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Axioms
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ISSN (Online) 2075-1680
Published by MDPI

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Axioms, Vol. 13, Pages 494: On Some Distance Spectral Characteristics of
Trees
- Authors: Sakander Hayat, Asad Khan, Mohammed J. F. Alenazi
  First page: 494
  Abstract: Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spectrum of graph-theoretic matrices. The study of graphs with “few eigenvalues” is a contemporary problem in spectral graph theory. This paper studies graphs with few distinct distance eigenvalues. After mentioning the classification of graphs with one and two distinct distance eigenvalues, we mainly focus on graphs with three distinct distance eigenvalues. Characterizing graphs with three distinct distance eigenvalues is “highly” non-trivial. In this paper, we classify all trees whose distance matrix has precisely three distinct eigenvalues. Our proof is different from earlier existing proof of the result as our proof is extendable to other similar families such as unicyclic and bicyclic graphs. The main tools which we employ include interlacing and equitable partitions. We also list all the connected graphs on ν ≤ 6 vertices and compute their distance spectra. Importantly, all these graphs on ν ≤ 6 vertices are determined from their distance spectra. We deliver a distance cospectral pair of order 7, thus making it a distance cospectral pair of the smallest order. This paper is concluded with some future directions.
  Citation: Axioms
  PubDate: 2024-07-23
  DOI: 10.3390/axioms13080494
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 495: Matrix Factorization and Some Fast Discrete
Transforms
- Authors: Iliya Bouyukliev, Mariya Dzhumalieva-Stoeva, Paskal Piperkov
  First page: 495
  Abstract: In this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh–Hadamard transform; for odd prime fields, the Vilenkin–Chrestenson transform; and for composite fields, the trace transform. A factorization of the transform matrices using Kronecker power is given so that the considered discrete transforms are reduced to the fast discrete transforms. Examples and applications are also presented of the considered transforms in coding theory for calculating the weight distribution of a linear code.
  Citation: Axioms
  PubDate: 2024-07-23
  DOI: 10.3390/axioms13080495
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 496: Some Results on the Free Poisson Distribution
- Authors: Ayed. R. A. Alanzi, Ohud A. Alqasem, Maysaa Elmahi Abd Elwahab, Raouf Fakhfakh
  First page: 496
  Abstract: Let K+(μi)={Qsiμi,si∈(m0μi,m+μi)}, i=1,2, be two CSK families generated by the nondegenerate probability measures μ1 and μ2 with support bounded from above. Define the set of measures L=K+(μ1)•K+(μ2)={Qs1μ1•Qs2μ2,s1∈(m0μ1,m+μ1)ands2∈(m0μ2,m+μ2)}, where Qs1μ1•Qs2μ2 denotes the Fermi convolution of Qs1μ1 and Qs2μ2. We prove that if L is still a CSK family (that is, L=K+(σ) for some nondegenerate probability measure ()σ), then the probability measures σ, μ1 and μ2 are of the free Poisson type and follow the free Poisson law up to affinity. The same result, regarding the free Poisson measure, is obtained if we consider the t-deformed free convolution t replacing the Fermi convolution • in the family of measures L.
  Citation: Axioms
  PubDate: 2024-07-24
  DOI: 10.3390/axioms13080496
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 497: On a Neumann Problem with an Intrinsic
Operator
- Authors: Dumitru Motreanu, Angela Sciammetta
  First page: 497
  Abstract: This paper investigates the existence and location of solutions for a Neumann problem driven by a (p,q) Laplacian operator and with a reaction term that depends not only on the solution and its gradient but also incorporates an intrinsic operator, which is its main novelty. This paper can be seen as the study of a quasilinear Neumann problem involving an elaborated perturbation with a Nemytskij operator. The approach proceeds through a version of the sub/supersolution method, exploiting an invariance property regarding the sub/supersolution ordered interval with respect to the intrinsic operator. An example illustrates the applicability of our result.
  Citation: Axioms
  PubDate: 2024-07-25
  DOI: 10.3390/axioms13080497
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 498: A Fuzzy Logic for Semi-Overlap Functions and
Their Residua
- Authors: Lei Du, Songsong Dai, Lvqing Bi
  First page: 498
  Abstract: Semi-overlap functions as a generalization of left-continuous t-norms also have residua. In this paper, we develop a new residuated logic, SOL-logic, based on semi-overlap functions and their residua. The corresponding algebraic structures, SOL-algebras, are defined, and the completeness of SOL with respect to SOL-algebras is proved.
  Citation: Axioms
  PubDate: 2024-07-25
  DOI: 10.3390/axioms13080498
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 499: Existence Result for a Class of
Time-Fractional Nonstationary Incompressible
Navier–Stokes–Voigt Equations
- Authors: Keji Xu, Biao Zeng
  First page: 499
  Abstract: We are devoted in this work to dealing with a class of time-fractional nonstationary incompressible Navier–Stokes–Voigt equation involving the Caputo fractional derivative. By exploiting the properties of the operators in the equation, we use the Rothe method to show the existence of weak solutions to the equation by verifying all the conditions of the surjectivity theorem for nonlinear weakly continuous operators.
  Citation: Axioms
  PubDate: 2024-07-25
  DOI: 10.3390/axioms13080499
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 500: The Impact of Quasi-Conformal Curvature Tensor
on Warped Product Manifolds
- Authors: Bang-Yen Chen, Sameh Shenawy, Uday Chand De, Alaa Rabie, Nasser Bin Turki
  First page: 500
  Abstract: This work investigates the effects on the factor manifolds of a singly warped product manifold resulting from the presence of a quasi-conformally flat, quasi-conformally symmetric, or divergence-free quasi-conformal curvature tensor. Quasi-conformally flat warped product manifolds exhibit three distinct scenarios: in one scenario, the base manifold has a constant curvature, while in the other two scenarios, it is quasi-Einstein. Alternatively, the fiber manifold has a constant curvature in two scenarios and is Einstein in one scenario. Quasi-conformally symmetric warped product manifolds present three distinct cases: in the first scenario, the base manifold is Ricci-symmetric and the fiber is Einstein; in the second case, the base manifold is Cartan-symmetric and the fiber has constant curvature; and in the last case, the fiber is Cartan-symmetric, and the Ricci tensor of the base manifold is of Codazzi type. Finally, conditions are provided for singly warped product manifolds that admit a divergence-free quasi-conformal curvature tensor to ensure that the Riemann curvature tensors of the factor manifolds are harmonic.
  Citation: Axioms
  PubDate: 2024-07-26
  DOI: 10.3390/axioms13080500
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 501: Numerical Solution of Third-Order
Rosenau–Hyman and Fornberg–Whitham Equations via B-Spline
Interpolation Approach
- Authors: Tanveer Akbar, Sirajul Haq, Shams Ul Arifeen, Azhar Iqbal
  First page: 501
  Abstract: This study aims to find the numerical solution of the Rosenau–Hyman and Fornberg–Whitham equations via the quintic B-spline collocation method. Quintic B-spline, along with finite difference and theta-weighted schemes, is used for the discretization and approximation purposes. The effectiveness and robustness of the procedure is assessed by comparing the computed results with the exact and available results in the literature using absolute and relative error norms. The stability of the proposed scheme is studied using von Neumann stability analysis. Graphical representations are drawn to analyze the behavior of the solution.
  Citation: Axioms
  PubDate: 2024-07-26
  DOI: 10.3390/axioms13080501
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 502: Efficiency of a New Iterative Algorithm Using
Fixed-Point Approach in the Settings of Uniformly Convex Banach Spaces
- Authors: Rekha Srivastava, Wakeel Ahmed, Asifa Tassaddiq, Nouf Alotaibi
  First page: 502
  Abstract: In the presence of Banach spaces, a novel iterative algorithm is presented in this study using the Chatterjea–Suzuki–C (CSC) condition, and the convergence theorems are established. The efficacy of the proposed algorithm is discussed analytically and numerically. We explain the solution of the Caputo fractional differential problem using our main result and then provide the numerical simulation to validate the results. Moreover, we use MATLAB R (2021a) to compare the obtained numerical results using the new iterative algorithm with some efficient existing algorithms. The work seems to contribute to the current advancement of fixed-point approximation iterative techniques in Banach spaces.
  Citation: Axioms
  PubDate: 2024-07-26
  DOI: 10.3390/axioms13080502
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 503: Modelling Up-and-Down Moves of Binomial Option
Pricing with Intuitionistic Fuzzy Numbers
- Authors: Jorge de Andrés-Sánchez
  First page: 503
  Abstract: Since the early 21st century, within fuzzy mathematics, there has been a stream of research in the field of option pricing that introduces vagueness in the parameters governing the movement of the underlying asset price through fuzzy numbers (FNs). This approach is commonly known as fuzzy random option pricing (FROP). In discrete time, most contributions use the binomial groundwork with up-and-down moves proposed by Cox, Ross, and Rubinstein (CRR), which introduces epistemic uncertainty associated with volatility through FNs. Thus, the present work falls within this stream of literature and contributes to the literature in three ways. First, analytical developments allow for the introduction of uncertainty with intuitionistic fuzzy numbers (IFNs), which are a generalization of FNs. Therefore, we can introduce bipolar uncertainty in parameter modelling. Second, a methodology is proposed that allows for adjusting the volatility with which the option is valued through an IFN. This approach is based on the existing developments in the literature on adjusting statistical parameters with possibility distributions via historical data. Third, we introduce into the debate on fuzzy random binomial option pricing the analytical framework that should be used in modelling upwards and downwards moves. In this sense, binomial modelling is usually employed to value path-dependent options that cannot be directly evaluated with the Black–Scholes–Merton (BSM) model. Thus, one way to assess the suitability of binomial moves for valuing a particular option is to approximate the results of the BSM in a European option with the same characteristics as the option of interest. In this study, we compared the moves proposed by Renddleman and Bartter (RB) with CRR. We have observed that, depending on the moneyness degree of the option and, without a doubt, on options traded at the money, RB modelling offers greater convergence to BSM prices than does CRR modelling.
  Citation: Axioms
  PubDate: 2024-07-26
  DOI: 10.3390/axioms13080503
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 504: Geometry of Torsion Gerbes and Flat Twisted
Vector Bundles
- Authors: Byungdo Park
  First page: 504
  Abstract: Gerbes and higher gerbes are geometric cocycles representing higher degree cohomology classes, and are attracting considerable interest in differential geometry and mathematical physics. We prove that a 2-gerbe has a torsion Dixmier–Douady class if and only if the gerbe has locally constant cocycle data. As an application, we give an alternative description of flat twisted vector bundles in terms of locally constant transition maps. These results generalize to n-gerbes for n=1 and n≥3, providing insights into the structure of higher gerbes and their applications to the geometry of twisted vector bundles.
  Citation: Axioms
  PubDate: 2024-07-26
  DOI: 10.3390/axioms13080504
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 505: On Lebesgue Constants
- Authors: Manuel Duarte Ortigueira, Gabriel Bengochea
  First page: 505
  Abstract: Simple formulae for Lebesgue constants arising in the classical Fourier series approximation are obtained. Both even and odd cases are addressed, extending Fejér’s results. Asymptotic formulae are also obtained.
  Citation: Axioms
  PubDate: 2024-07-26
  DOI: 10.3390/axioms13080505
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 506: The Unified Description of Abstract Convexity
Structures
- Authors: Chunrong Mo, Yanlong Yang
  First page: 506
  Abstract: The convexity of space is essential in nonlinear analysis, variational inequalities and optimization theory because it guarantees the existence and uniqueness of solutions to a certain extent. Because of its wide variety of applications, mathematicians have extensively promoted and researched convexity. This paper reviews some representative convexity structures and discusses their relations from their definitions, unifying them in the abstract convex structure. Moreover, applications of main convexity structures including KKM theory and fixed point theory will be reviewed.
  Citation: Axioms
  PubDate: 2024-07-26
  DOI: 10.3390/axioms13080506
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 507: Positive Fitted Finite Volume Method for
Semilinear Parabolic Systems on Unbounded Domain
- Authors: Miglena N. Koleva, Lubin G. Vulkov
  First page: 507
  Abstract: This work deals with a semilinear system of parabolic partial differential equations (PDEs) on an unbounded domain, related to environmental pollution modeling. Although we study a one-dimensional sub-model of a vertical advection–diffusion, the results can be extended in each direction for any number of spatial dimensions and different boundary conditions. The transformation of the independent variable is applied to convert the nonlinear problem into a finite interval, which can be selected in advance. We investigate the positivity of the solution of the new, degenerated parabolic system with a non-standard nonlinear right-hand side. Then, we design a fitted finite volume difference discretization in space and prove the non-negativity of the solution. The full discretization is obtained by implicit–explicit time stepping, taking into account the sign of the coefficients in the nonlinear term so as to preserve the non-negativity of the numerical solution and to avoid the iteration process. The method is realized on adaptive graded spatial meshes to attain second-order of accuracy in space. Some results from computations are presented.
  Citation: Axioms
  PubDate: 2024-07-27
  DOI: 10.3390/axioms13080507
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 508: Well-Posedness of the
Schrödinger–Korteweg–de Vries System with Robin Boundary
Conditions on the Half-Line
- Authors: Po-Chun Huang, Bo-Yu Pan
  First page: 508
  Abstract: The Schrödinger–Korteweg–de Vries (SKdV) system can describe the nonlinear dynamics of phenomena such as Langmuir and ion acoustic waves, which are highly valuable for studying wave behavior and interactions. The SKdV system has wide-ranging applications in physics and applied mathematics. In this article, we investigate the local well-posedness of the SKdV system with Robin boundary conditions and polynomial terms in the Sobolev space. We want to enhance the applicability of this type of SKdV system. Our verification process is as follows: We estimate Fokas solutions for the Robin problem with external forces. Next, we define an iteration map in suitable solution space and prove the iteration map is a contraction mapping and onto some closed ball B(0,r). Finally, by the contraction mapping theorem, we obtain the uniqueness solution. Moreover, we show that the data-to-solution map is locally Lipschitz continuous and conclude with the well-posedness of the SKdV system.
  Citation: Axioms
  PubDate: 2024-07-28
  DOI: 10.3390/axioms13080508
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 509: Coefficient Estimates for New Subclasses of
Bi-Univalent Functions with Bounded Boundary Rotation by Using Faber
Polynomial Technique
- Authors: Huo Tang, Prathviraj Sharma, Srikandan Sivasubramanian
  First page: 509
  Abstract: In this article, the authors use the Faber polynomial expansions to find the general coefficient estimates for a few new subclasses of bi-univalent functions with bounded boundary rotation and bounded radius rotation. Some of the results improve the existing coefficient bounds in the literature.
  Citation: Axioms
  PubDate: 2024-07-28
  DOI: 10.3390/axioms13080509
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 510: The Mean Square of the Hurwitz Zeta-Function
in Short Intervals
- Authors: Antanas Laurinčikas, Darius Šiaučiūnas
  First page: 510
  Abstract: The Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter 0<α⩽1 is a generalization of the Riemann zeta-function ζ(s) (ζ(s,1)=ζ(s)) and was introduced at the end of the 19th century. The function ζ(s,α) plays an important role in investigations of the distribution of prime numbers in arithmetic progression and has applications in special function theory, algebraic number theory, dynamical system theory, other fields of mathematics, and even physics. The function ζ(s,α) is the main example of zeta-functions without Euler’s product (except for the cases α=1, α=1/2), and its value distribution is governed by arithmetical properties of α. For the majority of zeta-functions, ζ(s,α) for some α is universal, i.e., its shifts ζ(s+iτ,α), τ∈R, approximate every analytic function defined in the strip {s:1/2<σ<1}. For needs of effectivization of the universality property for ζ(s,α), the interval for τ must be as short as possible, and this can be achieved by using the mean square estimate for ζ(σ+it,α) in short intervals. In this paper, we obtain the bound O(H) for that mean square over the interval [T−H,T+H], with T27/82⩽H⩽Tσ and 1/2<σ⩽7/12. This is the first result on the mean square for ζ(s,α) in short intervals. In forthcoming papers, this estimate will be applied for proof of universality for ζ(s,α) and other zeta-functions in short intervals.
  Citation: Axioms
  PubDate: 2024-07-28
  DOI: 10.3390/axioms13080510
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 511: Advancing the Analysis of Extended Negative
Dependence Random Variables: A New Concentration Inequality and Its
Applications for Linear Models
- Authors: Zouaoui Chikr Elmezouar, Abderrahmane Belguerna, Hamza Daoudi, Fatimah Alshahrani, Zoubeyr Kaddour
  First page: 511
  Abstract: This paper introduces an innovative concentration inequality for Extended Negative Dependence (END) random variables, providing new insights into their almost complete convergence. We apply this inequality to analyze END variable sequences, particularly focusing on the first-order auto-regressive (AR(1)) model. This application highlights the dynamics and convergence properties of END variables, expanding the analytical tools available for their study. Our findings contribute to both the theoretical understanding and practical applications of END variables in fields such as finance and machine learning, where understanding variable dependencies is crucial.
  Citation: Axioms
  PubDate: 2024-07-29
  DOI: 10.3390/axioms13080511
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 512: Measuring Sphericity in Positive Semi-Definite
Matrices
- Authors: Dário Ferreira, Sandra S. Ferreira
  First page: 512
  Abstract: The measure of sphericity for positive semi-definite matrices plays a crucial role in understanding their geometric properties, especially in high-dimensional settings. This paper introduces a robust measure of sphericity, which remains invariant under orthogonal transformations and scaling. We explore its behavior in finite-dimensional cases. Additionally, we investigate the stochastic case by considering a normal distribution, analyzing the asymptotic normality of random matrices and its implications on the convergence properties of the proposed measure.
  Citation: Axioms
  PubDate: 2024-07-29
  DOI: 10.3390/axioms13080512
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 513: Weighted Composition Operators between
Bers-Type Spaces on Generalized Hua–Cartan–Hartogs Domains
- Authors: Ziyan Wang, Jianbing Su
  First page: 513
  Abstract: We address weighted composition operators between Bers-type spaces on generalized Hua–Cartan–Hartogs domains and provide the necessary and sufficient conditions for their boundedness and compactness. We then apply our results to study the boundedness and the compactness of weighted composition operators between Bers-type spaces on four different domains: generalized Hua domains, generalized Cartan–Hartogs domains, generalized Cartan–Hartogs domains over different Cartan domains and generalized ellipsoidal-type domains, by proving that the above four different domains are special cases of the generalized Hua–Cartan–Hartogs domains.
  Citation: Axioms
  PubDate: 2024-07-29
  DOI: 10.3390/axioms13080513
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 514: A New Methodology for the Development of
Efficient Multistep Methods for First-Order Initial Value Problems with
Oscillating Solutions: III the Role of the Derivative of the Phase Lag and
the Derivative of the Amplification Factor
- Authors: Theodore E. Simos
  First page: 514
  Abstract: Recently, the author developed a theory for the computation of the phase lag and amplification factor for explicit and implicit multistep methods for first-order differential equations. In this paper, we will investigate the role of the derivatives of the phase lag and the derivatives of the amplification factor on the efficiency of the newly developed methods. We will also present the stability regions of the newly developed methods. We will also present numerical experiments and conclusions on the newly developed methodologies.
  Citation: Axioms
  PubDate: 2024-07-29
  DOI: 10.3390/axioms13080514
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 515: A Verifiable Multi-Secret Sharing Scheme for
Hierarchical Access Structure
- Authors: Irfan Alam, Amal S. Alali, Shakir Ali, Muhammad S. M. Asri
  First page: 515
  Abstract: Sharing confidential information is a critical concern in today’s world. Secret sharing schemes facilitate the sharing of secrets in a way that ensures only authorized participants (shareholders) can access the secret using their allocated shares. Hierarchical secret sharing schemes (HSSSs) build upon Shamir’s scheme by organizing participants into different levels based on priority. Within HSSS, participants at each level can reconstruct the secret if a specified number, denoted as the threshold value (t), or more of them are present. Each level has a predetermined threshold value. If the number of participants falls below the threshold at any level, higher-level participants must be involved in reconstructing the secret at lower levels. Our paper proposes schemes that implement hierarchical access structures and enable the sharing of multiple secrets. Additionally, our proposed scheme includes share verification. We have analyzed potential attacks and demonstrated the scheme’s resistance against them. Through security analysis and comparison with existing schemes, we highlight the novelty and superiority of our proposed approach, contributing to advancements in secure information-sharing practices.
  Citation: Axioms
  PubDate: 2024-07-30
  DOI: 10.3390/axioms13080515
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 516: Optimality Conditions for Mathematical
Programs with Vanishing Constraints Using Directional Convexificators
- Authors: Ram Narayan Mohapatra, Prachi Sachan, Vivek Laha
  First page: 516
  Abstract: This article deals with mathematical programs with vanishing constraints (MPVCs) involving lower semi-continuous functions. We introduce generalized Abadie constraint qualification (ACQ) and MPVC-ACQ in terms of directional convexificators and derive necessary KKT-type optimality conditions. We also derive sufficient conditions for global optimality for the MPVC under convexity utilizing directional convexificators. Further, we introduce a Wolfe-type dual model in terms of directional convexificators and derive duality results. The results are well illustrated by examples.
  Citation: Axioms
  PubDate: 2024-07-30
  DOI: 10.3390/axioms13080516
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 517: Transfer Learning for Logistic Regression with
Differential Privacy
- Authors: Yiming Hou, Yunquan Song
  First page: 517
  Abstract: Transfer learning, as a machine learning approach enhancing model generalization across different domains, has extensive applications in various fields. However, the risk of privacy leakage remains a crucial consideration during the transfer learning process. Differential privacy, with its rigorous mathematical foundation, has been proven to offer consistent and robust privacy protection. This study delves into the logistic regression transfer learning problem supported by differential privacy. In cases where transferable sources are known, we propose a two-step transfer learning algorithm. For scenarios with unknown transferable sources, a non-algorithmic, cross-validation-based transferable source detection method is introduced, to mitigate adverse effects from non-informative sources. The effectiveness of the proposed algorithm is validated through simulations and experiments with real-world data.
  Citation: Axioms
  PubDate: 2024-07-30
  DOI: 10.3390/axioms13080517
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 518: The Limiting Behaviors of the Gutman and
Schultz Indices in Random 2k-Sided Chains
- Authors: Chen Tao, Shengjun Tang, Xianya Geng
  First page: 518
  Abstract: The study of complex networks with topological indices has flourished in recent years. The aim of this paper is to study the limiting behaviors of Gutman and Schultz indices in random polygonal chains, whose graph-theoretic mathematical properties and their future applications have attracted the interest of scientists. By applying the concepts of symmetry and asymptotics as well as the knowledge of probability theory, we obtain explicit analytic expressions for the Gutman and Schultz indices of n random 2k-vertex chains and prove that they converge to a normal distribution, which contributes to a deeper understanding of the structural features of random polygonal chains and plays a crucial role in the study of the limiting behavior of topological indices and their applications.
  Citation: Axioms
  PubDate: 2024-07-30
  DOI: 10.3390/axioms13080518
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 519: On the Extremal Weighted Mostar Index of
Bicyclic Graphs
- Authors: Yuwei He, Mengmeng Liu
  First page: 519
  Abstract: Let G be a simple connected graph with edge set E(G) and vertex set V(G). The weighted Mostar index of a graph G is defined as w+Mo(G)=∑e=uv∈E(G)(dG(u)+dG(v)) nu(e)−nv(e) , where nu(e) denotes the number of vertices closer to u than to v for an edge uv in G. In this paper, we obtain the upper bound and lower bound of the weighted Mostar index among all bicyclic graphs and characterize the corresponding extremal graphs.
  Citation: Axioms
  PubDate: 2024-07-31
  DOI: 10.3390/axioms13080519
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 520: A Parametric Method for Proving Some Analytic
Inequalities
- Authors: Branko Malešević, Miloš Mićović, Bojana Mihailović
  First page: 520
  Abstract: In this paper, a parametric method for proving inequalities is described. The method is based on associating a considered inequality with the corresponding stratified family of functions. Many inequalities from the theory of analytic inequalities can be interpreted using families of functions that are stratified with respect to some parameter. By discussing the sign of the functions from the family by the parameter according to which the family is stratified, inequalities are obtained that contain the best possible constants, if they exist. The application of this method is demonstrated for four inequalities: the Cusa–Huygens inequality, the Wilker-type inequality and the two Mitrinović–Adamović-type inequalities. Significantly simpler proofs and improvements of all these inequalities are provided.
  Citation: Axioms
  PubDate: 2024-08-01
  DOI: 10.3390/axioms13080520
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 521: Toeplitz Matrices for a Class of
Bazilevič Functions and the λ-Pseudo-Starlike Functions
- Authors: Abbas Kareem Wanas, Salam Abdulhussein Sehen, Ágnes Orsolya Páll-Szabó
  First page: 521
  Abstract: In the present paper, we define and study a new family of holomorphic functions which involve the Bazilevič functions and the λ-pseudo-starlike functions. We establish coefficient estimates for the first four determinants of the symmetric Toeplitz matrices T2(2), T2(3), T3(1) and T3(2) for the functions in this family. Further, we investigate several special cases and consequences of our results.
  Citation: Axioms
  PubDate: 2024-08-02
  DOI: 10.3390/axioms13080521
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 522: Analysis of a Normalized Structure of a
Complex Fractal–Fractional Integral Transform Using Special
Functions
- Authors: Rabha W. Ibrahim, Soheil Salahshour, Ágnes Orsolya Páll-Szabó
  First page: 522
  Abstract: By using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal–fractional differential and integral operators of a complex variable in an open unit disk are defined and investigated analytically and geometrically. We address some inequalities involving the generalized fractal–fractional integral operator in some spaces of analytic functions. A novel complex fractal–fractional integral transform (CFFIT) is presented. A normalization of the proposed CFFIT is observed in the open unit disk. Examples are illustrated for power series of analytic functions.
  Citation: Axioms
  PubDate: 2024-08-02
  DOI: 10.3390/axioms13080522
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 523: Some Results on Certain Supercobalancing
Numbers
- Authors: Gül Karadeniz-Gözeri, Selin Sarı
  First page: 523
  Abstract: In this work, supercobalancing numbers are considered and some properties of these numbers are investigated. In the first part of this work, it is shown that every supercobalancing number is also a subbalancer. More specifically, B3-supercobalancing numbers which have not been considered before within the scope of this subject are examined. All the solution classes of the Diophantine equation of B3-supercobalancing numbers are determined exactly.
  Citation: Axioms
  PubDate: 2024-08-02
  DOI: 10.3390/axioms13080523
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 524: Linearized Stability Analysis of Nonlinear
Delay Differential Equations with Impulses
- Authors: Mostafa Bachar
  First page: 524
  Abstract: This paper explores the linearized stability of nonlinear delay differential equations (DDEs) with impulses. The classical results on the existence of periodic solutions are extended from ordinary differential equations (ODEs) to DDEs with impulses. Furthermore, the classical results of linearized stability for nonlinear semigroups are generalized to periodic DDEs with impulses. A significant challenge arises from the need for a discontinuous initial function to obtain periodic solutions. To address this, first-kind discontinuous spaces R([a,b],Rn) are introduced for defining DDEs with impulses, providing key existence and uniqueness results. This study also establishes linear stability results by linearizing the Poincaré operator for DDEs with impulses. Additionally, the stability properties of equilibrium solutions for these equations are analyzed, highlighting their importance due to the wide range of applications in various scientific fields.
  Citation: Axioms
  PubDate: 2024-08-02
  DOI: 10.3390/axioms13080524
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 525: Method for Approximating Solutions to
Equilibrium Problems and Fixed-Point Problems without Some Condition Using
Extragradient Algorithm
- Authors: Anchalee Sripattanet, Atid Kangtunyakarn
  First page: 525
  Abstract: The objective of this research is to present a novel approach to enhance the extragradient algorithm’s efficiency for finding an element within a set of fixed points of nonexpansive mapping and the set of solutions for equilibrium problems. Specifically, we focus on applications involving a pseudomonotone, Lipschitz-type continuous bifunction. Our main contribution lies in establishing a strong convergence theorem for this method, without relying on the assumption of limn→∞∥xn+1−xn∥=0. Moreover, the main theorem can be applied to effectively solve the combination of variational inequality problem (CVIP). In support of our main result, numerical examples are also presented.
  Citation: Axioms
  PubDate: 2024-08-02
  DOI: 10.3390/axioms13080525
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 526: Can Stiff Matter Solve the Hubble Tension'
- Authors: Øyvind G. Grøn
  First page: 526
  Abstract: A new form of the mathematical expression for the co-moving volume element of a flat universe with cosmological constant, cold matter, and stiff matter is presented. It is used to determine the constraints from the Planck measurements of the Hubble parameter on the amount of stiff matter in the universe. These constraints are used to investigate whether the presence of stiff matter can solve the Hubble tension. It is found that the Planck measurements lead to an upper bound on the present value of the density parameter of stiff matter ΩS0<5⋅10−23, and that this is too small to solve the Hubble tension. Report. The main objective of this article is to introduce a novel mathematical expression for the co-moving volume element in a flat universe that includes a cosmological constant, cold matter, and stiff matter. This expression is utilized to derive constraints on the amount of stiff matter in the universe based on the Planck measurements of the Hubble parameter. These constraints are then examined to assess whether stiff matter could potentially resolve the Hubble tension. The findings indicate that the Planck measurements impose an upper limit on the current value of the density parameter of stiff matter, ΩS0<5⋅10−23, which is insufficient to resolve the Hubble tension.
  Citation: Axioms
  PubDate: 2024-08-03
  DOI: 10.3390/axioms13080526
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 527: Two Schemes Based on the Collocation Method
Using Müntz–Legendre Wavelets for Solving the Fractional Bratu
Equation
- Authors: Haifa Bin Jebreen, Beatriz Hernández-Jiménez
  First page: 527
  Abstract: Our goal in this work is to solve the fractional Bratu equation, where the fractional derivative is of the Caputo type. As we know, the nonlinearity and derivative of the fractional type are two challenging subjects in solving various equations. In this paper, two approaches based on the collocation method using Müntz–Legendre wavelets are introduced and implemented to solve the desired equation. Three different types of collocation points are utilized, including Legendre and Chebyshev nodes, as well as uniform meshes. According to the experimental observations, we can confirm that the presented schemes efficiently solve the equation and yield superior results compared to other existing methods. Also, the schemes are convergent.
  Citation: Axioms
  PubDate: 2024-08-03
  DOI: 10.3390/axioms13080527
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 528: Quasi-Canonical Biholomorphically Projective
Mappings of Generalized Riemannian Space in the Eisenhart Sense
- Authors: Vladislava M. Milenković, Mića S. Stanković
  First page: 528
  Abstract: In this paper, quasi-canonical biholomorphically projective and equitorsion quasi-canonical biholomorphically projective mappings are defined. Some relations between the corresponding curvature tensors of the generalized Riemannian spaces GRN and GR¯N are obtained. At the end, the invariant geometric object of an equitorsion quasi-canonical biholomorphically projective mapping is found.
  Citation: Axioms
  PubDate: 2024-08-03
  DOI: 10.3390/axioms13080528
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 529: Numerical Analysis of the Cylindrical Shell
Pipe with Formed Holes Subjected to a Compressive Load Using Non-Uniform
Rational B-Splines and T-Splines for an Isogeometric Analysis Approach
- Authors: Said EL Fakkoussi, Ouadie Koubaiti, Ahmed Elkhalfi, Sorin Vlase, Marin Marin
  First page: 529
  Abstract: In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The Reissner–Mindlin (RM) hypothesis is considered for the investigation of the mechanical performance of a 3D cylindrical shell pipe without and with preformed hole problems under concentrated and compression loading in the linear elastic behavior for trimmed and untrimmed surfaces in structural engineering problems. Bézier extraction from T-Splines is integrated for an isogeometric analysis (IGA) approach. The numerical results obtained, particularly for the displacement and von Mises stress, are compared with and validated against the literature results, particularly with those for Non-Uniform Rational B-Spline (NURBS) IGA and the finite element method (FEM) Abaqus methods. The obtained results show that the computation time of the IGA based on the T-Spline method is shorter than that of the IGA NURBS and FEM Abaqus/CAE (computer-aided engineering) methods. Furthermore, the highlighted results confirm that the IGA approach based on the T-Spline method shows more success than numerical reference methods. We observed that the NURBS IGA method is very limited for studying trimmed surfaces. The T-Spline method shows its power and capability in computing trimmed and untrimmed surfaces.
  Citation: Axioms
  PubDate: 2024-08-03
  DOI: 10.3390/axioms13080529
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 530: Sums of Generalized Weighted Composition
Operators from Weighted Bergman Spaces Induced by Doubling Weights into
Bloch-Type Spaces
- Authors: Xiangling Zhu, Qinghua Hu
  First page: 530
  Abstract: The single generalized weighted composition operator Du,ψn on various spaces of analytic functions has been investigated for decades, i.e., Du,ψnf=u·(f(n)∘ψ), where f∈H(D). However, the study of the finite sum of generalized weighted composition operators with different orders, i.e., PU,ψkf=u0·f∘ψ+u1·f′∘ψ+⋯+uk·f(k)∘ψ, is far from complete. The boundedness, compactness and essential norm of sums of generalized weighted composition operators from weighted Bergman spaces with doubling weights into Bloch-type spaces are investigated. We show a rigidity property of PU,ψk. Specifically, the boundedness and compactness of the sum PU,ψk is equivalent to those of each Dun,ψn, 0≤n≤k.
  Citation: Axioms
  PubDate: 2024-08-05
  DOI: 10.3390/axioms13080530
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 531: Chen-Burr XII Model as a Competing Risks Model
with Applications to Real-Life Data Sets
- Authors: Zakiah I. Kalantan, Sulafah M. S. Binhimd, Heba N. Salem, Gannat R. AL-Dayian, Abeer A. EL-Helbawy, Mervat K. Abd Elaal
  First page: 531
  Abstract: In this paper Chen-Burr XII distribution is constructed and graphical description of the probability density function, hazard rate and reversed hazard rate functions of the proposed model is obtained. Also, some statistical characteristics of the Chen-Burr XII distribution are discussed and some new models as sub-models from the Chen-Burr XII distribution are introduced. Moreover, maximum likelihood estimation of the parameters, reliability, hazard rate and reversed hazard rate functions of the Chen-Burr XII distribution are considered. Also, the asymptotic confidence intervals of the distribution parameters, reliability, hazard rate and reversed hazard rate functions are presented. Finally, three real life data sets are applied to prove how the Chen-Burr XII distribution can be applied in real life and to confirm its superiority over some existing distributions.
  Citation: Axioms
  PubDate: 2024-08-05
  DOI: 10.3390/axioms13080531
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 532: Fox’s H-Functions: A Gentle Introduction
to Astrophysical Thermonuclear Functions
- Authors: Hans J. Haubold, Dilip Kumar, Ashik A. Kabeer
  First page: 532
  Abstract: Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three largely distinct velocity distributions, namely the Maxwell–Boltzmann distribution, the pathway distribution, and the Mittag-Leffler distribution. Moreover, a natural generalization of the Maxwell–Boltzmann velocity distribution is discussed. Furthermore, an explicit evaluation of the reaction rate integral in the high-energy cut-off case is carried out. Generalized special functions of mathematical physics like Meijer’s G-function and Fox’s H-functions and their utilization in mathematical physics are the prime focus of this paper.
  Citation: Axioms
  PubDate: 2024-08-06
  DOI: 10.3390/axioms13080532
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 533: Some Classical Inequalities Associated with
Generic Identity and Applications
- Authors: Muhammad Zakria Javed, Muhammad Uzair Awan, Bandar Bin-Mohsin, Hüseyin Budak, Silvestru Sever Dragomir
  First page: 533
  Abstract: In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski’s inequality, trapezoidal inequality, midpoint inequality, Simpson’s inequality, Newton-type inequalities, and several two-point open trapezoidal inequalities. Also, we provide the numerical and visual explanation of our principal findings. Later, we provide some novel applications to the theory of means, special functions, error bounds of composite quadrature schemes, and parametric iterative schemes to find the roots of linear functions. Also, we attain several already known and new bounds for different values of γ and parameter ξ.
  Citation: Axioms
  PubDate: 2024-08-06
  DOI: 10.3390/axioms13080533
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 534: On Voigt-Type Functions Extended by Neumann
Function in Kernels and Their Bounding Inequalities
- Authors: Rakesh K. Parmar, Tibor K. Pogány, Uthara Sabu
  First page: 534
  Abstract: The principal aim of this paper is to introduce the extended Voigt-type function Vμ,ν(x,y) and its counterpart extension Wμ,ν(x,y), involving the Neumann function Yν in the kernel of the representing integral. The newly defined integral reduces to the classical Voigt functions K(x,y) and L(x,y), and to their generalizations by Srivastava and Miller, by the unification of Klusch. Following an approach by Srivastava and Pogány, we also present the multiparameter and multivariable versions Vμ,ν(r)(x,y),Wμ,ν(r)(x,y) and the r positive integer of the initial extensions Vμ,ν(x,y),Wμ,ν(x,y). Several computable series expansions are obtained for the discussed Voigt-type functions in terms of Humbert confluent hypergeometric functions Ψ2(r). Furthermore, by transforming the input extended Voigt-type functions by the Grünwald–Letnikov fractional derivative, we establish representation formulae in terms of the associated Legendre functions of the second kind Qη−ν in the two-parameter and two-variable cases. Finally, functional bounding inequalities are given for Vμ,ν(x,y) and Wμ,ν(x,y). Particularly interesting results are presented for the Neumann function Yν and for the Struve Hν function in the form of several functional bounds. The article ends with a thorough discussion and closing remarks.
  Citation: Axioms
  PubDate: 2024-08-07
  DOI: 10.3390/axioms13080534
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 535: Ensuring Topological Data-Structure
Preservation under Autoencoder Compression Due to Latent Space
Regularization in Gauss–Legendre Nodes
- Authors: Chethan Krishnamurthy Ramanaik, Anna Willmann, Juan-Esteban Suarez Cardona, Pia Hanfeld, Nico Hoffmann, Michael Hecht
  First page: 535
  Abstract: We formulate a data-independent latent space regularization constraint for general unsupervised autoencoders. The regularization relies on sampling the autoencoder Jacobian at Legendre nodes, which are the centers of the Gauss–Legendre quadrature. Revisiting this classic allows us to prove that regularized autoencoders ensure a one-to-one re-embedding of the initial data manifold into its latent representation. Demonstrations show that previously proposed regularization strategies, such as contractive autoencoding, cause topological defects even in simple examples, as do convolutional-based (variational) autoencoders. In contrast, topological preservation is ensured by standard multilayer perceptron neural networks when regularized using our approach. This observation extends from the classic FashionMNIST dataset to (low-resolution) MRI brain scans, suggesting that reliable low-dimensional representations of complex high-dimensional datasets can be achieved using this regularization technique.
  Citation: Axioms
  PubDate: 2024-08-07
  DOI: 10.3390/axioms13080535
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 536: Fuzzy H-Quasi-Contraction and Fixed Point
Theorems in Tripled Fuzzy Metric Spaces
- Authors: Yunpeng Zhao, Fei He, Xuan Liu
  First page: 536
  Abstract: We consider the concept of fuzzy H-quasi-contraction (FH-QC for short) initiated by Ćirić in tripled fuzzy metric spaces (T-FMSs for short) and present a new fixed point theorem (FPT for short) for FH-QC in complete T-FMSs. As an application, we prove the corresponding results of the previous literature in setting fuzzy metric spaces (FMSs for short). Moreover, we obtain theorems of sufficient and necessary conditions which can be used to demonstrate the existence of fixed points. In addition, we construct relevant examples to illustrate the corresponding results. Finally, we show the existence and uniqueness of solutions for integral equations by applying our new results.
  Citation: Axioms
  PubDate: 2024-08-07
  DOI: 10.3390/axioms13080536
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 537: Review on Some Boundary Value Problems
Defining the Mean First-Passage Time in Cell Migration
- Authors: Hélia Serrano, Ramón F. Álvarez-Estrada
  First page: 537
  Abstract: The mean first-passage time represents the average time for a migrating cell within its environment, starting from a certain position, to reach a specific location or target for the first time. In this feature article, we provide an overview of the characterization of the mean first-passage time of cells moving inside two- or three-dimensional domains, subject to various boundary conditions (Dirichlet, Neumann, Robin, or mixed), through the so-called adjoint diffusion equation. We concentrate on reducing the latter to inhomogeneous linear integral equations for certain density functions on the boundaries. The integral equations yield the mean first-passage time exactly for a very reduced set of boundaries. For various boundary surfaces, which include small deformations of the exactly solvable boundaries, the integral equations provide approximate solutions. Moreover, the method also allows to deal approximately with mixed boundary conditions, which constitute a genuine long-standing and open problem. New plots, figures, and discussions are presented, aimed at clarifying the analysis.
  Citation: Axioms
  PubDate: 2024-08-08
  DOI: 10.3390/axioms13080537
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 538: A Normality Criterion for Sharing a
Holomorphic Function
- Authors: Sheng Wang, Xiaojun Huang
  First page: 538
  Abstract: In this paper, we scrutinize a collection of meromorphic functions known as normal families, prove the theorem that normal families share a holomorphic function, and present several illustrative counterexamples.
  Citation: Axioms
  PubDate: 2024-08-08
  DOI: 10.3390/axioms13080538
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 539: Boundedness and Compactness of Weighted
Composition Operators from (α, k)-Bloch Spaces to A(β,k) Spaces
on Generalized Hua Domains of the Fourth Kind
- Authors: Jiaqi Wang, Jianbing Su
  First page: 539
  Abstract: This paper addresses the weighted composition operators Cϕψ from the (α,k)-Bloch spaces to the A(β,k) spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the fourth kind. Additionally, we obtain some necessary and sufficient conditions for the boundedness and compactness of these operators.
  Citation: Axioms
  PubDate: 2024-08-08
  DOI: 10.3390/axioms13080539
  Issue No: Vol. 13, No. 8 (2024)
Axioms, Vol. 13, Pages 440: Brain Connectivity Dynamics and
Mittag–Leffler Synchronization in Asymmetric Complex Networks for a
Class of Coupled Nonlinear Fractional-Order Memristive Neural Network
System with Coupling Boundary Conditions
- Authors: Aziz Belmiloudi
  First page: 440
  Abstract: This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer’s disease, or Parkinson’s disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients.
  Citation: Axioms
  PubDate: 2024-06-28
  DOI: 10.3390/axioms13070440
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 441: On the Impact of Some Fixed Point Theorems on
Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like
Spaces
- Authors: Ekber Girgin, Abdurrahman Büyükkaya, Neslihan Kaplan Kuru, Mahpeyker Öztürk
  First page: 441
  Abstract: In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed point theorem for certain extensions of Geraghty-type contraction mappings, incorporating both Z simulation function and E-type contraction within this innovative structure. Moreover, we present several novel outcomes that stem from our newly defined notations. Afterwards, we introduce an unprecedented concept, the graphical modular b-metric-like space, which is derived from the binary relation R. Finally, we examine the existence of solutions for a class of functional equations that are pivotal in dynamic programming and in solving initial value problems related to the electric current in an RLC parallel circuit.
  Citation: Axioms
  PubDate: 2024-06-28
  DOI: 10.3390/axioms13070441
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 442: Sharp Coefficient Bounds for Starlike
Functions Associated with Cosine Function
- Authors: Rashid Ali, Mohsan Raza, Teodor Bulboacă
  First page: 442
  Abstract: Let Scos* denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf′(z)f(z)≺cosz. In the first result of this article, we find the sharp upper bounds for the initial coefficients a3, a4 and a5 and the sharp upper bound for module of the Hankel determinant H2,3(f) for the functions from the class Scos*. The next section deals with the sharp upper bounds of the logarithmic coefficients γ3 and γ4. Then, in addition, we found the sharp upper bound for H2,2Ff/2. To obtain these results we utilized the very useful and appropriate Lemma 2.4 of N.E. Cho et al. [Filomat 34(6) (2020), 2061–2072], which gave a most accurate description for the first five coefficients of the functions from the Carathéodory’s functions class, and provided a technique for finding the maximum value of a three-variable function on a closed cuboid. All the maximum found values were checked by using MAPLE™ 2016 computer software, and we also found the extremal functions in each case. All of our most recent results are the best ones and give sharp versions of those recently published in [Hacet. J. Math. Stat. 52, 596–618, 2023].
  Citation: Axioms
  PubDate: 2024-06-29
  DOI: 10.3390/axioms13070442
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 443: Statistical Inferences about Parameters of the
Pseudo Lindley Distribution with Acceptance Sampling Plans
- Authors: Fatehi Yahya Eissa, Chhaya Dhanraj Sonar, Osama Abdulaziz Alamri, Ahlam H. Tolba
  First page: 443
  Abstract: Different non-Bayesian and Bayesian techniques were used to estimate the pseudo-Lindley (PsL) distribution’s parameters in this study. To derive Bayesian estimators, one must assume appropriate priors on the parameters and use loss functions such as squared error (SE), general entropy (GE), and linear-exponential (LINEX). Since no closed-form solutions are accessible for Bayes estimates under these loss functions, the Markov Chain Monte Carlo (MCMC) approach was used. Simulation studies were conducted to evaluate the estimators’ performance under the given loss functions. Furthermore, we exhibited the adaptability and practicality of the PsL distribution through real-world data applications, which is essential for evaluating the various estimation techniques. Also, the acceptance sampling plans were developed in this work for items whose lifespans approximate the PsL distribution.
  Citation: Axioms
  PubDate: 2024-06-29
  DOI: 10.3390/axioms13070443
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 444: Strong Consistency of Incomplete Functional
Percentile Regression
- Authors: Mohammed B. Alamari, Fatimah A. Almulhim, Ouahiba Litimein, Boubaker Mechab
  First page: 444
  Abstract: This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data.
  Citation: Axioms
  PubDate: 2024-06-30
  DOI: 10.3390/axioms13070444
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 445: On a Version of Dontchev and Hager’s
Inverse Mapping Theorem
- Authors: Thanaa A. Alarfaj, Saud M. Alsulami
  First page: 445
  Abstract: By revisiting an open question raised by Kirk and Shahzad, we are able to prove a generalized version of Nadler’s fixed-point theorem in the context of strong b-metric space. Such a result leads us to prove a new version of Dontchev and Hager’s inverse mapping theorem. Some examples are provided to illustrate the results.
  Citation: Axioms
  PubDate: 2024-06-30
  DOI: 10.3390/axioms13070445
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 446: Quantization of the Rank Two
Heisenberg–Virasoro Algebra
- Authors: Xue Chen
  First page: 446
  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 Drinfel’d twists is presented, Lie bialgebra structures of which have been investigated by the authors recently.
  Citation: Axioms
  PubDate: 2024-07-01
  DOI: 10.3390/axioms13070446
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 447: Fractional-Order Sequential Linear
Differential Equations with Nabla Derivatives on Time Scales
- Authors: Cheng-Cheng Zhu, Jiang Zhu
  First page: 447
  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 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.
  Citation: Axioms
  PubDate: 2024-07-01
  DOI: 10.3390/axioms13070447
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 448: Center-like Subsets in Semiprime Rings with
Multiplicative Derivations
- Authors: Sarah Samah Aljohani, Emine Koç Sögütcü, Nadeem ur Rehman
  First page: 448
  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 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.
  Citation: Axioms
  PubDate: 2024-07-02
  DOI: 10.3390/axioms13070448
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 449: Uncertainty Degradation Model for Initiating
Explosive Devices Based on Uncertain Differential Equations
- Authors: Changli Ma, Li Jia, Meilin Wen
  First page: 449
  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 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.
  Citation: Axioms
  PubDate: 2024-07-03
  DOI: 10.3390/axioms13070449
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 450: Existence and Multiplicity of Nontrivial
Solutions for Semilinear Elliptic Equations Involving Hardy–Sobolev
Critical Exponents
- Authors: Yonghong Fan, Wenheng Sun, Linlin Wang
  First page: 450
  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 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.
  Citation: Axioms
  PubDate: 2024-07-03
  DOI: 10.3390/axioms13070450
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 451: Estimates of Eigenvalues and Approximation
Numbers for a Class of Degenerate Third-Order Partial Differential
Operators
- Authors: Mussakan Muratbekov, Ainash Suleimbekova, Mukhtar Baizhumanov
  First page: 451
  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 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.
  Citation: Axioms
  PubDate: 2024-07-03
  DOI: 10.3390/axioms13070451
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 452: Concerning Transformations of Bases Associated
with Unimodular diag(1, −1, −1)-Matrices
- Authors: I. A. Shilin, Junesang Choi
  First page: 452
  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 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.
  Citation: Axioms
  PubDate: 2024-07-04
  DOI: 10.3390/axioms13070452
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 453: Dynamic Pricing and Inventory Strategies for
Fashion Products Using Stochastic Fashion Level Function
- Authors: Wenhan Lu, Litan Yan
  First page: 453
  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 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.
  Citation: Axioms
  PubDate: 2024-07-04
  DOI: 10.3390/axioms13070453
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 454: Analyzing the Ricci Tensor for Slant
Submanifolds in Locally Metallic Product Space Forms with a Semi-Symmetric
Metric Connection
- Authors: Yanlin Li, Md Aquib, Meraj Ali Khan, Ibrahim Al-Dayel, Khalid Masood
  First page: 454
  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 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.
  Citation: Axioms
  PubDate: 2024-07-04
  DOI: 10.3390/axioms13070454
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 455: Some New Estimations of Ostrowski-Type
Inequalities for Harmonic Fuzzy Number Convexity via Gamma, Beta and
Hypergeometric Functions
- Authors: Azzh Saad Alshehry, Loredana Ciurdariu, Yaser Saber, Amal F. Soliman
  First page: 455
  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 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.
  Citation: Axioms
  PubDate: 2024-07-04
  DOI: 10.3390/axioms13070455
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 456: Fermatean Hesitant Fuzzy Multi-Attribute
- Authors: Ruan, Chen, Yan
  First page: 456
  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 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.
  Citation: Axioms
  PubDate: 2024-07-04
  DOI: 10.3390/axioms13070456
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 457: Visualization of Isometric Deformations of
Helicoidal CMC Surfaces
- Authors: Filip Vukojević, Miroslava Antić
  First page: 457
  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 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.
  Citation: Axioms
  PubDate: 2024-07-06
  DOI: 10.3390/axioms13070457
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 458: Achieving Optimal Order in a Novel Family of
Numerical Methods: Insights from Convergence and Dynamical Analysis
Results
- Authors: Marlon Moscoso-Martínez, Francisco I. Chicharro, Alicia Cordero, Juan R. Torregrosa, Gabriela Ureña-Callay
  First page: 458
  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, 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.
  Citation: Axioms
  PubDate: 2024-07-07
  DOI: 10.3390/axioms13070458
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 459: A Method for Calculating the Reliability of
2-Separable Networks and Its Applications
- Authors: Jing Liang, Haixing Zhao, Sun Xie
  First page: 459
  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 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.
  Citation: Axioms
  PubDate: 2024-07-08
  DOI: 10.3390/axioms13070459
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 460: The Split Equality Fixed-Point Problem and Its
Applications
- Authors: Lawan Bulama Mohammed, Adem Kilicman
  First page: 460
  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 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.
  Citation: Axioms
  PubDate: 2024-07-08
  DOI: 10.3390/axioms13070460
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 461: A Reduced-Dimension Weighted Explicit Finite
Difference Method Based on the Proper Orthogonal Decomposition Technique
for the Space-Fractional Diffusion Equation
- Authors: Xuehui Ren, Hong Li
  First page: 461
  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 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.
  Citation: Axioms
  PubDate: 2024-07-08
  DOI: 10.3390/axioms13070461
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 462: Smooth Logistic Real and Complex, Ordinary and
Fractional Neural Network Approximations over Infinite Domains
- Authors: George A. Anastassiou
  First page: 462
  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 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.
  Citation: Axioms
  PubDate: 2024-07-09
  DOI: 10.3390/axioms13070462
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 463: Special Geometric Objects in Generalized
Riemannian Spaces
- Authors: Marko Stefanović, Nenad Vesić, Dušan Simjanović, Branislav Randjelović
  First page: 463
  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 in physics.
  Citation: Axioms
  PubDate: 2024-07-09
  DOI: 10.3390/axioms13070463
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 464: Mathematical Modeling of Immune Dynamics in
Chronic Myeloid Leukemia Therapy: Unraveling Allergic Reactions and T Cell
Subset Modulation by Imatinib
- Authors: Rawan Abdullah, Irina Badralexi, Laurance Fakih, Andrei Halanay
  First page: 464
  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 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.
  Citation: Axioms
  PubDate: 2024-07-10
  DOI: 10.3390/axioms13070464
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 465: Fuzzy Milne, Ostrowski, and
Hermite–Hadamard-Type Inequalities for ħ-Godunova–Levin
Convexity and Their Applications
- Authors: Juan Wang, Valer-Daniel Breaz, Yasser Salah Hamed, Luminita-Ioana Cotirla, Xuewu Zuo
  First page: 465
  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 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.
  Citation: Axioms
  PubDate: 2024-07-10
  DOI: 10.3390/axioms13070465
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 466: Right Quantum Calculus on Finite Intervals
with Respect to Another Function and Quantum Hermite–Hadamard
Inequalities
- Authors: Asawathep Cuntavepanit, Sotiris K. Ntouyas, Jessada Tariboon
  First page: 466
  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 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.
  Citation: Axioms
  PubDate: 2024-07-10
  DOI: 10.3390/axioms13070466
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 467: Integral Equations: New Solutions via
Generalized Best Proximity Methods
- Authors: Amer Hassan Albargi, Jamshaid Ahmad
  First page: 467
  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 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.
  Citation: Axioms
  PubDate: 2024-07-11
  DOI: 10.3390/axioms13070467
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 468: Pole Analysis of the Inter-Replica Correlation
Function in a Two-Replica System as a Binary Mixture: Mean Overlap in the
Cluster Glass Phase
- Authors: Hiroshi Frusawa
  First page: 468
  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 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.
  Citation: Axioms
  PubDate: 2024-07-11
  DOI: 10.3390/axioms13070468
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 469: Impact of Risk Aversion in Fuzzy Bimatrix
Games
- Authors: Chuanyang Xu, Wanting Zhao, Zhongwei Feng
  First page: 469
  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, 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.
  Citation: Axioms
  PubDate: 2024-07-11
  DOI: 10.3390/axioms13070469
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 470: An Example of a Continuous Field of Roe
Algebras
- Authors: Vladimir Manuilov
  First page: 470
  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 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.
  Citation: Axioms
  PubDate: 2024-07-12
  DOI: 10.3390/axioms13070470
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 471: Generalized Fuzzy-Valued Convexity with
Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion
Relations and Their Applications
- Authors: Miguel Vivas Cortez, Ali Althobaiti, Abdulrahman F. Aljohani, Saad Althobaiti
  First page: 471
  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 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.
  Citation: Axioms
  PubDate: 2024-07-12
  DOI: 10.3390/axioms13070471
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 472: Adding a Degree of Certainty to Deductions in
a Fuzzy Temporal Constraint Prolog: FTCProlog
- Authors: María-Antonia Cárdenas-Viedma
  First page: 472
  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 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.
  Citation: Axioms
  PubDate: 2024-07-12
  DOI: 10.3390/axioms13070472
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 473: Modeling Data with Extreme Values Using
Three-Spliced Distributions
- Authors: Adrian Bâcă, Raluca Vernic
  First page: 473
  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 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.
  Citation: Axioms
  PubDate: 2024-07-13
  DOI: 10.3390/axioms13070473
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 474: Stability of Fixed Points of Partial
Contractivities and Fractal Surfaces
- Authors: María A. Navascués
  First page: 474
  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 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.
  Citation: Axioms
  PubDate: 2024-07-13
  DOI: 10.3390/axioms13070474
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 475: On Some New Dynamic Hilbert-Type Inequalities
Across Time Scales
- Authors: Mohammed Zakarya, Ahmed I. Saied, Amirah Ayidh I Al-Thaqfan, Maha Ali, Haytham M. Rezk
  First page: 475
  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 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.
  Citation: Axioms
  PubDate: 2024-07-14
  DOI: 10.3390/axioms13070475
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 476: On the Potential Vector Fields of Soliton-Type
Equations
- Authors: Adara M. Blaga
  First page: 476
  Abstract: We highlight some properties of a class of distinguished vector fields associated to a (1,1)-tensor field and to an affine connection on a Riemannian manifold, with a special view towards the Ricci vector fields, and we characterize them with respect to statistical, almost Kähler, and locally product structures. In particular, we provide conditions for these vector fields to be closed, Killing, parallel, or semi-torse forming. In the gradient case, we give a characterization of the Euclidean sphere. Among these vector fields, the Ricci and torse-forming-like vector fields are particular cases.
  Citation: Axioms
  PubDate: 2024-07-16
  DOI: 10.3390/axioms13070476
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 477: Nonlinear Contractions Employing Digraphs and
Comparison Functions with an Application to Singular Fractional
Differential Equations
- Authors: Doaa Filali, Mohammad Dilshad, Mohammad Akram
  First page: 477
  Abstract: After the initiation of Jachymski’s contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem.
  Citation: Axioms
  PubDate: 2024-07-16
  DOI: 10.3390/axioms13070477
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 478: On Some Properties of the Equilateral
Triangles with Vertices Located on the Support Sides of a Triangle
- Authors: Dorin Andrica, Ovidiu Bagdasar
  First page: 478
  Abstract: The possible positions of an equilateral triangle whose vertices are located on the support sides of a generic triangle are studied. Using complex coordinates, we show that there are infinitely many such configurations, then we prove that the centroids of these equilateral triangles are collinear, defining two lines perpendicular to the Euler’s line of the original triangle. Finally, we obtain the complex coordinates of the intersection points and study some particular cases.
  Citation: Axioms
  PubDate: 2024-07-17
  DOI: 10.3390/axioms13070478
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 479: A Note on the Multiplicity of the
Distinguished Points
- Authors: Weiping Li, Xiaoshen Wang
  First page: 479
  Abstract: Let P(x) be a system of polynomials in s variables, where x∈Cs. If z0 is an isolated zero of P, then the multiplicity and its structure at z0 can be revealed by the normal set of the quotient ring R(<P>) or its dual space R* or by certain numerical methods. In his book titled “Numerical Polynomial Algebra”, Stetter described the so-called distinguished points, which are embedded in a zero manifold of P, and the author defined their multiplicities. In this note, we will generalize the definition of distinguished points and give a more appropriate definition for their multiplicity, as well as show how to calculate the multiplicity of these points.
  Citation: Axioms
  PubDate: 2024-07-18
  DOI: 10.3390/axioms13070479
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 480: Stability Results for Some Classes of Cubic
Functional Equations
- Authors: El-sayed El-hady, Yamin Sayyari, Mehdi Dehghanian, Ymnah Alruwaily
  First page: 480
  Abstract: Applications involving functional equations (FUEQs) are commonplace. They are essential to various applications, such as fog computing. Ulam’s notion of stability is highly helpful since it provides a range of estimates between exact and approximate solutions. Using Brzdȩk’s fixed point technique (FPT), we establish the stability of the following cubic type functional equations (CFUEQs): Fξ13+ξ233+Fξ13−ξ233=2F(ξ1)+2F(ξ2),2Fξ13+ξ2323=F(ξ1)+F(ξ2) for all ξ1,ξ2∈R.
  Citation: Axioms
  PubDate: 2024-07-18
  DOI: 10.3390/axioms13070480
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 481: Integrable Couplings and Two-Dimensional
Unital Algebras
- Authors: Wen-Xiu Ma
  First page: 481
  Abstract: The paper aims to demonstrate that a linear expansion in a unital two-dimensional algebra can generate integrable couplings, proposing a novel approach for their construction. The integrable couplings presented encompass a range of perturbation equations and nonlinear integrable couplings. Their corresponding Lax pairs and hereditary recursion operators are explicitly detailed. Concrete applications to the KdV equation and the AKNS system of nonlinear Schrödinger equations are extensively explored.
  Citation: Axioms
  PubDate: 2024-07-18
  DOI: 10.3390/axioms13070481
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 482: Topological Degree via a Degree of
Nondensifiability and Applications
- Authors: N. Ouahab, J. J. Nieto, A. Ouahab
  First page: 482
  Abstract: The goal of this work is to introduce the notion of topological degree via the principle of the degree of nondensifiability (DND for short). We establish some new fixed point theorems, concerning, Schaefer’s fixed point theorem and the nonlinear alternative of Leray–Schauder type. As applications, we study the existence of mild solution of functional semilinear integro-differential equations.
  Citation: Axioms
  PubDate: 2024-07-18
  DOI: 10.3390/axioms13070482
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 483: Stability Analysis of a Credit Risk Contagion
Model with Distributed Delay
- Authors: Martin Anokye, Luca Guerrini, Albert L. Sackitey, Samuel E. Assabil, Henry Amankwah
  First page: 483
  Abstract: This research investigates the stability and occurrence of Hopf bifurcation in a credit risk contagion model, which includes distributed delay, using the chain trick method. The model is a generalized version of those previously examined. The model is an expanded version of those previously studied. Comparative analysis showed that unlike earlier models, which only used the nonlinear resistance coefficient to determine the rate of credit risk infection, the credit risk contagion rate is also affected by the weight given to past behaviors of credit risk participants. Therefore, it is recommended to model the transmission of credit risk contagion using dispersed delays.
  Citation: Axioms
  PubDate: 2024-07-18
  DOI: 10.3390/axioms13070483
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 484: Fractional Sequential Coupled Systems of
Hilfer and Caputo Integro-Differential Equations with Non-Separated
Boundary Conditions
- Authors: Ayub Samadi, Sotiris K. Ntouyas, Jessada Tariboon
  First page: 484
  Abstract: In studying boundary value problems and coupled systems of fractional order in (1,2], involving Hilfer fractional derivative operators, a zero initial condition is necessary. The consequence of this fact is that boundary value problems and coupled systems of fractional order with non-zero initial conditions cannot be studied. For example, such boundary value problems and coupled systems of fractional order are those including separated, non-separated, or periodic boundary conditions. In this paper, we propose a method for studying a coupled system of fractional order in (1,2], involving fractional derivative operators of Hilfer and Caputo with non-separated boundary conditions. More precisely, a sequential coupled system of fractional differential equations including Hilfer and Caputo fractional derivative operators and non-separated boundary conditions is studied in the present paper. As explained in the concluding section, the opposite combination of Caputo and Hilfer fractional derivative operators requires zero initial conditions. By using Banach’s fixed point theorem, the uniqueness of the solution is established, while by applying the Leray–Schauder alternative, the existence of solution is obtained. Numerical examples are constructed illustrating the main results.
  Citation: Axioms
  PubDate: 2024-07-18
  DOI: 10.3390/axioms13070484
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 485: Some Statistical and Direct Approximation
Properties for a New Form of the Generalization of q-Bernstein Operators
with the Parameter λ
- Authors: Lian-Ta Su, Esma Kangal, Ülkü Dinlemez Kantar, Qing-Bo Cai
  First page: 485
  Abstract: In this study, a different generalization of q-Bernstein operators with the parameter λ∈[−1,1] is created. The moments and central moments of these operators are calculated, a statistical approximation result for this new type of (λ,q)-Bernstein operators is obtained, and the convergence properties are analyzed using the Peetre K-functional and the modulus of continuity for this new operator. Finally, a numerical example is given to illustrate the convergence behavior of the newly defined operators.
  Citation: Axioms
  PubDate: 2024-07-18
  DOI: 10.3390/axioms13070485
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 486: Geometric Inequalities of Slant Submanifolds
in Locally Metallic Product Space Forms
- Authors: Yanlin Li, Md Aquib, Meraj Ali Khan, Ibrahim Al-Dayel, Maged Zakaria Youssef
  First page: 486
  Abstract: In this particular article, our focus revolves around the establishment of a geometric inequality, commonly referred to as Chen’s inequality. We specifically apply this inequality to assess the square norm of the mean curvature vector and the warping function of warped product slant submanifolds. Our investigation takes place within the context of locally metallic product space forms with quarter-symmetric metric connections. Additionally, we delve into the condition that determines when equality is achieved within the inequality. Furthermore, we explore a number of implications of our findings.
  Citation: Axioms
  PubDate: 2024-07-19
  DOI: 10.3390/axioms13070486
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 487: On the Relative Φ-Growth of Hadamard
Compositions of Dirichlet Series
- Authors: Myroslav Sheremeta, Oksana Mulyava
  First page: 487
  Abstract: For the Dirichlet series F(s)=∑n=1∞fnexp{sλn}, which is the Hadamard composition of the genus m of similar Dirichlet series Fj(s) with the same exponents, the growth with respect to the function G(s) given as the Dirichlet series is studied in terms of the Φ-type (the upper limit of MG−1(MF(σ))/Φ(σ) as σ↑A) and convergence Φ-class defined by the condition ∫σ0AΦ′(σ)MG−1(MF(σ))Φ2(σ)dσ<+∞, where MF(σ) is the maximum modulus of the function F at an imaginary line and A is the abscissa of the absolute convergence.
  Citation: Axioms
  PubDate: 2024-07-19
  DOI: 10.3390/axioms13070487
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 488: On Some Properties for Cofiniteness of
Submonoids and Ideals of an Affine Semigroup
- Authors: Carmelo Cisto
  First page: 488
  Abstract: Let S and C be affine semigroups in Nd such that S&sube;C. We provide a characterization for the set C∖S to be finite, together with a procedure and computational tools to check whether such a set is finite and, if so, compute its elements. As a consequence of this result, we provide a characterization for an ideal I of an affine semigroup S so that S∖I is a finite set. If so, we provide some procedures to compute the set S∖I.
  Citation: Axioms
  PubDate: 2024-07-20
  DOI: 10.3390/axioms13070488
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 489: Consistent Sampling Approximations in Abstract
Hilbert Spaces
- Authors: Sinuk Kang, Kil Hyun Kwon, Dae Gwan Lee
  First page: 489
  Abstract: This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples.
  Citation: Axioms
  PubDate: 2024-07-21
  DOI: 10.3390/axioms13070489
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 490: Numerical Computation of 2D Domain Integrals
in Boundary Element Method by (α, β) Distance Transformation
for Transient Heat Conduction Problems
- Authors: Yunqiao Dong, Zhengxu Tan, Hengbo Sun
  First page: 490
  Abstract: When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method.
  Citation: Axioms
  PubDate: 2024-07-22
  DOI: 10.3390/axioms13070490
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 491: Locally Convex Spaces with Sequential
Dunford–Pettis Type Properties
- Authors: Saak Gabriyelyan
  First page: 491
  Abstract: Let p,q,q′∈[1,∞], q′≤q. Several new characterizations of locally convex spaces with the sequential Dunford–Pettis property of order (p,q) are given. We introduce and thoroughly study the sequential Dunford–Pettis* property of order (p,q) of locally convex spaces (in the realm of Banach spaces, the sequential DP(p,∞)* property coincides with the well-known DPp* property). Being motivated by the coarse p-DP* property and the p-Dunford–Pettis relatively compact property for Banach spaces, we define and study the coarse sequential DP(p,q)* property, the coarse DPp* property and the p-Dunford–Pettis sequentially compact property of order (q′,q) in the class of all locally convex spaces.
  Citation: Axioms
  PubDate: 2024-07-22
  DOI: 10.3390/axioms13070491
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 492: Probabilistic and Average Gel’fand
Widths of Sobolev Space Equipped with Gaussian Measure in the Sq-Norm
- Authors: Ruihuan Wu, Yuqi Liu, Huan Li
  First page: 492
  Abstract: In this article, we mainly studied the Gel’fand widths of Sobolev space in the probabilistic and average settings. And, we estimated the sharp bounds of the probabilistic Gel’fand (N,δ)-widths of multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm by discretization methods. Later, we estimated the sharp bounds of the p-average Gel’fand N-widths of univariate Sobolev space W2r(T) and multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm.
  Citation: Axioms
  PubDate: 2024-07-22
  DOI: 10.3390/axioms13070492
  Issue No: Vol. 13, No. 7 (2024)
Axioms, Vol. 13, Pages 493: New Interval-Valued Soft Separation Axioms
- Authors: J. I. Baek, T. M. Al-shami, S. Jafari, M. Cheong, K. Hur
  First page: 493
  Abstract: Our research’s main aim is to study two viewpoints: First, we define partial interval-valued soft Ti(j)-spaces (i = 0, 1, 2, 3, 4; j = i, ii), study some of their properties and some of relationships among them, and give some examples. Second, we introduce the notions of partial total interval-valued soft Tj(i)-spaces (i = 0, 1, 2, 3, 4; j = i, ii) and discuss some of their properties. We present some relationships among them and give some examples.
  Citation: Axioms
  PubDate: 2024-07-22
  DOI: 10.3390/axioms13070493
  Issue No: Vol. 13, No. 7 (2024)

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