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Axioms, Volume 13, Issue 7 (July 2024) – 59 articles

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19 pages, 296 KiB  
Article
On Some New Dynamic Hilbert-Type Inequalities Across Time Scales
by Mohammed Zakarya, Ahmed I. Saied, Amirah Ayidh I Al-Thaqfan, Maha Ali and Haytham M. Rezk
Axioms 2024, 13(7), 475; https://doi.org/10.3390/axioms13070475 (registering DOI) - 14 Jul 2024
Viewed by 97
Abstract
In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales T. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our findings (when T=N and [...] Read more.
In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales T. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our findings (when T=N and T=R), we obtain the discrete and continuous analogues of previously established inequalities. Additionally, we derive other inequalities for different time scales, such as T=qN0 for q>1, which, to the best of the authors’ knowledge, is a largely novel conclusion. Full article
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
17 pages, 309 KiB  
Article
Stability of Fixed Points of Partial Contractivities and Fractal Surfaces
by María A. Navascués
Axioms 2024, 13(7), 474; https://doi.org/10.3390/axioms13070474 (registering DOI) - 13 Jul 2024
Viewed by 184
Abstract
In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations [...] Read more.
In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
21 pages, 476 KiB  
Article
Modeling Data with Extreme Values Using Three-Spliced Distributions
by Adrian Bâcă and Raluca Vernic
Axioms 2024, 13(7), 473; https://doi.org/10.3390/axioms13070473 (registering DOI) - 13 Jul 2024
Viewed by 118
Abstract
When data exhibit a high frequency of small to medium values and a low frequency of large values, fitting a classical distribution might fail. This is why spliced models defined from different distributions on distinct intervals are proposed in the literature. In contrast [...] Read more.
When data exhibit a high frequency of small to medium values and a low frequency of large values, fitting a classical distribution might fail. This is why spliced models defined from different distributions on distinct intervals are proposed in the literature. In contrast to the intensive study of two-spliced distributions, the case with more than two components is scarcely approached. In this paper, we focus on three-spliced distributions and on their ability to improve the modeling of extreme data. For this purpose, we consider a popular insurance data set related to Danish fire losses, to which we fit several three-spliced distributions; moreover, the results are compared to the best-fitted two-spliced distributions from previous studies. Full article
33 pages, 3534 KiB  
Article
Adding a Degree of Certainty to Deductions in a Fuzzy Temporal Constraint Prolog: FTCProlog
by María-Antonia Cárdenas-Viedma
Axioms 2024, 13(7), 472; https://doi.org/10.3390/axioms13070472 - 12 Jul 2024
Viewed by 260
Abstract
The management of time is essential in most AI-related applications. In addition, we know that temporal information is often not precise. In fact, in most cases, it is necessary to deal with imprecision and/or uncertainty. On the other hand, there is the need [...] Read more.
The management of time is essential in most AI-related applications. In addition, we know that temporal information is often not precise. In fact, in most cases, it is necessary to deal with imprecision and/or uncertainty. On the other hand, there is the need to handle the implicit common-sense information present in many temporal statements. In this paper, we present FTCProlog, a logic programming language capable of handling fuzzy temporal constraints soundly and efficiently. The main difference of FTCProlog with respect to its predecessor, PROLogic, is its ability to associate a certainty index with deductions obtained through SLD-resolution. This resolution is based on a proposal within the theoretical logical framework FTCLogic. This model integrates a first-order logic based on possibilistic logic with the Fuzzy Temporal Constraint Networks (FTCNs) that allow efficient time management. The calculation of the certainty index can be useful in applications where one wants to verify the extent to which the times elapsed between certain events follow a given temporal pattern. In this paper, we demonstrate that the calculation of this index respects the properties of the theoretical model regarding its semantics. FTCProlog is implemented in Haskell. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Its Applications)
25 pages, 541 KiB  
Article
Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications
by Miguel Vivas Cortez, Ali Althobaiti, Abdulrahman F. Aljohani and Saad Althobaiti
Axioms 2024, 13(7), 471; https://doi.org/10.3390/axioms13070471 - 12 Jul 2024
Viewed by 256
Abstract
Convex inequalities and fuzzy-valued calculus converge to form a comprehensive mathematical framework that can be employed to understand and analyze a broad spectrum of issues. This paper utilizes fuzzy Aumman’s integrals to establish integral inequalities of Hermite-Hahadard, Fejér, and Pachpatte types within up [...] Read more.
Convex inequalities and fuzzy-valued calculus converge to form a comprehensive mathematical framework that can be employed to understand and analyze a broad spectrum of issues. This paper utilizes fuzzy Aumman’s integrals to establish integral inequalities of Hermite-Hahadard, Fejér, and Pachpatte types within up and down (U·D) relations and over newly defined class U·D-ħ-Godunova–Levin convex fuzzy-number mappings. To demonstrate the unique properties of U·D-relations, recent findings have been developed using fuzzy Aumman’s, as well as various other fuzzy partial order relations that have notable deficiencies outlined in the literature. Several compelling examples were constructed to validate the derived results, and multiple notes were provided to illustrate, depending on the configuration, that this type of integral operator generalizes several previously documented conclusions. This endeavor can potentially advance mathematical theory, computational techniques, and applications across various fields. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities)
8 pages, 238 KiB  
Article
An Example of a Continuous Field of Roe Algebras
by Vladimir Manuilov
Axioms 2024, 13(7), 470; https://doi.org/10.3390/axioms13070470 - 12 Jul 2024
Viewed by 166
Abstract
The Roe algebra C*(X) is a noncommutative C*-algebra reflecting metric properties of a space X, and it is interesting to understand the correlation between the Roe algebra of X and the (uniform) Roe algebra of its [...] Read more.
The Roe algebra C*(X) is a noncommutative C*-algebra reflecting metric properties of a space X, and it is interesting to understand the correlation between the Roe algebra of X and the (uniform) Roe algebra of its discretization. Here, we perform a minor step in this direction in the simplest non-trivial example, namely X=R, by constructing a continuous field of C*-algebras over [0,1], with the fibers over non-zero points constituting the uniform C*-algebra of the integers, and the fibers over 0 constituting a C*-algebra related to R. Full article
(This article belongs to the Section Mathematical Analysis)
10 pages, 272 KiB  
Article
Impact of Risk Aversion in Fuzzy Bimatrix Games
by Chuanyang Xu, Wanting Zhao and Zhongwei Feng
Axioms 2024, 13(7), 469; https://doi.org/10.3390/axioms13070469 - 11 Jul 2024
Viewed by 232
Abstract
In bimatrix games with symmetric triangular fuzzy payoffs, our work defines an (α, β)-risk aversion Nash equilibrium ((α, β)-RANE) and presents its sufficient and necessary condition. Our work also discusses the relationships between the (α, [...] Read more.
In bimatrix games with symmetric triangular fuzzy payoffs, our work defines an (α, β)-risk aversion Nash equilibrium ((α, β)-RANE) and presents its sufficient and necessary condition. Our work also discusses the relationships between the (α, β)-RANE and a mixed-strategy Nash equilibrium (MSNE) in a bimatrix game with a risk-averse player 2 and certain payoffs. Finally, considering 2 × 2 bimatrix games with STFPs, we find the conditions where the increase in player 2’s risk-aversion level hurts or benefits himself/herself. Full article
20 pages, 1669 KiB  
Article
Pole Analysis of the Inter-Replica Correlation Function in a Two-Replica System as a Binary Mixture: Mean Overlap in the Cluster Glass Phase
by Hiroshi Frusawa
Axioms 2024, 13(7), 468; https://doi.org/10.3390/axioms13070468 - 11 Jul 2024
Viewed by 167
Abstract
To investigate the cluster glass phase of ultrasoft particles, we examine an annealed two-replica system endowed with an attractive inter-replica field similar to that of a binary symmetric electrolyte. Leveraging this analogy, we conduct pole analysis on the total correlation functions in the [...] Read more.
To investigate the cluster glass phase of ultrasoft particles, we examine an annealed two-replica system endowed with an attractive inter-replica field similar to that of a binary symmetric electrolyte. Leveraging this analogy, we conduct pole analysis on the total correlation functions in the two-replica system where the inter-replica field will eventually be switched off. By synthesizing discussions grounded in the pole analysis with a hierarchical view of the free-energy landscape, we derive an analytical form of the mean overlap between two replicas within the mean field approximation of the Gaussian core model. This formula elucidates novel numerical findings observed in the cluster glass phase. Full article
(This article belongs to the Section Mathematical Physics)
15 pages, 282 KiB  
Article
Integral Equations: New Solutions via Generalized Best Proximity Methods
by Amer Hassan Albargi and Jamshaid Ahmad
Axioms 2024, 13(7), 467; https://doi.org/10.3390/axioms13070467 - 11 Jul 2024
Viewed by 153
Abstract
This paper introduces the concept of proximal (α,F)-contractions in F-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial [...] Read more.
This paper introduces the concept of proximal (α,F)-contractions in F-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond. Full article
(This article belongs to the Special Issue Research on Fixed Point Theory and Application)
12 pages, 246 KiB  
Article
Right Quantum Calculus on Finite Intervals with Respect to Another Function and Quantum Hermite–Hadamard Inequalities
by Asawathep Cuntavepanit, Sotiris K. Ntouyas and Jessada Tariboon
Axioms 2024, 13(7), 466; https://doi.org/10.3390/axioms13070466 - 10 Jul 2024
Viewed by 203
Abstract
In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The [...] Read more.
In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The new definitions generalize the previous existing results in the literature. We provide applications of the newly defined quantum calculus by obtaining new Hermite–Hadamard-type inequalities for convex, h-convex, and modified h-convex functions. Full article
31 pages, 741 KiB  
Article
Fuzzy Milne, Ostrowski, and Hermite–Hadamard-Type Inequalities for ħ-Godunova–Levin Convexity and Their Applications
by Juan Wang, Valer-Daniel Breaz, Yasser Salah Hamed, Luminita-Ioana Cotirla and Xuewu Zuo
Axioms 2024, 13(7), 465; https://doi.org/10.3390/axioms13070465 - 10 Jul 2024
Viewed by 172
Abstract
In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann’s integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class, ħ-Godunova–Levin convex fuzzy number mappings, to derive [...] Read more.
In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann’s integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class, ħ-Godunova–Levin convex fuzzy number mappings, to derive Ostrowski’s and Hermite–Hadamard-type inequalities for fuzzy number mappings. Using the fuzzy Kulisch–Miranker order, we also establish connections with Hermite–Hadamard-type inequalities. Furthermore, we explore novel ideas and results based on Hermite–Hadamard–Fejér and provide examples and applications to illustrate our findings. Some very interesting examples are also provided to discuss the validation of the main results. Additionally, some new exceptional and classical outcomes have been obtained, which can be considered as applications of our main results. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
36 pages, 1658 KiB  
Article
Mathematical Modeling of Immune Dynamics in Chronic Myeloid Leukemia Therapy: Unraveling Allergic Reactions and T Cell Subset Modulation by Imatinib
by Rawan Abdullah, Irina Badralexi, Laurance Fakih and Andrei Halanay
Axioms 2024, 13(7), 464; https://doi.org/10.3390/axioms13070464 - 10 Jul 2024
Viewed by 458
Abstract
This mathematical model delves into the dynamics of the immune system during Chronic Myeloid Leukemia (CML) therapy with imatinib. The focus lies in elucidating the allergic reactions induced by imatinib, specifically its impact on T helper (Th) cells and Treg cells. The model [...] Read more.
This mathematical model delves into the dynamics of the immune system during Chronic Myeloid Leukemia (CML) therapy with imatinib. The focus lies in elucidating the allergic reactions induced by imatinib, specifically its impact on T helper (Th) cells and Treg cells. The model integrates cellular interactions, drug pharmacokinetics, and immune responses to unveil the mechanisms underlying the dominance of Th2 over Th1 and Treg cells, leading to allergic manifestations. Through a system of coupled delay differential equations, the interplay between healthy and leukemic cells, the influence of imatinib on T cell dynamics, and the emergence of allergic reactions during CML therapy are explored. Full article
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12 pages, 271 KiB  
Article
Special Geometric Objects in Generalized Riemannian Spaces
by Marko Stefanović, Nenad Vesić, Dušan Simjanović and Branislav Randjelović
Axioms 2024, 13(7), 463; https://doi.org/10.3390/axioms13070463 - 9 Jul 2024
Viewed by 190
Abstract
In this paper, we obtained the geometrical objects that are common in different definitions of the generalized Riemannian spaces. These objects are analogies to the Thomas projective parameter and the Weyl projective tensor. After that, we obtained some geometrical objects important for applications [...] Read more.
In this paper, we obtained the geometrical objects that are common in different definitions of the generalized Riemannian spaces. These objects are analogies to the Thomas projective parameter and the Weyl projective tensor. After that, we obtained some geometrical objects important for applications in physics. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
29 pages, 341 KiB  
Article
Smooth Logistic Real and Complex, Ordinary and Fractional Neural Network Approximations over Infinite Domains
by George A. Anastassiou
Axioms 2024, 13(7), 462; https://doi.org/10.3390/axioms13070462 - 9 Jul 2024
Viewed by 391
Abstract
In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All [...] Read more.
In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are obtained from the whole real line. The neural network operators used here are of the quasi-interpolation type: basic ones, Kantorovich-type ones, and those of the quadrature type. We provide pointwise and uniform approximations with rates. We finish with their applications. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory III)
21 pages, 747 KiB  
Article
A Reduced-Dimension Weighted Explicit Finite Difference Method Based on the Proper Orthogonal Decomposition Technique for the Space-Fractional Diffusion Equation
by Xuehui Ren and Hong Li
Axioms 2024, 13(7), 461; https://doi.org/10.3390/axioms13070461 - 8 Jul 2024
Viewed by 229
Abstract
A kind of reduced-dimension method based on a weighted explicit finite difference scheme and the proper orthogonal decomposition (POD) technique for diffusion equations with Riemann–Liouville fractional derivatives in space are discussed. The constructed approximation method written in matrix form can not only ensure [...] Read more.
A kind of reduced-dimension method based on a weighted explicit finite difference scheme and the proper orthogonal decomposition (POD) technique for diffusion equations with Riemann–Liouville fractional derivatives in space are discussed. The constructed approximation method written in matrix form can not only ensure a sufficient accuracy order but also reduce the degrees of freedom, decrease storage requirements, and accelerate the computation rate. Uniqueness, stabilization, and error estimation are demonstrated by matrix analysis. The procedural steps of the POD algorithm, which reduces dimensionality, are outlined. Numerical simulations to assess the viability and effectiveness of the reduced-dimension weighted explicit finite difference method are given. A comparison between the reduced-dimension method and the classical weighted explicit finite difference scheme is presented, including the error in the L2 norm, the accuracy order, and the CPU time. Full article
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19 pages, 355 KiB  
Article
The Split Equality Fixed-Point Problem and Its Applications
by Lawan Bulama Mohammed and Adem Kilicman
Axioms 2024, 13(7), 460; https://doi.org/10.3390/axioms13070460 - 8 Jul 2024
Viewed by 222
Abstract
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life. To address this issue, we studied the SEFPP [...] Read more.
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life. To address this issue, we studied the SEFPP involving a class of quasi-pseudocontractive mappings in Hilbert spaces and constructed novel algorithms in this regard, and we proved the algorithms’ convergences both with and without prior knowledge of the operator norm for bounded and linear mappings. Additionally, we gave applications and numerical examples of our findings. A variety of well-known discoveries revealed in the literature are generalized by the findings presented in this work. Full article
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12 pages, 593 KiB  
Article
A Method for Calculating the Reliability of 2-Separable Networks and Its Applications
by Jing Liang, Haixing Zhao and Sun Xie
Axioms 2024, 13(7), 459; https://doi.org/10.3390/axioms13070459 - 8 Jul 2024
Viewed by 234
Abstract
This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering [...] Read more.
This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering independent random failures of edges with equal probability q, this method can accurately calculate the reliability of 2-separable networks, and its effectiveness and accuracy are verified through examples. In addition, to demonstrate the generality of our method, we have also applied it to other 2-separable networks with fractal structures and proposed linear algorithms for calculating their all-terminal reliability. Full article
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31 pages, 1380 KiB  
Article
Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results
by Marlon Moscoso-Martínez, Francisco I. Chicharro, Alicia Cordero, Juan R. Torregrosa and Gabriela Ureña-Callay
Axioms 2024, 13(7), 458; https://doi.org/10.3390/axioms13070458 - 7 Jul 2024
Viewed by 250
Abstract
In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton’s scheme but includes an additional Newton step with a weight function and a “frozen” derivative, that is, [...] Read more.
In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton’s scheme but includes an additional Newton step with a weight function and a “frozen” derivative, that is, the same derivative than in the previous step. Initially, we develop a quad-parametric class with a first-order convergence rate. Subsequently, by restricting one of its parameters, we accelerate the convergence to achieve a third-order uni-parametric family. We thoroughly investigate the convergence properties of this final class of iterative methods, assess its stability through dynamical tools, and evaluate its performance on a set of test problems. We conclude that there exists one optimal fourth-order member of this class, in the sense of Kung–Traub’s conjecture. Our analysis includes stability surfaces and dynamical planes, revealing the intricate nature of this family. Notably, our exploration of stability surfaces enables the identification of specific family members suitable for scalar functions with a challenging convergence behavior, as they may exhibit periodical orbits and fixed points with attracting behavior in their corresponding dynamical planes. Furthermore, our dynamical study finds members of the family of iterative methods with exceptional stability. This property allows us to converge to the solution of practical problem-solving applications even from initial estimations very far from the solution. We confirm our findings with various numerical tests, demonstrating the efficiency and reliability of the presented family of iterative methods. Full article
20 pages, 10798 KiB  
Article
Visualization of Isometric Deformations of Helicoidal CMC Surfaces
by Filip Vukojević and Miroslava Antić
Axioms 2024, 13(7), 457; https://doi.org/10.3390/axioms13070457 - 6 Jul 2024
Viewed by 301
Abstract
Helicoidal surfaces of constant mean curvature were fully described by do Carmo and Dajczer. However, the obtained parameterizations are given in terms of somewhat complicated integrals, and as a consequence, not many examples of such surfaces are visualized. In this paper, by using [...] Read more.
Helicoidal surfaces of constant mean curvature were fully described by do Carmo and Dajczer. However, the obtained parameterizations are given in terms of somewhat complicated integrals, and as a consequence, not many examples of such surfaces are visualized. In this paper, by using these methods in some particular cases, we provide several interesting visualizations involving these surfaces, mostly as an isometric deformation of a rotational surface. We also give interpretations of some older results involving helicoidal surfaces, motivated by the work carried out by Malkowsky and Veličković. All of the graphics in this paper were created in Wolfram Mathematica. Full article
(This article belongs to the Special Issue Mathematics, Computer Graphics and Computational Visualizations)
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26 pages, 1523 KiB  
Article
Fermatean Hesitant Fuzzy Multi-Attribute Decision-Making Method with Probabilistic Information and Its Application
by Chuanyang Ruan, Xiangjing Chen and Lin Yan
Axioms 2024, 13(7), 456; https://doi.org/10.3390/axioms13070456 - 4 Jul 2024
Viewed by 284
Abstract
When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider [...] Read more.
When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider the stochastic nature of evaluation data and better quantify the importance of the attributes. To aggregate data by considering the location and importance degrees of each attribute, this paper develops a Fermatean hesitant fuzzy multi-attribute decision-making (MADM) method with probabilistic information and an ordered weighted averaging (OWA) method. The OWA method combines the concepts of weights and sorting to sort and weigh average property values based on those weights. Therefore, this novel approach assigns weights based on the decision-maker’s preferences and introduces probabilities to assess attribute importance under specific circumstances, thereby broadening the scope of information expression. Then, this paper presents four probabilistic aggregation operators under the Fermatean hesitant fuzzy environment, including the Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (FHFPOWA/FHFPOWG) operators and the generalized Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (GFHFPOWA/GFHFPOWG) operators. These new operators are designed to quantify the importance of attributes and characterize the attitudes of decision-makers using a probabilistic and weighted vector. Then, a MADM method based on these proposed operators is developed. Finally, an illustrative example of selecting the best new retail enterprise demonstrates the effectiveness and practicality of the method. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic and Multi-Criteria Decision Models)
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20 pages, 452 KiB  
Article
Some New Estimations of Ostrowski-Type Inequalities for Harmonic Fuzzy Number Convexity via Gamma, Beta and Hypergeometric Functions
by Azzh Saad Alshehry, Loredana Ciurdariu, Yaser Saber and Amal F. Soliman
Axioms 2024, 13(7), 455; https://doi.org/10.3390/axioms13070455 - 4 Jul 2024
Viewed by 254
Abstract
This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish [...] Read more.
This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish various Ostrowski-type inequalities for fuzzy-valued mappings (F·V·Ms). Furthermore, by employing diverse orders, we establish connections with the classical versions of Ostrowski-type inequalities. Additionally, we explore new ideas and results rooted in submodular measures, accompanied by examples and applications to illustrate our findings. Moreover, by using special functions, we have provided some applications of Ostrowski-type inequalities. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
13 pages, 263 KiB  
Article
Analyzing the Ricci Tensor for Slant Submanifolds in Locally Metallic Product Space Forms with a Semi-Symmetric Metric Connection
by Yanlin Li, Md Aquib, Meraj Ali Khan, Ibrahim Al-Dayel and Khalid Masood
Axioms 2024, 13(7), 454; https://doi.org/10.3390/axioms13070454 - 4 Jul 2024
Viewed by 196
Abstract
This article explores the Ricci tensor of slant submanifolds within locally metallic product space forms equipped with a semi-symmetric metric connection (SSMC). Our investigation includes the derivation of the Chen–Ricci inequality and an in-depth analysis of its equality case. More precisely, if the [...] Read more.
This article explores the Ricci tensor of slant submanifolds within locally metallic product space forms equipped with a semi-symmetric metric connection (SSMC). Our investigation includes the derivation of the Chen–Ricci inequality and an in-depth analysis of its equality case. More precisely, if the mean curvature vector at a point vanishes, then the equality case of this inequality is achieved by a unit tangent vector at the point if and only if the vector belongs to the normal space. Finally, we have shown that when a point is a totally geodesic point or is totally umbilical with n=2, the equality case of this inequality holds true for all unit tangent vectors at the point, and conversely. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application II)
20 pages, 2334 KiB  
Article
Dynamic Pricing and Inventory Strategies for Fashion Products Using Stochastic Fashion Level Function
by Wenhan Lu and Litan Yan
Axioms 2024, 13(7), 453; https://doi.org/10.3390/axioms13070453 - 4 Jul 2024
Viewed by 248
Abstract
The fashion apparel industry is facing an increasingly growing demand, compounded by the short sales lifecycle and strong seasonality of clothing, posing significant challenges to inventory management in the retail sector. Despite some retailers like Uniqlo and Zara implementing inventory management and dynamic [...] Read more.
The fashion apparel industry is facing an increasingly growing demand, compounded by the short sales lifecycle and strong seasonality of clothing, posing significant challenges to inventory management in the retail sector. Despite some retailers like Uniqlo and Zara implementing inventory management and dynamic pricing strategies, challenges persist due to the dynamic nature of fashion trends and the stochastic factors affecting inventory. To address these issues, we construct a mathematical model based on the mathematical expression of the deterministic fashion level function, where the geometric Brownian motion, widely applied in finance, is initially utilized in the stochastic fashion level function. Drawing on research findings from deteriorating inventory management and stochastic optimization, we investigate the fluctuation of inventory levels, optimal dynamic pricing, optimal production rates, and profits—four crucial indicators—via Pontryagin’s maximum principle. Analytical solutions are derived, and the numerical simulation is provided to verify and compare the proposed model with deterministic fashion level function models. The model emphasizes the importance of considering stochastic factors in decision-making processes and provides insights to enhance profitability, inventory management, and sustainable consumption in the fashion product industry. Full article
(This article belongs to the Special Issue Advances in Mathematical Modeling, Analysis and Optimization)
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11 pages, 299 KiB  
Article
Concerning Transformations of Bases Associated with Unimodular diag(1, −1, −1)-Matrices
by I. A. Shilin and Junesang Choi
Axioms 2024, 13(7), 452; https://doi.org/10.3390/axioms13070452 - 4 Jul 2024
Viewed by 276
Abstract
Considering a representation space for a group of unimodular diag(1, 1, 1)-matrices, we construct several bases whose elements are eigenfunctions of Casimir infinitesimal operators related to a reduction in the group to some [...] Read more.
Considering a representation space for a group of unimodular diag(1, 1, 1)-matrices, we construct several bases whose elements are eigenfunctions of Casimir infinitesimal operators related to a reduction in the group to some one-parameter subgroups. Finding the kernels of base transformation integral operators in terms of special functions, we consider the compositions of some of these transformations. Since composition is a ‘closed’ operation on the set of base transformations, we obtain some integral relations for the special functions involved in the above kernels. Full article
(This article belongs to the Special Issue Theory of Functions and Applications II)
11 pages, 253 KiB  
Article
Estimates of Eigenvalues and Approximation Numbers for a Class of Degenerate Third-Order Partial Differential Operators
by Mussakan Muratbekov, Ainash Suleimbekova and Mukhtar Baizhumanov
Axioms 2024, 13(7), 451; https://doi.org/10.3390/axioms13070451 - 3 Jul 2024
Viewed by 256
Abstract
In this paper, we study the spectral properties of a class of degenerate third-order partial differential operators with variable coefficients presented in a rectangle. Conditions are found to ensure the existence and compactness of the inverse operator. A theorem on estimates of approximation [...] Read more.
In this paper, we study the spectral properties of a class of degenerate third-order partial differential operators with variable coefficients presented in a rectangle. Conditions are found to ensure the existence and compactness of the inverse operator. A theorem on estimates of approximation numbers is proven. Here, we note that finding estimates of approximation numbers, as well as extremal subspaces, for a set of solutions to the equation is a task that is certainly important from both a theoretical and a practical point of view. The paper also obtained an upper bound for the eigenvalues. Note that, in this paper, estimates of eigenvalues and approximation numbers for the degenerate third-order partial differential operators are obtained for the first time. Full article
13 pages, 286 KiB  
Article
Existence and Multiplicity of Nontrivial Solutions for Semilinear Elliptic Equations Involving Hardy–Sobolev Critical Exponents
by Yonghong Fan, Wenheng Sun and Linlin Wang
Axioms 2024, 13(7), 450; https://doi.org/10.3390/axioms13070450 - 3 Jul 2024
Viewed by 277
Abstract
A class of semi-linear elliptic equations with the critical Hardy–Sobolev exponent has been considered. This model is widely used in hydrodynamics and glaciology, gas combustion in thermodynamics, quantum field theory, and statistical mechanics, as well as in gravity balance problems in galaxies. The [...] Read more.
A class of semi-linear elliptic equations with the critical Hardy–Sobolev exponent has been considered. This model is widely used in hydrodynamics and glaciology, gas combustion in thermodynamics, quantum field theory, and statistical mechanics, as well as in gravity balance problems in galaxies. The PSc sequence of energy functional was investigated, and then the mountain pass lemma was used to prove the existence of at least one nontrivial solution. Also a multiplicity result was obtained. Some known results were generalized. Full article
(This article belongs to the Section Mathematical Analysis)
11 pages, 1330 KiB  
Article
Uncertainty Degradation Model for Initiating Explosive Devices Based on Uncertain Differential Equations
by Changli Ma, Li Jia and Meilin Wen
Axioms 2024, 13(7), 449; https://doi.org/10.3390/axioms13070449 - 3 Jul 2024
Viewed by 220
Abstract
The performance degradation of initiating explosive devices is influenced by various internal and external factors, leading to uncertainties in their reliability and lifetime predictions. This paper proposes an uncertain degradation model based on uncertain differential equations, utilizing the Liu process to characterize the [...] Read more.
The performance degradation of initiating explosive devices is influenced by various internal and external factors, leading to uncertainties in their reliability and lifetime predictions. This paper proposes an uncertain degradation model based on uncertain differential equations, utilizing the Liu process to characterize the volatility in degradation rates. The ignition delay time is selected as the primary performance parameter, and the uncertain distributions, expected values and confidence intervals are derived for the model. Moment estimation techniques are employed to estimate the unknown parameters within the model. A real data analysis of ignition delay times under accelerated storage conditions demonstrates the practical applicability of the proposed method. Full article
(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)
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13 pages, 252 KiB  
Article
Center-like Subsets in Semiprime Rings with Multiplicative Derivations
by Sarah Samah Aljohani, Emine Koç Sögütcü and Nadeem ur Rehman
Axioms 2024, 13(7), 448; https://doi.org/10.3390/axioms13070448 - 2 Jul 2024
Viewed by 318
Abstract
We introduce center-like subsets Z*(A,d),Z**(A,d), where A is the ring and d is the multiplicative derivation. In the following, we take a new derivation for [...] Read more.
We introduce center-like subsets Z*(A,d),Z**(A,d), where A is the ring and d is the multiplicative derivation. In the following, we take a new derivation for the center-like subsets existing in the literature and establish the relations between these sets. In addition to these new sets, the theorems are generalized as multiplicative derivations instead of the derivations found in previous studies. Additionally, different proofs are provided for different center-like sets. Finally, we enrich this article with examples demonstrating that the hypotheses we use are necessary. Full article
27 pages, 364 KiB  
Article
Fractional-Order Sequential Linear Differential Equations with Nabla Derivatives on Time Scales
by Cheng-Cheng Zhu and Jiang Zhu
Axioms 2024, 13(7), 447; https://doi.org/10.3390/axioms13070447 - 1 Jul 2024
Viewed by 322
Abstract
In this paper, we present a general theory for fractional-order sequential differential equations with Riemann–Liouville nabla derivatives and Caputo nabla derivatives on time scales. The explicit solution, in the case of constant coefficients, for both the homogeneous and the non-homogeneous problems, are given [...] Read more.
In this paper, we present a general theory for fractional-order sequential differential equations with Riemann–Liouville nabla derivatives and Caputo nabla derivatives on time scales. The explicit solution, in the case of constant coefficients, for both the homogeneous and the non-homogeneous problems, are given using the ∇-Mittag-Leffler function, Laplace transform method, operational method and operational decomposition method. In addition, we also provide some results about a solution to a new class of fractional-order sequential differential equations with convolutional-type variable coefficients using the Laplace transform method. Full article
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
16 pages, 323 KiB  
Article
Quantization of the Rank Two Heisenberg–Virasoro Algebra
by Xue Chen
Axioms 2024, 13(7), 446; https://doi.org/10.3390/axioms13070446 - 1 Jul 2024
Viewed by 234
Abstract
Quantum groups occupy a significant position in both mathematics and physics, contributing to progress in these fields. It is interesting to obtain new quantum groups by the quantization of Lie bialgebras. In this paper, the quantization of the rank two Heisenberg–Virasoro algebra by [...] Read more.
Quantum groups occupy a significant position in both mathematics and physics, contributing to progress in these fields. It is interesting to obtain new quantum groups by the quantization of Lie bialgebras. In this paper, the quantization of the rank two Heisenberg–Virasoro algebra by Drinfel’d twists is presented, Lie bialgebra structures of which have been investigated by the authors recently. Full article
(This article belongs to the Section Algebra and Number Theory)
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