important application in plat-metal-based industries. Relating to the purpose, this discussion aims to obtain some formulas for constructing the regular developable B&amp;eacute;zier patches, in which each boundary curve must be laid in two parallel planes. The results as follows: We find some formulas of the equation systems that are described by the constant, linear, and quadratic control parameters of the regular developable B&amp;eacute;zier patches criteria. The new approach is numerically tested for constructing the regular developable B&amp;eacute;zier patches, in which their boundary curves are defined, respectively, by the combination of four, five, and six degrees. MCA, Vol. 24, Pages 4: Construction of Regular Developable Bézier Patches

Mathematical and Computational Applications doi: 10.3390/mca24010004

Authors: Kusno

The modeling of developable surfaces is considered a very important application in plat-metal-based industries. Relating to the purpose, this discussion aims to obtain some formulas for constructing the regular developable B&amp;eacute;zier patches, in which each boundary curve must be laid in two parallel planes. The results as follows: We find some formulas of the equation systems that are described by the constant, linear, and quadratic control parameters of the regular developable B&amp;eacute;zier patches criteria. The new approach is numerically tested for constructing the regular developable B&amp;eacute;zier patches, in which their boundary curves are defined, respectively, by the combination of four, five, and six degrees.

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Construction of Regular Developable Bézier Patches Kusno doi: 10.3390/mca24010004 Mathematical and Computational Applications 2019-01-02 Mathematical and Computational Applications 2019-01-02 24 1 Article 4 10.3390/mca24010004 http://www.mdpi.com/2297-8747/24/1/4
MCA, Vol. 24, Pages 3: Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations http://www.mdpi.com/2297-8747/24/1/3 In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra&amp;ndash;Pt&amp;aacute;k method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3 r + 6 , r = 0 , 1 , 2 , &amp;hellip; . The sixth order method is the special case of this multi-step scheme for r = 0 . The family gives a four-step ninth order method for r = 1 . As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods. MCA, Vol. 24, Pages 3: Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations

Mathematical and Computational Applications doi: 10.3390/mca24010003

Authors: Himani Arora Juan R. Torregrosa Alicia Cordero

In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra&amp;ndash;Pt&amp;aacute;k method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3 r + 6 , r = 0 , 1 , 2 , &amp;hellip; . The sixth order method is the special case of this multi-step scheme for r = 0 . The family gives a four-step ninth order method for r = 1 . As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods.

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Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations Himani Arora Juan R. Torregrosa Alicia Cordero doi: 10.3390/mca24010003 Mathematical and Computational Applications 2018-12-27 Mathematical and Computational Applications 2018-12-27 24 1 Article 3 10.3390/mca24010003 http://www.mdpi.com/2297-8747/24/1/3
MCA, Vol. 24, Pages 2: Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal http://www.mdpi.com/2297-8747/24/1/2 Active optics techniques in astronomy provide high imaging quality. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces&amp;mdash;or freeform surfaces&amp;mdash;by use of a minimum number of actuators. The aspheric mirror is obtained from a single uniform load that acts over the surface of a closed-form substrate whilst under axial reaction to its elliptical perimeter ring during spherical polishing. MESSIER space proposal is a wide-field low-central-obstruction folded-two-mirror-anastigmat or here called briefly three-mirror-anastigmat (TMA) telescope. The optical design is a folded reflective Schmidt. Basic telescope features are 36 cm aperture, f/2.5, with 1.6&amp;deg; &amp;times; 2.6&amp;deg; field of view and a curved field detector allowing null distortion aberration for drift-scan observations. The freeform mirror is generated by spherical stress polishing that provides super-polished freeform surfaces after elastic relaxation. Preliminary analysis required use of the optics theory of 3rd-order aberrations and elasticity theory of thin elliptical plates. Final cross-optimizations were carried out with Zemax raytracing code and Nastran FEA elasticity code in order to determine the complete geometry of a glass ceramic Zerodur deformable substrate. MCA, Vol. 24, Pages 2: Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal

Mathematical and Computational Applications doi: 10.3390/mca24010002

Authors: Gerard Rene Lemaitre Pascal Vola Eduard Muslimov

Active optics techniques in astronomy provide high imaging quality. This paper is dedicated to highly deformable active optics that can generate non-axisymmetric aspheric surfaces&amp;mdash;or freeform surfaces&amp;mdash;by use of a minimum number of actuators. The aspheric mirror is obtained from a single uniform load that acts over the surface of a closed-form substrate whilst under axial reaction to its elliptical perimeter ring during spherical polishing. MESSIER space proposal is a wide-field low-central-obstruction folded-two-mirror-anastigmat or here called briefly three-mirror-anastigmat (TMA) telescope. The optical design is a folded reflective Schmidt. Basic telescope features are 36 cm aperture, f/2.5, with 1.6&amp;deg; &amp;times; 2.6&amp;deg; field of view and a curved field detector allowing null distortion aberration for drift-scan observations. The freeform mirror is generated by spherical stress polishing that provides super-polished freeform surfaces after elastic relaxation. Preliminary analysis required use of the optics theory of 3rd-order aberrations and elasticity theory of thin elliptical plates. Final cross-optimizations were carried out with Zemax raytracing code and Nastran FEA elasticity code in order to determine the complete geometry of a glass ceramic Zerodur deformable substrate.

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Active Optics in Astronomy: Freeform Mirror for the MESSIER Telescope Proposal Gerard Rene Lemaitre Pascal Vola Eduard Muslimov doi: 10.3390/mca24010002 Mathematical and Computational Applications 2018-12-27 Mathematical and Computational Applications 2018-12-27 24 1 Article 2 10.3390/mca24010002 http://www.mdpi.com/2297-8747/24/1/2
MCA, Vol. 24, Pages 1: Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions http://www.mdpi.com/2297-8747/24/1/1 In this article, we present a modified auxiliary equation method. We harness this modification in three fundamental models in the biological branch of science. These models are the biological population model, equal width model and modified equal width equation. The three models represent the population density occurring as a result of population supply, a lengthy wave propagating in the positive x-direction, and the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes, respectively. We discuss these models in nonlinear fractional partial differential equation formulas. We used the conformable derivative properties to convert them into nonlinear ordinary differential equations with integer order. After adapting, we applied our new modification to these models to obtain solitary solutions of them. We obtained many novel solutions of these models, which serve to understand more about their properties. All obtained solutions were verified by putting them back into the original equations via computer software such as Maple, Mathematica, and Matlab. MCA, Vol. 24, Pages 1: Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions

Mathematical and Computational Applications doi: 10.3390/mca24010001

Authors: Mostafa M. A. Khater Raghda A. M. Attia Dianchen Lu

In this article, we present a modified auxiliary equation method. We harness this modification in three fundamental models in the biological branch of science. These models are the biological population model, equal width model and modified equal width equation. The three models represent the population density occurring as a result of population supply, a lengthy wave propagating in the positive x-direction, and the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes, respectively. We discuss these models in nonlinear fractional partial differential equation formulas. We used the conformable derivative properties to convert them into nonlinear ordinary differential equations with integer order. After adapting, we applied our new modification to these models to obtain solitary solutions of them. We obtained many novel solutions of these models, which serve to understand more about their properties. All obtained solutions were verified by putting them back into the original equations via computer software such as Maple, Mathematica, and Matlab.

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Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions Mostafa M. A. Khater Raghda A. M. Attia Dianchen Lu doi: 10.3390/mca24010001 Mathematical and Computational Applications 2018-12-20 Mathematical and Computational Applications 2018-12-20 24 1 Article 1 10.3390/mca24010001 http://www.mdpi.com/2297-8747/24/1/1
MCA, Vol. 23, Pages 80: CFD Investigation of the Effect of the Feed Spacer on Hydrodynamics in Spiral Wound Membrane Modules http://www.mdpi.com/2297-8747/23/4/80 Spacers are designed to create a feed channel, but they are also obstacles to the flow in spiral wound membrane modules. The geometry of the feed spacer influences the flow pattern, which was investigated by using a three-dimensional Computational Fluid Dynamics (CFD) model. For the conventional feed spacer, unavoidable disadvantages were caused by its line contact with the membrane. The pillar-like feed spacer was designed to achieve area contact, which made it possible to enhance the porosity and minimize the adverse effects from the dead zone caused by the transverse filament. Through reductions in the connecting filament&amp;rsquo;s diameter, the channel porosity reached 0.979. Regarding the maximum porosity, the dimensionless power number was reduced by 47.31% at Reynolds number 150 in comparison with a previously studied commercial spacer. Furthermore, a modified friction factor, as a dimensionless parameter, was employed to investigate the shear stress at the membrane&amp;rsquo;s surface. At dimensionless power number 106, the enhancement of the modified friction factor increased by approximately 22.27% in comparison with the results of a previous study. Based on the numerical prediction, the homogenization of shear stress distribution, which changed the flow profile near the membrane, was featured through contour plots. MCA, Vol. 23, Pages 80: CFD Investigation of the Effect of the Feed Spacer on Hydrodynamics in Spiral Wound Membrane Modules

Mathematical and Computational Applications doi: 10.3390/mca23040080

Authors: Zhiming Han Mitsuharu Terashima Bing Liu Hidenari Yasui

Spacers are designed to create a feed channel, but they are also obstacles to the flow in spiral wound membrane modules. The geometry of the feed spacer influences the flow pattern, which was investigated by using a three-dimensional Computational Fluid Dynamics (CFD) model. For the conventional feed spacer, unavoidable disadvantages were caused by its line contact with the membrane. The pillar-like feed spacer was designed to achieve area contact, which made it possible to enhance the porosity and minimize the adverse effects from the dead zone caused by the transverse filament. Through reductions in the connecting filament&amp;rsquo;s diameter, the channel porosity reached 0.979. Regarding the maximum porosity, the dimensionless power number was reduced by 47.31% at Reynolds number 150 in comparison with a previously studied commercial spacer. Furthermore, a modified friction factor, as a dimensionless parameter, was employed to investigate the shear stress at the membrane&amp;rsquo;s surface. At dimensionless power number 106, the enhancement of the modified friction factor increased by approximately 22.27% in comparison with the results of a previous study. Based on the numerical prediction, the homogenization of shear stress distribution, which changed the flow profile near the membrane, was featured through contour plots.

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CFD Investigation of the Effect of the Feed Spacer on Hydrodynamics in Spiral Wound Membrane Modules Zhiming Han Mitsuharu Terashima Bing Liu Hidenari Yasui doi: 10.3390/mca23040080 Mathematical and Computational Applications 2018-12-13 Mathematical and Computational Applications 2018-12-13 23 4 Article 80 10.3390/mca23040080 http://www.mdpi.com/2297-8747/23/4/80
MCA, Vol. 23, Pages 79: U-Shaped Assembly Line Balancing by Using Differential Evolution Algorithm http://www.mdpi.com/2297-8747/23/4/79 The objective of this research is to develop metaheuristic methods by using the differential evolution (DE) algorithm for solving the U-shaped assembly line balancing problem Type 1 (UALBP-1). The proposed DE algorithm is applied for balancing the lines (manufacturing a single product within a fixed given cycle time), where the aim is to minimize the number of workstations. After establishing the method, the results from previous research studies were compared with the results from this study. For the UALBP, two groups of benchmark problems were used for the experiments: (1) For the medium-sized UALBP (21&amp;ndash;45 tasks), it was found that the DE algorithm DE/best/2 to Exponential Crossover 1 produced better solutions when compared to the other metaheuristic methods: it could generate 25 optimal solutions from a total of 25 instances, and the average time used for the calculation was 0.10 seconds/instance; (2) for the large-scale UALBP (75&amp;ndash;297 tasks), it was found that the basic DE algorithm and improved differential evolution algorithm generated better solutions, and DE/best/2 to Exponential Crossover 1 generated the optimal solutions and achieved the minimum solution search time when compared to the other metaheuristic methods: it could generate 36 optimal solutions from a total of 62 instances, and the average time used for the calculation was 4.88 seconds/instance. From the comparison of the DE algorithms, it was found that the improved differential evolution algorithm generated optimal solutions with a better solution search time than the search time of the basic differential evolution algorithm. The basic and improved DE algorithm are the effective methods for balancing UALBP-1 when compared to the other metaheuristic methods. MCA, Vol. 23, Pages 79: U-Shaped Assembly Line Balancing by Using Differential Evolution Algorithm

Mathematical and Computational Applications doi: 10.3390/mca23040079

Authors: Poontana Sresracoo Nuchsara Kriengkorakot Preecha Kriengkorakot Krit Chantarasamai

The objective of this research is to develop metaheuristic methods by using the differential evolution (DE) algorithm for solving the U-shaped assembly line balancing problem Type 1 (UALBP-1). The proposed DE algorithm is applied for balancing the lines (manufacturing a single product within a fixed given cycle time), where the aim is to minimize the number of workstations. After establishing the method, the results from previous research studies were compared with the results from this study. For the UALBP, two groups of benchmark problems were used for the experiments: (1) For the medium-sized UALBP (21&amp;ndash;45 tasks), it was found that the DE algorithm DE/best/2 to Exponential Crossover 1 produced better solutions when compared to the other metaheuristic methods: it could generate 25 optimal solutions from a total of 25 instances, and the average time used for the calculation was 0.10 seconds/instance; (2) for the large-scale UALBP (75&amp;ndash;297 tasks), it was found that the basic DE algorithm and improved differential evolution algorithm generated better solutions, and DE/best/2 to Exponential Crossover 1 generated the optimal solutions and achieved the minimum solution search time when compared to the other metaheuristic methods: it could generate 36 optimal solutions from a total of 62 instances, and the average time used for the calculation was 4.88 seconds/instance. From the comparison of the DE algorithms, it was found that the improved differential evolution algorithm generated optimal solutions with a better solution search time than the search time of the basic differential evolution algorithm. The basic and improved DE algorithm are the effective methods for balancing UALBP-1 when compared to the other metaheuristic methods.

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U-Shaped Assembly Line Balancing by Using Differential Evolution Algorithm Poontana Sresracoo Nuchsara Kriengkorakot Preecha Kriengkorakot Krit Chantarasamai doi: 10.3390/mca23040079 Mathematical and Computational Applications 2018-12-12 Mathematical and Computational Applications 2018-12-12 23 4 Article 79 10.3390/mca23040079 http://www.mdpi.com/2297-8747/23/4/79
MCA, Vol. 23, Pages 78: Nanofluid Convective Heat Transfer Enhancement Elliptical Tube inside Circular Tube under Turbulent Flow http://www.mdpi.com/2297-8747/23/4/78 Heat transfer enhancement employing an elliptical tube inside a circular tube to increase the heat transfer rate without increasing in pressure drop is investigated. The flow rate inside the narrow is in the range of Reynolds number 10,000 to 100,000. Commercial software is used to solve the governing equations (continuity, momentum, and energy) by adopting a finite volume method (FVM). The electrical heater is connected around the circular tube to apply uniform heat flux (3000 W/m2) as a boundary condition. The volume concentrations are in the range of 0.25% to 1% with different TiO2 nanoparticle diameters in the range of 27 nm to 50 nm dispersed in water. The results indicate that the elliptical annulus tube can enhance heat transfer and friction factor by approximately 19% and 6% than the circular tube respectively. Results show that the heat transfer enhancement is significantly increasing as the volume concentrations increase and the nanoparticles size diameter decrease. MCA, Vol. 23, Pages 78: Nanofluid Convective Heat Transfer Enhancement Elliptical Tube inside Circular Tube under Turbulent Flow

Mathematical and Computational Applications doi: 10.3390/mca23040078

Authors: Suad Hassan Danook Qusay Kamel Jasim Adnan Mohammed Hussein

Heat transfer enhancement employing an elliptical tube inside a circular tube to increase the heat transfer rate without increasing in pressure drop is investigated. The flow rate inside the narrow is in the range of Reynolds number 10,000 to 100,000. Commercial software is used to solve the governing equations (continuity, momentum, and energy) by adopting a finite volume method (FVM). The electrical heater is connected around the circular tube to apply uniform heat flux (3000 W/m2) as a boundary condition. The volume concentrations are in the range of 0.25% to 1% with different TiO2 nanoparticle diameters in the range of 27 nm to 50 nm dispersed in water. The results indicate that the elliptical annulus tube can enhance heat transfer and friction factor by approximately 19% and 6% than the circular tube respectively. Results show that the heat transfer enhancement is significantly increasing as the volume concentrations increase and the nanoparticles size diameter decrease.

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Nanofluid Convective Heat Transfer Enhancement Elliptical Tube inside Circular Tube under Turbulent Flow Suad Hassan Danook Qusay Kamel Jasim Adnan Mohammed Hussein doi: 10.3390/mca23040078 Mathematical and Computational Applications 2018-12-06 Mathematical and Computational Applications 2018-12-06 23 4 Article 78 10.3390/mca23040078 http://www.mdpi.com/2297-8747/23/4/78
MCA, Vol. 23, Pages 77: On the Moving Trajectory of a Ball in a Viscous Liquid between Two Concentric Rigid Spheres http://www.mdpi.com/2297-8747/23/4/77 In the paper, the dynamic motion of a point ball with a mass of m , sliding in a viscous liquid between two concentric spheres under the influence of gravity and viscous and dry resistance, is investigated. In addition, it is considered that the ball starts its motion from some arbitrary point M 0 = M ( &amp;theta; 0 , &amp;phi; 0 ) . A system of nonlinear differential equations in a spheroidal coordinate system is obtained for the angular variables &amp;theta; and &amp;phi; to account for all the forces acting on the ball. The dependence of the reaction force on the angular variables is found, and the solution of the resulting system of equations is numerically analyzed. The projections of the trajectories on the plane x &amp;minus; y , &amp;nbsp; y &amp;minus; z , &amp;nbsp; x &amp;minus; z are found. MCA, Vol. 23, Pages 77: On the Moving Trajectory of a Ball in a Viscous Liquid between Two Concentric Rigid Spheres

Mathematical and Computational Applications doi: 10.3390/mca23040077

Authors: Sergey Gladkov Sophie Bogdanova

In the paper, the dynamic motion of a point ball with a mass of m , sliding in a viscous liquid between two concentric spheres under the influence of gravity and viscous and dry resistance, is investigated. In addition, it is considered that the ball starts its motion from some arbitrary point M 0 = M ( &amp;theta; 0 , &amp;phi; 0 ) . A system of nonlinear differential equations in a spheroidal coordinate system is obtained for the angular variables &amp;theta; and &amp;phi; to account for all the forces acting on the ball. The dependence of the reaction force on the angular variables is found, and the solution of the resulting system of equations is numerically analyzed. The projections of the trajectories on the plane x &amp;minus; y , &amp;nbsp; y &amp;minus; z , &amp;nbsp; x &amp;minus; z are found.

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On the Moving Trajectory of a Ball in a Viscous Liquid between Two Concentric Rigid Spheres Sergey Gladkov Sophie Bogdanova doi: 10.3390/mca23040077 Mathematical and Computational Applications 2018-12-04 Mathematical and Computational Applications 2018-12-04 23 4 Article 77 10.3390/mca23040077 http://www.mdpi.com/2297-8747/23/4/77
MCA, Vol. 23, Pages 76: Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling http://www.mdpi.com/2297-8747/23/4/76 The objective of this paper is to complete certain issues from our recent contribution (Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Adv. Differ. Equ. 2018, 392, 1–29, doi:10.1186/s13662-018-1848-8). We restate the main theorem therein that deals with the homogeneous case, so that the hypotheses are clearer and also easier to check in applications. Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. We also prove the uniqueness of mean square solution via a habitual Lipschitz condition that extends the classical Picard theorem to mean square calculus. In this manner, the study on general random non-autonomous second order linear differential equations with analytic data processes is completely resolved. Finally, we relate our exposition based on random power series with polynomial chaos expansions and the random differential transform method, the latter being a reformulation of our random Fröbenius method. MCA, Vol. 23, Pages 76: Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling

Mathematical and Computational Applications doi: 10.3390/mca23040076

Authors: Julia Calatayud Gregori Juan Cortés López Marc Jornet Sanz

The objective of this paper is to complete certain issues from our recent contribution (Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Adv. Differ. Equ. 2018, 392, 1–29, doi:10.1186/s13662-018-1848-8). We restate the main theorem therein that deals with the homogeneous case, so that the hypotheses are clearer and also easier to check in applications. Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. We also prove the uniqueness of mean square solution via a habitual Lipschitz condition that extends the classical Picard theorem to mean square calculus. In this manner, the study on general random non-autonomous second order linear differential equations with analytic data processes is completely resolved. Finally, we relate our exposition based on random power series with polynomial chaos expansions and the random differential transform method, the latter being a reformulation of our random Fröbenius method.

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Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling Julia Calatayud Gregori Juan Cortés López Marc Jornet Sanz doi: 10.3390/mca23040076 Mathematical and Computational Applications 2018-11-27 Mathematical and Computational Applications 2018-11-27 23 4 Article 76 10.3390/mca23040076 http://www.mdpi.com/2297-8747/23/4/76
MCA, Vol. 23, Pages 75: Cellular Automata and Artificial Brain Dynamics http://www.mdpi.com/2297-8747/23/4/75 Brain dynamics, neuron activity, information transfer in brains, etc., are a vast field where a large number of questions remain unsolved. Nowadays, computer simulation is playing a key role in the study of such an immense variety of problems. In this work, we explored the possibility of studying brain dynamics using cellular automata, more precisely the famous Game of Life (GoL). The model has some important features (i.e., pseudo-criticality, 1/f noise, universal computing), which represent good reasons for its use in brain dynamics modelling. We have also considered that the model maintains sufficient flexibility. For instance, the timestep is arbitrary, as are the spatial dimensions. As first steps in our study, we used the GoL to simulate the evolution of several neurons (i.e., a statistically significant set, typically a million neurons) and their interactions with the surrounding ones, as well as signal transfer in some simple scenarios. The way that signals (or life) propagate across the grid was described, along with a discussion on how this model could be compared with brain dynamics. Further work and variations of the model were also examined. MCA, Vol. 23, Pages 75: Cellular Automata and Artificial Brain Dynamics

Mathematical and Computational Applications doi: 10.3390/mca23040075

Authors: Alberto Fraile Emmanouil Panagiotakis Nicholas Christakis Luis Acedo

Brain dynamics, neuron activity, information transfer in brains, etc., are a vast field where a large number of questions remain unsolved. Nowadays, computer simulation is playing a key role in the study of such an immense variety of problems. In this work, we explored the possibility of studying brain dynamics using cellular automata, more precisely the famous Game of Life (GoL). The model has some important features (i.e., pseudo-criticality, 1/f noise, universal computing), which represent good reasons for its use in brain dynamics modelling. We have also considered that the model maintains sufficient flexibility. For instance, the timestep is arbitrary, as are the spatial dimensions. As first steps in our study, we used the GoL to simulate the evolution of several neurons (i.e., a statistically significant set, typically a million neurons) and their interactions with the surrounding ones, as well as signal transfer in some simple scenarios. The way that signals (or life) propagate across the grid was described, along with a discussion on how this model could be compared with brain dynamics. Further work and variations of the model were also examined.

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Cellular Automata and Artificial Brain Dynamics Alberto Fraile Emmanouil Panagiotakis Nicholas Christakis Luis Acedo doi: 10.3390/mca23040075 Mathematical and Computational Applications 2018-11-16 Mathematical and Computational Applications 2018-11-16 23 4 Article 75 10.3390/mca23040075 http://www.mdpi.com/2297-8747/23/4/75
MCA, Vol. 23, Pages 74: A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping http://www.mdpi.com/2297-8747/23/4/74 Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low DoF models of locomotion are thoroughly analyzed in the literature; however, these models do not describe the geometry accurately. We contribute by narrowing the gap between the two modeling approaches. Our goal is to develop a dynamic analysis methodology for the study of self-stable controlled multibody models of legged locomotion. An efficient way of modeling multibody systems is to use geometric constraints among the rigid bodies. It is especially effective when closed kinematic loops are present, such as in the case of walking models, when both legs are in contact with the ground. The mathematical representation of such constrained systems is the differential algebraic equation (DAE). We focus on the mathematical analysis methods of piecewise-smooth dynamic systems and we present their application for constrained multibody models of self-stable locomotion represented by DAE. Our numerical approach is demonstrated on a linear model of hopping and compared with analytically obtained reference results. MCA, Vol. 23, Pages 74: A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping

Mathematical and Computational Applications doi: 10.3390/mca23040074

Authors: Roland Reginald Zana Bálint Bodor László Bencsik Ambrus Zelei

Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low DoF models of locomotion are thoroughly analyzed in the literature; however, these models do not describe the geometry accurately. We contribute by narrowing the gap between the two modeling approaches. Our goal is to develop a dynamic analysis methodology for the study of self-stable controlled multibody models of legged locomotion. An efficient way of modeling multibody systems is to use geometric constraints among the rigid bodies. It is especially effective when closed kinematic loops are present, such as in the case of walking models, when both legs are in contact with the ground. The mathematical representation of such constrained systems is the differential algebraic equation (DAE). We focus on the mathematical analysis methods of piecewise-smooth dynamic systems and we present their application for constrained multibody models of self-stable locomotion represented by DAE. Our numerical approach is demonstrated on a linear model of hopping and compared with analytically obtained reference results.

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A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping Roland Reginald Zana Bálint Bodor László Bencsik Ambrus Zelei doi: 10.3390/mca23040074 Mathematical and Computational Applications 2018-11-14 Mathematical and Computational Applications 2018-11-14 23 4 Tutorial 74 10.3390/mca23040074 http://www.mdpi.com/2297-8747/23/4/74
MCA, Vol. 23, Pages 73: Iterated Petrov–Galerkin Method with Regular Pairs for Solving Fredholm Integral Equations of the Second Kind http://www.mdpi.com/2297-8747/23/4/73 In this work we obtain approximate solutions for Fredholm integral equations of the second kind by means of Petrov&amp;ndash;Galerkin method, choosing &amp;ldquo;regular pairs&amp;rdquo; of subspaces, { X n , Y n } , which are simply characterized by the positive definitiveness of a correlation matrix. This choice guarantees the solvability and numerical stability of the approximation scheme in an easy way, and the selection of orthogonal basis for the subspaces make the calculations quite simple. Afterwards, we explore an interesting phenomenon called &amp;ldquo;superconvergence&amp;rdquo;, observed in the 1970s by Sloan: once the approximations u n &amp;isin; X n to the solution of the operator equation u &amp;minus; K u = g are obtained, the convergence can be notably improved by means of an iteration of the method, u n * = g + K u n . We illustrate both procedures of approximation by means of two numerical examples: one for a continuous kernel, and the other for a weakly singular one. MCA, Vol. 23, Pages 73: Iterated Petrov–Galerkin Method with Regular Pairs for Solving Fredholm Integral Equations of the Second Kind

Mathematical and Computational Applications doi: 10.3390/mca23040073

Authors: Silvia Alejandra Seminara María Inés Troparevsky

In this work we obtain approximate solutions for Fredholm integral equations of the second kind by means of Petrov&amp;ndash;Galerkin method, choosing &amp;ldquo;regular pairs&amp;rdquo; of subspaces, { X n , Y n } , which are simply characterized by the positive definitiveness of a correlation matrix. This choice guarantees the solvability and numerical stability of the approximation scheme in an easy way, and the selection of orthogonal basis for the subspaces make the calculations quite simple. Afterwards, we explore an interesting phenomenon called &amp;ldquo;superconvergence&amp;rdquo;, observed in the 1970s by Sloan: once the approximations u n &amp;isin; X n to the solution of the operator equation u &amp;minus; K u = g are obtained, the convergence can be notably improved by means of an iteration of the method, u n * = g + K u n . We illustrate both procedures of approximation by means of two numerical examples: one for a continuous kernel, and the other for a weakly singular one.

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Iterated Petrov–Galerkin Method with Regular Pairs for Solving Fredholm Integral Equations of the Second Kind Silvia Alejandra Seminara María Inés Troparevsky doi: 10.3390/mca23040073 Mathematical and Computational Applications 2018-11-13 Mathematical and Computational Applications 2018-11-13 23 4 Article 73 10.3390/mca23040073 http://www.mdpi.com/2297-8747/23/4/73
MCA, Vol. 23, Pages 72: Magnetic Field Analytical Solution for Non-homogeneous Permeability in Retaining Sleeve of a High-Speed Permanent-Magnet Machine http://www.mdpi.com/2297-8747/23/4/72 This work presents a novel solution for magnetic field calculation in two-dimensional problems in which one region is defined with space-varying magnetic parameter. The proposed solution extends the well-established Maxwell&amp;ndash;Fourier method for calculating magnetic fields in surface-mounted cylindrical high-speed permanent-magnet machines. This contribution is effective to evaluate more realistic magnetic parameters, where measurements of a high-speed permanent-magnet generator prototype indicate saturation in the retaining sleeve due to pole-to-pole leakage flux. The saturation profile is a function of mechanical angle and can be modeled with the aid of a space-varying relative permeability, expressed in terms of a Fourier series. As an example, the presented solution has been applied to a surface-mounted PM machine at no-load condition. Magnetic field calculations show that a simple saturation profile, with low order space-varying permeability in the retaining sleeve significantly affects the magnetic flux density distribution in the air-gap. The analytical solution is confronted with finite-element method, which confirms validity of the proposed methodology. MCA, Vol. 23, Pages 72: Magnetic Field Analytical Solution for Non-homogeneous Permeability in Retaining Sleeve of a High-Speed Permanent-Magnet Machine

Mathematical and Computational Applications doi: 10.3390/mca23040072

Authors: Gabriel A. Mendonça Thales A. C. Maia Braz J. Cardoso Filho

This work presents a novel solution for magnetic field calculation in two-dimensional problems in which one region is defined with space-varying magnetic parameter. The proposed solution extends the well-established Maxwell&amp;ndash;Fourier method for calculating magnetic fields in surface-mounted cylindrical high-speed permanent-magnet machines. This contribution is effective to evaluate more realistic magnetic parameters, where measurements of a high-speed permanent-magnet generator prototype indicate saturation in the retaining sleeve due to pole-to-pole leakage flux. The saturation profile is a function of mechanical angle and can be modeled with the aid of a space-varying relative permeability, expressed in terms of a Fourier series. As an example, the presented solution has been applied to a surface-mounted PM machine at no-load condition. Magnetic field calculations show that a simple saturation profile, with low order space-varying permeability in the retaining sleeve significantly affects the magnetic flux density distribution in the air-gap. The analytical solution is confronted with finite-element method, which confirms validity of the proposed methodology.

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Magnetic Field Analytical Solution for Non-homogeneous Permeability in Retaining Sleeve of a High-Speed Permanent-Magnet Machine Gabriel A. Mendonça Thales A. C. Maia Braz J. Cardoso Filho doi: 10.3390/mca23040072 Mathematical and Computational Applications 2018-11-10 Mathematical and Computational Applications 2018-11-10 23 4 Article 72 10.3390/mca23040072 http://www.mdpi.com/2297-8747/23/4/72
MCA, Vol. 23, Pages 71: Memory Efficient Method for Electromagnetic Multi-Region Models Using Scattering Matrices http://www.mdpi.com/2297-8747/23/4/71 This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification. MCA, Vol. 23, Pages 71: Memory Efficient Method for Electromagnetic Multi-Region Models Using Scattering Matrices

Mathematical and Computational Applications doi: 10.3390/mca23040071

Authors: C. H. H. M. Custers J. W. Jansen E. A. Lomonova

This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification.

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Memory Efficient Method for Electromagnetic Multi-Region Models Using Scattering Matrices C. H. H. M. Custers J. W. Jansen E. A. Lomonova doi: 10.3390/mca23040071 Mathematical and Computational Applications 2018-11-09 Mathematical and Computational Applications 2018-11-09 23 4 Article 71 10.3390/mca23040071 http://www.mdpi.com/2297-8747/23/4/71
MCA, Vol. 23, Pages 70: Modeling and Simulation of a Hydraulic Network for Leak Diagnosis http://www.mdpi.com/2297-8747/23/4/70 This work presents the modeling and simulation of a hydraulic network with four nodes and two branches that form a two-level water distribution system. It also proposes a distribution of hydraulic valves that allows emulating a leak using a valve and different network configurations, e.g., simple ducts, closed networks and branched networks. The network is modeled in the steady state considering turbulent flow. Numerical experiments are performed, and the results show that the proposed network is useful for the design of leakage diagnosis and control algorithms in different configurations and leakage scenarios. MCA, Vol. 23, Pages 70: Modeling and Simulation of a Hydraulic Network for Leak Diagnosis

Mathematical and Computational Applications doi: 10.3390/mca23040070

Authors: José-Roberto Bermúdez Francisco-Ronay López-Estrada Gildas Besançon Guillermo Valencia-Palomo Lizeth Torres Héctor-Ricardo Hernández

This work presents the modeling and simulation of a hydraulic network with four nodes and two branches that form a two-level water distribution system. It also proposes a distribution of hydraulic valves that allows emulating a leak using a valve and different network configurations, e.g., simple ducts, closed networks and branched networks. The network is modeled in the steady state considering turbulent flow. Numerical experiments are performed, and the results show that the proposed network is useful for the design of leakage diagnosis and control algorithms in different configurations and leakage scenarios.

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Modeling and Simulation of a Hydraulic Network for Leak Diagnosis José-Roberto Bermúdez Francisco-Ronay López-Estrada Gildas Besançon Guillermo Valencia-Palomo Lizeth Torres Héctor-Ricardo Hernández doi: 10.3390/mca23040070 Mathematical and Computational Applications 2018-11-06 Mathematical and Computational Applications 2018-11-06 23 4 Article 70 10.3390/mca23040070 http://www.mdpi.com/2297-8747/23/4/70
MCA, Vol. 23, Pages 69: Bipolar Fuzzy UP-Algebras http://www.mdpi.com/2297-8747/23/4/69 In this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras and prove their generalizations. We provide a condition for a bipolar fuzzy UP-filter to be a bipolar fuzzy UP-ideal. Further, we discuss the relation between bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) and their level cuts. MCA, Vol. 23, Pages 69: Bipolar Fuzzy UP-Algebras

Mathematical and Computational Applications doi: 10.3390/mca23040069

Authors: Korawut Kawila Chaiphon Udomsetchai Aiyared Iampan

In this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras and prove their generalizations. We provide a condition for a bipolar fuzzy UP-filter to be a bipolar fuzzy UP-ideal. Further, we discuss the relation between bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) and their level cuts.

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Bipolar Fuzzy UP-Algebras Korawut Kawila Chaiphon Udomsetchai Aiyared Iampan doi: 10.3390/mca23040069 Mathematical and Computational Applications 2018-11-03 Mathematical and Computational Applications 2018-11-03 23 4 Article 69 10.3390/mca23040069 http://www.mdpi.com/2297-8747/23/4/69
MCA, Vol. 23, Pages 68: Decision Making Approach Based on Competition Graphs and Extended TOPSIS Method under Bipolar Fuzzy Environment http://www.mdpi.com/2297-8747/23/4/68 A wide variety of human decision-making is based on double-sided or bipolar judgmental thinking on a positive side and a negative side. This paper develops a new method called bipolar fuzzy extended TOPSIS based on entropy weights to address the multi-criteria decision-making problems involving bipolar measurements with positive and negative values. The extended bipolar fuzzy TOPSIS method incorporates the capability of bipolar information into the TOPSIS to address the interactions between criteria and measure the aggregate values on a bipolar scale. In practical problems, this method can be used to measure the benefits and side effects of medical treatments. We also discuss some novel applications of bipolar fuzzy competition graphs in food webs and present certain algorithms to compute the strength of competition between species. MCA, Vol. 23, Pages 68: Decision Making Approach Based on Competition Graphs and Extended TOPSIS Method under Bipolar Fuzzy Environment

Mathematical and Computational Applications doi: 10.3390/mca23040068

Authors: Musavarah Sarwar Muhammad Akram Fariha Zafar

A wide variety of human decision-making is based on double-sided or bipolar judgmental thinking on a positive side and a negative side. This paper develops a new method called bipolar fuzzy extended TOPSIS based on entropy weights to address the multi-criteria decision-making problems involving bipolar measurements with positive and negative values. The extended bipolar fuzzy TOPSIS method incorporates the capability of bipolar information into the TOPSIS to address the interactions between criteria and measure the aggregate values on a bipolar scale. In practical problems, this method can be used to measure the benefits and side effects of medical treatments. We also discuss some novel applications of bipolar fuzzy competition graphs in food webs and present certain algorithms to compute the strength of competition between species.

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Decision Making Approach Based on Competition Graphs and Extended TOPSIS Method under Bipolar Fuzzy Environment Musavarah Sarwar Muhammad Akram Fariha Zafar doi: 10.3390/mca23040068 Mathematical and Computational Applications 2018-10-28 Mathematical and Computational Applications 2018-10-28 23 4 Article 68 10.3390/mca23040068 http://www.mdpi.com/2297-8747/23/4/68
MCA, Vol. 23, Pages 67: Managing Human Factors to Reduce Organisational Risk in Industry http://www.mdpi.com/2297-8747/23/4/67 Human factors are intrinsically involved at virtually any level of most industrial/business activities, and may be responsible for several accidents and incidents, if not correctly identified and managed. Focusing on the significance of human behaviour in industry, this article proposes a multi-criteria decision-making (MCDM)-based approach to support organizational risk assessment in industrial environments. The decision-making trial and evaluation laboratory (DEMATEL) method is proposed as a mathematical framework to evaluate mutual relationships within a set of human factors involved in industrial processes, with the aim of highlighting priorities of intervention. A case study related to a manufacturing process of a real-world winery is presented, and the proposed approach is applied to rank human factors resulting from a previous organisational risk evaluation from which suitable inference engines may be developed to better support risk management. MCA, Vol. 23, Pages 67: Managing Human Factors to Reduce Organisational Risk in Industry

Mathematical and Computational Applications doi: 10.3390/mca23040067

Authors: Silvia Carpitella Fortunato Carpitella Antonella Certa Julio Benítez Joaquín Izquierdo

Human factors are intrinsically involved at virtually any level of most industrial/business activities, and may be responsible for several accidents and incidents, if not correctly identified and managed. Focusing on the significance of human behaviour in industry, this article proposes a multi-criteria decision-making (MCDM)-based approach to support organizational risk assessment in industrial environments. The decision-making trial and evaluation laboratory (DEMATEL) method is proposed as a mathematical framework to evaluate mutual relationships within a set of human factors involved in industrial processes, with the aim of highlighting priorities of intervention. A case study related to a manufacturing process of a real-world winery is presented, and the proposed approach is applied to rank human factors resulting from a previous organisational risk evaluation from which suitable inference engines may be developed to better support risk management.

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Managing Human Factors to Reduce Organisational Risk in Industry Silvia Carpitella Fortunato Carpitella Antonella Certa Julio Benítez Joaquín Izquierdo doi: 10.3390/mca23040067 Mathematical and Computational Applications 2018-10-25 Mathematical and Computational Applications 2018-10-25 23 4 Article 67 10.3390/mca23040067 http://www.mdpi.com/2297-8747/23/4/67
MCA, Vol. 23, Pages 66: Metrics for Single-Edged Graphs over a Fixed Set of Vertices http://www.mdpi.com/2297-8747/23/4/66 Graphs have powerful representations of all kinds of theoretical or experimental mathematical objects. A technique to measure the distance between graphs has become an important issue. In this article, we show how to define distance functions measuring the distance between graphs with directed edges over a fixed set of named and unnamed vertices, respectively. Furthermore, we show how to implement these distance functions via computational matrix operations. MCA, Vol. 23, Pages 66: Metrics for Single-Edged Graphs over a Fixed Set of Vertices

Mathematical and Computational Applications doi: 10.3390/mca23040066

Authors: Ray-Ming Chen

Graphs have powerful representations of all kinds of theoretical or experimental mathematical objects. A technique to measure the distance between graphs has become an important issue. In this article, we show how to define distance functions measuring the distance between graphs with directed edges over a fixed set of named and unnamed vertices, respectively. Furthermore, we show how to implement these distance functions via computational matrix operations.

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Metrics for Single-Edged Graphs over a Fixed Set of Vertices Ray-Ming Chen doi: 10.3390/mca23040066 Mathematical and Computational Applications 2018-10-24 Mathematical and Computational Applications 2018-10-24 23 4 Article 66 10.3390/mca23040066 http://www.mdpi.com/2297-8747/23/4/66
MCA, Vol. 23, Pages 65: Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme http://www.mdpi.com/2297-8747/23/4/65 In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan&amp;ndash;Ivrissimtzis&amp;rsquo;s scheme, Siddiqi&amp;ndash;Rehan&amp;rsquo;s scheme, and Siddiqi&amp;ndash;Ahmad&amp;rsquo;s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values. MCA, Vol. 23, Pages 65: Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

Mathematical and Computational Applications doi: 10.3390/mca23040065

Authors: Kaijun Peng Jieqing Tan Zhiming Li Li Zhang

In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan&amp;ndash;Ivrissimtzis&amp;rsquo;s scheme, Siddiqi&amp;ndash;Rehan&amp;rsquo;s scheme, and Siddiqi&amp;ndash;Ahmad&amp;rsquo;s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

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Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme Kaijun Peng Jieqing Tan Zhiming Li Li Zhang doi: 10.3390/mca23040065 Mathematical and Computational Applications 2018-10-23 Mathematical and Computational Applications 2018-10-23 23 4 Article 65 10.3390/mca23040065 http://www.mdpi.com/2297-8747/23/4/65
MCA, Vol. 23, Pages 64: Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem http://www.mdpi.com/2297-8747/23/4/64 In this paper, we attempt to determine the optimal duration of an anti-epidemic control strategy which targets susceptible people, under the isoperimetric condition that we could not control all individuals of this category due to restricted health resources. We state and prove the local and global stability conditions of free and endemic equilibria of a simple epidemic compartmental model devised in the form of four ordinary differential equations which describe the dynamics of susceptible-controlled-infected-removed populations and where it is taken into account that the controlled people cannot acquire long-lived immunity to move towards the removed compartment due to the temporary effect of the control parameter. Thereafter, we characterize the sought optimal control and we show the effectiveness of this limited control policy along with the research of the optimal duration that is needed to reduce the size of the infected population. The isoperimetric constraint is defined over a fixed horizon, while the objective function is defined over a free horizon present under a quadratic form in the payoff term. The complexity of this optimal control problem requires the execution of three numerical methods all combined together at the same time, namely, the forward–backward sweep method to generate the optimal state and control functions, the secant method adapted to the isoperimetric restriction, and, finally, the fixed point method to obtain the optimal final time. MCA, Vol. 23, Pages 64: Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem

Mathematical and Computational Applications doi: 10.3390/mca23040064

Authors: Imane Abouelkheir Fadwa El Kihal Mostafa Rachik Ilias Elmouki

In this paper, we attempt to determine the optimal duration of an anti-epidemic control strategy which targets susceptible people, under the isoperimetric condition that we could not control all individuals of this category due to restricted health resources. We state and prove the local and global stability conditions of free and endemic equilibria of a simple epidemic compartmental model devised in the form of four ordinary differential equations which describe the dynamics of susceptible-controlled-infected-removed populations and where it is taken into account that the controlled people cannot acquire long-lived immunity to move towards the removed compartment due to the temporary effect of the control parameter. Thereafter, we characterize the sought optimal control and we show the effectiveness of this limited control policy along with the research of the optimal duration that is needed to reduce the size of the infected population. The isoperimetric constraint is defined over a fixed horizon, while the objective function is defined over a free horizon present under a quadratic form in the payoff term. The complexity of this optimal control problem requires the execution of three numerical methods all combined together at the same time, namely, the forward–backward sweep method to generate the optimal state and control functions, the secant method adapted to the isoperimetric restriction, and, finally, the fixed point method to obtain the optimal final time.

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Time Needed to Control an Epidemic with Restricted Resources in SIR Model with Short-Term Controlled Population: A Fixed Point Method for a Free Isoperimetric Optimal Control Problem Imane Abouelkheir Fadwa El Kihal Mostafa Rachik Ilias Elmouki doi: 10.3390/mca23040064 Mathematical and Computational Applications 2018-10-22 Mathematical and Computational Applications 2018-10-22 23 4 Article 64 10.3390/mca23040064 http://www.mdpi.com/2297-8747/23/4/64
MCA, Vol. 23, Pages 63: A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions http://www.mdpi.com/2297-8747/23/4/63 A complete MAPLE procedure is designed to effectively implement an algorithm for approximating trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval&amp;ndash;polynomial as its output that we can easily exploit in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both rational and irrational arguments as well as drawing the graph of the piecewise approximate functions are presented. Moreover, from the approximate integration on [ a , b ] with integrands of the form x m sin x , another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best L 2 -approximation of the sine function in the vector space P ℓ of polynomials of degree at most ℓ, a subspace of L 2 ( a , b ) . MCA, Vol. 23, Pages 63: A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions

Mathematical and Computational Applications doi: 10.3390/mca23040063

Authors: Le Phuong Quan

A complete MAPLE procedure is designed to effectively implement an algorithm for approximating trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval&amp;ndash;polynomial as its output that we can easily exploit in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both rational and irrational arguments as well as drawing the graph of the piecewise approximate functions are presented. Moreover, from the approximate integration on [ a , b ] with integrands of the form x m sin x , another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best L 2 -approximation of the sine function in the vector space P ℓ of polynomials of degree at most ℓ, a subspace of L 2 ( a , b ) .

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A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions Le Phuong Quan doi: 10.3390/mca23040063 Mathematical and Computational Applications 2018-10-17 Mathematical and Computational Applications 2018-10-17 23 4 Article 63 10.3390/mca23040063 http://www.mdpi.com/2297-8747/23/4/63
MCA, Vol. 23, Pages 62: Application of Approximate Analytical Technique Using the Homotopy Perturbation Method to Study the Inclination Effect on the Thermal Behavior of Porous Fin Heat Sink http://www.mdpi.com/2297-8747/23/4/62 This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length&amp;ndash;thickness aspect ratio. The study further reveals that increase in the internal heat generation variable decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The obtained results using HPM highlights the accuracy of the present method for the analysis of nonlinear heat transfer problems, as it agrees well with the established results of Runge&amp;ndash;Kutta. MCA, Vol. 23, Pages 62: Application of Approximate Analytical Technique Using the Homotopy Perturbation Method to Study the Inclination Effect on the Thermal Behavior of Porous Fin Heat Sink

Mathematical and Computational Applications doi: 10.3390/mca23040062

Authors: George Oguntala Gbeminiyi Sobamowo Yinusa Ahmed Raed Abd-Alhameed

This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length&amp;ndash;thickness aspect ratio. The study further reveals that increase in the internal heat generation variable decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The obtained results using HPM highlights the accuracy of the present method for the analysis of nonlinear heat transfer problems, as it agrees well with the established results of Runge&amp;ndash;Kutta.

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Application of Approximate Analytical Technique Using the Homotopy Perturbation Method to Study the Inclination Effect on the Thermal Behavior of Porous Fin Heat Sink George Oguntala Gbeminiyi Sobamowo Yinusa Ahmed Raed Abd-Alhameed doi: 10.3390/mca23040062 Mathematical and Computational Applications 2018-10-15 Mathematical and Computational Applications 2018-10-15 23 4 Article 62 10.3390/mca23040062 http://www.mdpi.com/2297-8747/23/4/62
MCA, Vol. 23, Pages 61: On a Graph Associated to UP-Algebras http://www.mdpi.com/2297-8747/23/4/61 In this article, we introduce the concept of graphs associated with commutative UP-algebra, which we say is a UP-graph whose vertices are the elements of commutative UP-algebra and whose edges are the association of two vertices, that is two elements from commutative UP-algebra. We also define a graph of equivalence classes of a commutative UP-algebra and prove some related results based on the algebraic properties of the graph. We show that two graphs are the same and complete bipartite if they are formed by equivalence classes of UP-algebra and the graph folding of commutative UP-algebra. An algorithm for checking whether a given set is a UP-algebra or not has also been given. MCA, Vol. 23, Pages 61: On a Graph Associated to UP-Algebras

Mathematical and Computational Applications doi: 10.3390/mca23040061

Authors: Moin A. Ansari Azeem Haidar Ali N.A. Koam

In this article, we introduce the concept of graphs associated with commutative UP-algebra, which we say is a UP-graph whose vertices are the elements of commutative UP-algebra and whose edges are the association of two vertices, that is two elements from commutative UP-algebra. We also define a graph of equivalence classes of a commutative UP-algebra and prove some related results based on the algebraic properties of the graph. We show that two graphs are the same and complete bipartite if they are formed by equivalence classes of UP-algebra and the graph folding of commutative UP-algebra. An algorithm for checking whether a given set is a UP-algebra or not has also been given.

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On a Graph Associated to UP-Algebras Moin A. Ansari Azeem Haidar Ali N.A. Koam doi: 10.3390/mca23040061 Mathematical and Computational Applications 2018-10-15 Mathematical and Computational Applications 2018-10-15 23 4 Article 61 10.3390/mca23040061 http://www.mdpi.com/2297-8747/23/4/61
MCA, Vol. 23, Pages 60: Surrogate-Based Optimization Using an Open-Source Framework: The Bulbous Bow Shape Optimization Case http://www.mdpi.com/2297-8747/23/4/60 Shape optimization is a very time-consuming and expensive task, especially if experimental tests need to be performed. To overcome the challenges of geometry optimization, the industry is increasingly relying on numerical simulations. These kinds of problems typically involve the interaction of three main applications: a solid modeler, a multi-physics solver, and an optimizer. In this manuscript, we present a shape optimization work-flow entirely based on open-source tools; it is fault tolerant and software agnostic, allows for asynchronous simulations, and has a high degree of automation. To demonstrate the usability and flexibility of the proposed methodology, we tested it in a practical case related to the naval industry, where we aimed at optimizing the shape of a bulbous bow in order to minimize the hydrodynamic resistance. As design variables, we considered the protrusion and immersion of the bulbous bow, and we used surrogate-based optimization. From the results presented, a non-negligible resistance reduction is obtainable using the proposed work-flow and optimization strategy. MCA, Vol. 23, Pages 60: Surrogate-Based Optimization Using an Open-Source Framework: The Bulbous Bow Shape Optimization Case

Mathematical and Computational Applications doi: 10.3390/mca23040060

Authors: Joel Guerrero Alberto Cominetti Jan Pralits Diego Villa

Shape optimization is a very time-consuming and expensive task, especially if experimental tests need to be performed. To overcome the challenges of geometry optimization, the industry is increasingly relying on numerical simulations. These kinds of problems typically involve the interaction of three main applications: a solid modeler, a multi-physics solver, and an optimizer. In this manuscript, we present a shape optimization work-flow entirely based on open-source tools; it is fault tolerant and software agnostic, allows for asynchronous simulations, and has a high degree of automation. To demonstrate the usability and flexibility of the proposed methodology, we tested it in a practical case related to the naval industry, where we aimed at optimizing the shape of a bulbous bow in order to minimize the hydrodynamic resistance. As design variables, we considered the protrusion and immersion of the bulbous bow, and we used surrogate-based optimization. From the results presented, a non-negligible resistance reduction is obtainable using the proposed work-flow and optimization strategy.

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Surrogate-Based Optimization Using an Open-Source Framework: The Bulbous Bow Shape Optimization Case Joel Guerrero Alberto Cominetti Jan Pralits Diego Villa doi: 10.3390/mca23040060 Mathematical and Computational Applications 2018-10-13 Mathematical and Computational Applications 2018-10-13 23 4 Article 60 10.3390/mca23040060 http://www.mdpi.com/2297-8747/23/4/60
MCA, Vol. 23, Pages 59: Two-Dimensional Exact Subdomain Technique of Switched Reluctance Machines with Sinusoidal Current Excitation http://www.mdpi.com/2297-8747/23/4/59 This paper presents a two-dimensional (2D) exact subdomain technique in polar coordinates considering the iron relative permeability in 6/4 switched reluctance machines (SRM) supplied by sinusoidal waveform of current (aka, variable flux reluctance machines). In non-periodic regions (e.g., rotor and/or stator slots/teeth), magnetostatic Maxwell&amp;rsquo;s equations are solved considering non-homogeneous Neumann boundary conditions (BCs). The general solutions of magnetic vector potential in all subdomains are obtained by applying the interface conditions (ICs) in both directions (i.e., r- and &amp;theta;-edges ICs). The global saturation effect is taken into account, with a constant magnetic permeability corresponding to the linear zone of the nonlinear B(H) curve. In this investigation, the magnetic flux density distribution inside the electrical machine, the static/dynamic electromagnetic torques, the magnetic flux linkage, the self-/mutual inductances, the magnetic pressures, and the unbalanced magnetic forces (UMFs) have been calculated for 6/4 SRM with two various non-overlapping (or concentrated) windings. One of the case studies is a M1 with a non-overlapping all teeth wound winding (double-layer winding with left and right layer) and the other is a M2 with a non-overlapping alternate teeth wound winding (single-layer winding). It is important to note that the developed semi-analytical model based on the 2D exact subdomain technique is also valid for any number of slot/pole combinations and for non-overlapping teeth wound windings with a single/double layer. Finally, the semi-analytical results have been performed for different values of iron core relative permeability (viz., 100 and 800), and compared with those obtained by the 2D finite-element method (FEM). The comparisons with FEM show good results for the proposed approach. MCA, Vol. 23, Pages 59: Two-Dimensional Exact Subdomain Technique of Switched Reluctance Machines with Sinusoidal Current Excitation

Mathematical and Computational Applications doi: 10.3390/mca23040059

Authors: Mohammed Ben Yahia Kamel Boughrara Frédéric Dubas Lazhar Roubache Rachid Ibtiouen

This paper presents a two-dimensional (2D) exact subdomain technique in polar coordinates considering the iron relative permeability in 6/4 switched reluctance machines (SRM) supplied by sinusoidal waveform of current (aka, variable flux reluctance machines). In non-periodic regions (e.g., rotor and/or stator slots/teeth), magnetostatic Maxwell&amp;rsquo;s equations are solved considering non-homogeneous Neumann boundary conditions (BCs). The general solutions of magnetic vector potential in all subdomains are obtained by applying the interface conditions (ICs) in both directions (i.e., r- and &amp;theta;-edges ICs). The global saturation effect is taken into account, with a constant magnetic permeability corresponding to the linear zone of the nonlinear B(H) curve. In this investigation, the magnetic flux density distribution inside the electrical machine, the static/dynamic electromagnetic torques, the magnetic flux linkage, the self-/mutual inductances, the magnetic pressures, and the unbalanced magnetic forces (UMFs) have been calculated for 6/4 SRM with two various non-overlapping (or concentrated) windings. One of the case studies is a M1 with a non-overlapping all teeth wound winding (double-layer winding with left and right layer) and the other is a M2 with a non-overlapping alternate teeth wound winding (single-layer winding). It is important to note that the developed semi-analytical model based on the 2D exact subdomain technique is also valid for any number of slot/pole combinations and for non-overlapping teeth wound windings with a single/double layer. Finally, the semi-analytical results have been performed for different values of iron core relative permeability (viz., 100 and 800), and compared with those obtained by the 2D finite-element method (FEM). The comparisons with FEM show good results for the proposed approach.

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Two-Dimensional Exact Subdomain Technique of Switched Reluctance Machines with Sinusoidal Current Excitation Mohammed Ben Yahia Kamel Boughrara Frédéric Dubas Lazhar Roubache Rachid Ibtiouen doi: 10.3390/mca23040059 Mathematical and Computational Applications 2018-10-11 Mathematical and Computational Applications 2018-10-11 23 4 Article 59 10.3390/mca23040059 http://www.mdpi.com/2297-8747/23/4/59
MCA, Vol. 23, Pages 58: An Efficient Golden Ratio Method for Secure Cryptographic Applications http://www.mdpi.com/2297-8747/23/4/58 With the increase in the use of electronic transactions in everyday life, secure communications and data storage to withstand any kind of attack is warranted. The golden ratio, being the most irrational among irrational numbers, can be used in elliptic curve cryptosystems, power analysis security, and other applications. However, in such applications, cryptographic operations should take place very quickly before the keys are extracted or decoded by the attackers. This paper proposes an efficient method of golden ratio computation in cryptography to resist information security breaches. We compare our new golden ratio method with the well-known Fibonacci sequence method. The experimental results show that our proposed method is more efficient than the Fibonacci sequence method. Our golden ratio method with infinite precision provides reliable counter measure strategy to address the escalating security attacks. MCA, Vol. 23, Pages 58: An Efficient Golden Ratio Method for Secure Cryptographic Applications

Mathematical and Computational Applications doi: 10.3390/mca23040058

Authors: Anthony Overmars Sitalakshmi Venkatraman

With the increase in the use of electronic transactions in everyday life, secure communications and data storage to withstand any kind of attack is warranted. The golden ratio, being the most irrational among irrational numbers, can be used in elliptic curve cryptosystems, power analysis security, and other applications. However, in such applications, cryptographic operations should take place very quickly before the keys are extracted or decoded by the attackers. This paper proposes an efficient method of golden ratio computation in cryptography to resist information security breaches. We compare our new golden ratio method with the well-known Fibonacci sequence method. The experimental results show that our proposed method is more efficient than the Fibonacci sequence method. Our golden ratio method with infinite precision provides reliable counter measure strategy to address the escalating security attacks.

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An Efficient Golden Ratio Method for Secure Cryptographic Applications Anthony Overmars Sitalakshmi Venkatraman doi: 10.3390/mca23040058 Mathematical and Computational Applications 2018-10-10 Mathematical and Computational Applications 2018-10-10 23 4 Article 58 10.3390/mca23040058 http://www.mdpi.com/2297-8747/23/4/58
MCA, Vol. 23, Pages 57: An Analytical Expression for Magnet Shape Optimization in Surface-Mounted Permanent Magnet Machines http://www.mdpi.com/2297-8747/23/4/57 Surface-mounted permanent magnet machines are widely used in low and medium speed applications. Pulsating torque components is the most crucial challenge, especially in low-speed applications. Magnet pole shape optimization can be used to mitigate these components. In this research, an analytical model is proposed to calculate the magnetic vector potential in surface-mounted permanent magnet machines. A mathematical expression is also derived for optimal the magnet shape to reduce the cogging torque and electromagnetic torque components. The presented model is based on the resolution of the Laplace&amp;rsquo;s and Poisson&amp;rsquo;s equations in polar coordinates by using the subdomain method and applying hyperbolic functions. The proposed method is applied to the performance computation of a surface-mounted permanent magnet machine, i.e., a 3-phase 12S-10P motor. The analytical results are validated through the finite element analysis (FEA) method. MCA, Vol. 23, Pages 57: An Analytical Expression for Magnet Shape Optimization in Surface-Mounted Permanent Magnet Machines

Mathematical and Computational Applications doi: 10.3390/mca23040057

Authors: Ali Jabbari

Surface-mounted permanent magnet machines are widely used in low and medium speed applications. Pulsating torque components is the most crucial challenge, especially in low-speed applications. Magnet pole shape optimization can be used to mitigate these components. In this research, an analytical model is proposed to calculate the magnetic vector potential in surface-mounted permanent magnet machines. A mathematical expression is also derived for optimal the magnet shape to reduce the cogging torque and electromagnetic torque components. The presented model is based on the resolution of the Laplace&amp;rsquo;s and Poisson&amp;rsquo;s equations in polar coordinates by using the subdomain method and applying hyperbolic functions. The proposed method is applied to the performance computation of a surface-mounted permanent magnet machine, i.e., a 3-phase 12S-10P motor. The analytical results are validated through the finite element analysis (FEA) method.

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An Analytical Expression for Magnet Shape Optimization in Surface-Mounted Permanent Magnet Machines Ali Jabbari doi: 10.3390/mca23040057 Mathematical and Computational Applications 2018-10-05 Mathematical and Computational Applications 2018-10-05 23 4 Article 57 10.3390/mca23040057 http://www.mdpi.com/2297-8747/23/4/57
MCA, Vol. 23, Pages 56: Green’s Function of the Linearized Logarithmic Keller–Segel–Fisher/KPP System http://www.mdpi.com/2297-8747/23/4/56 We consider a Keller–Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity in the system is removed via the inverse Hopf–Cole transformation. We then linearize the system around a constant equilibrium state, and obtain a detailed, pointwise description of the Green’s function. The result provides a complete solution picture for the linear problem. It also helps to shed light on small solutions of the nonlinear system. MCA, Vol. 23, Pages 56: Green’s Function of the Linearized Logarithmic Keller–Segel–Fisher/KPP System

Mathematical and Computational Applications doi: 10.3390/mca23040056

Authors: Jean Rugamba Yanni Zeng

We consider a Keller–Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity in the system is removed via the inverse Hopf–Cole transformation. We then linearize the system around a constant equilibrium state, and obtain a detailed, pointwise description of the Green’s function. The result provides a complete solution picture for the linear problem. It also helps to shed light on small solutions of the nonlinear system.

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Green’s Function of the Linearized Logarithmic Keller–Segel–Fisher/KPP System Jean Rugamba Yanni Zeng doi: 10.3390/mca23040056 Mathematical and Computational Applications 2018-10-03 Mathematical and Computational Applications 2018-10-03 23 4 Article 56 10.3390/mca23040056 http://www.mdpi.com/2297-8747/23/4/56
MCA, Vol. 23, Pages 55: Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation http://www.mdpi.com/2297-8747/23/4/55 This study aims to solve the real-world multistage assignment problem. The proposed problem is composed of two stages of assignment: (1) different types of trucks are assigned to chicken farms to transport young chickens to egg farms, and (2) chicken farms are assigned to egg farms. Assigning different trucks to the egg farms and different egg farms to the chicken farms generates different costs and consumes different resources. The distance and the idle space in the truck have to be minimized, while constraints such as the minimum number of chickens needed for all egg farms and the longest time that chickens can be in the truck remain. This makes the problem a special case of the multistage assignment (S-MSA) problem. A mathematical model representing the problem was developed and solved to optimality using Lingo v.11 optimization software. Lingo v.11 can solve to optimality only small- and medium-sized test instances. To solve large-sized test instances, the differential evolution (DE) algorithm was designed. An excellent decoding method was developed to increase the search performance of DE. The proposed algorithm was tested with three randomly generated datasets (small, medium, and large test instances) and one real case study. Each dataset is composed of 12 problems, therefore we tested with 37 instances, including the case study. The results show that for small- and medium-sized test instances, DE has 0.03% and 0.05% higher cost than Lingo v.11. For large test instances, DE has 3.52% lower cost than Lingo v.11. Lingo v.11 uses an average computation time of 5.8, 103, and 4320 s for small, medium and large test instances, while DE uses 0.86, 1.68, and 8.79 s, which is, at most, 491 times less than Lingo v.11. Therefore, the proposed heuristics are an effective algorithm that can find a good solution while using less computation time. MCA, Vol. 23, Pages 55: Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation

Mathematical and Computational Applications doi: 10.3390/mca23040055

Authors: Sasitorn Kaewman Tassin Srivarapongse Chalermchat Theeraviriya Ganokgarn Jirasirilerd

This study aims to solve the real-world multistage assignment problem. The proposed problem is composed of two stages of assignment: (1) different types of trucks are assigned to chicken farms to transport young chickens to egg farms, and (2) chicken farms are assigned to egg farms. Assigning different trucks to the egg farms and different egg farms to the chicken farms generates different costs and consumes different resources. The distance and the idle space in the truck have to be minimized, while constraints such as the minimum number of chickens needed for all egg farms and the longest time that chickens can be in the truck remain. This makes the problem a special case of the multistage assignment (S-MSA) problem. A mathematical model representing the problem was developed and solved to optimality using Lingo v.11 optimization software. Lingo v.11 can solve to optimality only small- and medium-sized test instances. To solve large-sized test instances, the differential evolution (DE) algorithm was designed. An excellent decoding method was developed to increase the search performance of DE. The proposed algorithm was tested with three randomly generated datasets (small, medium, and large test instances) and one real case study. Each dataset is composed of 12 problems, therefore we tested with 37 instances, including the case study. The results show that for small- and medium-sized test instances, DE has 0.03% and 0.05% higher cost than Lingo v.11. For large test instances, DE has 3.52% lower cost than Lingo v.11. Lingo v.11 uses an average computation time of 5.8, 103, and 4320 s for small, medium and large test instances, while DE uses 0.86, 1.68, and 8.79 s, which is, at most, 491 times less than Lingo v.11. Therefore, the proposed heuristics are an effective algorithm that can find a good solution while using less computation time.

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Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation Sasitorn Kaewman Tassin Srivarapongse Chalermchat Theeraviriya Ganokgarn Jirasirilerd doi: 10.3390/mca23040055 Mathematical and Computational Applications 2018-10-02 Mathematical and Computational Applications 2018-10-02 23 4 Article 55 10.3390/mca23040055 http://www.mdpi.com/2297-8747/23/4/55

Mathematical and Computational Applications doi: 10.3390/mca23040054

Authors: Chahid Kamel Ghaddar

We devise a practical and systematic spreadsheet solution paradigm for general optimal control problems. The paradigm is based on an adaptation of a partial-parametrization direct solution method which preserves the original mathematical optimization statement, but transforms it into a simplified nonlinear programming problem (NLP) suitable for Excel NLP solver. A rapid solution strategy is implemented by a tiered arrangement of pure elementary calculus functions in conjunction with Excel NLP solver. With the aid of the calculus functions, a cost index and constraints are represented by equivalent formulas that fully encapsulate an underlining parametrized dynamical system. Excel NLP solver is then employed to minimize (or maximize) the cost index formula, by varying decision parameters, subject to the constraints formulas. The paradigm is demonstrated for several fixed and free-time nonlinear optimal control problems involving integral and implicit dynamic constraints with direct comparison to published results obtained by fundamentally different methods. Practically, applying the paradigm involves no more than defining a few formulas using basic Excel spreadsheet skills.

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Rapid Solution of Optimal Control Problems by a Functional Spreadsheet Paradigm: A Practical Method for the Non-Programmer Chahid Kamel Ghaddar doi: 10.3390/mca23040054 Mathematical and Computational Applications 2018-09-28 Mathematical and Computational Applications 2018-09-28 23 4 Article 54 10.3390/mca23040054 http://www.mdpi.com/2297-8747/23/4/54
MCA, Vol. 23, Pages 53: Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method http://www.mdpi.com/2297-8747/23/4/53 The present study aimed at solving the stochastic generalized fractional diffusion equation (SGFDE) by means of the random finite difference method (FDM). Moreover, the conditions of mean square convergence of the numerical solution are studied and numerical examples are presented to demonstrate the validity and accuracy of the method. MCA, Vol. 23, Pages 53: Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method

Mathematical and Computational Applications doi: 10.3390/mca23040053

The present study aimed at solving the stochastic generalized fractional diffusion equation (SGFDE) by means of the random finite difference method (FDM). Moreover, the conditions of mean square convergence of the numerical solution are studied and numerical examples are presented to demonstrate the validity and accuracy of the method.

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Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method Amaneh Sepahvandzadeh Bahman Ghazanfari Nader Asadian doi: 10.3390/mca23040053 Mathematical and Computational Applications 2018-09-26 Mathematical and Computational Applications 2018-09-26 23 4 Article 53 10.3390/mca23040053 http://www.mdpi.com/2297-8747/23/4/53
MCA, Vol. 23, Pages 52: Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System http://www.mdpi.com/2297-8747/23/4/52 We consider a discrete-time susceptible-infected-removed-susceptible &amp;ldquo;again&amp;rdquo; (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem. MCA, Vol. 23, Pages 52: Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System

Mathematical and Computational Applications doi: 10.3390/mca23040052

Authors: Fadwa El Kihal Imane Abouelkheir Mostafa Rachik Ilias Elmouki

We consider a discrete-time susceptible-infected-removed-susceptible &amp;ldquo;again&amp;rdquo; (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem.

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Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System Fadwa El Kihal Imane Abouelkheir Mostafa Rachik Ilias Elmouki doi: 10.3390/mca23040052 Mathematical and Computational Applications 2018-09-24 Mathematical and Computational Applications 2018-09-24 23 4 Article 52 10.3390/mca23040052 http://www.mdpi.com/2297-8747/23/4/52
MCA, Vol. 23, Pages 51: A (p,q)-Averaged Hausdorff Distance for Arbitrary Measurable Sets http://www.mdpi.com/2297-8747/23/3/51 The Hausdorff distance is a widely used tool to measure the distance between different sets. For the approximation of certain objects via stochastic search algorithms this distance is, however, of limited use as it punishes single outliers. As a remedy in the context of evolutionary multi-objective optimization (EMO), the averaged Hausdorff distance &amp;Delta; p has been proposed that is better suited as an indicator for the performance assessment of EMO algorithms since such methods tend to generate outliers. Later on, the two-parameter indicator &amp;Delta; p , q has been proposed for finite sets as an extension to &amp;Delta; p which also averages distances, but which yields some desired metric properties. In this paper, we extend &amp;Delta; p , q to a continuous function between general bounded subsets of finite measure inside a metric measure space. In particular, this extension applies to bounded subsets of R k endowed with the Euclidean metric, which is the natural context for EMO applications. We show that our extension preserves the nice metric properties of the finite case, and finally provide some useful numerical examples that arise in EMO. MCA, Vol. 23, Pages 51: A (p,q)-Averaged Hausdorff Distance for Arbitrary Measurable Sets

Mathematical and Computational Applications doi: 10.3390/mca23030051

Authors: Johan M. Bogoya Andrés Vargas Oliver Cuate Oliver Schütze

The Hausdorff distance is a widely used tool to measure the distance between different sets. For the approximation of certain objects via stochastic search algorithms this distance is, however, of limited use as it punishes single outliers. As a remedy in the context of evolutionary multi-objective optimization (EMO), the averaged Hausdorff distance &amp;Delta; p has been proposed that is better suited as an indicator for the performance assessment of EMO algorithms since such methods tend to generate outliers. Later on, the two-parameter indicator &amp;Delta; p , q has been proposed for finite sets as an extension to &amp;Delta; p which also averages distances, but which yields some desired metric properties. In this paper, we extend &amp;Delta; p , q to a continuous function between general bounded subsets of finite measure inside a metric measure space. In particular, this extension applies to bounded subsets of R k endowed with the Euclidean metric, which is the natural context for EMO applications. We show that our extension preserves the nice metric properties of the finite case, and finally provide some useful numerical examples that arise in EMO.

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A (p,q)-Averaged Hausdorff Distance for Arbitrary Measurable Sets Johan M. Bogoya Andrés Vargas Oliver Cuate Oliver Schütze doi: 10.3390/mca23030051 Mathematical and Computational Applications 2018-09-18 Mathematical and Computational Applications 2018-09-18 23 3 Article 51 10.3390/mca23030051 http://www.mdpi.com/2297-8747/23/3/51
MCA, Vol. 23, Pages 50: Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid http://www.mdpi.com/2297-8747/23/3/50 The main objective of this article is to determine the existing linear correlation between the real left ventricular volume (RV) from the heart of bovines and the volumes obtained by Teichholz&amp;rsquo;s mathematical model and the volume of the truncated prolate spheroid (TPS) to identify which model has a higher proximity to the RV. For that, ten silicon rubber molds of the left ventricle (LV) were manufactured, and their real volumes were obtained through Archimedes&amp;rsquo; principle, and their linear dimensions were also obtained. These dimensions were used to feed Teichholz&amp;rsquo;s and the TPS models. It was verified that, for ventricles of lower volume, the models showed relatively close results, and Teichholz&amp;rsquo;s model was the most accurate one. The TPS method shows a grave accuracy mistake for higher volume ventricles. Besides, both methods showed strong linear correlations with the RV, and both with high significance. MCA, Vol. 23, Pages 50: Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid

Mathematical and Computational Applications doi: 10.3390/mca23030050

Authors: José Sérgio Domingues Ravel Alvarenga Coelho Francielly dos Santos Bento Brenda Cristina Almeida Ayanne Oliveira De Castro

The main objective of this article is to determine the existing linear correlation between the real left ventricular volume (RV) from the heart of bovines and the volumes obtained by Teichholz&amp;rsquo;s mathematical model and the volume of the truncated prolate spheroid (TPS) to identify which model has a higher proximity to the RV. For that, ten silicon rubber molds of the left ventricle (LV) were manufactured, and their real volumes were obtained through Archimedes&amp;rsquo; principle, and their linear dimensions were also obtained. These dimensions were used to feed Teichholz&amp;rsquo;s and the TPS models. It was verified that, for ventricles of lower volume, the models showed relatively close results, and Teichholz&amp;rsquo;s model was the most accurate one. The TPS method shows a grave accuracy mistake for higher volume ventricles. Besides, both methods showed strong linear correlations with the RV, and both with high significance.

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Left Ventricular Volume in Bovines: The Correlation between Teichholz’s Medical Mathematical Method and the Volume of the Truncated Prolate Spheroid José Sérgio Domingues Ravel Alvarenga Coelho Francielly dos Santos Bento Brenda Cristina Almeida Ayanne Oliveira De Castro doi: 10.3390/mca23030050 Mathematical and Computational Applications 2018-09-11 Mathematical and Computational Applications 2018-09-11 23 3 Communication 50 10.3390/mca23030050 http://www.mdpi.com/2297-8747/23/3/50
MCA, Vol. 23, Pages 49: Algebraic Operations on Delta-Sigma Bit-Streams http://www.mdpi.com/2297-8747/23/3/49 Operations in the Delta-Sigma ( &amp;Delta; &amp;Sigma; ) domain are a broad field of research. In this article the main, focus is on applications in control systems, nevertheless the results are generally applicable for &amp;Delta; &amp;Sigma; -signal processing ( &amp;Delta; &amp;Sigma; SP) in other fields. As the bit-stream does not have an instantaneous value, algebraic operations cannot be executed directly. The first approaches were made in the 1980s based on small-scale integration logic chips by Kouvaras and by Lagoyannis. Further algebraic operations and other implementations were introduced by Zrilic, by Ng, by Bradshaw and by Homann. Other publications utilize complex networks and operations to achieve the desired algebraic operations. These presented operations can be divided into different operation classes by the based implementation idea. In this paper, the known algebraic operation classes are further developed and new operation classes are presented. All implementations are compared and evaluated. For linear operations in control applications, the introduced Bipolar Interpretation is best rated. It compensates for the signal offset of bipolar bit-streams and results in the best signal quality by mapping the logic values true and false of bit-stream to plus and minus one before the algebraic operation. The output of the algebraic operation is a multibit value, to achieve a bit-stream as output value a third step is taken. The result is modulated by a digital &amp;Delta; &amp;Sigma; -modulator ( &amp;Delta; &amp;Sigma; -M). For nonlinear operations the most universal implementation is also based on three steps. In the first stage, the bit-streams are processed with short sinc 3 filters, resulting in multibit values. This signal is processed by digital signal processing (DSP). The output stage is a &amp;Delta; &amp;Sigma; -M. For some nonlinear algebraic operations there can be better solutions than DSP, like shown for limiting. In short, this paper gives a detailed overview about different &amp;Delta; &amp;Sigma; SP classes for linear and nonlinear operations. Newly presented are the scaling with Bit-Stream Modification, the Bipolar Interpretation class, the nonlinear operation class based on digital signal processing (DSP), the modified multiplication based on Delta Adder and benchmarks of all presented operations. MCA, Vol. 23, Pages 49: Algebraic Operations on Delta-Sigma Bit-Streams

Mathematical and Computational Applications doi: 10.3390/mca23030049

Authors: Axel Klein Walter Schumacher

Operations in the Delta-Sigma ( &amp;Delta; &amp;Sigma; ) domain are a broad field of research. In this article the main, focus is on applications in control systems, nevertheless the results are generally applicable for &amp;Delta; &amp;Sigma; -signal processing ( &amp;Delta; &amp;Sigma; SP) in other fields. As the bit-stream does not have an instantaneous value, algebraic operations cannot be executed directly. The first approaches were made in the 1980s based on small-scale integration logic chips by Kouvaras and by Lagoyannis. Further algebraic operations and other implementations were introduced by Zrilic, by Ng, by Bradshaw and by Homann. Other publications utilize complex networks and operations to achieve the desired algebraic operations. These presented operations can be divided into different operation classes by the based implementation idea. In this paper, the known algebraic operation classes are further developed and new operation classes are presented. All implementations are compared and evaluated. For linear operations in control applications, the introduced Bipolar Interpretation is best rated. It compensates for the signal offset of bipolar bit-streams and results in the best signal quality by mapping the logic values true and false of bit-stream to plus and minus one before the algebraic operation. The output of the algebraic operation is a multibit value, to achieve a bit-stream as output value a third step is taken. The result is modulated by a digital &amp;Delta; &amp;Sigma; -modulator ( &amp;Delta; &amp;Sigma; -M). For nonlinear operations the most universal implementation is also based on three steps. In the first stage, the bit-streams are processed with short sinc 3 filters, resulting in multibit values. This signal is processed by digital signal processing (DSP). The output stage is a &amp;Delta; &amp;Sigma; -M. For some nonlinear algebraic operations there can be better solutions than DSP, like shown for limiting. In short, this paper gives a detailed overview about different &amp;Delta; &amp;Sigma; SP classes for linear and nonlinear operations. Newly presented are the scaling with Bit-Stream Modification, the Bipolar Interpretation class, the nonlinear operation class based on digital signal processing (DSP), the modified multiplication based on Delta Adder and benchmarks of all presented operations.

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Algebraic Operations on Delta-Sigma Bit-Streams Axel Klein Walter Schumacher doi: 10.3390/mca23030049 Mathematical and Computational Applications 2018-09-10 Mathematical and Computational Applications 2018-09-10 23 3 Article 49 10.3390/mca23030049 http://www.mdpi.com/2297-8747/23/3/49
MCA, Vol. 23, Pages 48: First Order Hadamard Variation of the Harmonic Navigation Function on a Sphere World http://www.mdpi.com/2297-8747/23/3/48 Planning conflict-free trajectories is a long-standing problem in Air Traffic Management. Navigation functions designed specifically to produce flyable trajectories have been previously considered, but lack the robustness to uncertain weather conditions needed for use in an operational context. These uncertainties can be taken into account be modifying the boundary of the domain on which the navigation function is computed. In the following work, we present a method for efficiently taking into account boundary variations, using the Hadamard variation. MCA, Vol. 23, Pages 48: First Order Hadamard Variation of the Harmonic Navigation Function on a Sphere World

Mathematical and Computational Applications doi: 10.3390/mca23030048

Authors: Isabelle Santos Stéphane Puechmorel Guillaume Dufour

Planning conflict-free trajectories is a long-standing problem in Air Traffic Management. Navigation functions designed specifically to produce flyable trajectories have been previously considered, but lack the robustness to uncertain weather conditions needed for use in an operational context. These uncertainties can be taken into account be modifying the boundary of the domain on which the navigation function is computed. In the following work, we present a method for efficiently taking into account boundary variations, using the Hadamard variation.

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First Order Hadamard Variation of the Harmonic Navigation Function on a Sphere World Isabelle Santos Stéphane Puechmorel Guillaume Dufour doi: 10.3390/mca23030048 Mathematical and Computational Applications 2018-09-10 Mathematical and Computational Applications 2018-09-10 23 3 Article 48 10.3390/mca23030048 http://www.mdpi.com/2297-8747/23/3/48
MCA, Vol. 23, Pages 47: TL-Moments for Type-I Censored Data with an Application to the Weibull Distribution http://www.mdpi.com/2297-8747/23/3/47 This paper aims to provide an adaptation of the trimmed L (TL)-moments method to censored data. The present study concentrates on Type-I censored data. The idea of using TL-moments with censored data may seem conflicting. However, our perspective is that we can use data censored from one side and trimmed from the other side. This study is applied to estimate the two unknown parameters of the Weibull distribution. The suggested point is compared with direct L-moments and maximum likelihood (ML) methods. A Monte Carlo simulation study is carried out to compare these methods in terms of estimate average, root of mean square error (RMSE), and relative absolute biases (RABs). MCA, Vol. 23, Pages 47: TL-Moments for Type-I Censored Data with an Application to the Weibull Distribution

Mathematical and Computational Applications doi: 10.3390/mca23030047

Authors: Hager A. Ibrahim Mahmoud Riad Mahmoud Fatma A. Khalil Ghada A. El-Kelany

This paper aims to provide an adaptation of the trimmed L (TL)-moments method to censored data. The present study concentrates on Type-I censored data. The idea of using TL-moments with censored data may seem conflicting. However, our perspective is that we can use data censored from one side and trimmed from the other side. This study is applied to estimate the two unknown parameters of the Weibull distribution. The suggested point is compared with direct L-moments and maximum likelihood (ML) methods. A Monte Carlo simulation study is carried out to compare these methods in terms of estimate average, root of mean square error (RMSE), and relative absolute biases (RABs).

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TL-Moments for Type-I Censored Data with an Application to the Weibull Distribution Hager A. Ibrahim Mahmoud Riad Mahmoud Fatma A. Khalil Ghada A. El-Kelany doi: 10.3390/mca23030047 Mathematical and Computational Applications 2018-09-09 Mathematical and Computational Applications 2018-09-09 23 3 Article 47 10.3390/mca23030047 http://www.mdpi.com/2297-8747/23/3/47
MCA, Vol. 23, Pages 46: An Authentication Code over Galois Rings with Optimal Impersonation and Substitution Probabilities http://www.mdpi.com/2297-8747/23/3/46 Two new systematic authentication codes based on the Gray map over a Galois ring are introduced. The first introduced code attains optimal impersonation and substitution probabilities. The second code improves space sizes, but it does not attain optimal probabilities. Additionally, it is conditioned to the existence of a special class of bent maps on Galois rings. MCA, Vol. 23, Pages 46: An Authentication Code over Galois Rings with Optimal Impersonation and Substitution Probabilities

Mathematical and Computational Applications doi: 10.3390/mca23030046

Authors: Juan Carlos Ku-Cauich Guillermo Morales-Luna Horacio Tapia-Recillas

Two new systematic authentication codes based on the Gray map over a Galois ring are introduced. The first introduced code attains optimal impersonation and substitution probabilities. The second code improves space sizes, but it does not attain optimal probabilities. Additionally, it is conditioned to the existence of a special class of bent maps on Galois rings.

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An Authentication Code over Galois Rings with Optimal Impersonation and Substitution Probabilities Juan Carlos Ku-Cauich Guillermo Morales-Luna Horacio Tapia-Recillas doi: 10.3390/mca23030046 Mathematical and Computational Applications 2018-09-06 Mathematical and Computational Applications 2018-09-06 23 3 Article 46 10.3390/mca23030046 http://www.mdpi.com/2297-8747/23/3/46
MCA, Vol. 23, Pages 45: Optimal Strategies for Psoriasis Treatment http://www.mdpi.com/2297-8747/23/3/45 Within a given time interval we consider a nonlinear system of differential equations describing psoriasis treatment. Its phase variables define the concentrations of T-lymphocytes, keratinocytes and dendritic cells. Two scalar bounded controls are introduced into this system to reflect medication dosages aimed at suppressing interactions between T-lymphocytes and keratinocytes, and between T-lymphocytes and dendritic cells. For such a controlled system, a minimization problem of the concentration of keratinocytes at the terminal time is considered. For its analysis, the Pontryagin maximum principle is applied. As a result of this analysis, the properties of the optimal controls and their possible types are established. It is shown that each of these controls is either a bang-bang type on the entire time interval or (in addition to bang-bang type) contains a singular arc. The obtained analytical results are confirmed by numerical calculations using the software “BOCOP-2.0.5”. Their detailed analysis and the corresponding conclusions are presented. MCA, Vol. 23, Pages 45: Optimal Strategies for Psoriasis Treatment

Mathematical and Computational Applications doi: 10.3390/mca23030045

Authors: Ellina Grigorieva Evgenii Khailov

Within a given time interval we consider a nonlinear system of differential equations describing psoriasis treatment. Its phase variables define the concentrations of T-lymphocytes, keratinocytes and dendritic cells. Two scalar bounded controls are introduced into this system to reflect medication dosages aimed at suppressing interactions between T-lymphocytes and keratinocytes, and between T-lymphocytes and dendritic cells. For such a controlled system, a minimization problem of the concentration of keratinocytes at the terminal time is considered. For its analysis, the Pontryagin maximum principle is applied. As a result of this analysis, the properties of the optimal controls and their possible types are established. It is shown that each of these controls is either a bang-bang type on the entire time interval or (in addition to bang-bang type) contains a singular arc. The obtained analytical results are confirmed by numerical calculations using the software “BOCOP-2.0.5”. Their detailed analysis and the corresponding conclusions are presented.

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Optimal Strategies for Psoriasis Treatment Ellina Grigorieva Evgenii Khailov doi: 10.3390/mca23030045 Mathematical and Computational Applications 2018-09-04 Mathematical and Computational Applications 2018-09-04 23 3 Article 45 10.3390/mca23030045 http://www.mdpi.com/2297-8747/23/3/45
MCA, Vol. 23, Pages 44: Retraction: Hang, Y.; Liu, Y.; Xu, X.; Chen, Y.; Mo, S. Sensitivity Analysis Based on Markovian Integration by Parts Formula. Math. Comput. Appl. 2017, 22, 40 http://www.mdpi.com/2297-8747/23/3/44 We, the authors, have requested that the title paper  is retracted[...] MCA, Vol. 23, Pages 44: Retraction: Hang, Y.; Liu, Y.; Xu, X.; Chen, Y.; Mo, S. Sensitivity Analysis Based on Markovian Integration by Parts Formula. Math. Comput. Appl. 2017, 22, 40

Mathematical and Computational Applications doi: 10.3390/mca23030044

Authors: Yongsheng Hang Yue Liu Xiaoyang Xu Yan Chen Shu Mo

We, the authors, have requested that the title paper  is retracted[...]

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Retraction: Hang, Y.; Liu, Y.; Xu, X.; Chen, Y.; Mo, S. Sensitivity Analysis Based on Markovian Integration by Parts Formula. Math. Comput. Appl. 2017, 22, 40 Yongsheng Hang Yue Liu Xiaoyang Xu Yan Chen Shu Mo doi: 10.3390/mca23030044 Mathematical and Computational Applications 2018-08-30 Mathematical and Computational Applications 2018-08-30 23 3 Retraction 44 10.3390/mca23030044 http://www.mdpi.com/2297-8747/23/3/44
MCA, Vol. 23, Pages 43: A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification http://www.mdpi.com/2297-8747/23/3/43 A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable method and continuity boundary conditions are used to determine stress and displacement within the tunnel lining and within the surrounding rock. The coefficients in the conformal mapping function and stress functions are determined by the optimal design and complex variable method, respectively. The new method is validated by FLAC3D finite difference software through an example. Both the new method and the numerical simulation obtained similar results for the stress concentration and the minimum radial displacement occurred at a similar place in the tunnel. It is demonstrated that the new complex variable method is reliable and reasonable. The new method also provides another way to solve non-circular tunnel excavation problems in a faster and more accurate way. MCA, Vol. 23, Pages 43: A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification

Mathematical and Computational Applications doi: 10.3390/mca23030043

Authors: Yansong Li Shougen Chen

A new complex variable method is presented for stress and displacement problems in a non-circular deep tunnel with certain given boundary conditions at infinity. In order to overcome the complex problems caused by non-circular geometric configurations and the multiply-connected region, a complex variable method and continuity boundary conditions are used to determine stress and displacement within the tunnel lining and within the surrounding rock. The coefficients in the conformal mapping function and stress functions are determined by the optimal design and complex variable method, respectively. The new method is validated by FLAC3D finite difference software through an example. Both the new method and the numerical simulation obtained similar results for the stress concentration and the minimum radial displacement occurred at a similar place in the tunnel. It is demonstrated that the new complex variable method is reliable and reasonable. The new method also provides another way to solve non-circular tunnel excavation problems in a faster and more accurate way.

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A Complex Variable Solution for Lining Stress and Deformation in a Non-Circular Deep Tunnel II Practical Application and Verification Yansong Li Shougen Chen doi: 10.3390/mca23030043 Mathematical and Computational Applications 2018-08-30 Mathematical and Computational Applications 2018-08-30 23 3 Article 43 10.3390/mca23030043 http://www.mdpi.com/2297-8747/23/3/43
MCA, Vol. 23, Pages 42: Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making http://www.mdpi.com/2297-8747/23/3/42 The purpose of this research study is to present some new operations, including rejection, symmetric difference, residue product, and maximal product of Pythagorean fuzzy graphs (PFGs), and to explore some of their properties. This research article introduces certain notions, including intuitionistic fuzzy graphs of 3-type (IFGs3T), intuitionistic fuzzy graphs of 4-type (IFGs4T), and intuitionistic fuzzy graphs of n-type (IFGsnT), and proves that every IFG(n &amp;minus; 1)T is an IFGnT (for n &amp;ge; 2). Moreover, this study discusses the application of Pythagorean fuzzy graphs in decision making. MCA, Vol. 23, Pages 42: Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making

Mathematical and Computational Applications doi: 10.3390/mca23030042

Authors: Muhammad Akram Amna Habib Farwa Ilyas Jawaria Mohsan Dar

The purpose of this research study is to present some new operations, including rejection, symmetric difference, residue product, and maximal product of Pythagorean fuzzy graphs (PFGs), and to explore some of their properties. This research article introduces certain notions, including intuitionistic fuzzy graphs of 3-type (IFGs3T), intuitionistic fuzzy graphs of 4-type (IFGs4T), and intuitionistic fuzzy graphs of n-type (IFGsnT), and proves that every IFG(n &amp;minus; 1)T is an IFGnT (for n &amp;ge; 2). Moreover, this study discusses the application of Pythagorean fuzzy graphs in decision making.

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Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making Muhammad Akram Amna Habib Farwa Ilyas Jawaria Mohsan Dar doi: 10.3390/mca23030042 Mathematical and Computational Applications 2018-08-23 Mathematical and Computational Applications 2018-08-23 23 3 Article 42 10.3390/mca23030042 http://www.mdpi.com/2297-8747/23/3/42
MCA, Vol. 23, Pages 41: The Average Hull Dimension of Negacyclic Codes over Finite Fields http://www.mdpi.com/2297-8747/23/3/41 Hulls of linear codes have been extensively studied due to their wide applications and links with the efficiency of some algorithms in coding theory. In this paper, the average dimension of the Euclidean hull of negacyclic codes of length n over finite fields F q , denoted by E ( n , &amp;minus; 1 , q ) , has been investigated. The formula for E ( n , &amp;minus; 1 , q ) has been determined. Some upper and lower bounds of E ( n , &amp;minus; 1 , q ) have been given as well. Asymptotically, it has been shown that either E ( n , &amp;minus; 1 , q ) is zero or it grows the same rate as n. MCA, Vol. 23, Pages 41: The Average Hull Dimension of Negacyclic Codes over Finite Fields

Mathematical and Computational Applications doi: 10.3390/mca23030041

Authors: Somphong Jitman Ekkasit Sangwisut

Hulls of linear codes have been extensively studied due to their wide applications and links with the efficiency of some algorithms in coding theory. In this paper, the average dimension of the Euclidean hull of negacyclic codes of length n over finite fields F q , denoted by E ( n , &amp;minus; 1 , q ) , has been investigated. The formula for E ( n , &amp;minus; 1 , q ) has been determined. Some upper and lower bounds of E ( n , &amp;minus; 1 , q ) have been given as well. Asymptotically, it has been shown that either E ( n , &amp;minus; 1 , q ) is zero or it grows the same rate as n.

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The Average Hull Dimension of Negacyclic Codes over Finite Fields Somphong Jitman Ekkasit Sangwisut doi: 10.3390/mca23030041 Mathematical and Computational Applications 2018-08-20 Mathematical and Computational Applications 2018-08-20 23 3 Article 41 10.3390/mca23030041 http://www.mdpi.com/2297-8747/23/3/41
MCA, Vol. 23, Pages 40: An Improved Differential Evolution Algorithm for Crop Planning in the Northeastern Region of Thailand http://www.mdpi.com/2297-8747/23/3/40 This research aimed to solve the economic crop planning problem, considering transportation logistics to maximize the profit from cultivated activities. Income is derived from the selling price and production rate of the plants; costs are due to operating and transportation expenses. Two solving methods are presented: (1) developing a mathematical model and solving it using Lingo v.11, and (2) using three improved Differential Evolution (DE) Algorithms&amp;mdash;I-DE-SW, I-DE-CY, and I-DE-KV&amp;mdash;which are DE with swap, cyclic moves (CY), and K-variables moves (KV) respectively. The algorithms were tested by 16 test instances, including this case study. The computational results showed that Lingo v.11 and all DE algorithms can find the optimal solution eight out of 16 times. Regarding the remaining test instances, Lingo v.11 was unable to find the optimal solution within 400 h. The results for the DE algorithms were compared with the best solution generated within that time. The DE solutions were 1.196&amp;ndash;1.488% better than the best solution generated by Lingo v.11 and used 200 times less computational time. Comparing the three DE algorithms, MDE-KV was the DE that was the most flexible, with the biggest neighborhood structure, and outperformed the other DE algorithms. MCA, Vol. 23, Pages 40: An Improved Differential Evolution Algorithm for Crop Planning in the Northeastern Region of Thailand

Mathematical and Computational Applications doi: 10.3390/mca23030040

Authors: Udompong Ketsripongsa Rapeepan Pitakaso Kanchana Sethanan Tassin Srivarapongse

This research aimed to solve the economic crop planning problem, considering transportation logistics to maximize the profit from cultivated activities. Income is derived from the selling price and production rate of the plants; costs are due to operating and transportation expenses. Two solving methods are presented: (1) developing a mathematical model and solving it using Lingo v.11, and (2) using three improved Differential Evolution (DE) Algorithms&amp;mdash;I-DE-SW, I-DE-CY, and I-DE-KV&amp;mdash;which are DE with swap, cyclic moves (CY), and K-variables moves (KV) respectively. The algorithms were tested by 16 test instances, including this case study. The computational results showed that Lingo v.11 and all DE algorithms can find the optimal solution eight out of 16 times. Regarding the remaining test instances, Lingo v.11 was unable to find the optimal solution within 400 h. The results for the DE algorithms were compared with the best solution generated within that time. The DE solutions were 1.196&amp;ndash;1.488% better than the best solution generated by Lingo v.11 and used 200 times less computational time. Comparing the three DE algorithms, MDE-KV was the DE that was the most flexible, with the biggest neighborhood structure, and outperformed the other DE algorithms.

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An Improved Differential Evolution Algorithm for Crop Planning in the Northeastern Region of Thailand Udompong Ketsripongsa Rapeepan Pitakaso Kanchana Sethanan Tassin Srivarapongse doi: 10.3390/mca23030040 Mathematical and Computational Applications 2018-08-10 Mathematical and Computational Applications 2018-08-10 23 3 Article 40 10.3390/mca23030040 http://www.mdpi.com/2297-8747/23/3/40
MCA, Vol. 23, Pages 39: Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm http://www.mdpi.com/2297-8747/23/3/39 We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE). The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver. Two alternative least-square dynamical minimization schemes are devised and demonstrated on a complex parameterized PDAE system with discontinues properties and coupled time derivatives. Applying the method involves no more than defining a few formulas that closely parallel the original mathematical equations, without any programming skills. It offers a simpler alternative to more complex environments which require nontrivial programming skill and effort. MCA, Vol. 23, Pages 39: Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm

Mathematical and Computational Applications doi: 10.3390/mca23030039

Authors: Chahid Kamel Ghaddar

We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE). The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver. Two alternative least-square dynamical minimization schemes are devised and demonstrated on a complex parameterized PDAE system with discontinues properties and coupled time derivatives. Applying the method involves no more than defining a few formulas that closely parallel the original mathematical equations, without any programming skills. It offers a simpler alternative to more complex environments which require nontrivial programming skill and effort.

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Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm Chahid Kamel Ghaddar doi: 10.3390/mca23030039 Mathematical and Computational Applications 2018-08-03 Mathematical and Computational Applications 2018-08-03 23 3 Article 39 10.3390/mca23030039 http://www.mdpi.com/2297-8747/23/3/39
MCA, Vol. 23, Pages 38: Cost-Effective Analysis of Control Strategies to Reduce the Prevalence of Cutaneous Leishmaniasis, Based on a Mathematical Model http://www.mdpi.com/2297-8747/23/3/38 Leishmaniasis is a neglected tropical vector-borne epidemic disease, and its transmission is a complex process. Zoonotic transmission to humans or animals occurs through the bites of female Phlebotominae sand flies. Here, reservoir is considered as a major source of endemic pathogen pool for disease outbreak, and the role of more than one reservoir animal becomes indispensable. To study the role of the reservoir animals on disease dynamics, a mathematical model was constructed consisting of susceptible and infected populations of humans and two types of reservoir (animal) and vector populations, respectively. Our aim is to prevent the disease by applying a control theoretic approach, when more than one type of reservoir animal exists in the region. We use drugs like sodium stibogluconate and meglumine antimoniate to control the disease for humans and spray insecticide to control the sand fly population. Similarly, drugs are applied for infected reservoir animals of Types A and B. We calculated the cost-effectiveness of all possible combinations of the intervention and control policies. One of our findings is that the most cost-effective case for Leishmania control is the spray of insecticides for infected sand fly vector. Alternate strategic cases were compared to address the critical shortcomings of single strategic cases, and a range of control strategies were estimated for effective control and economical benefit of the overall control strategy. Our findings provide the most innovative techniques available for application to the successful eradication of cutaneous leishmaniasis in the future. MCA, Vol. 23, Pages 38: Cost-Effective Analysis of Control Strategies to Reduce the Prevalence of Cutaneous Leishmaniasis, Based on a Mathematical Model

Mathematical and Computational Applications doi: 10.3390/mca23030038

Authors: Dibyendu Biswas Suman Dolai Jahangir Chowdhury Priti K. Roy Ellina V. Grigorieva

Leishmaniasis is a neglected tropical vector-borne epidemic disease, and its transmission is a complex process. Zoonotic transmission to humans or animals occurs through the bites of female Phlebotominae sand flies. Here, reservoir is considered as a major source of endemic pathogen pool for disease outbreak, and the role of more than one reservoir animal becomes indispensable. To study the role of the reservoir animals on disease dynamics, a mathematical model was constructed consisting of susceptible and infected populations of humans and two types of reservoir (animal) and vector populations, respectively. Our aim is to prevent the disease by applying a control theoretic approach, when more than one type of reservoir animal exists in the region. We use drugs like sodium stibogluconate and meglumine antimoniate to control the disease for humans and spray insecticide to control the sand fly population. Similarly, drugs are applied for infected reservoir animals of Types A and B. We calculated the cost-effectiveness of all possible combinations of the intervention and control policies. One of our findings is that the most cost-effective case for Leishmania control is the spray of insecticides for infected sand fly vector. Alternate strategic cases were compared to address the critical shortcomings of single strategic cases, and a range of control strategies were estimated for effective control and economical benefit of the overall control strategy. Our findings provide the most innovative techniques available for application to the successful eradication of cutaneous leishmaniasis in the future.

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Cost-Effective Analysis of Control Strategies to Reduce the Prevalence of Cutaneous Leishmaniasis, Based on a Mathematical Model Dibyendu Biswas Suman Dolai Jahangir Chowdhury Priti K. Roy Ellina V. Grigorieva doi: 10.3390/mca23030038 Mathematical and Computational Applications 2018-07-25 Mathematical and Computational Applications 2018-07-25 23 3 Article 38 10.3390/mca23030038 http://www.mdpi.com/2297-8747/23/3/38
MCA, Vol. 23, Pages 37: Applying Computer Algebra Systems in Approximating the Trigonometric Functions http://www.mdpi.com/2297-8747/23/3/37 We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor&amp;rsquo;s expansion about a point having a form of k p , k &amp;isin; Z and p = &amp;pi; / 2 , and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating &amp;pi; with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE. MCA, Vol. 23, Pages 37: Applying Computer Algebra Systems in Approximating the Trigonometric Functions

Mathematical and Computational Applications doi: 10.3390/mca23030037

Authors: Le Phuong Quan Thái Anh Nhan

We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor&amp;rsquo;s expansion about a point having a form of k p , k &amp;isin; Z and p = &amp;pi; / 2 , and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating &amp;pi; with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE.

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Applying Computer Algebra Systems in Approximating the Trigonometric Functions Le Phuong Quan Thái Anh Nhan doi: 10.3390/mca23030037 Mathematical and Computational Applications 2018-07-14 Mathematical and Computational Applications 2018-07-14 23 3 Article 37 10.3390/mca23030037 http://www.mdpi.com/2297-8747/23/3/37
MCA, Vol. 23, Pages 36: Existence of Solutions for Fractional Integro-Differential Equations with Non-Local Boundary Conditions http://www.mdpi.com/2297-8747/23/3/36 In this paper, we study the existence of solutions for a new class of boundary value problems of non-linear fractional integro-differential equations. The existence result is obtained with the aid of Schauder type fixed point theorem while the uniqueness of solution is established by means of contraction mapping principle. Then, we present some examples to illustrate our results. MCA, Vol. 23, Pages 36: Existence of Solutions for Fractional Integro-Differential Equations with Non-Local Boundary Conditions

Mathematical and Computational Applications doi: 10.3390/mca23030036

Authors: Hamed Bazgir Bahman Ghazanfari

In this paper, we study the existence of solutions for a new class of boundary value problems of non-linear fractional integro-differential equations. The existence result is obtained with the aid of Schauder type fixed point theorem while the uniqueness of solution is established by means of contraction mapping principle. Then, we present some examples to illustrate our results.

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Existence of Solutions for Fractional Integro-Differential Equations with Non-Local Boundary Conditions Hamed Bazgir Bahman Ghazanfari doi: 10.3390/mca23030036 Mathematical and Computational Applications 2018-07-14 Mathematical and Computational Applications 2018-07-14 23 3 Article 36 10.3390/mca23030036 http://www.mdpi.com/2297-8747/23/3/36
MCA, Vol. 23, Pages 35: Exact Solutions of Non-Linear Evolution Models in Physics and Biosciences Using the Hyperbolic Tangent Method http://www.mdpi.com/2297-8747/23/3/35 There has been considerable interest in seeking exact solutions of non-linear evolution equations that describe important physical and biological processes. Nonetheless, it is a difficult undertaking to determine closed form solutions of mathematical models that describe natural phenomena. This is because of their high non-linearity and the huge number of parameters of which they consist. In this article we determine, using the hyperbolic tangent (tanh) method, travelling wave solutions to non-linear evolution models of interest in biology and physics. These solutions have recognizable properties expected of other solutions and thus can be used to deduce properties of the general solutions. MCA, Vol. 23, Pages 35: Exact Solutions of Non-Linear Evolution Models in Physics and Biosciences Using the Hyperbolic Tangent Method

Mathematical and Computational Applications doi: 10.3390/mca23030035

Authors: Joseph Malinzi Paul Amarh Quaye

There has been considerable interest in seeking exact solutions of non-linear evolution equations that describe important physical and biological processes. Nonetheless, it is a difficult undertaking to determine closed form solutions of mathematical models that describe natural phenomena. This is because of their high non-linearity and the huge number of parameters of which they consist. In this article we determine, using the hyperbolic tangent (tanh) method, travelling wave solutions to non-linear evolution models of interest in biology and physics. These solutions have recognizable properties expected of other solutions and thus can be used to deduce properties of the general solutions.

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Exact Solutions of Non-Linear Evolution Models in Physics and Biosciences Using the Hyperbolic Tangent Method Joseph Malinzi Paul Amarh Quaye doi: 10.3390/mca23030035 Mathematical and Computational Applications 2018-07-06 Mathematical and Computational Applications 2018-07-06 23 3 Article 35 10.3390/mca23030035 http://www.mdpi.com/2297-8747/23/3/35
MCA, Vol. 23, Pages 34: Modified Differential Evolution Algorithm Solving the Special Case of Location Routing Problem http://www.mdpi.com/2297-8747/23/3/34 This research article aims to solve the special case of the location routing problem (SLRP) when the objective function is the fuel consumption. The fuel consumption depends on the distance of travel and the condition of the road. The condition of the road causes the vehicle to use a different speed, which affects fuel usage. This turns the original LRP into a more difficult problem. Moreover, the volume of the goods that are produced in each node could be more or less than the capacity of the vehicle, and as the case study requires the transportation of latex, which is a sensitive good and needs to be carried within a reasonable time so that it does not form solid before being used in the latex process, the maximum time that the latex can be in the truck is limited. All of these attributes are added into the LRP and make it a special case of LRP: a so-called SLRP (a special case of location routing problem). The differential evolution algorithms (DE) are proposed to solve the SLRP. We modified two points in the original DE, which are that (1) the mutation formula is introduced and (2) the new rule of a local search is presented. We call this the modified differential evolution algorithm (MDE). From the computational result, we can see that MDE generates a 13.82% better solution than that of the original version of DE in solving the test instances. MCA, Vol. 23, Pages 34: Modified Differential Evolution Algorithm Solving the Special Case of Location Routing Problem

Mathematical and Computational Applications doi: 10.3390/mca23030034

Authors: Raknoi Akararungruangkul Sasitorn Kaewman

This research article aims to solve the special case of the location routing problem (SLRP) when the objective function is the fuel consumption. The fuel consumption depends on the distance of travel and the condition of the road. The condition of the road causes the vehicle to use a different speed, which affects fuel usage. This turns the original LRP into a more difficult problem. Moreover, the volume of the goods that are produced in each node could be more or less than the capacity of the vehicle, and as the case study requires the transportation of latex, which is a sensitive good and needs to be carried within a reasonable time so that it does not form solid before being used in the latex process, the maximum time that the latex can be in the truck is limited. All of these attributes are added into the LRP and make it a special case of LRP: a so-called SLRP (a special case of location routing problem). The differential evolution algorithms (DE) are proposed to solve the SLRP. We modified two points in the original DE, which are that (1) the mutation formula is introduced and (2) the new rule of a local search is presented. We call this the modified differential evolution algorithm (MDE). From the computational result, we can see that MDE generates a 13.82% better solution than that of the original version of DE in solving the test instances.

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Modified Differential Evolution Algorithm Solving the Special Case of Location Routing Problem Raknoi Akararungruangkul Sasitorn Kaewman doi: 10.3390/mca23030034 Mathematical and Computational Applications 2018-07-03 Mathematical and Computational Applications 2018-07-03 23 3 Article 34 10.3390/mca23030034 http://www.mdpi.com/2297-8747/23/3/34
MCA, Vol. 23, Pages 33: Qualitative Analysis of a Dengue Fever Model http://www.mdpi.com/2297-8747/23/3/33 In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh–Hurwitz criterion, along with Descartes’ rule of signs change, established the local asymptotically stability of the model whenever R0&amp;lt;1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model. MCA, Vol. 23, Pages 33: Qualitative Analysis of a Dengue Fever Model

Mathematical and Computational Applications doi: 10.3390/mca23030033

Authors: Babatunde Gbadamosi Mayowa Ojo Segun Oke Maba Matadi

In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh–Hurwitz criterion, along with Descartes’ rule of signs change, established the local asymptotically stability of the model whenever R0&amp;lt;1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model.

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Qualitative Analysis of a Dengue Fever Model Babatunde Gbadamosi Mayowa Ojo Segun Oke Maba Matadi doi: 10.3390/mca23030033 Mathematical and Computational Applications 2018-06-21 Mathematical and Computational Applications 2018-06-21 23 3 Article 33 10.3390/mca23030033 http://www.mdpi.com/2297-8747/23/3/33
MCA, Vol. 23, Pages 32: Total Controllability of the Second Order Semi-Linear Differential Equation with Infinite Delay and Non-Instantaneous Impulses http://www.mdpi.com/2297-8747/23/3/32 In this manuscript, a stronger concept of exact controllability called Total Controllability has been introduced. Sufficient conditions have been established for the total controllability of the proposed problem. The proposed control problem is a second-order semi-linear differential equation with infinite delay and non-instantaneous impulses. The tools for study include the strongly continuous cosine family and Sadovskii&amp;rsquo;s fixed point theorem. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. In addition, the total controllability of an integrodifferential problem has been investigated. Finally, an example is provided to illustrate the analytical findings. MCA, Vol. 23, Pages 32: Total Controllability of the Second Order Semi-Linear Differential Equation with Infinite Delay and Non-Instantaneous Impulses

Mathematical and Computational Applications doi: 10.3390/mca23030032

Authors: Dimplekumar N. Chalishajar Avadhesh Kumar

In this manuscript, a stronger concept of exact controllability called Total Controllability has been introduced. Sufficient conditions have been established for the total controllability of the proposed problem. The proposed control problem is a second-order semi-linear differential equation with infinite delay and non-instantaneous impulses. The tools for study include the strongly continuous cosine family and Sadovskii&amp;rsquo;s fixed point theorem. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. In addition, the total controllability of an integrodifferential problem has been investigated. Finally, an example is provided to illustrate the analytical findings.

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Total Controllability of the Second Order Semi-Linear Differential Equation with Infinite Delay and Non-Instantaneous Impulses Dimplekumar N. Chalishajar Avadhesh Kumar doi: 10.3390/mca23030032 Mathematical and Computational Applications 2018-06-21 Mathematical and Computational Applications 2018-06-21 23 3 Article 32 10.3390/mca23030032 http://www.mdpi.com/2297-8747/23/3/32
MCA, Vol. 23, Pages 31: Dual Methods for Optimal Allocation of Telecommunication Network Resources with Several Classes of Users http://www.mdpi.com/2297-8747/23/2/31 We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The network users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users’ requirements. This approach leads to a convex optimization problem with balance and capacity constraints. We present several decomposition type methods to find a solution to this problem, which exploit its special features. We suggest applying first the dual Lagrangian method with respect to the total capacity constraint, which gives the one-dimensional dual problem. However, calculation of the value of the dual cost function requires solving several optimization problems. Our methods differ in approaches for solving these auxiliary problems. We consider three basic methods: Dual Multi Layer (DML), Conditional Gradient Dual Multilayer (CGDM) and Bisection (BS). Besides these methods we consider their modifications adjusted to different kind of cost functions. Our comparison of the performance of the suggested methods on several series of test problems show satisfactory convergence. Nevertheless, proper decomposition techniques enhance the convergence essentially. MCA, Vol. 23, Pages 31: Dual Methods for Optimal Allocation of Telecommunication Network Resources with Several Classes of Users

Mathematical and Computational Applications doi: 10.3390/mca23020031

Authors: Igor Konnov Aleksey Kashuba Erkki Laitinen

We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The network users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users’ requirements. This approach leads to a convex optimization problem with balance and capacity constraints. We present several decomposition type methods to find a solution to this problem, which exploit its special features. We suggest applying first the dual Lagrangian method with respect to the total capacity constraint, which gives the one-dimensional dual problem. However, calculation of the value of the dual cost function requires solving several optimization problems. Our methods differ in approaches for solving these auxiliary problems. We consider three basic methods: Dual Multi Layer (DML), Conditional Gradient Dual Multilayer (CGDM) and Bisection (BS). Besides these methods we consider their modifications adjusted to different kind of cost functions. Our comparison of the performance of the suggested methods on several series of test problems show satisfactory convergence. Nevertheless, proper decomposition techniques enhance the convergence essentially.

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Dual Methods for Optimal Allocation of Telecommunication Network Resources with Several Classes of Users Igor Konnov Aleksey Kashuba Erkki Laitinen doi: 10.3390/mca23020031 Mathematical and Computational Applications 2018-06-17 Mathematical and Computational Applications 2018-06-17 23 2 Article 31 10.3390/mca23020031 http://www.mdpi.com/2297-8747/23/2/31
MCA, Vol. 23, Pages 30: A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction http://www.mdpi.com/2297-8747/23/2/30 Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort. MCA, Vol. 23, Pages 30: A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

Mathematical and Computational Applications doi: 10.3390/mca23020030

Authors: Sebastian Peitz Michael Dellnitz

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

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A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction Sebastian Peitz Michael Dellnitz doi: 10.3390/mca23020030 Mathematical and Computational Applications 2018-06-01 Mathematical and Computational Applications 2018-06-01 23 2 Review 30 10.3390/mca23020030 http://www.mdpi.com/2297-8747/23/2/30

Mathematical and Computational Applications doi: 10.3390/mca23020029

Authors: Serge Dumont Franck Jourdan Tarik Madani

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4D Remeshing Using a Space-Time Finite Element Method for Elastodynamics Problems Serge Dumont Franck Jourdan Tarik Madani doi: 10.3390/mca23020029 Mathematical and Computational Applications 2018-05-25 Mathematical and Computational Applications 2018-05-25 23 2 Article 29 10.3390/mca23020029 http://www.mdpi.com/2297-8747/23/2/29
MCA, Vol. 23, Pages 28: The Impact of the Implementation Cost of Replication in Data Grid Job Scheduling http://www.mdpi.com/2297-8747/23/2/28 Data Grids deal with geographically-distributed large-scale data-intensive applications. Schemes scheduled for data grids attempt to not only improve data access time, but also aim to improve the ratio of data availability to a node, where the data requests are generated. Data replication techniques manage large data by storing a number of data files efficiently. In this paper, we propose centralized dynamic scheduling strategy-replica placement strategies (CDSS-RPS). CDSS-RPS schedule the data and task so that it minimizes the implementation cost and data transfer time. CDSS-RPS consists of two algorithms, namely (a) centralized dynamic scheduling (CDS) and (b) replica placement strategy (RPS). CDS considers the computing capacity of a node and finds an appropriate location for the job. RPS attempts to improve file access time by using replication on the basis of number of accesses, storage capacity of a computing node, and response time of a requested file. Extensive simulations are carried out to demonstrate the effectiveness of the proposed strategy. Simulation results demonstrate that the replication and scheduling strategies improve the implementation cost and average access time significantly. MCA, Vol. 23, Pages 28: The Impact of the Implementation Cost of Replication in Data Grid Job Scheduling

Mathematical and Computational Applications doi: 10.3390/mca23020028

Authors: Babar Nazir Faiza Ishaq Shahaboddin Shamshirband Anthony T. Chronopoulos

Data Grids deal with geographically-distributed large-scale data-intensive applications. Schemes scheduled for data grids attempt to not only improve data access time, but also aim to improve the ratio of data availability to a node, where the data requests are generated. Data replication techniques manage large data by storing a number of data files efficiently. In this paper, we propose centralized dynamic scheduling strategy-replica placement strategies (CDSS-RPS). CDSS-RPS schedule the data and task so that it minimizes the implementation cost and data transfer time. CDSS-RPS consists of two algorithms, namely (a) centralized dynamic scheduling (CDS) and (b) replica placement strategy (RPS). CDS considers the computing capacity of a node and finds an appropriate location for the job. RPS attempts to improve file access time by using replication on the basis of number of accesses, storage capacity of a computing node, and response time of a requested file. Extensive simulations are carried out to demonstrate the effectiveness of the proposed strategy. Simulation results demonstrate that the replication and scheduling strategies improve the implementation cost and average access time significantly.

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The Impact of the Implementation Cost of Replication in Data Grid Job Scheduling Babar Nazir Faiza Ishaq Shahaboddin Shamshirband Anthony T. Chronopoulos doi: 10.3390/mca23020028 Mathematical and Computational Applications 2018-05-25 Mathematical and Computational Applications 2018-05-25 23 2 Article 28 10.3390/mca23020028 http://www.mdpi.com/2297-8747/23/2/28
MCA, Vol. 23, Pages 27: Nonlinear Elimination of Drugs in One-Compartment Pharmacokinetic Models: Nonstandard Finite Difference Approach for Various Routes of Administration http://www.mdpi.com/2297-8747/23/2/27 The motivation for this study is to introduce and motivate the use of nonstandard finite difference (NSFD) schemes, capable of solving one-compartment pharmacokinetic models. These models are modeled by both linear and nonlinear ordinary differential equations. &amp;ldquo;Exact&amp;rdquo; finite difference schemes, which are a special NSFD, are provided for the linear models while we apply the NSFD rules, based on Mickens&amp;rsquo; idea of transferring nonlinear models into discrete schemes. The method used was compared with other established methods to verify its efficiency and accuracy. One-compartment pharmacokinetic models are considered for different routes of administration: I.V. bolus injection, I.V. bolus infusion and extravascular administration. MCA, Vol. 23, Pages 27: Nonlinear Elimination of Drugs in One-Compartment Pharmacokinetic Models: Nonstandard Finite Difference Approach for Various Routes of Administration

Mathematical and Computational Applications doi: 10.3390/mca23020027

Authors: Oluwaseun Egbelowo

The motivation for this study is to introduce and motivate the use of nonstandard finite difference (NSFD) schemes, capable of solving one-compartment pharmacokinetic models. These models are modeled by both linear and nonlinear ordinary differential equations. &amp;ldquo;Exact&amp;rdquo; finite difference schemes, which are a special NSFD, are provided for the linear models while we apply the NSFD rules, based on Mickens&amp;rsquo; idea of transferring nonlinear models into discrete schemes. The method used was compared with other established methods to verify its efficiency and accuracy. One-compartment pharmacokinetic models are considered for different routes of administration: I.V. bolus injection, I.V. bolus infusion and extravascular administration.

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Nonlinear Elimination of Drugs in One-Compartment Pharmacokinetic Models: Nonstandard Finite Difference Approach for Various Routes of Administration Oluwaseun Egbelowo doi: 10.3390/mca23020027 Mathematical and Computational Applications 2018-05-23 Mathematical and Computational Applications 2018-05-23 23 2 Article 27 10.3390/mca23020027 http://www.mdpi.com/2297-8747/23/2/27
MCA, Vol. 23, Pages 26: A New Analytical Procedure to Solve Two Phase Flow in Tubes http://www.mdpi.com/2297-8747/23/2/26 A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves whereas when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature. MCA, Vol. 23, Pages 26: A New Analytical Procedure to Solve Two Phase Flow in Tubes

Mathematical and Computational Applications doi: 10.3390/mca23020026

Authors: Terry E. Moschandreou

A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves whereas when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.

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A New Analytical Procedure to Solve Two Phase Flow in Tubes Terry E. Moschandreou doi: 10.3390/mca23020026 Mathematical and Computational Applications 2018-05-23 Mathematical and Computational Applications 2018-05-23 23 2 Article 26 10.3390/mca23020026 http://www.mdpi.com/2297-8747/23/2/26
MCA, Vol. 23, Pages 25: The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm http://www.mdpi.com/2297-8747/23/2/25 Among the numerous alphabetical optimality criteria is the IV-criterion that is focused on prediction variance. We propose a new criterion, called the weighted IV-optimality. It is similar to IV-optimality, because the researcher must first specify a model. However, unlike IV-optimality, a suite of &amp;ldquo;reduced&amp;rdquo; models is also proposed if the original model is misspecified via over-parameterization. In this research, weighted IV-optimality is applied to mixture experiments with a set of prior weights assigned to the potential mixture models of interest. To address the issue of implementation, a genetic algorithm was developed to generate weighted IV-optimal mixture designs that are robust across multiple models. In our examples, we assign models with p parameters to have equal weights, but weights will vary based on varying p. Fraction-of-design-space (FDS) plots are used to compare the performance of an experimental design in terms of the prediction variance properties. An illustrating example is presented. The result shows that the GA-generated designs studied are robust across a set of potential mixture models. MCA, Vol. 23, Pages 25: The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm

Mathematical and Computational Applications doi: 10.3390/mca23020025

Authors: Wanida Limmun Boonorm Chomtee John J. Borkowski

Among the numerous alphabetical optimality criteria is the IV-criterion that is focused on prediction variance. We propose a new criterion, called the weighted IV-optimality. It is similar to IV-optimality, because the researcher must first specify a model. However, unlike IV-optimality, a suite of &amp;ldquo;reduced&amp;rdquo; models is also proposed if the original model is misspecified via over-parameterization. In this research, weighted IV-optimality is applied to mixture experiments with a set of prior weights assigned to the potential mixture models of interest. To address the issue of implementation, a genetic algorithm was developed to generate weighted IV-optimal mixture designs that are robust across multiple models. In our examples, we assign models with p parameters to have equal weights, but weights will vary based on varying p. Fraction-of-design-space (FDS) plots are used to compare the performance of an experimental design in terms of the prediction variance properties. An illustrating example is presented. The result shows that the GA-generated designs studied are robust across a set of potential mixture models.

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The Construction of a Model-Robust IV-Optimal Mixture Designs Using a Genetic Algorithm Wanida Limmun Boonorm Chomtee John J. Borkowski doi: 10.3390/mca23020025 Mathematical and Computational Applications 2018-05-17 Mathematical and Computational Applications 2018-05-17 23 2 Article 25 10.3390/mca23020025 http://www.mdpi.com/2297-8747/23/2/25
MCA, Vol. 23, Pages 24: Integration of Direction Fields with Standard Options in Finite Element Programs http://www.mdpi.com/2297-8747/23/2/24 The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. The differential equation to be integrated with arbitrary boundaries is idealized as an FE model with thermal 2D elements. Its orthotropic thermal conductivities are specified as k1 = 1 and k2 = 0. In doing so, k1 is parallel to y´, and k2 is oriented perpendicular to this. For this extreme case, it is shown that the isotherms are identical to the solution of y’ = f(x,y). The direction fields, for example, can be velocity vectors in fluid mechanics or principal stress directions in structural mechanics. In the case of the latter, possibilities for application in the construction of fiber-reinforced plastics (FRP) arise, since fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers. MCA, Vol. 23, Pages 24: Integration of Direction Fields with Standard Options in Finite Element Programs

Mathematical and Computational Applications doi: 10.3390/mca23020024

Authors: Herbert Moldenhauer

The two-dimensional differential equation y’ = f(x,y) can be interpreted as a direction field. Commercial Finite Element (FE) programs can be used for this integration task without additional programming, provided that these programs have options for the calculation of orthotropic heat conduction problems. The differential equation to be integrated with arbitrary boundaries is idealized as an FE model with thermal 2D elements. Its orthotropic thermal conductivities are specified as k1 = 1 and k2 = 0. In doing so, k1 is parallel to y´, and k2 is oriented perpendicular to this. For this extreme case, it is shown that the isotherms are identical to the solution of y’ = f(x,y). The direction fields, for example, can be velocity vectors in fluid mechanics or principal stress directions in structural mechanics. In the case of the latter, possibilities for application in the construction of fiber-reinforced plastics (FRP) arise, since fiber courses, which follow the local principal stress directions, make use of the superior stiffness and strength of the fibers.

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Integration of Direction Fields with Standard Options in Finite Element Programs Herbert Moldenhauer doi: 10.3390/mca23020024 Mathematical and Computational Applications 2018-05-07 Mathematical and Computational Applications 2018-05-07 23 2 Article 24 10.3390/mca23020024 http://www.mdpi.com/2297-8747/23/2/24
MCA, Vol. 23, Pages 23: A Simple Spectral Observer http://www.mdpi.com/2297-8747/23/2/23 The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier Transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 1 December 2014 to 8 January 2018 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis. MCA, Vol. 23, Pages 23: A Simple Spectral Observer

Mathematical and Computational Applications doi: 10.3390/mca23020023

Authors: Lizeth Torres Javier Jiménez-Cabas José Gómez-Aguilar Pablo Pérez-Alcazar

The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier Transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 1 December 2014 to 8 January 2018 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis.

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A Simple Spectral Observer Lizeth Torres Javier Jiménez-Cabas José Gómez-Aguilar Pablo Pérez-Alcazar doi: 10.3390/mca23020023 Mathematical and Computational Applications 2018-05-01 Mathematical and Computational Applications 2018-05-01 23 2 Article 23 10.3390/mca23020023 http://www.mdpi.com/2297-8747/23/2/23
MCA, Vol. 23, Pages 22: Solution of Optimal Harvesting Problem by Finite Difference Approximations of Size-Structured Population Model http://www.mdpi.com/2297-8747/23/2/22 We solve numerically a forest management optimization problem governed by a nonlinear partial differential equation (PDE), which is a size-structured population model. The formulated problem is supplemented with a natural constraint for a solution to be non-negative. PDE is approximated by an explicit or implicit in time finite difference scheme, whereas the cost function is taken from the very beginning in the finite-dimensional form used in practice. We prove the stability of the constructed nonlinear finite difference schemes on the set of non-negative vectors and the solvability of the formulated discrete optimal control problems. The gradient information is derived by constructing discrete adjoint state equations. The projected gradient method is used for finding the extremal points. The results of numerical testing for several real problems show good agreement with the known results and confirm the theoretical statements. MCA, Vol. 23, Pages 22: Solution of Optimal Harvesting Problem by Finite Difference Approximations of Size-Structured Population Model

Mathematical and Computational Applications doi: 10.3390/mca23020022

Authors: Johanna Pyy Anssi Ahtikoski Alexander Lapin Erkki Laitinen

We solve numerically a forest management optimization problem governed by a nonlinear partial differential equation (PDE), which is a size-structured population model. The formulated problem is supplemented with a natural constraint for a solution to be non-negative. PDE is approximated by an explicit or implicit in time finite difference scheme, whereas the cost function is taken from the very beginning in the finite-dimensional form used in practice. We prove the stability of the constructed nonlinear finite difference schemes on the set of non-negative vectors and the solvability of the formulated discrete optimal control problems. The gradient information is derived by constructing discrete adjoint state equations. The projected gradient method is used for finding the extremal points. The results of numerical testing for several real problems show good agreement with the known results and confirm the theoretical statements.

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Solution of Optimal Harvesting Problem by Finite Difference Approximations of Size-Structured Population Model Johanna Pyy Anssi Ahtikoski Alexander Lapin Erkki Laitinen doi: 10.3390/mca23020022 Mathematical and Computational Applications 2018-04-26 Mathematical and Computational Applications 2018-04-26 23 2 Article 22 10.3390/mca23020022 http://www.mdpi.com/2297-8747/23/2/22
MCA, Vol. 23, Pages 21: Optimal Control Analysis of a Mathematical Model for Breast Cancer http://www.mdpi.com/2297-8747/23/2/21 In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analyses were carried out using a variety of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs, ketogenic diet, and cancer emission when anti-cancer drugs, immune-booster, and ketogenic diet are included were established. Furthermore, optimal control theory is applied to discover the optimal drug adjustment as an input control of the system therapies in order to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin&amp;rsquo;s maximum principle. Numerical simulations are presented to validate our theoretical results. MCA, Vol. 23, Pages 21: Optimal Control Analysis of a Mathematical Model for Breast Cancer

Mathematical and Computational Applications doi: 10.3390/mca23020021

Authors: Segun Isaac Oke Maba Boniface Matadi Sibusiso Southwell Xulu

In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analyses were carried out using a variety of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs, ketogenic diet, and cancer emission when anti-cancer drugs, immune-booster, and ketogenic diet are included were established. Furthermore, optimal control theory is applied to discover the optimal drug adjustment as an input control of the system therapies in order to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin&amp;rsquo;s maximum principle. Numerical simulations are presented to validate our theoretical results.

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Optimal Control Analysis of a Mathematical Model for Breast Cancer Segun Isaac Oke Maba Boniface Matadi Sibusiso Southwell Xulu doi: 10.3390/mca23020021 Mathematical and Computational Applications 2018-04-24 Mathematical and Computational Applications 2018-04-24 23 2 Article 21 10.3390/mca23020021 http://www.mdpi.com/2297-8747/23/2/21

Mathematical and Computational Applications doi: 10.3390/mca23020020

Authors: Abdullah Dawar Zahir Shah Muhammad Idrees Waris Khan Saeed Islam Taza Gul

The main intention of this article is to examine the heat transmission of the flow of Eyring–Powell fluid over an unstable oscillatory porous stretching surface. The effect of thermal radiation on the fluid flow is investigated, where the flow is actuated by the unbounded flexible surface which is extended occasionally to and fro on its plane. The rudimentary leading equations are changed to differential equations through the use of applicable similarity variables. An optimal and numerical approach was used to find the solution to the modeled problems. The convergence of the homotopy analysis method (HAM) is shown numerically. The homotopy analysis method predictions of the structures formed are in close agreement with the obtained results from the numerical method. Comparisons between HAM and numerical methods are shown graphically as well as numerically. The convergence of this method is shown numerically. The impacts of the skin friction and heat flux are shown through a table. The influence of the porosity, oscillation, thermal radiation, and heat absorption/generation are the main focus of this work. The consequences of emerging parameters are demonstrated through graphs.

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Impact of Thermal Radiation and Heat Source/Sink on Eyring–Powell Fluid Flow over an Unsteady Oscillatory Porous Stretching Surface Abdullah Dawar Zahir Shah Muhammad Idrees Waris Khan Saeed Islam Taza Gul doi: 10.3390/mca23020020 Mathematical and Computational Applications 2018-04-09 Mathematical and Computational Applications 2018-04-09 23 2 Article 20 10.3390/mca23020020 http://www.mdpi.com/2297-8747/23/2/20
MCA, Vol. 23, Pages 19: How Am I Driving? Using Genetic Programming to Generate Scoring Functions for Urban Driving Behavior http://www.mdpi.com/2297-8747/23/2/19 Road traffic injuries are a serious concern in emerging economies. Their death toll and economic impact are shocking, with 9 out of 10 deaths occurring in low or middle-income countries; and road traffic crashes representing 3% of their gross domestic product. One way to mitigate these issues is to develop technology to effectively assist the driver, perhaps making him more aware about how her (his) decisions influence safety. Following this idea, in this paper we evaluate computational models that can score the behavior of a driver based on a risky-safety scale. Potential applications of these models include car rental agencies, insurance companies or transportation service providers. In a previous work, we showed that Genetic Programming (GP) was a successful methodology to evolve mathematical functions with the ability to learn how people subjectively score a road trip. The input to this model was a vector of frequencies of risky maneuvers, which were supposed to be detected in a sensor layer. Moreover, GP was shown, even with statistical significance, to be better than six other Machine Learning strategies, including Neural Networks, Support Vector Regression and a Fuzzy Inference system, among others. A pending task, since then, was to evaluate if a more detailed comparison of different strategies based on GP could improve upon the best GP model. In this work, we evaluate, side by side, scoring functions evolved by three different variants of GP. In the end, the results suggest that two of these strategies are very competitive in terms of accuracy and simplicity, both generating models that could be implemented in current technology that seeks to assist the driver in real-world scenarios. MCA, Vol. 23, Pages 19: How Am I Driving? Using Genetic Programming to Generate Scoring Functions for Urban Driving Behavior

Mathematical and Computational Applications doi: 10.3390/mca23020019

Authors: Roberto López Luis González Gurrola Leonardo Trujillo Olanda Prieto Graciela Ramírez Antonio Posada Perla Juárez-Smith Leticia Méndez

Road traffic injuries are a serious concern in emerging economies. Their death toll and economic impact are shocking, with 9 out of 10 deaths occurring in low or middle-income countries; and road traffic crashes representing 3% of their gross domestic product. One way to mitigate these issues is to develop technology to effectively assist the driver, perhaps making him more aware about how her (his) decisions influence safety. Following this idea, in this paper we evaluate computational models that can score the behavior of a driver based on a risky-safety scale. Potential applications of these models include car rental agencies, insurance companies or transportation service providers. In a previous work, we showed that Genetic Programming (GP) was a successful methodology to evolve mathematical functions with the ability to learn how people subjectively score a road trip. The input to this model was a vector of frequencies of risky maneuvers, which were supposed to be detected in a sensor layer. Moreover, GP was shown, even with statistical significance, to be better than six other Machine Learning strategies, including Neural Networks, Support Vector Regression and a Fuzzy Inference system, among others. A pending task, since then, was to evaluate if a more detailed comparison of different strategies based on GP could improve upon the best GP model. In this work, we evaluate, side by side, scoring functions evolved by three different variants of GP. In the end, the results suggest that two of these strategies are very competitive in terms of accuracy and simplicity, both generating models that could be implemented in current technology that seeks to assist the driver in real-world scenarios.

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How Am I Driving? Using Genetic Programming to Generate Scoring Functions for Urban Driving Behavior Roberto López Luis González Gurrola Leonardo Trujillo Olanda Prieto Graciela Ramírez Antonio Posada Perla Juárez-Smith Leticia Méndez doi: 10.3390/mca23020019 Mathematical and Computational Applications 2018-04-03 Mathematical and Computational Applications 2018-04-03 23 2 Article 19 10.3390/mca23020019 http://www.mdpi.com/2297-8747/23/2/19
MCA, Vol. 23, Pages 18: A Family of 5-Point Nonlinear Ternary Interpolating Subdivision Schemes with C2 Smoothness http://www.mdpi.com/2297-8747/23/2/18 The occurrence of the Gibbs phenomenon near irregular initial data points is a widely known fact in curve generation by interpolating subdivision schemes. In this article, we propose a family of 5-point nonlinear ternary interpolating subdivision schemes. We provide the convergence analysis and prove that this family of subdivision schemes is C 2 continuous. Numerical results are presented to show that nonlinear schemes reduce the Gibbs phenomenon significantly while keeping the same order of smoothness. MCA, Vol. 23, Pages 18: A Family of 5-Point Nonlinear Ternary Interpolating Subdivision Schemes with C2 Smoothness

Mathematical and Computational Applications doi: 10.3390/mca23020018

The occurrence of the Gibbs phenomenon near irregular initial data points is a widely known fact in curve generation by interpolating subdivision schemes. In this article, we propose a family of 5-point nonlinear ternary interpolating subdivision schemes. We provide the convergence analysis and prove that this family of subdivision schemes is C 2 continuous. Numerical results are presented to show that nonlinear schemes reduce the Gibbs phenomenon significantly while keeping the same order of smoothness.

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A Family of 5-Point Nonlinear Ternary Interpolating Subdivision Schemes with C2 Smoothness Muhammad Aslam doi: 10.3390/mca23020018 Mathematical and Computational Applications 2018-03-23 Mathematical and Computational Applications 2018-03-23 23 2 Article 18 10.3390/mca23020018 http://www.mdpi.com/2297-8747/23/2/18
MCA, Vol. 23, Pages 17: An Improved Digital Signature Protocol to Multi-User Broadcast Authentication Based on Elliptic Curve Cryptography in Wireless Sensor Networks (WSNs) http://www.mdpi.com/2297-8747/23/2/17 In wireless sensor networks (WSNs), users can use broadcast authentication mechanisms to connect to the target network and disseminate their messages within the network. Since data transfer for sensor networks is wireless, as a result, attackers can easily eavesdrop deployed sensor nodes and the data sent between them or modify the content of eavesdropped data and inject false data into the sensor network. Hence, the implementation of the message authentication mechanisms (in order to avoid changes and injecting messages into the network) of wireless sensor networks is essential. In this paper, we present an improved protocol based on elliptic curve cryptography (ECC) to accelerate authentication of multi-user message broadcasting. In comparison with previous ECC-based schemes, complexity and computational overhead of proposed scheme is significantly decreased. Also, the proposed scheme supports user anonymity, which is an important property in broadcast authentication schemes for WSNs to preserve user privacy and user untracking. MCA, Vol. 23, Pages 17: An Improved Digital Signature Protocol to Multi-User Broadcast Authentication Based on Elliptic Curve Cryptography in Wireless Sensor Networks (WSNs)

Mathematical and Computational Applications doi: 10.3390/mca23020017

Authors: Hamed Bashirpour Saman Bashirpour Shahaboddin Shamshirband Anthony Chronopoulos

In wireless sensor networks (WSNs), users can use broadcast authentication mechanisms to connect to the target network and disseminate their messages within the network. Since data transfer for sensor networks is wireless, as a result, attackers can easily eavesdrop deployed sensor nodes and the data sent between them or modify the content of eavesdropped data and inject false data into the sensor network. Hence, the implementation of the message authentication mechanisms (in order to avoid changes and injecting messages into the network) of wireless sensor networks is essential. In this paper, we present an improved protocol based on elliptic curve cryptography (ECC) to accelerate authentication of multi-user message broadcasting. In comparison with previous ECC-based schemes, complexity and computational overhead of proposed scheme is significantly decreased. Also, the proposed scheme supports user anonymity, which is an important property in broadcast authentication schemes for WSNs to preserve user privacy and user untracking.

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An Improved Digital Signature Protocol to Multi-User Broadcast Authentication Based on Elliptic Curve Cryptography in Wireless Sensor Networks (WSNs) Hamed Bashirpour Saman Bashirpour Shahaboddin Shamshirband Anthony Chronopoulos doi: 10.3390/mca23020017 Mathematical and Computational Applications 2018-03-21 Mathematical and Computational Applications 2018-03-21 23 2 Article 17 10.3390/mca23020017 http://www.mdpi.com/2297-8747/23/2/17
MCA, Vol. 23, Pages 16: Numerical Solution for Fuzzy Enzyme Kinetic Equations by the Runge–Kutta Method http://www.mdpi.com/2297-8747/23/1/16 One of the most important biochemical reactions is catalyzed by enzymes. A numerical method to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten equations, together with fuzzy initial values is introduced. The numerical method is based on the fourth order Runge–Kutta method, which is generalized for a fuzzy system of differential equations. The convergence and stability of the method are also presented. The capability of the method in fuzzy enzyme kinetics is demonstrated by some numerical examples. MCA, Vol. 23, Pages 16: Numerical Solution for Fuzzy Enzyme Kinetic Equations by the Runge–Kutta Method

Mathematical and Computational Applications doi: 10.3390/mca23010016

Authors: Yousef Barazandeh Bahman Ghazanfari

One of the most important biochemical reactions is catalyzed by enzymes. A numerical method to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten equations, together with fuzzy initial values is introduced. The numerical method is based on the fourth order Runge–Kutta method, which is generalized for a fuzzy system of differential equations. The convergence and stability of the method are also presented. The capability of the method in fuzzy enzyme kinetics is demonstrated by some numerical examples.

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Numerical Solution for Fuzzy Enzyme Kinetic Equations by the Runge–Kutta Method Yousef Barazandeh Bahman Ghazanfari doi: 10.3390/mca23010016 Mathematical and Computational Applications 2018-03-18 Mathematical and Computational Applications 2018-03-18 23 1 Article 16 10.3390/mca23010016 http://www.mdpi.com/2297-8747/23/1/16
MCA, Vol. 23, Pages 15: Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain http://www.mdpi.com/2297-8747/23/1/15 In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM) equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary differential equations (ODEs). Some of these ODEs had no quadrature. We here derive several new solutions for these non-solvable ODEs. MCA, Vol. 23, Pages 15: Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain

Mathematical and Computational Applications doi: 10.3390/mca23010015

Authors: Rahma Sadat Magda Kassem

In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM) equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary differential equations (ODEs). Some of these ODEs had no quadrature. We here derive several new solutions for these non-solvable ODEs.

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Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain Rahma Sadat Magda Kassem doi: 10.3390/mca23010015 Mathematical and Computational Applications 2018-03-16 Mathematical and Computational Applications 2018-03-16 23 1 Article 15 10.3390/mca23010015 http://www.mdpi.com/2297-8747/23/1/15
MCA, Vol. 23, Pages 14: A New Hybrid Whale Optimizer Algorithm with Mean Strategy of Grey Wolf Optimizer for Global Optimization http://www.mdpi.com/2297-8747/23/1/14 The quest for an efficient nature-inspired optimization technique has continued over the last few decades. In this paper, a hybrid nature-inspired optimization technique has been proposed. The hybrid algorithm has been constructed using Mean Grey Wolf Optimizer (MGWO) and Whale Optimizer Algorithm (WOA). We have utilized the spiral equation of Whale Optimizer Algorithm for two procedures in the Hybrid Approach GWO (HAGWO) algorithm: (i) firstly, we used the spiral equation in Grey Wolf Optimizer algorithm for balance between the exploitation and the exploration process in the new hybrid approach; and (ii) secondly, we also applied this equation in the whole population in order to refrain from the premature convergence and trapping in local minima. The feasibility and effectiveness of the hybrid algorithm have been tested by solving some standard benchmarks, XOR, Baloon, Iris, Breast Cancer, Welded Beam Design, Pressure Vessel Design problems and comparing the results with those obtained through other metaheuristics. The solutions prove that the newly existing hybrid variant has higher stronger stability, faster convergence rate and computational accuracy than other nature-inspired metaheuristics on the maximum number of problems and can successfully resolve the function of constrained nonlinear optimization in reality. MCA, Vol. 23, Pages 14: A New Hybrid Whale Optimizer Algorithm with Mean Strategy of Grey Wolf Optimizer for Global Optimization

Mathematical and Computational Applications doi: 10.3390/mca23010014

Authors: Narinder Singh Hanaa Hachimi

The quest for an efficient nature-inspired optimization technique has continued over the last few decades. In this paper, a hybrid nature-inspired optimization technique has been proposed. The hybrid algorithm has been constructed using Mean Grey Wolf Optimizer (MGWO) and Whale Optimizer Algorithm (WOA). We have utilized the spiral equation of Whale Optimizer Algorithm for two procedures in the Hybrid Approach GWO (HAGWO) algorithm: (i) firstly, we used the spiral equation in Grey Wolf Optimizer algorithm for balance between the exploitation and the exploration process in the new hybrid approach; and (ii) secondly, we also applied this equation in the whole population in order to refrain from the premature convergence and trapping in local minima. The feasibility and effectiveness of the hybrid algorithm have been tested by solving some standard benchmarks, XOR, Baloon, Iris, Breast Cancer, Welded Beam Design, Pressure Vessel Design problems and comparing the results with those obtained through other metaheuristics. The solutions prove that the newly existing hybrid variant has higher stronger stability, faster convergence rate and computational accuracy than other nature-inspired metaheuristics on the maximum number of problems and can successfully resolve the function of constrained nonlinear optimization in reality.

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A New Hybrid Whale Optimizer Algorithm with Mean Strategy of Grey Wolf Optimizer for Global Optimization Narinder Singh Hanaa Hachimi doi: 10.3390/mca23010014 Mathematical and Computational Applications 2018-03-12 Mathematical and Computational Applications 2018-03-12 23 1 Article 14 10.3390/mca23010014 http://www.mdpi.com/2297-8747/23/1/14
MCA, Vol. 23, Pages 13: Impact Evaluation of Electric Vehicle Parking on Solving Security-Constrained Unit Commitment Problem http://www.mdpi.com/2297-8747/23/1/13 In this paper, the employment of a vehicle-to-grid (V2G) system in the security-constrained unit commitment (SCUC) problem is considered. SCUC has gained remarkable attention from researchers in the field of electric power systems, aiming to determine the generation schedule in which the system operator maximizes the system security and minimizes the generation costs, while satisfying the system and units’ constraints. Tremendous technological advances in recent years have attracted the attention of system operators to utilize novel sources of electricity, accompanied with thermal units. To this end, V2G technology recently drew remarkable consideration as a new energy resource. V2G reduces the dependence of electricity production procedures on small-scale and costly thermal units, and subsequently has a strong impact on the operation costs and ameliorates the management of load vacillations. This paper presents the use of V2G in scheduling and operating power systems. A successful technique for investigating the impacts of V2G on a real power system is running SCUC on power systems in which electric vehicle parking is installed on different buses. In order to assess its applicability, the proposed method has been applied in two case studies: the IEEE 6-bus system and the extended IEEE 30-bus system. This study presents two simulation scenarios: the SCUC problem was first evaluated separately, and then in the presence of some electrical vehicles connected to the grid. The results demonstrate the reduction of the total operation cost. In addition, by using the proposed method, the operator can specify the optimal number of vehicles needed in the parking each hour. The results can help the system operators and designers in designing, planning, and operating such power systems. MCA, Vol. 23, Pages 13: Impact Evaluation of Electric Vehicle Parking on Solving Security-Constrained Unit Commitment Problem

Mathematical and Computational Applications doi: 10.3390/mca23010013

Authors: Mahmood Hosseini Imani Mojtaba Jabbari Ghadi Shahaboddin Shamshirband Marius M. Balas

In this paper, the employment of a vehicle-to-grid (V2G) system in the security-constrained unit commitment (SCUC) problem is considered. SCUC has gained remarkable attention from researchers in the field of electric power systems, aiming to determine the generation schedule in which the system operator maximizes the system security and minimizes the generation costs, while satisfying the system and units’ constraints. Tremendous technological advances in recent years have attracted the attention of system operators to utilize novel sources of electricity, accompanied with thermal units. To this end, V2G technology recently drew remarkable consideration as a new energy resource. V2G reduces the dependence of electricity production procedures on small-scale and costly thermal units, and subsequently has a strong impact on the operation costs and ameliorates the management of load vacillations. This paper presents the use of V2G in scheduling and operating power systems. A successful technique for investigating the impacts of V2G on a real power system is running SCUC on power systems in which electric vehicle parking is installed on different buses. In order to assess its applicability, the proposed method has been applied in two case studies: the IEEE 6-bus system and the extended IEEE 30-bus system. This study presents two simulation scenarios: the SCUC problem was first evaluated separately, and then in the presence of some electrical vehicles connected to the grid. The results demonstrate the reduction of the total operation cost. In addition, by using the proposed method, the operator can specify the optimal number of vehicles needed in the parking each hour. The results can help the system operators and designers in designing, planning, and operating such power systems.

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Impact Evaluation of Electric Vehicle Parking on Solving Security-Constrained Unit Commitment Problem Mahmood Hosseini Imani Mojtaba Jabbari Ghadi Shahaboddin Shamshirband Marius M. Balas doi: 10.3390/mca23010013 Mathematical and Computational Applications 2018-03-07 Mathematical and Computational Applications 2018-03-07 23 1 Article 13 10.3390/mca23010013 http://www.mdpi.com/2297-8747/23/1/13