Journal Description
Axioms
Axioms
is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA) and Union of Slovak Mathematicians and Physicists (JSMF) are affiliated with Axioms and their members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High visibility: indexed within SCIE (Web of Science), dblp, and other databases.
- Journal Rank: JCR - Q2 (Mathematics, Applied)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.8 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Companion journal: Logics.
Impact Factor:
2.0 (2022);
5-Year Impact Factor:
1.9 (2022)
Latest Articles
Cutting-Edge Monte Carlo Framework: Novel “Walk on Equations” Algorithm for Linear Algebraic Systems
Axioms 2024, 13(1), 53; https://doi.org/10.3390/axioms13010053 - 15 Jan 2024
Abstract
In this paper, we introduce the “Walk on Equations” (WE) Monte Carlo algorithm, a novel approach for solving linear algebraic systems. This algorithm shares similarities with the recently developed WE MC method by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. This method
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In this paper, we introduce the “Walk on Equations” (WE) Monte Carlo algorithm, a novel approach for solving linear algebraic systems. This algorithm shares similarities with the recently developed WE MC method by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. This method is particularly effective for large matrices, both real- and complex-valued, and shows significant improvements over traditional methods. Our comprehensive comparison with the Gauss–Seidel method highlights the WE algorithm’s superior performance, especially in reducing relative errors within fewer iterations. We also introduce a unique dominancy number, which plays a crucial role in the algorithm’s efficiency. A pivotal outcome of our research is the convergence theorem we established for the WE algorithm, demonstrating its optimized performance through a balanced iteration matrix. Furthermore, we incorporated a sequential Monte Carlo method, enhancing the algorithm’s efficacy. The most-notable application of our algorithm is in solving a large system derived from a finite-element approximation in constructive mechanics, specifically for a beam structure problem. Our findings reveal that the proposed WE Monte Carlo algorithm, especially when combined with sequential MC, converges significantly faster than well-known deterministic iterative methods such as the Jacobi method. This enhanced convergence is more pronounced in larger matrices. Additionally, our comparative analysis with the preconditioned conjugate gradient (PCG) method shows that the WE MC method can outperform traditional methods for certain matrices. The introduction of a new random variable as an unbiased estimator of the solution vector and the analysis of the relative stochastic error structure further illustrate the potential of our novel algorithm in computational mathematics.
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(This article belongs to the Special Issue Advances in Numerical Algorithms for Machine Learning)
Open AccessArticle
A Convergence Criterion for a Class of Stationary Inclusions in Hilbert Spaces
by
and
Axioms 2024, 13(1), 52; https://doi.org/10.3390/axioms13010052 - 15 Jan 2024
Abstract
Here, we consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A, and an element . Under appropriate assumptions on the data, the inclusion has a
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Here, we consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A, and an element . Under appropriate assumptions on the data, the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence , which guarantee its convergence to the solution u. We then present several applications that provide the continuous dependence of the solution with respect to the data K, A and f on the one hand, and the convergence of an associate penalty problem on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials that, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the analysis of two nonlinear elastic constitutive laws.
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(This article belongs to the Section Hilbert’s Sixth Problem)
Open AccessArticle
On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions
Axioms 2024, 13(1), 51; https://doi.org/10.3390/axioms13010051 - 15 Jan 2024
Abstract
In this paper, we investigate a nonlinear coupled integro-differential system involving generalized Hilfer fractional derivative operators ( -Hilfer type) of different orders and equipped with non-local multi-point ordinary and fractional integral boundary conditions. The uniqueness results for the
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In this paper, we investigate a nonlinear coupled integro-differential system involving generalized Hilfer fractional derivative operators ( -Hilfer type) of different orders and equipped with non-local multi-point ordinary and fractional integral boundary conditions. The uniqueness results for the given problem are obtained by applying Banach’s contraction mapping principle and the Boyd–Wong fixed point theorem for nonlinear contractions. Based on the Laray–Schauder alternative and the well-known fixed-point theorem due to Krasnosel’skiĭ, the existence of solutions for the problem at hand is established under different criteria. Illustrative examples for the main results are constructed.
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(This article belongs to the Section Mathematical Analysis)
Open AccessArticle
Minimal and Primitive Terracini Loci of a Four-Dimensional Projective Space
Axioms 2024, 13(1), 50; https://doi.org/10.3390/axioms13010050 - 14 Jan 2024
Abstract
We study two quite different types of Terracini loci for the order d-Veronese embedding of an n-dimensional projective space: the minimal one and the primitive one (defined in this paper). The main result is that if ,
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We study two quite different types of Terracini loci for the order d-Veronese embedding of an n-dimensional projective space: the minimal one and the primitive one (defined in this paper). The main result is that if , and , no subset with x points is a minimal Terracini set. We give examples that show that the result is sharp. We raise several open questions.
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(This article belongs to the Special Issue Yang-Baxter Equations, Nonassociative Structures and Applications—In Memoriam, Stefan Papadima)
Open AccessArticle
Application of Gradient Optimization Methods in Defining Neural Dynamics
by
, , , , , and
Axioms 2024, 13(1), 49; https://doi.org/10.3390/axioms13010049 - 14 Jan 2024
Abstract
Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation which changes over time is studied using the novel GNN
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Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation which changes over time is studied using the novel GNN model, termed as GGNN . The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN design converges asymptotically to the solution of the matrix equation , for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.
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(This article belongs to the Special Issue Numerical Analysis and Optimization)
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Open AccessArticle
Hybrid Quantum Genetic Algorithm with Fuzzy Adaptive Rotation Angle for Efficient Placement of Unmanned Aerial Vehicles in Natural Disaster Areas
Axioms 2024, 13(1), 48; https://doi.org/10.3390/axioms13010048 - 13 Jan 2024
Abstract
A Hybrid Quantum Genetic Algorithm with Fuzzy Adaptive Rotation Angle (HQGAFARA) is introduced in this work to determine the optimal placements for Unmanned Aerial Vehicles (UAVs) aimed at maximizing coverage in disaster-stricken areas. The HQGAFARA is a hybrid quantum fuzzy meta-heuristic that uses
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A Hybrid Quantum Genetic Algorithm with Fuzzy Adaptive Rotation Angle (HQGAFARA) is introduced in this work to determine the optimal placements for Unmanned Aerial Vehicles (UAVs) aimed at maximizing coverage in disaster-stricken areas. The HQGAFARA is a hybrid quantum fuzzy meta-heuristic that uses the Deutsch–Jozsa quantum circuit to generate quantum populations synergistically working as haploid recombination and mutation operators that take advantage of quantum entanglement, providing exploitative and explorative features to produce new individuals. In place of the conventional lookup table or mathematical equation, we introduced a fuzzy heuristic to adapt the rotation angle employed in quantum gates. The hybrid nature of this algorithm becomes evident through its utilization of both classical and quantum computing components. Experimental evaluations were conducted using two distinct test sets. The first set, termed the “best case”, represents conditions that are the most favorable for determining the UAV positions, while the second set, the “worst-case”, simulates highly challenging conditions for locating the UAV positions, thereby posing a significant test for the proposed algorithm. We carried out statistical comparative analyses, assessing the HQGAFARA against other hybrid quantum algorithms that employ different rotation angles and against the classical genetic algorithm. The experimental results demonstrated that the HQGAFARA performed comparably, if not better, to the classical genetic algorithm regarding precision. Furthermore, quantum algorithms showcased their computational prowess in experiments related to the convergence time.
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(This article belongs to the Special Issue Applications of Quantum Computing in Artificial Intelligence)
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Open AccessTutorial
Multilevel Ordinal Logit Models: A Proportional Odds Application Using Data from Brazilian Higher Education Institutions
Axioms 2024, 13(1), 47; https://doi.org/10.3390/axioms13010047 - 12 Jan 2024
Abstract
This tutorial delves into the application of proportional odds-type ordinal logistic regression to assess the impact of incorporating both fixed and random effects when predicting the rankings of Brazilian universities in a well-established international academic assessment utilizing authentic data. In addition to offering
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This tutorial delves into the application of proportional odds-type ordinal logistic regression to assess the impact of incorporating both fixed and random effects when predicting the rankings of Brazilian universities in a well-established international academic assessment utilizing authentic data. In addition to offering valuable insights into the estimation of ordinal logistic models, this study underscores the significance of integrating random effects into the analysis and addresses the potential pitfalls associated with the inappropriate treatment of phenomena exhibiting categorical ordinal characteristics. Furthermore, we have made the R language code and dataset available as supplementary resources for the replication.
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(This article belongs to the Special Issue Statistical Modeling of Modern Multivariate Data)
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Open AccessArticle
Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model
Axioms 2024, 13(1), 46; https://doi.org/10.3390/axioms13010046 - 11 Jan 2024
Abstract
This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus
[...] Read more.
This study introduces a new two-parameter Liu estimator (PMTPLE) for addressing the multicollinearity problem in the Poisson regression model (PRM). The estimation of the PRM is traditionally accomplished through the Poisson maximum likelihood estimator (PMLE). However, when the explanatory variables are correlated, thus leading to multicollinearity, the variance or standard error of the PMLE is inflated. To address this issue, several alternative estimators have been introduced, including the Poisson ridge regression estimator (PRRE), Liu estimator (PLE), and adjusted Liu estimator (PALE), each of them relying on a single shrinkage parameter. The PMTPLE uses two shrinkage parameters, which enhances its adaptability and robustness in the presence of multicollinearity between explanatory variables. To assess the performance of the PMTPLE compared to the four existing estimators (the PMLE, PRRE, PLE, and PALE), a simulation study is conducted that encompasses various scenarios and two empirical applications. The evaluation of the performance is based on the mean square error (MSE) criterion. The theoretical comparison, simulation results, and findings of the two applications consistently demonstrate the superiority of the PMTPLE over the other estimators, establishing it as a robust solution for count data analysis under multicollinearity conditions.
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(This article belongs to the Special Issue Computational Statistics and Its Applications)
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Open AccessEditorial
Special Issue “Optimisation Models and Applications”
Axioms 2024, 13(1), 45; https://doi.org/10.3390/axioms13010045 - 11 Jan 2024
Abstract
Optimisation models have transcended their origins to become indispensable tools across many fields, including engineering, economics, the environment, health, systems of systems, businesses, and beyond [...]
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(This article belongs to the Special Issue Optimization Models and Applications)
Open AccessArticle
A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method
Axioms 2024, 13(1), 44; https://doi.org/10.3390/axioms13010044 - 11 Jan 2024
Abstract
In this work, the time-fractional Navier–Stokes equation is discussed using a calculational method, which is called the Sumudu-generalized Laplace transform decomposition method (DGLTDM). The fractional derivatives are defined in the Caputo sense. The (DGLTDM) is a hybrid of the Sumudu-generalized Laplace transform and
[...] Read more.
In this work, the time-fractional Navier–Stokes equation is discussed using a calculational method, which is called the Sumudu-generalized Laplace transform decomposition method (DGLTDM). The fractional derivatives are defined in the Caputo sense. The (DGLTDM) is a hybrid of the Sumudu-generalized Laplace transform and the decomposition method. Three examples of the time-fractional Navier–Stokes equation are studied to check the validity and demonstrate the effectiveness of the current method. The results show that the suggested method succeeds remarkably well in terms of proficiency and can be utilized to study more problems in the field of nonlinear fractional differential equations (FDEs).
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(This article belongs to the Special Issue Fractional Calculus - Theory and Applications II)
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Specific Features of Polynomials in Several Examples
Axioms 2024, 13(1), 43; https://doi.org/10.3390/axioms13010043 - 11 Jan 2024
Abstract
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This paper considers polynomial characteristics useful for a better understanding of the behaviour of these functions. Taylor series for the polynomials are described by the items with even and odd derivatives and powered changes in the argument, which leads to more specific studying
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This paper considers polynomial characteristics useful for a better understanding of the behaviour of these functions. Taylor series for the polynomials are described by the items with even and odd derivatives and powered changes in the argument, which leads to more specific studying of their properties. Connections between the derivative and antiderivative of the polynomial functions are defined. The structure of polynomial functions reveals their specific characteristic that the mean value of their roots equals the mean value of the locations of the critical points such as the extrema and inflection points. Derivatives of the quadratic exponent in relation to an interesting connection of two transcendental numbers are also described. The discussed properties of the polynomials can be helpful for practical implementations and educational purposes.
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Open AccessArticle
Results of Third-Order Strong Differential Subordinations
Axioms 2024, 13(1), 42; https://doi.org/10.3390/axioms13010042 - 10 Jan 2024
Abstract
In this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions. Furthermore, we extend certain definitions, presenting novel and fascinating results. We also derive several interesting properties
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In this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions. Furthermore, we extend certain definitions, presenting novel and fascinating results. We also derive several interesting properties of the results of third-order strong differential subordinations for analytic functions associated with the Srivastava–Attiya operator.
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(This article belongs to the Special Issue New Developments in Geometric Function Theory II)
Open AccessArticle
A Probabilistic Physico-Chemical Diffusion Model of the Key Drifting Parameter of Measuring Equipment
Axioms 2024, 13(1), 41; https://doi.org/10.3390/axioms13010041 - 09 Jan 2024
Abstract
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(1) Background: A new probabilistic physico-chemical model of the drifting key parameter of measuring equipment is proposed. The model allows for the integrated consideration of degradation processes (electrolytic corrosion, oxidation, plastic accumulation of dislocations, etc.) in nodes and elements of measuring equipment. The
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(1) Background: A new probabilistic physico-chemical model of the drifting key parameter of measuring equipment is proposed. The model allows for the integrated consideration of degradation processes (electrolytic corrosion, oxidation, plastic accumulation of dislocations, etc.) in nodes and elements of measuring equipment. The novelty of this article lies in the analytical solutions that are a combination of the Fokker–Planck–Kolmogorov equation and the equation of chemical kinetics. The novelty also consists of the simultaneous simulation and analysis of probabilistic, physical and chemical processes in one model. (2) Research literature review: Research works related to the topic of the study were analyzed. The need for a probabilistic formulation of the problem is argued, since classical statistical methods are not applicable due to the lack of statistical data. (3) Statement of the research problem: A probabilistic formulation of the problem is given taking into account the physical and chemical laws of aging and degradation. (4) Methods: The author uses methods of probability theory and mathematical statistics, methods for solving the stochastic differential equations, the methods of mathematical modeling, the methods of chemical kinetics and the methods for solving a partial differential equations. (5) Results: A mathematical model of a drifting key parameter of measuring equipment is developed. The conditional transition density of the probability distribution of the key parameter of measuring equipment is constructed using a solution to the Fokker–Planck–Kolmogorov equation. The results of the study on the developed model and the results of solving the applied problem of constructing the function of the failure rate of measuring equipment are presented. (6) Discussion: The results of comparison between the model developed in this paper and the known two-parameter models of diffusion monotonic distribution and diffusion non-monotonic distribution are discussed. The results of comparison between the model and the three-parameter diffusion probabilistic physical model developed by the author earlier are also discussed. (7) Conclusions: The developed model facilitates the construction and analysis of a wide range of metrological characteristics such as measurement errors and measurement ranges and acquisition of their statistical estimates. The developed model is used to forecast and simulate the reliability of measuring equipment in general, as well as soldered joints of integrated circuits in special equipment and machinery, which is also operated in harsh conditions and corrosive environments.
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Open AccessArticle
Integer-Valued Split-BREAK Process with a General Family of Innovations and Application to Accident Count Data Modeling
by
, , , and
Axioms 2024, 13(1), 40; https://doi.org/10.3390/axioms13010040 - 07 Jan 2024
Abstract
This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and correlation structure. In addition, the marginal distribution,
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This paper presents a novel count time-series model, named integer-valued Split-BREAK process of the first order, abbr. INSB(1) model. This process is examined in terms of its basic stochastic properties, such as stationarity, mean, variance and correlation structure. In addition, the marginal distribution, over-dispersion and zero-inflation properties of the INSB(1) process are also examined. To estimate the unknown parameters of the INSB(1) process, an estimation procedure based on probability generating functions (PGFs) is proposed. For the obtained estimators, their asymptotic properties, as well as the appropriate simulation study, are examined. Finally, the INSB(1) process is applied in the dynamic analysis of some real-world series, namely, the numbers of serious traffic accidents in Serbia and forest fires in Greece.
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(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)
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Finite-Time Passivity and Synchronization for a Class of Fuzzy Inertial Complex-Valued Neural Networks with Time-Varying Delays
by
Axioms 2024, 13(1), 39; https://doi.org/10.3390/axioms13010039 - 07 Jan 2024
Abstract
This article investigates finite-time passivity for fuzzy inertial complex-valued neural networks (FICVNNs) with time-varying delays. First, by using the existing passivity theory, several related definitions of finite-time passivity are illustrated. Consequently, by adopting a reduced-order method and dividing complex-valued parameters into real and
[...] Read more.
This article investigates finite-time passivity for fuzzy inertial complex-valued neural networks (FICVNNs) with time-varying delays. First, by using the existing passivity theory, several related definitions of finite-time passivity are illustrated. Consequently, by adopting a reduced-order method and dividing complex-valued parameters into real and imaginary parts, the proposed FICVNNs are turned into first-order real-valued neural network systems. Moreover, appropriate controllers and the Lyapunov functional method are established to obtain the finite-time passivity of FICVNNs with time delays. Furthermore, some essential conditions are established to ensure finite-time synchronization for finite-time passive FICVNNs. In the end, corresponding simulations certify the feasibility of the proposed theoretical outcomes.
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(This article belongs to the Special Issue Control Theory and Control Systems: Algorithms and Methods)
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The AA-Viscosity Algorithm for Fixed-Point, Generalized Equilibrium and Variational Inclusion Problems
Axioms 2024, 13(1), 38; https://doi.org/10.3390/axioms13010038 - 05 Jan 2024
Abstract
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The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained
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The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained through the proposed method is proved under some mild assumptions. Consequently, approximations of the solution of the split feasibility problem, the relaxed split feasibility problem, the split common null point problem and the split minimization problem are given. The applicability of our proposed algorithm has been illustrated with the help of a numerical example. Our iterative method was then compared graphically with different comparable methods in the existing literature.
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Open AccessArticle
Heuristic Ensemble Construction Methods of Automatically Designed Dispatching Rules for the Unrelated Machines Environment
by
and
Axioms 2024, 13(1), 37; https://doi.org/10.3390/axioms13010037 - 05 Jan 2024
Abstract
Dynamic scheduling represents an important class of combinatorial optimisation problems that are usually solved with simple heuristics, the so-called dispatching rules (DRs). Designing efficient DRs is a tedious task, which is why it has been automated through the application of genetic programming (GP).
[...] Read more.
Dynamic scheduling represents an important class of combinatorial optimisation problems that are usually solved with simple heuristics, the so-called dispatching rules (DRs). Designing efficient DRs is a tedious task, which is why it has been automated through the application of genetic programming (GP). Various approaches have been used to improve the results of automatically generated DRs, with ensemble learning being one of the best-known. The goal of ensemble learning is to create sets of automatically designed DRs that perform better together. One of the main problems in ensemble learning is the selection of DRs to form the ensemble. To this end, various ensemble construction methods have been proposed over the years. However, these methods are quite computationally intensive and require a lot of computation time to obtain good ensembles. Therefore, in this study, we propose several simple heuristic ensemble construction methods that can be used to construct ensembles quite efficiently and without the need to evaluate their performance. The proposed methods construct the ensembles solely based on certain properties of the individual DRs used for their construction. The experimental study shows that some of the proposed heuristic construction methods perform better than more complex state-of-the-art approaches for constructing ensembles.
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(This article belongs to the Special Issue Applied Mathematics, Intelligence and Operations Research)
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On Construction of Bounded Sets Not Admitting a General Type of Riesz Spectrum
by
Axioms 2024, 13(1), 36; https://doi.org/10.3390/axioms13010036 - 05 Jan 2024
Abstract
We construct a bound set that does not admit a Riesz spectrum containing a nonempty periodic set for which the period is a rational multiple of a fixed constant. As a consequence, we obtain a bounded set V with an arbitrarily small Lebesgue
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We construct a bound set that does not admit a Riesz spectrum containing a nonempty periodic set for which the period is a rational multiple of a fixed constant. As a consequence, we obtain a bounded set V with an arbitrarily small Lebesgue measure such that for any positive integer N, the set of exponentials with frequencies in any union of cosets of cannot be a frame for the space of square integrable functions over V. These results are based on the proof technique of Olevskii and Ulanovskii from 2008.
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(This article belongs to the Special Issue Theory of Functions and Applications II)
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A New Criterion for Improving Convergence of Fuzzy C-Means Clustering
by
, , , , , and
Axioms 2024, 13(1), 35; https://doi.org/10.3390/axioms13010035 - 02 Jan 2024
Abstract
One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for
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One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for its initialization and convergence. In this research, a new convergence strategy is proposed, which is based on the difference of the objective function values, in two consecutive iterations, expressed as a percentage of its value in the next to the last one. Additionally, a new method is proposed to optimize the selection of values of the convergence or stop threshold of the algorithm, which is based on the Pareto principle. To validate our approach, a collection of real datasets was solved, and a significant reduction in the number of iterations was observed, without affecting significantly the solution quality. Based on the proposed method and the experiments carried out, we found it is convenient to use threshold values equal to 0.73 and 0.35 if a decrease in the number of iterations of approximately 75.2% and 64.56%, respectively, is wanted, at the expense of a reduction in solution quality of 2% and 1%, respectively. It is worth mentioning that, as the size of the datasets is increased, the proposed approach tends to obtain better results, and therefore, its use is suggested for datasets found in Big Data and Data Science.
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(This article belongs to the Special Issue Computational and Mathematical Methods in Science and Engineering II)
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Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations
Axioms 2024, 13(1), 34; https://doi.org/10.3390/axioms13010034 - 31 Dec 2023
Abstract
In this paper, a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations is presented. After the convergence analysis, a study of the stability of this class is made using the tools of complex discrete dynamics, allowing
[...] Read more.
In this paper, a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations is presented. After the convergence analysis, a study of the stability of this class is made using the tools of complex discrete dynamics, allowing those elements of the class with lower dependence on initial estimations to be selected in order to find a very stable subfamily. Numerical tests indicate that the stable members perform better on quadratic polynomials than the unstable ones when applied to other non-polynomial functions. Moreover, the performance of the best elements of the family are compared with known methods, showing robust and stable behaviour.
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(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)
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