Axioms

17 pages, 323 KiB

Open AccessReview

Recent Progress on Point-Countable Covers and Sequence-Covering Mappings

by Shou Lin and Jing Zhang

Axioms 2024, 13(10), 728; https://doi.org/10.3390/axioms13100728 - 21 Oct 2024

Viewed by 618

This paper is dedicated to the memory of Professor Gary Gruenhage (1947–2023). This survey introduces the formation and early development of the topic of point-countable covers and sequence-covering mappings, and lists the recent progress of 38 questions on this topic proposed before 2015, [...] Read more.

This paper is dedicated to the memory of Professor Gary Gruenhage (1947–2023). This survey introduces the formation and early development of the topic of point-countable covers and sequence-covering mappings, and lists the recent progress of 38 questions on this topic proposed before 2015, which involve the theory of generalized metric spaces. These questions are related to point-countable covers and sequence-covering mappings, including point-countable covers with certain networks, sequence-covering mappings, images of metric spaces, and hereditarily closure-preserving families. Full article

(This article belongs to the Special Issue Topics in General Topology and Applications)

22 pages, 1273 KiB

Open AccessArticle

Estimation of Lifetime Performance Index for Generalized Inverse Lindley Distribution Under Adaptive Progressive Type-II Censored Lifetime Test

by Shixiao Xiao, Xue Hu and Haiping Ren

Axioms 2024, 13(10), 727; https://doi.org/10.3390/axioms13100727 - 18 Oct 2024

Viewed by 649

Abstract

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II [...] Read more.

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II censored lifetime test, assuming that the product’s lifetime follows a generalized inverse Lindley distribution. At first, the maximum likelihood estimator of the LPI is derived, and the Newton–Raphson iterative method is adopted to solve the numerical solution due to the log-likelihood equations having no analytical solutions. If the exact distribution of the LPI is not available, then the asymptotic confidence interval and bootstrap confidence interval of the LPI are constructed. For the Bayesian estimation, the Bayesian estimators of the LPI are derived under three different loss functions. Due to the complex multiple integrals involved in these estimators, the MCMC method is used to draw samples and further construct the HPD credible interval of the LPI. Finally, Monte Carlo simulations are used to observe the performance of these estimators in terms of the average bias and mean squared error, and two practical examples are used to illustrate the application of the proposed estimation method. Full article

(This article belongs to the Special Issue Reliability and Risk of Complex Systems: Modelling, Analysis and Optimization)

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13 pages, 292 KiB

Open AccessArticle

Fixed Point Results in Modular b-Metric-like Spaces with an Application

by Nizamettin Ufuk Bostan and Banu Pazar Varol

Axioms 2024, 13(10), 726; https://doi.org/10.3390/axioms13100726 - 18 Oct 2024

Viewed by 615

Abstract

In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of

ξ

-convergence,

ξ

-Cauchy sequence,

ξ

-completeness and

ξ

-contraction. The existence and uniqueness of fixed points in [...] Read more.

In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of

ξ

-convergence,

ξ

-Cauchy sequence,

ξ

-completeness and

ξ

-contraction. The existence and uniqueness of fixed points in the modular b-metric-like space are handled. Moreover, we give some examples and an application to an integral equation to illustrate the usability of the obtained results. Full article

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

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12 pages, 270 KiB

Open AccessArticle

Symmetry Reductions of the (1 + 1)-Dimensional Broer–Kaup System Using the Generalized Double Reduction Method

by Molahlehi Charles Kakuli, Winter Sinkala and Phetogo Masemola

Axioms 2024, 13(10), 725; https://doi.org/10.3390/axioms13100725 - 18 Oct 2024

Viewed by 528

Abstract

The generalized theory of the double reduction of systems of partial differential equations (PDEs) based on the association of conservation laws with Lie–Bäcklund symmetries is one of the most effective algorithms for performing symmetry reductions of PDEs. In this article, we apply the [...] Read more.

The generalized theory of the double reduction of systems of partial differential equations (PDEs) based on the association of conservation laws with Lie–Bäcklund symmetries is one of the most effective algorithms for performing symmetry reductions of PDEs. In this article, we apply the theory to a (1 + 1)-dimensional Broer–Kaup (BK) system, which is a pair of nonlinear PDEs that arise in the modeling of the propagation of long waves in shallow water. We find symmetries and construct six local conservation laws of the BK system arising from low-order multipliers. We establish associations between the Lie point symmetries and conservation laws and exploit the association to perform double reductions of the system, reducing it to first-order ordinary differential equations or algebraic equations. Our paper contributes to the broader understanding and application of the generalized double reduction method in the analysis of nonlinear PDEs. Full article

54 pages, 554 KiB

Open AccessReview

A Comprehensive Review of Golden Riemannian Manifolds

by Bang-Yen Chen, Majid Ali Choudhary and Afshan Perween

Axioms 2024, 13(10), 724; https://doi.org/10.3390/axioms13100724 - 18 Oct 2024

Viewed by 1109

Abstract

In differential geometry, the concept of golden structure represents a compelling area with wide-ranging applications. The exploration of golden Riemannian manifolds was initiated by C. E. Hretcanu and M. Crasmareanu in 2008, following the principles of the golden structure. Subsequently, numerous researchers have [...] Read more.

In differential geometry, the concept of golden structure represents a compelling area with wide-ranging applications. The exploration of golden Riemannian manifolds was initiated by C. E. Hretcanu and M. Crasmareanu in 2008, following the principles of the golden structure. Subsequently, numerous researchers have contributed significant insights with respect to golden Riemannian manifolds. The purpose of this paper is to provide a comprehensive survey of research on golden Riemannian manifolds conducted over the past decade. Full article

(This article belongs to the Section Geometry and Topology)

16 pages, 295 KiB

Open AccessArticle

Unified Generalizations of Hardy-Type Inequalities Through the Nabla Framework on Time Scales

by Haytham M. Rezk, Oluwafemi Samson Balogun and Mahmoud E. Bakr

Axioms 2024, 13(10), 723; https://doi.org/10.3390/axioms13100723 - 18 Oct 2024

Viewed by 490

Abstract

This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative functions. We extend these inequalities within a cohesive framework that integrates elements [...] Read more.

This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative functions. We extend these inequalities within a cohesive framework that integrates elements of both continuous and discrete calculus. Furthermore, our study revisits specific integral inequalities from the existing literature, showcasing the wide-ranging relevance of our results. Full article

(This article belongs to the Special Issue Differential and Dynamic Equations on Time Scales and Their Applications)

24 pages, 499 KiB

Open AccessArticle

Constrained Bayesian Method for Testing Equi-Correlation Coefficient

by Kartlos Kachiashvili and Ashis SenGupta

Axioms 2024, 13(10), 722; https://doi.org/10.3390/axioms13100722 - 17 Oct 2024

Viewed by 445

Abstract

The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are examined. For the investigation of the obtained theoretical results and choosing the [...] Read more.

The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are examined. For the investigation of the obtained theoretical results and choosing the best among them, different practical examples are analyzed. The simulation results showed that the constrained Bayesian method (CBM) using Stein’s approach has the advantage of making decisions with higher reliability for testing hypotheses concerning the equi-correlation coefficient than the Bayes method. Also, the use of this approach with the probability distribution of linear combinations of chi-square random variables gives better results compared to that of using the integrated probability distributions in terms of providing both the necessary precisions as well as convenience of implementation in practice. Recommendations towards the use of the proposed methods for solving practical problems are given. Full article

(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)

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17 pages, 334 KiB

Open AccessFeature PaperArticle

A Penalty Method for Elliptic Variational–Hemivariational Inequalities

by Mircea Sofonea and Domingo A. Tarzia

Axioms 2024, 13(10), 721; https://doi.org/10.3390/axioms13100721 - 17 Oct 2024

Viewed by 524

Abstract

We consider an elliptic variational–hemivariational inequality

P

in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution

u \in K

. We associate inequality

P

to a [...] Read more.

We consider an elliptic variational–hemivariational inequality

P

in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution

u \in K

. We associate inequality

P

to a sequence of elliptic variational–hemivariational inequalities

{P_{n}}

, governed by a set of constraints

\tilde{K} \supset K

, a sequence of parameters

{λ_{n}} \subset R_{+}

, and a function

ψ

. We prove that if, for each

n \in N

, the element

u_{n} \in \tilde{K}

represents a solution to Problem

P_{n}

, then the sequence

{u_{n}}

converges to u as

λ_{n} \to 0

. Based on this general result, we recover convergence results for various associated penalty methods previously obtained in the literature. These convergence results are obtained by considering particular choices of the set

\tilde{K}

and the function

ψ

. The corresponding penalty methods can be applied in the study of various inequality problems. To provide an example, we consider a purely hemivariational inequality that describes the equilibrium of an elastic membrane in contact with an obstacle, the so-called foundation. Full article

(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)

17 pages, 1994 KiB

Open AccessArticle

Notes on Modified Planar Kelvin–Stuart Models: Simulations, Applications, Probabilistic Control on the Perturbations

by Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev, Vesselin Kyurkchiev and Asen Rahnev

Axioms 2024, 13(10), 720; https://doi.org/10.3390/axioms13100720 - 17 Oct 2024

Viewed by 502

Abstract

In this paper, we propose a new modified planar Kelvin–Stuart model. We demonstrate some modules for investigating the dynamics of the proposed model. This will be included as an integral part of a planned, much more general Web-based application for scientific computing. Investigations [...] Read more.

In this paper, we propose a new modified planar Kelvin–Stuart model. We demonstrate some modules for investigating the dynamics of the proposed model. This will be included as an integral part of a planned, much more general Web-based application for scientific computing. Investigations in light of Melnikov’s approach are considered. Some simulations and applications are also presented. The proposed new modifications of planar Kelvin–Stuart models contain many free parameters (the coefficients

g_{i}, i = 1, 2, \dots, N

), which makes them attractive for use in engineering applications such as the antenna feeder technique (a possible generating and simulating of antenna factors) and the theory of approximations (a possible good approximation of a given electrical stage). The probabilistic control of the perturbations is discussed. Full article

(This article belongs to the Special Issue Differential Equations and Related Topics, 2nd Edition)

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13 pages, 272 KiB

Open AccessArticle

Some Remarks on Existence of a Complex Structure on the Compact Six Sphere

by Daniel Guan, Na Li and Zhonghua Wang

Axioms 2024, 13(10), 719; https://doi.org/10.3390/axioms13100719 - 17 Oct 2024

Viewed by 690

Abstract

The existence or nonexistence of a complex structure on a differential manifold is a central problem in differential geometry. In particular, this problem on

S^{6}

was a long-standing unsolved problem, and differential geometry is an important tool. Recently, G. Clemente found a [...] Read more.

The existence or nonexistence of a complex structure on a differential manifold is a central problem in differential geometry. In particular, this problem on

S^{6}

was a long-standing unsolved problem, and differential geometry is an important tool. Recently, G. Clemente found a necessary and sufficient condition for almost-complex structures on a general differential manifold to be complex structures by using a covariant exterior derivative in three articles. However, in two of them, G. Clemente used a stronger condition instead of the published one. From there, G. Clemente proved the nonexistence of the complex structure on

S^{6}

. We study the related differential operators and give some examples of nilmanifolds. And we prove that the earlier condition is too strong for an almost complex structure to be integrable. In another word, we clarify the situation of this problem. Full article

(This article belongs to the Section Geometry and Topology)

16 pages, 495 KiB

Open AccessArticle

A Kinematic Approach to the Classical SIR Model

by Fernando Córdova-Lepe, Juan Pablo Gutiérrez-Jara and Katia Vogt-Geisse

Axioms 2024, 13(10), 718; https://doi.org/10.3390/axioms13100718 - 16 Oct 2024

Viewed by 494

Abstract

Given the risk and impact of infectious-contagious X diseases, which are expected to increase in frequency and unpredictability due to climate change and anthropogenic penetration of the wilderness, it is crucial to advance descriptions and explanations that improve the understanding and applicability of [...] Read more.

Given the risk and impact of infectious-contagious X diseases, which are expected to increase in frequency and unpredictability due to climate change and anthropogenic penetration of the wilderness, it is crucial to advance descriptions and explanations that improve the understanding and applicability of current theories. An inferential approach is to find analogies with better-studied contexts from which new questions and hypotheses can be raised through their concepts, propositions, and methods. Kinematics emerges as a promising analog field in physics by interpreting states’ changes in a contagion process as a movement. Consequently, this work explores, for a contagion process, the representations and conceptual equivalents for position, displacement, velocity, momentum, and acceleration, introducing some metrics. It also discusses some epistemological aspects and proposes future perspectives. Full article

(This article belongs to the Special Issue Advances in Mathematical Modeling and Related Topics)

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15 pages, 270 KiB

Open AccessArticle

Symmetric Reverse n-Derivations on Ideals of Semiprime Rings

by Shakir Ali, Ali Yahya Hummdi, Naira N. Rafiquee, Vaishali Varshney and Kok Bin Wong

Axioms 2024, 13(10), 717; https://doi.org/10.3390/axioms13100717 - 16 Oct 2024

Viewed by 483

Abstract

This paper focuses on examining a new type of n-additive map called the symmetric reverse n-derivation. As implied by its name, it combines the ideas of n-additive maps and reverse derivations, with a 1-reverse derivation being the ordinary reverse derivation. [...] Read more.

This paper focuses on examining a new type of n-additive map called the symmetric reverse n-derivation. As implied by its name, it combines the ideas of n-additive maps and reverse derivations, with a 1-reverse derivation being the ordinary reverse derivation. We explore several findings that expand our knowledge of these maps, particularly their presence in semiprime rings and the way rings respond to specific functional identities involving elements of ideals. Also, we provide examples to help clarify the concept of symmetric reverse n-derivations. This study aims to deepen our understanding of these symmetric maps and their properties within mathematical structures. Full article

(This article belongs to the Section Algebra and Number Theory)

17 pages, 450 KiB

Open AccessArticle

Transient and Steady-State Analysis of an M/PH₂/1 Queue with Catastrophes

by Youxin Liu, Liwei Liu, Tao Jiang and Xudong Chai

Axioms 2024, 13(10), 716; https://doi.org/10.3390/axioms13100716 - 16 Oct 2024

Viewed by 612

Abstract

In the paper, we consider the

P H_{2}

-distribution, which is a particular case of the

P H

-distribution. In other words, The first service phase is exponentially distributed, and the service rate is

μ

. After the first service phase, the [...] Read more.

In the paper, we consider the

P H_{2}

-distribution, which is a particular case of the

P H

-distribution. In other words, The first service phase is exponentially distributed, and the service rate is

μ

. After the first service phase, the customer can to go away with probability p or continue the service with probability

(1 - p)

and service rate

μ^{'}

. We study an analysis of an

M / P H_{2} / 1

queue model with catastrophes, which is regarded as a generalization of an

M / M / 1

queue model with catastrophes. Whenever a catastrophe happens, all customers will be cleaned up immediately, and the queuing system is empty. The customers arrive at the queuing system based on a Poisson process, and the total service duration has two phases. Transient probabilities and steady-state probabilities of this queuing system are considered using practical applications of the modified Bessel function of the first kind, the Laplace transform, and probability-generating function techniques. Moreover, some important performance measures are obtained in the system. Finally, numerical illustrations are used to discuss the system’s behavior, and conclusions and future directions of the model are given. Full article

(This article belongs to the Special Issue Stochastic and Statistical Analysis in Natural Sciences)

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12 pages, 257 KiB

Open AccessArticle

The Orthogonal Riesz Fractional Derivative

by Fethi Bouzeffour

Axioms 2024, 13(10), 715; https://doi.org/10.3390/axioms13100715 - 16 Oct 2024

Viewed by 553

Abstract

The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials

C_{n}^{(ν)} (x)

[...] Read more.

The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials

C_{n}^{(ν)} (x)

, where

ν > - \frac{1}{2}

. Building on the work of Diekema and Koornwinder, the n-th derivative is obtained as the limit of an integral involving Gegenbauer polynomials as the kernel. When this limit is omitted, it results in the approximate Gegenbauer orthogonal derivative, which serves as an effective approximation of the n-th order derivative. Using this operator, we introduce a novel extension of the fractional Riesz derivative, denoted as

{}_{x}D^{α}

, providing an alternative framework for fractional calculus. Full article

(This article belongs to the Special Issue Fractional Calculus—Theory and Applications, 3rd Edition)

14 pages, 275 KiB

Open AccessArticle

Strong Stability for a Viscoelastic Transmission Problem Under a Nonlocal Boundary Control

by Noureddine Touati Brahim, Abderrahmane Beniani, Abderrazak Chaoui, Zayd Hajjej, Perikles Papadopoulos and Khaled Zennir

Axioms 2024, 13(10), 714; https://doi.org/10.3390/axioms13100714 - 16 Oct 2024

Viewed by 661

Abstract

The purpose of this paper is to consider a transmission problem of a viscoelastic wave with nonlocal boundary control. It should be noted that the present paper is based on the previous C. G. Gal and M. Warma works, together with H. Atoui [...] Read more.

The purpose of this paper is to consider a transmission problem of a viscoelastic wave with nonlocal boundary control. It should be noted that the present paper is based on the previous C. G. Gal and M. Warma works, together with H. Atoui and A. Benaissa. Namely, they focused on a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with an emphasis on rough interfaces and nonlinear dynamic (possibly, nonlocal) boundary conditions along the interface, where a transmission problem in the presence of a boundary control condition of a nonlocal type was investigated in these papers. Owing to the semigroup theory, we prove the question of well-posedness. For the very rare cases, we combined between the frequency domain approach and the Borichev–Tomilov theorem to establish strong stability results. Full article

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

14 pages, 275 KiB

Open AccessArticle

Homogeneous Grand Mixed Herz–Morrey Spaces and Their Applications

by Xiaoxi Xia and Jiang Zhou

Axioms 2024, 13(10), 713; https://doi.org/10.3390/axioms13100713 - 16 Oct 2024

Viewed by 430

Abstract

In this paper, we introduce the homogeneous grand mixed Herz–Morrey spaces

M {\dot{K}}_{\tilde{q}, λ}^{α, p), θ} (R^{n})

and investigate their fundamental properties. We further explore the boundedness of sublinear operators and fractional-type [...] Read more.

In this paper, we introduce the homogeneous grand mixed Herz–Morrey spaces

M {\dot{K}}_{\tilde{q}, λ}^{α, p), θ} (R^{n})

and investigate their fundamental properties. We further explore the boundedness of sublinear operators and fractional-type operators on these spaces, establishing new results that contribute to the broader understanding of their applications. Full article

15 pages, 275 KiB

Open AccessArticle

Fredholm Determinant and Wronskian Representations of the Solutions to the Schrödinger Equation with a KdV-Potential

by Pierre Gaillard

Axioms 2024, 13(10), 712; https://doi.org/10.3390/axioms13100712 - 15 Oct 2024

Viewed by 493

Abstract

From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants. For this we establish a connection between Riemann theta functions and [...] Read more.

From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants. For this we establish a connection between Riemann theta functions and Fredholm determinants and we obtain multi-parametric solutions to this equation. As a consequence, a double Wronskian representation of the solutions to this equation is constructed. We also give quasi-rational solutions to this Schrödinger equation with rational KdV potentials. Full article

(This article belongs to the Special Issue Differential Equations and Related Topics, 2nd Edition)

15 pages, 418 KiB

Open AccessArticle

Using Artificial Neural Networks to Solve the Gross–Pitaevskii Equation

by Ioannis G. Tsoulos, Vasileios N. Stavrou and Dimitrios Tsalikakis

Axioms 2024, 13(10), 711; https://doi.org/10.3390/axioms13100711 - 15 Oct 2024

Viewed by 665

Abstract

The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials. With the assistance of neural networks, a model is formed that is capable of solving this equation. The adaptation [...] Read more.

The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials. With the assistance of neural networks, a model is formed that is capable of solving this equation. The adaptation of the parameters for the constructed model is performed using some evolutionary techniques, such as genetic algorithms and particle swarm optimization. The proposed model is used to solve the GPE for the linear case (

γ = 0

) and the nonlinear case (

γ \neq 0

), where

γ

is the nonlinearity parameter in GPE. The results are close to the reported results regarding the behavior and the amplitudes of the wavefunctions. Full article

(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)

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24 pages, 17859 KiB

Open AccessArticle

The Reduced-Dimension Method for Crank–Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher–Kolmogorov Equation

by Xiaohui Chang and Hong Li

Axioms 2024, 13(10), 710; https://doi.org/10.3390/axioms13100710 - 14 Oct 2024

Viewed by 459

Abstract

A reduced-dimension (RD) method based on the proper orthogonal decomposition (POD) technology and the linearized Crank–Nicolson mixed finite element (CNMFE) scheme for solving the 2D nonlinear extended Fisher–Kolmogorov (EFK) equation is proposed. The method reduces CPU runtime and error accumulation by reducing the [...] Read more.

A reduced-dimension (RD) method based on the proper orthogonal decomposition (POD) technology and the linearized Crank–Nicolson mixed finite element (CNMFE) scheme for solving the 2D nonlinear extended Fisher–Kolmogorov (EFK) equation is proposed. The method reduces CPU runtime and error accumulation by reducing the dimension of the unknown CNMFE solution coefficient vectors. For this purpose, the CNMFE scheme of the above EFK equation is established, and the uniqueness, stability and convergence of the CNMFE solutions are discussed. Subsequently, the matrix-based RDCNMFE scheme is derived by applying the POD method. Furthermore, the uniqueness, stability and error estimates of the linearized RDCNMFE solution are proved. Finally, numerical experiments are carried out to validate the theoretical findings. In addition, we contrast the RDCNMFE method with the CNMFE method, highlighting the advantages of the dimensionality reduction method. Full article

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13 pages, 315 KiB

Open AccessArticle

Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities

by Milena Dimova, Natalia Kolkovska and Nikolai Kutev

Axioms 2024, 13(10), 709; https://doi.org/10.3390/axioms13100709 - 14 Oct 2024

Viewed by 479

Abstract

In this paper, we study the initial boundary value problem for wave equations with combined logarithmic and power-type nonlinearities. For arbitrary initial energy, we prove a necessary and sufficient condition for blow up at infinity of the global weak solutions. In addition, we [...] Read more.

In this paper, we study the initial boundary value problem for wave equations with combined logarithmic and power-type nonlinearities. For arbitrary initial energy, we prove a necessary and sufficient condition for blow up at infinity of the global weak solutions. In addition, we derive a growth estimate for the blowing up global solutions. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems)

12 pages, 316 KiB

Open AccessArticle

Modified

F (R, T^{2})

-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry

by Mohd Danish Siddiqi and Fatemah Mofarreh

Axioms 2024, 13(10), 708; https://doi.org/10.3390/axioms13100708 - 14 Oct 2024

Viewed by 613

Abstract

In the present research note, we discuss the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the

F (R, T^{2})

-gravity [...] Read more.

In the present research note, we discuss the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the

F (R, T^{2})

-gravity model. Furthermore, we deal with the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to

F (R, T^{2})

-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential

U_{n}

with hyperbolic Ricci solitons in the

F (R, T^{2})

-gravity model coupled with perfect fluid and a phantom barrier. Full article

27 pages, 436 KiB

Open AccessArticle

On the Conflation of Negative Binomial and Logarithmic Distributions

by Anfal A. Alqefari, Abdulhamid A. Alzaid and Najla Qarmalah

Axioms 2024, 13(10), 707; https://doi.org/10.3390/axioms13100707 - 13 Oct 2024

Viewed by 650

Abstract

In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for instance, is the negative binomial [...] Read more.

In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for instance, is the negative binomial distribution (NBD), which performs well with over-dispersed data. In this paper, a new count distribution is introduced, called the conflation of negative binomial and logarithmic distributions, which is formed by conflating the negative binomial and logarithmic distributions, resulting in a distribution that possesses some of the properties of negative binomial and logarithmic distributions. The distribution has two parameters and is verified by a positive integer. Two modifications are proposed to the distribution, which includes zero as a support point. The new distribution is valuable from a theoretical perspective since it is a member of the weighted negative binomial distribution family. In addition, the distribution differs from the NBD in the sense that the probability of lower counts is inflated. This study discusses the characteristics of the proposed distribution and its modified versions, such as moments, probability generating functions, likelihood stochastic ordering, log-concavity, and unimodality properties. Real-world data are used to evaluate the performance of the proposed models against other models. All computations shown in this paper were produced using the R programming language. Full article

(This article belongs to the Special Issue Probability, Statistics and Estimations, 2nd Edition)

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13 pages, 4219 KiB

Open AccessArticle

Dynamic Sliding Mode Control of Spherical Bubble for Cavitation Suppression

by Ali Karami-Mollaee and Oscar Barambones

Axioms 2024, 13(10), 706; https://doi.org/10.3390/axioms13100706 - 13 Oct 2024

Viewed by 697

Abstract

Cavitation is a disadvantageous phenomenon that occurs when fluid pressure drops below its vapor pressure. Under these conditions, bubbles form in the fluid. When these bubbles flow into a high-pressure area or tube, they erupt, causing harm to mechanical parts such as centrifugal [...] Read more.

Cavitation is a disadvantageous phenomenon that occurs when fluid pressure drops below its vapor pressure. Under these conditions, bubbles form in the fluid. When these bubbles flow into a high-pressure area or tube, they erupt, causing harm to mechanical parts such as centrifugal pumps. The difference in pressure in a fluid is the result of varying temperatures. One way to eliminate cavitation is to reduce the radius of the bubbles to zero before they reach high-pressure areas, using a robust approach. In this paper, sliding mode control is used for this purpose due to its invariance property. To force the radius of the bubbles toward zero and prevent chattering, a new dynamic sliding mode control approach is used. In dynamic sliding mode control, chattering is removed by passing the input control through a low-pass filter, such as an integrator. A general model of the spherical bubble is used, transferred to the state space, and then a state proportional-integral feedback is applied to obtain a linear system with a new input control signal. A comparison is also made with traditional sliding mode control using state feedback, providing a trusted comparison. Full article

(This article belongs to the Special Issue New Perspectives in Control Theory)

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11 pages, 257 KiB

Open AccessReview

Join Spaces and Lattices

by Violeta Leoreanu-Fotea and Sarka Hoskova-Mayerova

Axioms 2024, 13(10), 705; https://doi.org/10.3390/axioms13100705 - 12 Oct 2024

Viewed by 417

Abstract

Hypergroups represent a generalization of groups, introduced by Marty, that are rich in applications in several sectors of mathematics and in other fields. An important class of hypergroups called join spaces is presented in this paper, along with some connections to lattice theory, [...] Read more.

Hypergroups represent a generalization of groups, introduced by Marty, that are rich in applications in several sectors of mathematics and in other fields. An important class of hypergroups called join spaces is presented in this paper, along with some connections to lattice theory, in particular, to modular and to distributive lattices. In particular, we study join spaces associated with chains through functions and we analyze when such join spaces are isomorphic. Moreover, a combinatorial problem is presented for a finite context, focusing on calculating the number of isomorphisms classes of join spaces. Full article

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

28 pages, 11701 KiB

Open AccessArticle

Bifurcation of a Leslie–Gower Predator–Prey Model with Nonlinear Harvesting and a Generalist Predator

by Mengxin He and Zhong Li

Axioms 2024, 13(10), 704; https://doi.org/10.3390/axioms13100704 - 12 Oct 2024

Viewed by 617

Abstract

A Leslie–Gower predator–prey model with nonlinear harvesting and a generalist predator is considered in this paper. It is shown that the degenerate positive equilibrium of the system is a cusp of codimension up to 4, and the system admits the cusp-type degenerate Bogdanov–Takens [...] Read more.

A Leslie–Gower predator–prey model with nonlinear harvesting and a generalist predator is considered in this paper. It is shown that the degenerate positive equilibrium of the system is a cusp of codimension up to 4, and the system admits the cusp-type degenerate Bogdanov–Takens bifurcation of codimension 4. Moreover, the system has a weak focus of at least order 3 and can undergo degenerate Hopf bifurcation of codimension 3. We verify, through numerical simulations, that the system admits three different stable states, such as a stable fixed point and three limit cycles (the middle one is unstable), or two stable fixed points and two limit cycles. Our results reveal that nonlinear harvesting and a generalist predator can lead to richer dynamics and bifurcations (such as three limit cycles or tristability); specifically, harvesting can cause the extinction of prey, but a generalist predator provides some protection for the predator in the absence of prey. Full article

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16 pages, 298 KiB

Open AccessArticle

Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms

by Asma Al-Jaser, Insaf F. Ben Saoud, Higinio Ramos and Belgees Qaraad

Axioms 2024, 13(10), 703; https://doi.org/10.3390/axioms13100703 - 11 Oct 2024

Viewed by 532

Abstract

In this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for excluding increasing [...] Read more.

In this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for excluding increasing positive solutions and decreasing positive solutions so that the resulting criteria are easier to apply than other criteria that have appeared in the literature. We have obtained new oscillation criteria that hold up more robustly upon application. Some examples are presented to illustrate the significance of our main findings. Full article

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

15 pages, 326 KiB

Open AccessArticle

Non-Fragile Sampled Control Design for an Interconnected Large-Scale System via Wirtinger Inequality

by Volodymyr Lynnyk and Branislav Rehák

Axioms 2024, 13(10), 702; https://doi.org/10.3390/axioms13100702 - 10 Oct 2024

Viewed by 544

Abstract

A control design for a linear large-scale interconnected system composed of identical subsystems is presented in this paper. The control signal of all subsystems is sampled. For different subsystems, the sampling times are not identical. Nonetheless, it is assumed that a bound exists [...] Read more.

A control design for a linear large-scale interconnected system composed of identical subsystems is presented in this paper. The control signal of all subsystems is sampled. For different subsystems, the sampling times are not identical. Nonetheless, it is assumed that a bound exists for the maximal sampling time. The control algorithm is designed using the Wirtinger inequality, and the non-fragile control law is proposed. The size of the linear matrix inequalities to be solved by the proposed control algorithm is independent of the number of subsystems composing the overall system. Hence, the algorithm is computationally effective. The results are illustrated by two examples. The first example graphically illustrates the function of the proposed algorithm while the second one compares with a method for stabilizing a large-scale system obtained earlier, thus illustrating the improved capabilities of the presented algorithm. Full article

(This article belongs to the Special Issue Advances in Mathematical Methods in Optimal Control and Applications)

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17 pages, 892 KiB

Open AccessArticle

Bivariate Pareto–Feller Distribution Based on Appell Hypergeometric Function

by Christian Caamaño-Carrillo, Moreno Bevilacqua, Michael Zamudio-Monserratt and Javier E. Contreras-Reyes

Axioms 2024, 13(10), 701; https://doi.org/10.3390/axioms13100701 - 9 Oct 2024

Viewed by 663

Abstract

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate distribution based on the Appell hypergeometric function with [...] Read more.

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate distribution based on the Appell hypergeometric function with marginal Pareto–Feller distributions obtained from two independent gamma random variables. The proposed distribution has the beta prime marginal distributions as special case, which were obtained using a Kibble-type bivariate gamma distribution, and the stochastic representation was obtained by the quotient of a scale mixture of two gamma random variables. This result can be viewed as a generalization of the standard bivariate beta I (or inverted bivariate beta distribution). Moreover, the obtained bivariate density is based on two confluent hypergeometric functions. Then, we derive the probability distribution function, the cumulative distribution function, the moment-generating function, the characteristic function, the approximated differential entropy, and the approximated mutual information index. Based on numerical examples, the exact and approximated expressions are shown. Full article

(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)

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22 pages, 19554 KiB

Open AccessArticle

Computational Study of Shocked V-Shaped N₂/SF₆ Interface across Varying Mach Numbers

by Salman Saud Alsaeed and Satyvir Singh

Axioms 2024, 13(10), 700; https://doi.org/10.3390/axioms13100700 - 9 Oct 2024

Cited by 1 | Viewed by 707

Abstract

The Mach number effect on the Richtmyer–Meshkov instability (RMI) evolution of the shocked V-shaped

N_{2}

/

{SF}_{6}

interface is numerically studied in this research. Four distinct Mach numbers are taken into consideration for this purpose: [...] Read more.

The Mach number effect on the Richtmyer–Meshkov instability (RMI) evolution of the shocked V-shaped

N_{2}

/

{SF}_{6}

interface is numerically studied in this research. Four distinct Mach numbers are taken into consideration for this purpose:

M_{s} = 1.12, 1.22, 1.42

, and 1.62. A two-dimensional space of compressible two-component Euler equations is simulated using a high-order modal discontinuous Galerkin approach to computational simulations. The numerical results show good consistency when compared to the available experimental data. The computational results show that the RMI evolution in the shocked V-shaped

N_{2}

/

{SF}_{6}

interface is critically dependent on the Mach number. The flow field, interface deformation, intricate wave patterns, inward jet development, and vorticity generation are all strongly impacted by the shock Mach number. As the Mach number increases, the V-shaped interface deforms differently, and the distance between the Mach stem and the triple points varies depending on the Mach number. Compared to lower Mach numbers, higher ones produce larger rolled-up vortex chains. A thorough analysis of the Mach number effect identifies the factors that propel the creation of vorticity during the interaction phase. Moreover, kinetic energy and enstrophy both dramatically rise with increasing Mach number. Lastly, a detailed analysis is carried out to determine how the Mach number affects the temporal variations in the V-shaped interface’s features. Full article

(This article belongs to the Special Issue Recent Progress in Computational Fluid Dynamics)

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16 pages, 344 KiB

Open AccessArticle

Reformulation and Enhancement of Distributed Robust Optimization Framework Incorporating Decision-Adaptive Uncertainty Sets

by Jie Zhang, Shuang Lin and Yifei Wang

Axioms 2024, 13(10), 699; https://doi.org/10.3390/axioms13100699 - 8 Oct 2024

Viewed by 707

Abstract

Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the probability [...] Read more.

Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introduce a novel class of DRO challenges where the probability distribution of random variables is contingent upon the decision variables, and the ambiguity set is defined through parameterization involving the mean and a covariance matrix, which also depend on the decision variables. This dependency makes DRO difficult to solve directly; therefore, first, we demonstrate that under the condition of a full-space support set, the original problem can be reduced to a second-order cone programming (SOCP) problem. Subsequently, we solve this second-order cone programming problem using a projection differential equation approach. Compared with the traditional methods, the differential equation method offers advantages in providing continuous and smooth solutions, offering inherent stability analysis, and possessing a rich mathematical toolbox, which make the differential equation a powerful and versatile tool for addressing complex optimization challenges. Full article

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Axioms, Volume 13, Issue 10 (October 2024) – 74 articles

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