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
AHD-SLE: Anomalous Hyperedge Detection on Hypergraph Symmetric Line Expansion
Axioms 2024, 13(6), 387; https://doi.org/10.3390/axioms13060387 - 7 Jun 2024
Abstract
Graph anomaly detection aims to identify unusual patterns or structures in graph-structured data. Most existing research focuses on anomalous nodes in ordinary graphs with pairwise relationships. However, complex real-world systems often involve relationships that go beyond pairwise relationships, and insufficient attention is paid
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Graph anomaly detection aims to identify unusual patterns or structures in graph-structured data. Most existing research focuses on anomalous nodes in ordinary graphs with pairwise relationships. However, complex real-world systems often involve relationships that go beyond pairwise relationships, and insufficient attention is paid to hypergraph anomaly detection, especially anomalous hyperedge detection. Some existing methods for researching hypergraphs involve transforming hypergraphs into ordinary graphs for learning, which can result in poor detection performance due to the loss of high-order information. We propose a new method for Anomalous Hyperedge Detection on Symmetric Line Expansion (AHD-SLE). The SLE of a hypergraph is an ordinary graph with pairwise relationships and can be backmapped to the hypergraph, so the SLE is able to preserve the higher-order information of the hypergraph. The AHD-SLE first maps the hypergraph to the SLE; then, the information is aggregated by Graph Convolutional Networks (GCNs) in the SLE. After that, the hyperedge embedding representation is obtained through a backmapping operation. Finally, an anomaly function is designed to detect anomalous hyperedges using the hyperedge embedding representation. Experiments on five different types of real hypergraph datasets show that AHD-SLE outperforms the baseline algorithm in terms of Area Under the receiver operating characteristic Curve(AUC) and Recall metrics.
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(This article belongs to the Special Issue Mathematical Modelling of Complex Systems)
Open AccessArticle
Characterization of Isoclinic, Transversally Geodesic and Grassmannizable Webs
by
Jihad Saab and Rafik Absi
Axioms 2024, 13(6), 386; https://doi.org/10.3390/axioms13060386 - 6 Jun 2024
Abstract
One of the most relevant topics in web theory is linearization. A particular class of linearizable webs is the Grassmannizable web. Akivis gave a characterization of such a web, showing that Grassmannizable webs are equivalent to isoclinic and transversally geodesic webs. The obstructions
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One of the most relevant topics in web theory is linearization. A particular class of linearizable webs is the Grassmannizable web. Akivis gave a characterization of such a web, showing that Grassmannizable webs are equivalent to isoclinic and transversally geodesic webs. The obstructions given by Akivis that characterize isoclinic and transversally geodesic webs are computed locally, and it is difficult to give them an interpretation in relation to torsion or curvature of the unique Chern connection associated with a web. In this paper, using Nagy’s web formalism, Frölisher—Nejenhuis theory for derivation associated with vector differential forms, and Grifone’s connection theory for tensorial algebra on the tangent bundle, we find invariants associated with almost-Grassmann structures expressed in terms of torsion, curvature, and Nagy’s tensors, and we provide an interpretation in terms of these invariants for the isoclinic, transversally geodesic, Grassmannizable, and parallelizable webs.
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(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)
Open AccessArticle
The New G-Double-Laplace Transforms and One-Dimensional Coupled Sine-Gordon Equations
by
Hassan Eltayeb and Said Mesloub
Axioms 2024, 13(6), 385; https://doi.org/10.3390/axioms13060385 - 5 Jun 2024
Abstract
This paper establishes a novel technique, which is called the G-double-Laplace transform. This technique is an extension of the generalized Laplace transform. We study its properties with examples and various theorems related to the G-double-Laplace transform that have been addressed and proven. Finally,
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This paper establishes a novel technique, which is called the G-double-Laplace transform. This technique is an extension of the generalized Laplace transform. We study its properties with examples and various theorems related to the G-double-Laplace transform that have been addressed and proven. Finally, we apply the G-double-Laplace transform decomposition method to solve the nonlinear sine-Gordon and coupled sine-Gordon equations. This method is a combination of the G-double-Laplace transform and decomposition method. In addition, some examples are examined to establish the accuracy and effectiveness of this technique.
Full article
(This article belongs to the Special Issue Advances in Generalized Hypergeometric Functions, Integral Transforms and Number Theory)
Open AccessArticle
A Proportional–Integral Observer-Based Dynamic Event-Triggered Consensus Protocol for Nonlinear Positive Multi-Agent Systems
by
Xiaogang Yang, Mengxing Huang, Yuanyuan Wu and Xuegang Tan
Axioms 2024, 13(6), 384; https://doi.org/10.3390/axioms13060384 - 5 Jun 2024
Abstract
This paper investigates the state estimation and event-triggered control for positive nonlinear multi-agent systems. Firstly, a proportional–integral observer is established to estimate the states of the considered nonlinear positive multi-agent systems based on the matrix decomposition method. Then, a dynamic event-triggered mechanism is
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This paper investigates the state estimation and event-triggered control for positive nonlinear multi-agent systems. Firstly, a proportional–integral observer is established to estimate the states of the considered nonlinear positive multi-agent systems based on the matrix decomposition method. Then, a dynamic event-triggered mechanism is constructed, and a control protocol is proposed based on the proportional–integral observer and event-triggered mechanism. By combining linear programming with linear co-positive Lyapunov functions, the considered multi-agent systems are guaranteed to be positive and achieve consensus. Moreover, by introducing three new variables and a finite vector, the final convergence point can be changed based on the given vector. Finally, two illustrative examples demonstrate the validity of the proposed theoretical results.
Full article
(This article belongs to the Special Issue Cooperative Control of Multi-agent Systems and Security Control of Cyber-Physical Systems)
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The Existence and Uniqueness of Radial Solutions for Biharmonic Elliptic Equations in an Annulus
by
Yongxiang Li and Yanyan Wang
Axioms 2024, 13(6), 383; https://doi.org/10.3390/axioms13060383 - 4 Jun 2024
Abstract
This paper concerns with the existence of radial solutions of the biharmonic elliptic equation in an annular domain
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This paper concerns with the existence of radial solutions of the biharmonic elliptic equation in an annular domain ( ) with the boundary conditions and , where is continuous. Under certain inequality conditions on f involving the principal eigenvalue of the Laplace operator with boundary condition , an existence result and a uniqueness result are obtained. The inequality conditions allow for to be a superlinear growth on as . Our discussion is based on the Leray–Schauder fixed point theorem, spectral theory of linear operators and technique of prior estimates.
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(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems)
Open AccessArticle
Exploring Clique Transversal Problems for d-degenerate Graphs with Fixed d: From Polynomial-Time Solvability to Parameterized Complexity
by
Chuan-Min Lee
Axioms 2024, 13(6), 382; https://doi.org/10.3390/axioms13060382 - 4 Jun 2024
Abstract
This paper explores the computational challenges of clique transversal problems in d-degenerate graphs, which are commonly encountered across theoretical computer science and various network applications. We examine d-degenerate graphs to highlight their utility in representing sparse structures and assess several variations
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This paper explores the computational challenges of clique transversal problems in d-degenerate graphs, which are commonly encountered across theoretical computer science and various network applications. We examine d-degenerate graphs to highlight their utility in representing sparse structures and assess several variations of clique transversal problems, including the b-fold and -clique transversal problems, focusing on their computational complexities for different graph categories. Our analysis identifies that certain instances of these problems are polynomial-time solvable in specific graph classes, such as 1-degenerate or 2-degenerate graphs. However, for d-degenerate graphs where , these problems generally escalate to NP-completeness. We also explore the parameterized complexity, pinpointing specific conditions that render these problems fixed-parameter tractable.
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(This article belongs to the Special Issue Advances in Graph Theory and Combinatorial Optimization)
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A Selberg Trace Formula for GL3(
by
Daksh Aggarwal, Asghar Ghorbanpour, Masoud Khalkhali, Jiyuan Lu, Balázs Németh and C Shijia Yu
Axioms 2024, 13(6), 381; https://doi.org/10.3390/axioms13060381 - 4 Jun 2024
Abstract
In this paper, we prove a discrete analog of the Selberg Trace Formula for the group By considering a cubic extension of the finite field , we define an analog of the upper half-space
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In this paper, we prove a discrete analog of the Selberg Trace Formula for the group By considering a cubic extension of the finite field , we define an analog of the upper half-space and an action of on it. To compute the orbital sums, we explicitly identify the double coset spaces and fundamental domains in our upper half space. To understand the spectral side of the trace formula, we decompose the induced representation for and
Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)
Open AccessArticle
Abelian Extensions of Modified λ-Differential Left-Symmetric Algebras and Crossed Modules
by
Fuyang Zhu, Taijie You and Wen Teng
Axioms 2024, 13(6), 380; https://doi.org/10.3390/axioms13060380 - 4 Jun 2024
Abstract
In this paper, we define a cohomology theory of a modified -differential left-symmetric algebra. Moreover, we introduce the notion of modified -differential left-symmetric 2-algebras, which is the categorization of a modified -differential left-symmetric algebra. As applications of cohomology, we classify
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In this paper, we define a cohomology theory of a modified -differential left-symmetric algebra. Moreover, we introduce the notion of modified -differential left-symmetric 2-algebras, which is the categorization of a modified -differential left-symmetric algebra. As applications of cohomology, we classify linear deformations and abelian extensions of modified -differential left-symmetric algebras using the second cohomology group and classify skeletal modified -differential left-symmetric 2-algebra using the third cohomology group. Finally, we show that strict modified -differential left-symmetric 2-algebras are equivalent to crossed modules of modified -differential left-symmetric algebras.
Full article
(This article belongs to the Section Algebra and Number Theory)
Open AccessArticle
Fuzzy Testing Model Built on Confidence Interval of Process Capability Index CPMK
by
Wei Lo, Tsun-Hung Huang, Kuen-Suan Chen, Chun-Min Yu and Chun-Ming Yang
Axioms 2024, 13(6), 379; https://doi.org/10.3390/axioms13060379 - 4 Jun 2024
Abstract
A variety of process capability indices are applied to the quantitative measurement of the potential and performance of processes in manufacturing. As it is easy to understand the formulae of these indices, this method is easy to apply. Furthermore, a process capability index
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A variety of process capability indices are applied to the quantitative measurement of the potential and performance of processes in manufacturing. As it is easy to understand the formulae of these indices, this method is easy to apply. Furthermore, a process capability index is frequently utilized by a manufacturer to gauge the quality of a process. This index can be utilized by not only an internal process engineer to assess the quality of the process but also as a communication tool for an external sales department. When the manufacturing process deviates from the target value T, the process capability index CPMK can be quickly detected, which is conducive to the promotion of smart manufacturing. Therefore, this study applied the index CPMK as an evaluation tool for process quality. As noted by some studies, process capability indices have unknown parameters and therefore must be estimated from sample data. Additionally, numerous studies have addressed that it is essential for companies to establish a rapid response mechanism, as they wish to make decisions quickly when using a small sample size. Considering the small sample size, this study proposed a 100 (1 − α)% confidence interval for the process capability index CPMK based on suggestions from previous studies. Subsequently, this study built a fuzzy testing model on the 100 (1 − α)% confidence interval for the process capability index CPMK. This fuzzy testing model can help enterprises make decisions rapidly with a small sample size, meeting their expectation of having a rapid response mechanism.
Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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Research on the Validity of Bootstrap LM-Error Test in Spatial Random Effect Models
by
Tongxian Ren, Lin Xu and Zhengliang Ren
Axioms 2024, 13(6), 378; https://doi.org/10.3390/axioms13060378 - 4 Jun 2024
Abstract
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Under the condition of non-classical distributed errors, the test for spatial dependence in spatial panel data models is still a problem waiting to be solved. In this paper, we apply the FDB (Fast Double Bootstrap) method to spatial panel data models to test
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Under the condition of non-classical distributed errors, the test for spatial dependence in spatial panel data models is still a problem waiting to be solved. In this paper, we apply the FDB (Fast Double Bootstrap) method to spatial panel data models to test spatial dependence. In order to research the validity of the Bootstrap LM-Error test in spatial random effect models under the condition that the error term obeys a normal distribution, heteroscedasticity, or time-series correlation, we construct Bootstrap LM-Error statistics and make use of Monte Carlo simulation from size distortion and power aspects to carry out our research. The Monte Carlo simulation results show that the asymptotic LM-Error test in the spatial random effects model has a large size of distortion when the error term disobeys classical distribution. However, the FDB LM-Error test can effectively correct the size distortion of the asymptotic test with the precondition that there is nearly no loss of power in the FDB test. Obviously, compared to the asymptotic LM-Error test, the FDB LM-Error test is a more valid method to test spatial dependence in a spatial random effects model.
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Open AccessArticle
Analytical and Numerical Investigation for the Inhomogeneous Pantograph Equation
by
Faten Aldosari and Abdelhalim Ebaid
Axioms 2024, 13(6), 377; https://doi.org/10.3390/axioms13060377 - 4 Jun 2024
Abstract
This paper investigates the inhomogeneous version of the pantograph equation. The current model includes the exponential function as the inhomogeneous part of the pantograph equation. The Maclaurin series expansion (MSE) is a well-known standard method for solving initial value problems; it may be
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This paper investigates the inhomogeneous version of the pantograph equation. The current model includes the exponential function as the inhomogeneous part of the pantograph equation. The Maclaurin series expansion (MSE) is a well-known standard method for solving initial value problems; it may be easier than any other approaches. Moreover, the MSE can be used in a straightforward manner in contrast to the other analytical methods. Thus, the MSE is extended in this paper to treat the inhomogeneous pantograph equation. The solution is obtained in a closed series form with an explicit formula for the series coefficients and the convergence of the series is proved. Also, the analytic solutions of some models in the literature are recovered as special cases of the present work. The accuracy of the results is examined through several comparisons with the available exact solutions of some classes in the relevant literature. Finally, the residuals are calculated and then used to validate the accuracy of the present approximations for some classes which have no exact solutions.
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(This article belongs to the Special Issue Difference, Functional, and Related Equations)
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Asymptotic Conformality and Polygonal Approximation
by
Samuel L. Krushkal
Axioms 2024, 13(6), 376; https://doi.org/10.3390/axioms13060376 - 3 Jun 2024
Abstract
Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichmüller space theory and have important applications involving conformal and quasiconformal
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Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichmüller space theory and have important applications involving conformal and quasiconformal maps. The paper provides an approximative characterization of local conformality and its connection with univalent polynomials. Also, some other quantitative applications of this connection are given.
Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications II)
Open AccessArticle
Edge DP-Coloring in K4-Minor Free Graphs and Planar Graphs
by
Jingxiang He and Ming Han
Axioms 2024, 13(6), 375; https://doi.org/10.3390/axioms13060375 - 3 Jun 2024
Abstract
The edge DP-chromatic number of G, denoted by , is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of
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The edge DP-chromatic number of G, denoted by , is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of -minor free graph G with is . In this paper, we prove that if G is a -minor free graph, then , and equality holds for some -minor free graph G with . Moreover, if G is a planar graph with and with no intersecting triangles, then .
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(This article belongs to the Special Issue Advances in Mathematics: Theory and Applications)
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An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion
by
FeiXiang Yang, TingLei Wang and Yun Huang
Axioms 2024, 13(6), 374; https://doi.org/10.3390/axioms13060374 - 2 Jun 2024
Abstract
The problem of inverting dynamic complex matrices remains a central and intricate challenge that has garnered significant attention in scientific and mathematical research. The zeroing neural network (ZNN) has been a notable approach, utilizing time derivatives for real-time solutions in noiseless settings. However,
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The problem of inverting dynamic complex matrices remains a central and intricate challenge that has garnered significant attention in scientific and mathematical research. The zeroing neural network (ZNN) has been a notable approach, utilizing time derivatives for real-time solutions in noiseless settings. However, real-world disturbances pose a significant challenge to a ZNN’s convergence. We design an accelerated dual-integral structure zeroing neural network (ADISZNN), which can enhance convergence and restrict linear noise, particularly in complex domains. Based on the Lyapunov principle, theoretical analysis proves the convergence and robustness of ADISZNN. We have selectively integrated the SBPAF activation function, and through theoretical dissection and comparative experimental validation we have affirmed the efficacy and accuracy of our activation function selection strategy. After conducting numerous experiments, we discovered oscillations and improved the model accordingly, resulting in the ADISZNN-Stable model. This advanced model surpasses current models in both linear noisy and noise-free environments, delivering a more rapid and stable convergence, marking a significant leap forward in the field.
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(This article belongs to the Special Issue Differential Equations and Inverse Problems)
Open AccessArticle
On Properties and Classification of a Class of 4-Dimensional 3-Hom-Lie Algebras with a Nilpotent Twisting Map
by
Abdennour Kitouni and Sergei Silvestrov
Axioms 2024, 13(6), 373; https://doi.org/10.3390/axioms13060373 - 2 Jun 2024
Abstract
The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map and eight structure constants as parameters. Derived series and central descending series are studied for all algebras
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The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map and eight structure constants as parameters. Derived series and central descending series are studied for all algebras in this class and are used to divide it into five non-isomorphic subclasses. The levels of solvability and nilpotency of the 3-Hom-Lie algebras in these five classes are obtained. Building upon that, all algebras of this class are classified up to Hom-algebra isomorphism. Necessary and sufficient conditions for multiplicativity of general -dimensional n-Hom-Lie algebras, as well as for algebras in the considered class, are obtained in terms of the structure constants and the twisting map. Furthermore, for some algebras in this class, it is determined whether the terms of the derived and central descending series are weak subalgebras, Hom-subalgebras, weak ideals, or Hom-ideals.
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(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications)
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Mathematical Model of the Evolution of a Simple Dynamic System with Dry Friction
by
Stelian Alaci, Florina-Carmen Ciornei, Costica Lupascu and Ionut-Cristian Romanu
Axioms 2024, 13(6), 372; https://doi.org/10.3390/axioms13060372 - 31 May 2024
Abstract
A simple dynamic system with dry friction is studied theoretically and numerically. Models of systems including dry friction are not easily obtained, as defining the relationship between the friction force and the relative velocity presents a significant challenge. It is known that friction
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A simple dynamic system with dry friction is studied theoretically and numerically. Models of systems including dry friction are not easily obtained, as defining the relationship between the friction force and the relative velocity presents a significant challenge. It is known that friction forces exhibit notable discontinuities when there is a change in the direction of motion. Additionally, when the relative motion ceases, the friction force can assume any value within a certain range. In the literature, numerous models of dry friction are presented, and most of them assume a biunivocal dependency of the friction force with respect to relative velocity. The dynamic system considered here is a tilted rod with spherical ends, initially at rest. Dry friction forces are evident at the contact point with the horizontal plane. The ball–plane contact highlights the rolling friction or/and sliding friction. The problem is theoretically solved after adopting one of the two cases of friction: rolling friction or sliding friction. The nonlinear differential equations of motion have been derived, along with expressions for the magnitude of the normal reaction and the friction force. The results of the model are displayed graphically for three different sets of values for the coefficient of friction. It is revealed that there is a critical value of the coefficient of friction that determines the transition from rolling to sliding regimes. To validate the theoretical model, dynamic simulation software was utilised. The excellent match between the theoretical predictions and the results from the numerical simulation confirms the accuracy of the proposed analytical solution.
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(This article belongs to the Special Issue Applied Mathematical Modeling and Optimization)
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On Approximate Variational Inequalities and Bilevel Programming Problems
by
Balendu Bhooshan Upadhyay, Ioan Stancu-Minasian, Subham Poddar and Priyanka Mishra
Axioms 2024, 13(6), 371; https://doi.org/10.3390/axioms13060371 - 30 May 2024
Abstract
In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local -quasi solutions of the BLPP,
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In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local -quasi solutions of the BLPP, under generalized approximate convexity assumptions, via limiting subdifferentials. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (KKM)-Fan’s lemma, we derive some existence results for the solutions of AMTVI and ASTVI. We have furnished suitable, non-trivial, illustrative examples to demonstrate the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that explores relationships between the approximate variational inequalities and BLPP under the assumptions of generalized approximate convexity by employing the powerful tool of limiting subdifferentials.
Full article
(This article belongs to the Special Issue Research on Fixed Point Theory and Application)
Open AccessArticle
Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor
by
Mohd Danish Siddiqi and Rawan Bossly
Axioms 2024, 13(6), 370; https://doi.org/10.3390/axioms13060370 - 30 May 2024
Abstract
In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient
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In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient Ricci solitons. We also characterize anti-invariant, invariant, quasi-umbilical submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection for which the same inequality case holds. Finally, we deduce the above inequalities in terms of a scalar concircular field on submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection.
Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)
Open AccessArticle
A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions
by
Jean-Renaud Pycke
Axioms 2024, 13(6), 369; https://doi.org/10.3390/axioms13060369 - 30 May 2024
Abstract
We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy enables us to introduce a discrete Cramér–von Mises
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We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy enables us to introduce a discrete Cramér–von Mises statistic and show that this statistic satisfies a property of local asymptotic Bahadur optimality for a statistical test involving the classical hypergeometric distributions. Our statistic and the goodness-of-fit problem we deal with are based on basic properties of Hahn polynomials and are, therefore, subject to some extension to all families of classical orthogonal polynomials, as well as their q-analogues. Due probably to computational difficulties, the family of discrete Cramér–von Mises statistics has received less attention than its continuous counterpart—the aim of this article is to bridge part of this gap.
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(This article belongs to the Special Issue New Trends in Discrete Probability and Statistics)
Open AccessArticle
A New Hybrid Approach for Clustering, Classification, and Prediction of World Development Indicators Combining General Type-2 Fuzzy Systems and Neural Networks
by
Martha Ramírez, Patricia Melin and Oscar Castillo
Axioms 2024, 13(6), 368; https://doi.org/10.3390/axioms13060368 - 30 May 2024
Abstract
Economic risk is a probability that measures the possible alterations, as well as the uncertainty, generated by multiple internal or external factors. Sometimes it could cause the impossibility of guaranteeing the level of compliance with organizational goals and objectives, which is why for
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Economic risk is a probability that measures the possible alterations, as well as the uncertainty, generated by multiple internal or external factors. Sometimes it could cause the impossibility of guaranteeing the level of compliance with organizational goals and objectives, which is why for their administration they are frequently divided into multiple categories according to their consequences and impact. Global indicators are dynamic and sometimes the correlation is uncertain because they depend largely on a combination of economic, social, and environmental factors. Thus, our proposal consists of a model for prediction and classification of multivariate risk factors such as birth rate and population growth, among others, using multiple neural networks and General Type-2 fuzzy systems. The contribution is the proposal to integrate multiple variables of several time series using both supervised and unsupervised neural networks, and a generalized Type-2 fuzzy integration. Results show the advantages of utilizing the method for the fuzzy integration of multiple time series attributes, with which the user can then prevent future threats from the global environment that impact the scheduled compliance process.
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(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Fuzzy Modeling, Optimization and Computational Intelligence)
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Differential Equations and Dynamical Systems
Collection Editor: Feliz Manuel Minhós