Schröder approximations of the first kind, modified for the inverse function approximation case, are utilized to establish general analytical approximation forms for an inverse function. Such general forms are used to establish arbitrarily accurate analytical approximations, with a set relative error bound, for an inverse function when an initial approximation, typically with low accuracy, is known. Approximations for arcsine, the inverse of x − sin(x), the inverse Langevin function and the Lambert W function are used to illustrate this approach. Several applications are detailed. For the root approximation of a function, Schröder approximations of the first kind, based on the inverse of a function, have an advantage over the corresponding generalization of the standard Newton–Raphson method, as explicit analytical expressions for all orders of approximation can be obtained.
{"title":"Schröder-Based Inverse Function Approximation","authors":"Roy M. Howard","doi":"10.3390/axioms12111042","DOIUrl":"https://doi.org/10.3390/axioms12111042","url":null,"abstract":"Schröder approximations of the first kind, modified for the inverse function approximation case, are utilized to establish general analytical approximation forms for an inverse function. Such general forms are used to establish arbitrarily accurate analytical approximations, with a set relative error bound, for an inverse function when an initial approximation, typically with low accuracy, is known. Approximations for arcsine, the inverse of x − sin(x), the inverse Langevin function and the Lambert W function are used to illustrate this approach. Several applications are detailed. For the root approximation of a function, Schröder approximations of the first kind, based on the inverse of a function, have an advantage over the corresponding generalization of the standard Newton–Raphson method, as explicit analytical expressions for all orders of approximation can be obtained.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"332 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Innovation plays a crucial role in the economy of nations worldwide. In Latin America, countries foster competitiveness through public and private incentives to support innovation. Moreover, entrepreneurship incentives seek to improve countries’ performance, although factors such as low business growth rates and informality can compromise it. Despite the efforts, there are several difficulties in achieving competitiveness, and few studies in developing countries. Therefore, the article explores the relationship between the factors that influence competitiveness, especially the role of innovation and entrepreneurship in Brazil and Peru. The research uses quantitative-qualitative methodology through modeling and simulation and a case study. The authors use the Affinities Theory to verify the relationship between the indicators that make up the competitiveness landscape and its most significant and attractive factors, adapting the methodology established by the International Institute for Management Development (IMD) World Competitiveness ranking. As a result, this algorithm allows us to know the relationships between five factors of economic attractiveness and four competitiveness indicators. As its main contributions, the study advances the frontier of knowledge about innovation and entrepreneurship, as few studies explore competitiveness in developing countries. Also, it offers a detailed explanation of the application of this algorithm, allowing researchers to reproduce this methodology in other scenarios. Practically, it might support policymakers in formulating development strategies and stimuli for business competitiveness. In addition, academic and business leaders can strengthen university-business collaboration with applied research in innovation and entrepreneurship. One limitation would be the number of countries participating in the research. The authors suggest future lines of research.
{"title":"Fuzzy Algorithm Applied to Factors Influencing Competitiveness: A Case Study of Brazil and Peru through Affinities Theory","authors":"Luciano Barcellos-Paula, Aline Castro-Rezende, Daniela Fantoni Alvares","doi":"10.3390/axioms12111038","DOIUrl":"https://doi.org/10.3390/axioms12111038","url":null,"abstract":"Innovation plays a crucial role in the economy of nations worldwide. In Latin America, countries foster competitiveness through public and private incentives to support innovation. Moreover, entrepreneurship incentives seek to improve countries’ performance, although factors such as low business growth rates and informality can compromise it. Despite the efforts, there are several difficulties in achieving competitiveness, and few studies in developing countries. Therefore, the article explores the relationship between the factors that influence competitiveness, especially the role of innovation and entrepreneurship in Brazil and Peru. The research uses quantitative-qualitative methodology through modeling and simulation and a case study. The authors use the Affinities Theory to verify the relationship between the indicators that make up the competitiveness landscape and its most significant and attractive factors, adapting the methodology established by the International Institute for Management Development (IMD) World Competitiveness ranking. As a result, this algorithm allows us to know the relationships between five factors of economic attractiveness and four competitiveness indicators. As its main contributions, the study advances the frontier of knowledge about innovation and entrepreneurship, as few studies explore competitiveness in developing countries. Also, it offers a detailed explanation of the application of this algorithm, allowing researchers to reproduce this methodology in other scenarios. Practically, it might support policymakers in formulating development strategies and stimuli for business competitiveness. In addition, academic and business leaders can strengthen university-business collaboration with applied research in innovation and entrepreneurship. One limitation would be the number of countries participating in the research. The authors suggest future lines of research.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"18 S27","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Felix D. Ajibade, Francis Monday Nkwuda, Hussaini Joshua, Taiwo P. Fajusigbe, Kayode Oshinubi
In the context of uniformly convex Banach space, this paper focuses on examining the strong convergence of the F* iterative algorithm to the fixed point of a strongly pseudocontractive mapping. Furthermore, we demonstrate through numerical methods that the F* iterative algorithm converges strongly and faster than other current iterative schemes in the literature and extends to the fixed point of a strong pseudocontractive mapping. Finally, under a nonlinear quadratic Volterra integral equation, the application of our findings is shown.
{"title":"Investigation of the F* Algorithm on Strong Pseudocontractive Mappings and Its Application","authors":"Felix D. Ajibade, Francis Monday Nkwuda, Hussaini Joshua, Taiwo P. Fajusigbe, Kayode Oshinubi","doi":"10.3390/axioms12111041","DOIUrl":"https://doi.org/10.3390/axioms12111041","url":null,"abstract":"In the context of uniformly convex Banach space, this paper focuses on examining the strong convergence of the F* iterative algorithm to the fixed point of a strongly pseudocontractive mapping. Furthermore, we demonstrate through numerical methods that the F* iterative algorithm converges strongly and faster than other current iterative schemes in the literature and extends to the fixed point of a strong pseudocontractive mapping. Finally, under a nonlinear quadratic Volterra integral equation, the application of our findings is shown.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"327 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nikolaos P. Theodorakatos, Rohit Babu, Angelos P. Moschoudis
Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary polynomial models to encounter the optimal number of PMUs with suitable PMU positioning sites. All optimization models are implemented with powerful optimization solvers in MATLAB to obtain the global solution point.
{"title":"The Branch-and-Bound Algorithm in Optimizing Mathematical Programming Models to Achieve Power Grid Observability","authors":"Nikolaos P. Theodorakatos, Rohit Babu, Angelos P. Moschoudis","doi":"10.3390/axioms12111040","DOIUrl":"https://doi.org/10.3390/axioms12111040","url":null,"abstract":"Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary polynomial models to encounter the optimal number of PMUs with suitable PMU positioning sites. All optimization models are implemented with powerful optimization solvers in MATLAB to obtain the global solution point.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"28 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Manan A. Maisuria, Priti V. Tandel, Trushitkumar Patel
This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.
{"title":"Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method","authors":"Manan A. Maisuria, Priti V. Tandel, Trushitkumar Patel","doi":"10.3390/axioms12111039","DOIUrl":"https://doi.org/10.3390/axioms12111039","url":null,"abstract":"This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p<2, if the boundary value is in the vector-valued Lp,1≤p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2≤p≤∞. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1≤p≤∞.
{"title":"Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values","authors":"Richard D. Carmichael","doi":"10.3390/axioms12111036","DOIUrl":"https://doi.org/10.3390/axioms12111036","url":null,"abstract":"Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p<2, if the boundary value is in the vector-valued Lp,1≤p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2≤p≤∞. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1≤p≤∞.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"372 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng’s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature.
{"title":"A Regularized Tseng Method for Solving Various Variational Inclusion Problems and Its Application to a Statistical Learning Model","authors":"Adeolu Taiwo, Simeon Reich","doi":"10.3390/axioms12111037","DOIUrl":"https://doi.org/10.3390/axioms12111037","url":null,"abstract":"We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng’s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"223 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135679925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique continuation and a suitable reflection principle are enough to proceed with the constructions without any other assumption on the underlying partial differential equation or the boundary condition. We also aim to keep the geometric constructions and their proofs as simple as possible. To illustrate the applicability of this theory, we show how several uniqueness results present in the literature immediately follow from our arguments. Indeed, we believe that this theory may serve as a roadmap for establishing similar uniqueness results for other partial differential equations or boundary conditions.
{"title":"On Unique Determination of Polyhedral Sets","authors":"Luca Rondi","doi":"10.3390/axioms12111035","DOIUrl":"https://doi.org/10.3390/axioms12111035","url":null,"abstract":"In this paper, we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique continuation and a suitable reflection principle are enough to proceed with the constructions without any other assumption on the underlying partial differential equation or the boundary condition. We also aim to keep the geometric constructions and their proofs as simple as possible. To illustrate the applicability of this theory, we show how several uniqueness results present in the literature immediately follow from our arguments. Indeed, we believe that this theory may serve as a roadmap for establishing similar uniqueness results for other partial differential equations or boundary conditions.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"47 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135726493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For a quantale I, the unit interval endowed with a continuous triangular norm, we introduce the canonical, op-canonical and Kleisli extensions of the conical I-semifilter monad to I-Rel. It is proved that the op-canonical extension coincides with the Kleisli extension.
{"title":"Lax Extensions of Conical I-Semifilter Monads","authors":"Gao Zhang, Shao-Qun Zhang","doi":"10.3390/axioms12111034","DOIUrl":"https://doi.org/10.3390/axioms12111034","url":null,"abstract":"For a quantale I, the unit interval endowed with a continuous triangular norm, we introduce the canonical, op-canonical and Kleisli extensions of the conical I-semifilter monad to I-Rel. It is proved that the op-canonical extension coincides with the Kleisli extension.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"38 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135725447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The 4×4 trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure. Additionally, we give the Darboux matrix T, whose elements are connected to the spectral parameter in accordance with the various positions and numbers of the spectral parameter λ. The Darboux transformation approach has also been successfully applicated to superintegrable systems.
{"title":"Solution of High-Order Nonlinear Integrable Systems Using Darboux Transformation","authors":"Xinhui Wu, Jiawei Hu, Ning Zhang","doi":"10.3390/axioms12111032","DOIUrl":"https://doi.org/10.3390/axioms12111032","url":null,"abstract":"The 4×4 trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure. Additionally, we give the Darboux matrix T, whose elements are connected to the spectral parameter in accordance with the various positions and numbers of the spectral parameter λ. The Darboux transformation approach has also been successfully applicated to superintegrable systems.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"8 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135821498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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