Axioms

25 pages, 367 KiB

Open AccessFeature PaperArticle

New Interval-Valued Soft Separation Axioms

by Jong Il Baek, Tareq M. Al-shami, Saeid Jafari, Minseok Cheong and Kul Hur

Axioms 2024, 13(7), 493; https://doi.org/10.3390/axioms13070493 - 22 Jul 2024

Viewed by 739

Our research’s main aim is to study two viewpoints: First, we define partial interval-valued soft T

_{i}

(j)-spaces (i = 0, 1, 2, 3, 4; j = i, ii), study some of their properties and some of relationships among them, and give [...] Read more.

Our research’s main aim is to study two viewpoints: First, we define partial interval-valued soft T

_{i}

(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 T

_{j}

(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. Full article

(This article belongs to the Special Issue Advances in Octahedron Sets and Its Applications)

21 pages, 331 KiB

Open AccessArticle

Probabilistic and Average Gel’fand Widths of Sobolev Space Equipped with Gaussian Measure in the S_q-Norm

by Ruihuan Wu, Yuqi Liu and Huan Li

Axioms 2024, 13(7), 492; https://doi.org/10.3390/axioms13070492 - 22 Jul 2024

Viewed by 650

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 [...] Read more.

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

M W_{2}^{r} (T^{d})

with mixed derivative equipped with the Gaussian measure in the

S_{q}

-norm by discretization methods. Later, we estimated the sharp bounds of the p-average Gel’fand N-widths of univariate Sobolev space

W_{2}^{r} (T)

and multivariate Sobolev space

M W_{2}^{r} (T^{d})

with mixed derivative equipped with the Gaussian measure in the

S_{q}

-norm. Full article

(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications, 2nd Edition)

28 pages, 436 KiB

Open AccessArticle

Locally Convex Spaces with Sequential Dunford–Pettis Type Properties

by Saak Gabriyelyan

Axioms 2024, 13(7), 491; https://doi.org/10.3390/axioms13070491 - 22 Jul 2024

Viewed by 815

Abstract

Let

p, q, q^{'} \in [1, \infty]

,

q^{'} \leq q

. Several new characterizations of locally convex spaces with the sequential Dunford–Pettis property of order

(p, q)

are given. We introduce and [...] Read more.

Let

p, q, q^{'} \in [1, \infty]

,

q^{'} \leq 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

D P_{(p, \infty)}^{*}

property coincides with the well-known

D P_{p}^{*}

property). Being motivated by the coarse p-

D P^{*}

property and the p-Dunford–Pettis relatively compact property for Banach spaces, we define and study the coarse sequential

D P_{(p, q)}^{*}

property, the coarse

D P_{p}^{*}

property and the p-Dunford–Pettis sequentially compact property of order

(q^{'}, q)

in the class of all locally convex spaces. Full article

(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)

14 pages, 3346 KiB

Open AccessArticle

Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems

by Yunqiao Dong, Zhengxu Tan and Hengbo Sun

Axioms 2024, 13(7), 490; https://doi.org/10.3390/axioms13070490 - 22 Jul 2024

Viewed by 680

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Numerical Computation, Approximation of Functions and Applied Mathematics, 2nd Edition)

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10 pages, 268 KiB

Open AccessArticle

Consistent Sampling Approximations in Abstract Hilbert Spaces

by Sinuk Kang, Kil Hyun Kwon and Dae Gwan Lee

Axioms 2024, 13(7), 489; https://doi.org/10.3390/axioms13070489 - 21 Jul 2024

Viewed by 597

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)

14 pages, 348 KiB

Open AccessArticle

On Some Properties for Cofiniteness of Submonoids and Ideals of an Affine Semigroup

by Carmelo Cisto

Axioms 2024, 13(7), 488; https://doi.org/10.3390/axioms13070488 - 20 Jul 2024

Viewed by 831

Abstract

Let S and

C

be affine semigroups in

N^{d}

such that

S \subseteq 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 [...] Read more.

Let S and

C

be affine semigroups in

N^{d}

such that

S \subseteq 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

. Full article

(This article belongs to the Special Issue Advances in Linear Algebra with Applications)

16 pages, 307 KiB

Open AccessArticle

On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series

by Myroslav Sheremeta and Oksana Mulyava

Axioms 2024, 13(7), 487; https://doi.org/10.3390/axioms13070487 - 19 Jul 2024

Viewed by 528

Abstract

For the Dirichlet series

F (s) = \sum_{n = 1}^{\infty} f_{n} exp {s λ_{n}}

, which is the Hadamard composition of the genus m of similar Dirichlet series

F_{j} (s)

with the [...] Read more.

For the Dirichlet series

F (s) = \sum_{n = 1}^{\infty} f_{n} exp {s λ_{n}}

, which is the Hadamard composition of the genus m of similar Dirichlet series

F_{j} (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

M_{G}^{- 1} (M_{F} (σ)) / Φ (σ)

as

σ ↑ A

) and convergence

Φ

-class defined by the condition

\int_{σ_{0}}^{A} \frac{Φ^{'} (σ) M_{G}^{- 1} (M_{F} (σ))}{Φ^{2} (σ)} d σ < + \infty

, where

M_{F} (σ)

is the maximum modulus of the function F at an imaginary line and A is the abscissa of the absolute convergence. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)

16 pages, 283 KiB

Open AccessArticle

Geometric Inequalities of Slant Submanifolds in Locally Metallic Product Space Forms

by Yanlin Li, Md Aquib, Meraj Ali Khan, Ibrahim Al-Dayel and Maged Zakaria Youssef

Axioms 2024, 13(7), 486; https://doi.org/10.3390/axioms13070486 - 19 Jul 2024

Cited by 7 | Viewed by 645

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 2nd Edition)

14 pages, 402 KiB

Open AccessArticle

Some Statistical and Direct Approximation Properties for a New Form of the Generalization of q-Bernstein Operators with the Parameter λ

by Lian-Ta Su, Esma Kangal, Ülkü Dinlemez Kantar and Qing-Bo Cai

Axioms 2024, 13(7), 485; https://doi.org/10.3390/axioms13070485 - 18 Jul 2024

Viewed by 587

Abstract

In this study, a different generalization of q-Bernstein operators with the parameter

λ \in [- 1, 1]

is created. The moments and central moments of these operators are calculated, a statistical approximation result for this new type of [...] Read more.

In this study, a different generalization of q-Bernstein operators with the parameter

λ \in [- 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. Full article

(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)

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17 pages, 298 KiB

Open AccessArticle

Fractional Sequential Coupled Systems of Hilfer and Caputo Integro-Differential Equations with Non-Separated Boundary Conditions

by Ayub Samadi, Sotiris K. Ntouyas and Jessada Tariboon

Axioms 2024, 13(7), 484; https://doi.org/10.3390/axioms13070484 - 18 Jul 2024

Viewed by 684

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Fractional Calculus and Its Applications: Historical and Recent Developments)

12 pages, 339 KiB

Open AccessArticle

Stability Analysis of a Credit Risk Contagion Model with Distributed Delay

by Martin Anokye, Luca Guerrini, Albert L. Sackitey, Samuel E. Assabil and Henry Amankwah

Axioms 2024, 13(7), 483; https://doi.org/10.3390/axioms13070483 - 18 Jul 2024

Viewed by 671

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue New Perspectives in Applied Mathematics with Nonlinear Equations and Dynamical Systems)

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14 pages, 280 KiB

Open AccessArticle

Topological Degree via a Degree of Nondensifiability and Applications

by Noureddine Ouahab, Juan J. Nieto and Abdelghani Ouahab

Axioms 2024, 13(7), 482; https://doi.org/10.3390/axioms13070482 - 18 Jul 2024

Viewed by 626

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. [...] Read more.

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. Full article

(This article belongs to the Special Issue New Perspectives in Applied Mathematics with Nonlinear Equations and Dynamical Systems)

8 pages, 220 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Integrable Couplings and Two-Dimensional Unital Algebras

by Wen-Xiu Ma

Axioms 2024, 13(7), 481; https://doi.org/10.3390/axioms13070481 - 18 Jul 2024

Cited by 16 | Viewed by 1008

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 [...] Read more.

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. Full article

12 pages, 260 KiB

Open AccessArticle

Stability Results for Some Classes of Cubic Functional Equations

by El-sayed El-hady, Yamin Sayyari, Mehdi Dehghanian and Ymnah Alruwaily

Axioms 2024, 13(7), 480; https://doi.org/10.3390/axioms13070480 - 18 Jul 2024

Cited by 1 | Viewed by 706

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 [...] Read more.

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):

F (\sqrt[3]{ξ_{1}^{3} + ξ_{2}^{3}}) + F (\sqrt[3]{ξ_{1}^{3} - ξ_{2}^{3}}) = 2 F (ξ_{1}) + 2 F (ξ_{2}),

2 F (\sqrt[3]{\frac{ξ_{1}^{3} + ξ_{2}^{3}}{2}}) = F (ξ_{1}) + F (ξ_{2})

for all

ξ_{1}, ξ_{2} \in R

. Full article

(This article belongs to the Special Issue Difference, Functional, and Related Equations)

6 pages, 213 KiB

Open AccessArticle

A Note on the Multiplicity of the Distinguished Points

by Weiping Li and Xiaoshen Wang

Axioms 2024, 13(7), 479; https://doi.org/10.3390/axioms13070479 - 18 Jul 2024

Viewed by 672

Abstract

Let

P (x)

be a system of polynomials in s variables, where

x \in C^{s}

. If

z_{0}

is an isolated zero of P, then the multiplicity and its structure at

z_{0}

can be revealed by the normal [...] Read more.

Let

P (x)

be a system of polynomials in s variables, where

x \in C^{s}

. If

z_{0}

is an isolated zero of P, then the multiplicity and its structure at

z_{0}

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. Full article

15 pages, 617 KiB

Open AccessArticle

On Some Properties of the Equilateral Triangles with Vertices Located on the Support Sides of a Triangle

by Dorin Andrica and Ovidiu Bagdasar

Axioms 2024, 13(7), 478; https://doi.org/10.3390/axioms13070478 - 17 Jul 2024

Viewed by 659

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)

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12 pages, 327 KiB

Open AccessArticle

Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations

by Doaa Filali, Mohammad Dilshad and Mohammad Akram

Axioms 2024, 13(7), 477; https://doi.org/10.3390/axioms13070477 - 16 Jul 2024

Viewed by 644

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)

13 pages, 258 KiB

Open AccessArticle

On the Potential Vector Fields of Soliton-Type Equations

by Adara M. Blaga

Axioms 2024, 13(7), 476; https://doi.org/10.3390/axioms13070476 - 16 Jul 2024

Viewed by 618

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Discrete Curvatures and Laplacians)

19 pages, 300 KiB

Open AccessArticle

On Some New Dynamic Hilbert-Type Inequalities across Time Scales

by Mohammed Zakarya, Ahmed I. Saied, Amirah Ayidh I Al-Thaqfan, Maha Ali and Haytham M. Rezk

Axioms 2024, 13(7), 475; https://doi.org/10.3390/axioms13070475 - 14 Jul 2024

Viewed by 869

Abstract

In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales

T

. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our findings (when

T = N

and [...] Read more.

In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales

T

. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our findings (when

T = N

and

T = R

), we obtain the discrete and continuous analogues of previously established inequalities. Additionally, we derive other inequalities for different time scales, such as

T = q^{N_{0}}

for

q > 1,

which, to the best of the authors’ knowledge, is a largely novel conclusion. Full article

(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)

17 pages, 312 KiB

Open AccessArticle

Stability of Fixed Points of Partial Contractivities and Fractal Surfaces

by María A. Navascués

Axioms 2024, 13(7), 474; https://doi.org/10.3390/axioms13070474 - 13 Jul 2024

Viewed by 692

Abstract

In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations [...] Read more.

In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. Full article

(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)

21 pages, 482 KiB

Open AccessArticle

Modeling Data with Extreme Values Using Three-Spliced Distributions

by Adrian Bâcă and Raluca Vernic

Axioms 2024, 13(7), 473; https://doi.org/10.3390/axioms13070473 - 13 Jul 2024

Viewed by 564

Abstract

When data exhibit a high frequency of small to medium values and a low frequency of large values, fitting a classical distribution might fail. This is why spliced models defined from different distributions on distinct intervals are proposed in the literature. In contrast [...] Read more.

When data exhibit a high frequency of small to medium values and a low frequency of large values, fitting a classical distribution might fail. This is why spliced models defined from different distributions on distinct intervals are proposed in the literature. In contrast to the intensive study of two-spliced distributions, the case with more than two components is scarcely approached. In this paper, we focus on three-spliced distributions and on their ability to improve the modeling of extreme data. For this purpose, we consider a popular insurance data set related to Danish fire losses, to which we fit several three-spliced distributions; moreover, the results are compared to the best-fitted two-spliced distributions from previous studies. Full article

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33 pages, 3475 KiB

Open AccessArticle

Adding a Degree of Certainty to Deductions in a Fuzzy Temporal Constraint Prolog: FTCProlog

by María-Antonia Cárdenas-Viedma

Axioms 2024, 13(7), 472; https://doi.org/10.3390/axioms13070472 - 12 Jul 2024

Viewed by 784

Abstract

The management of time is essential in most AI-related applications. In addition, we know that temporal information is often not precise. In fact, in most cases, it is necessary to deal with imprecision and/or uncertainty. On the other hand, there is the need [...] Read more.

The management of time is essential in most AI-related applications. In addition, we know that temporal information is often not precise. In fact, in most cases, it is necessary to deal with imprecision and/or uncertainty. On the other hand, there is the need to handle the implicit common-sense information present in many temporal statements. In this paper, we present FTCProlog, a logic programming language capable of handling fuzzy temporal constraints soundly and efficiently. The main difference of FTCProlog with respect to its predecessor, PROLogic, is its ability to associate a certainty index with deductions obtained through SLD-resolution. This resolution is based on a proposal within the theoretical logical framework FTCLogic. This model integrates a first-order logic based on possibilistic logic with the Fuzzy Temporal Constraint Networks (FTCNs) that allow efficient time management. The calculation of the certainty index can be useful in applications where one wants to verify the extent to which the times elapsed between certain events follow a given temporal pattern. In this paper, we demonstrate that the calculation of this index respects the properties of the theoretical model regarding its semantics. FTCProlog is implemented in Haskell. Full article

(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications)

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27 pages, 1378 KiB

Open AccessArticle

Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications

by Miguel Vivas Cortez, Ali Althobaiti, Abdulrahman F. Aljohani and Saad Althobaiti

Axioms 2024, 13(7), 471; https://doi.org/10.3390/axioms13070471 - 12 Jul 2024

Viewed by 752

Abstract

Convex inequalities and fuzzy-valued calculus converge to form a comprehensive mathematical framework that can be employed to understand and analyze a broad spectrum of issues. This paper utilizes fuzzy Aumman’s integrals to establish integral inequalities of Hermite-Hahadard, Fejér, and Pachpatte types within up [...] Read more.

Convex inequalities and fuzzy-valued calculus converge to form a comprehensive mathematical framework that can be employed to understand and analyze a broad spectrum of issues. This paper utilizes fuzzy Aumman’s integrals to establish integral inequalities of Hermite-Hahadard, Fejér, and Pachpatte types within up and down (

U

·

D

) relations and over newly defined class

U

·

D

-ħ-Godunova–Levin convex fuzzy-number mappings. To demonstrate the unique properties of

U

·

D

-relations, recent findings have been developed using fuzzy Aumman’s, as well as various other fuzzy partial order relations that have notable deficiencies outlined in the literature. Several compelling examples were constructed to validate the derived results, and multiple notes were provided to illustrate, depending on the configuration, that this type of integral operator generalizes several previously documented conclusions. This endeavor can potentially advance mathematical theory, computational techniques, and applications across various fields. Full article

(This article belongs to the Special Issue Theory and Application of Integral Inequalities)

8 pages, 239 KiB

Open AccessArticle

An Example of a Continuous Field of Roe Algebras

by Vladimir Manuilov

Axioms 2024, 13(7), 470; https://doi.org/10.3390/axioms13070470 - 12 Jul 2024

Viewed by 544

Abstract

The Roe algebra

C^{*} (X)

is a noncommutative

C^{*}

-algebra reflecting metric properties of a space X, and it is interesting to understand the correlation between the Roe algebra of X and the (uniform) Roe algebra of its [...] Read more.

The Roe algebra

C^{*} (X)

is a noncommutative

C^{*}

-algebra reflecting metric properties of a space X, and it is interesting to understand the correlation between the Roe algebra of X and the (uniform) Roe algebra of its discretization. Here, we perform a minor step in this direction in the simplest non-trivial example, namely

X = R

, by constructing a continuous field of

C^{*}

-algebras over

[0, 1]

, with the fibers over non-zero points constituting the uniform

C^{*}

-algebra of the integers, and the fibers over 0 constituting a

C^{*}

-algebra related to

R

. Full article

(This article belongs to the Section Mathematical Analysis)

10 pages, 272 KiB

Open AccessArticle

Impact of Risk Aversion in Fuzzy Bimatrix Games

by Chuanyang Xu, Wanting Zhao and Zhongwei Feng

Axioms 2024, 13(7), 469; https://doi.org/10.3390/axioms13070469 - 11 Jul 2024

Viewed by 793

Abstract

In bimatrix games with symmetric triangular fuzzy payoffs, our work defines an (α, β)-risk aversion Nash equilibrium ((α, β)-RANE) and presents its sufficient and necessary condition. Our work also discusses the relationships between the (α, [...] Read more.

In bimatrix games with symmetric triangular fuzzy payoffs, our work defines an (α, β)-risk aversion Nash equilibrium ((α, β)-RANE) and presents its sufficient and necessary condition. Our work also discusses the relationships between the (α, β)-RANE and a mixed-strategy Nash equilibrium (MSNE) in a bimatrix game with a risk-averse player 2 and certain payoffs. Finally, considering 2 × 2 bimatrix games with STFPs, we find the conditions where the increase in player 2’s risk-aversion level hurts or benefits himself/herself. Full article

20 pages, 1690 KiB

Open AccessArticle

Pole Analysis of the Inter-Replica Correlation Function in a Two-Replica System as a Binary Mixture: Mean Overlap in the Cluster Glass Phase

by Hiroshi Frusawa

Axioms 2024, 13(7), 468; https://doi.org/10.3390/axioms13070468 - 11 Jul 2024

Viewed by 693

Abstract

To investigate the cluster glass phase of ultrasoft particles, we examine an annealed two-replica system endowed with an attractive inter-replica field similar to that of a binary symmetric electrolyte. Leveraging this analogy, we conduct pole analysis on the total correlation functions in the [...] Read more.

To investigate the cluster glass phase of ultrasoft particles, we examine an annealed two-replica system endowed with an attractive inter-replica field similar to that of a binary symmetric electrolyte. Leveraging this analogy, we conduct pole analysis on the total correlation functions in the two-replica system where the inter-replica field will eventually be switched off. By synthesizing discussions grounded in the pole analysis with a hierarchical view of the free-energy landscape, we derive an analytical form of the mean overlap between two replicas within the mean field approximation of the Gaussian core model. This formula elucidates novel numerical findings observed in the cluster glass phase. Full article

(This article belongs to the Section Mathematical Physics)

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15 pages, 286 KiB

Open AccessArticle

Integral Equations: New Solutions via Generalized Best Proximity Methods

by Amer Hassan Albargi and Jamshaid Ahmad

Axioms 2024, 13(7), 467; https://doi.org/10.3390/axioms13070467 - 11 Jul 2024

Cited by 1 | Viewed by 587

Abstract

This paper introduces the concept of proximal

(α, F)

-contractions in

F

-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial [...] Read more.

This paper introduces the concept of proximal

(α, F)

-contractions in

F

-metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond. Full article

(This article belongs to the Special Issue Research on Fixed Point Theory and Application)

12 pages, 250 KiB

Open AccessArticle

Right Quantum Calculus on Finite Intervals with Respect to Another Function and Quantum Hermite–Hadamard Inequalities

by Asawathep Cuntavepanit, Sotiris K. Ntouyas and Jessada Tariboon

Axioms 2024, 13(7), 466; https://doi.org/10.3390/axioms13070466 - 10 Jul 2024

Viewed by 667

Abstract

In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The [...] Read more.

In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The new definitions generalize the previous existing results in the literature. We provide applications of the newly defined quantum calculus by obtaining new Hermite–Hadamard-type inequalities for convex, h-convex, and modified h-convex functions. Full article

(This article belongs to the Special Issue New Perspectives in Applied Mathematics with Nonlinear Equations and Dynamical Systems)

31 pages, 431 KiB

Open AccessArticle

Fuzzy Milne, Ostrowski, and Hermite–Hadamard-Type Inequalities for ħ-Godunova–Levin Convexity and Their Applications

by Juan Wang, Valer-Daniel Breaz, Yasser Salah Hamed, Luminita-Ioana Cotirla and Xuewu Zuo

Axioms 2024, 13(7), 465; https://doi.org/10.3390/axioms13070465 - 10 Jul 2024

Viewed by 588

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 [...] Read more.

In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann’s integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class,

ħ

-Godunova–Levin convex fuzzy number mappings, to derive Ostrowski’s and Hermite–Hadamard-type inequalities for fuzzy number mappings. Using the fuzzy Kulisch–Miranker order, we also establish connections with Hermite–Hadamard-type inequalities. Furthermore, we explore novel ideas and results based on Hermite–Hadamard–Fejér and provide examples and applications to illustrate our findings. Some very interesting examples are also provided to discuss the validation of the main results. Additionally, some new exceptional and classical outcomes have been obtained, which can be considered as applications of our main results. Full article

(This article belongs to the Special Issue Analysis of Mathematical Inequalities)

36 pages, 1658 KiB

Open AccessArticle

Mathematical Modeling of Immune Dynamics in Chronic Myeloid Leukemia Therapy: Unraveling Allergic Reactions and T Cell Subset Modulation by Imatinib

by Rawan Abdullah, Irina Badralexi, Laurance Fakih and Andrei Halanay

Axioms 2024, 13(7), 464; https://doi.org/10.3390/axioms13070464 - 10 Jul 2024

Viewed by 1130

Abstract

This mathematical model delves into the dynamics of the immune system during Chronic Myeloid Leukemia (CML) therapy with imatinib. The focus lies in elucidating the allergic reactions induced by imatinib, specifically its impact on T helper (Th) cells and Treg cells. The model [...] Read more.

This mathematical model delves into the dynamics of the immune system during Chronic Myeloid Leukemia (CML) therapy with imatinib. The focus lies in elucidating the allergic reactions induced by imatinib, specifically its impact on T helper (Th) cells and Treg cells. The model integrates cellular interactions, drug pharmacokinetics, and immune responses to unveil the mechanisms underlying the dominance of Th2 over Th1 and Treg cells, leading to allergic manifestations. Through a system of coupled delay differential equations, the interplay between healthy and leukemic cells, the influence of imatinib on T cell dynamics, and the emergence of allergic reactions during CML therapy are explored. Full article

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Axioms, Volume 13, Issue 7 (July 2024) – 77 articles

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