Journal Description
Axioms
Axioms
is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA) and Union of Slovak Mathematicians and Physicists (JSMF) are affiliated with Axioms and their members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High visibility: indexed within SCIE (Web of Science), dblp, and other databases.
- Journal Rank: JCR - Q2 (Mathematics, Applied)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.8 days after submission; acceptance to publication is undertaken in 2.8 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Companion journal: Logics.
Impact Factor:
2.0 (2022);
5-Year Impact Factor:
1.9 (2022)
Latest Articles
On Approximate Variational Inequalities and Bilevel Programming Problems
Axioms 2024, 13(6), 371; https://doi.org/10.3390/axioms13060371 - 30 May 2024
Abstract
In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local -quasi solutions of the BLPP,
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In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local -quasi solutions of the BLPP, under generalized approximate convexity assumptions, via limiting subdifferentials. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (KKM)-Fan’s lemma, we derive some existence results for the solutions of AMTVI and ASTVI. We have furnished suitable, non-trivial, illustrative examples to demonstrate the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that explores relationships between the approximate variational inequalities and BLPP under the assumptions of generalized approximate convexity by employing the powerful tool of limiting subdifferentials.
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(This article belongs to the Special Issue Research on Fixed Point Theory and Application)
Open AccessArticle
Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor
by
Mohd Danish Siddiqi and Rawan Bossly
Axioms 2024, 13(6), 370; https://doi.org/10.3390/axioms13060370 - 30 May 2024
Abstract
In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient
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In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient Ricci solitons. We also characterize anti-invariant, invariant, quasi-umbilical submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection for which the same inequality case holds. Finally, we deduce the above inequalities in terms of a scalar concircular field on submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection.
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(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)
Open AccessArticle
A Discrete Cramér–Von Mises Statistic Related to Hahn Polynomials with Application to Goodness-of-Fit Testing for Hypergeometric Distributions
by
Jean-Renaud Pycke
Axioms 2024, 13(6), 369; https://doi.org/10.3390/axioms13060369 - 30 May 2024
Abstract
We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy enables us to introduce a discrete Cramér–von Mises
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We give the Karhunen–Loève expansion of the covariance function of a family of discrete weighted Brownian bridges, appearing as discrete analogues of continuous Gaussian processes related to Cramér –von Mises and Anderson–Darling statistics. This analogy enables us to introduce a discrete Cramér–von Mises statistic and show that this statistic satisfies a property of local asymptotic Bahadur optimality for a statistical test involving the classical hypergeometric distributions. Our statistic and the goodness-of-fit problem we deal with are based on basic properties of Hahn polynomials and are, therefore, subject to some extension to all families of classical orthogonal polynomials, as well as their q-analogues. Due probably to computational difficulties, the family of discrete Cramér–von Mises statistics has received less attention than its continuous counterpart—the aim of this article is to bridge part of this gap.
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(This article belongs to the Special Issue New Trends in Discrete Probability and Statistics)
Open AccessArticle
A New Hybrid Approach for Clustering, Classification, and Prediction of World Development Indicators Combining General Type-2 Fuzzy Systems and Neural Networks
by
Martha Ramírez, Patricia Melin and Oscar Castillo
Axioms 2024, 13(6), 368; https://doi.org/10.3390/axioms13060368 - 30 May 2024
Abstract
Economic risk is a probability that measures the possible alterations, as well as the uncertainty, generated by multiple internal or external factors. Sometimes it could cause the impossibility of guaranteeing the level of compliance with organizational goals and objectives, which is why for
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Economic risk is a probability that measures the possible alterations, as well as the uncertainty, generated by multiple internal or external factors. Sometimes it could cause the impossibility of guaranteeing the level of compliance with organizational goals and objectives, which is why for their administration they are frequently divided into multiple categories according to their consequences and impact. Global indicators are dynamic and sometimes the correlation is uncertain because they depend largely on a combination of economic, social, and environmental factors. Thus, our proposal consists of a model for prediction and classification of multivariate risk factors such as birth rate and population growth, among others, using multiple neural networks and General Type-2 fuzzy systems. The contribution is the proposal to integrate multiple variables of several time series using both supervised and unsupervised neural networks, and a generalized Type-2 fuzzy integration. Results show the advantages of utilizing the method for the fuzzy integration of multiple time series attributes, with which the user can then prevent future threats from the global environment that impact the scheduled compliance process.
Full article
(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Fuzzy Modeling, Optimization and Computational Intelligence)
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Bivariate Random Coefficient Integer-Valued Autoregressive Model Based on a ρ-Thinning Operator
by
Chang Liu and Dehui Wang
Axioms 2024, 13(6), 367; https://doi.org/10.3390/axioms13060367 - 29 May 2024
Abstract
While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter
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While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter and integrates random coefficients. This approach combines characteristics from both binomial and negative binomial thinning operators, thereby offering a flexible framework capable of generating counting series exhibiting equidispersion, overdispersion, or underdispersion. Notably, our model includes two distinct classes of first-order bivariate geometric integer-valued autoregressive models: one class employs binomial thinning (BVGINAR(1)), and the other adopts negative binomial thinning (BVNGINAR(1)). We establish the stationarity and ergodicity of the model and estimate its parameters using a combination of the Yule–Walker (YW) and conditional maximum likelihood (CML) methods. Furthermore, Monte Carlo simulation experiments are conducted to evaluate the finite sample performances of the proposed estimators across various parameter configurations, and the Anderson-Darling (AD) test is employed to assess the asymptotic normality of the estimators under large sample sizes. Ultimately, we highlight the practical applicability of the examined model by analyzing two real-world datasets on crime counts in New South Wales (NSW) and comparing its performance with other popular overdispersed BINAR(1) models.
Full article
(This article belongs to the Section Mathematical Analysis)
Open AccessArticle
Certain New Applications of Symmetric q-Calculus for New Subclasses of Multivalent Functions Associated with the Cardioid Domain
by
Hari M. Srivastava, Daniel Breaz, Shahid Khan and Fairouz Tchier
Axioms 2024, 13(6), 366; https://doi.org/10.3390/axioms13060366 - 29 May 2024
Abstract
In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We
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In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are additionally taken into consideration to show how the findings of this research relate to those of earlier studies.
Full article
(This article belongs to the Special Issue Advances in Geometric Function Theory and Related Topics)
Open AccessArticle
Analyzing Richtmyer–Meshkov Phenomena Triggered by Forward-Triangular Light Gas Bubbles: A Numerical Perspective
by
Satyvir Singh and Ahmed Hussein Msmali
Axioms 2024, 13(6), 365; https://doi.org/10.3390/axioms13060365 - 29 May 2024
Abstract
In this paper, we present a numerical investigation into elucidating the complex dynamics of Richtmyer–Meshkov (RM) phenomena initiated by the interaction of shock waves with forward-triangular light gas bubbles. The triangular bubble is filled with neon, helium, or hydrogen gas, and is surrounded
[...] Read more.
In this paper, we present a numerical investigation into elucidating the complex dynamics of Richtmyer–Meshkov (RM) phenomena initiated by the interaction of shock waves with forward-triangular light gas bubbles. The triangular bubble is filled with neon, helium, or hydrogen gas, and is surrounded by nitrogen gas. Three different shock Mach numbers are considered: and 1.41. For the numerical simulations, a two-dimensional system of compressible Euler equations for two-component gas flows is solved by utilizing the high-fidelity explicit modal discontinuous Galerkin technique. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The numerical model explores the impact of the Atwood number on the underlying mechanisms of the shock-induced forward-triangle bubble, encompassing aspects such as flow evolution, wave characteristics, jet formation, generation of vorticity, interface features, and integral diagnostics. Furthermore, the impacts of shock strengths and positive Atwood numbers on the flow evolution are also analyzed. Insights gained from this numerical perspective enhance our understanding of RM phenomena triggered by forward-triangular light gas bubbles, with implications for diverse applications in engineering, astrophysics, and fusion research.
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(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)
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Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures
by
Evgeniya Egorova, Vladislav Leonov, Aleksey Mokryakov and Vladimir Tsurkov
Axioms 2024, 13(6), 364; https://doi.org/10.3390/axioms13060364 - 29 May 2024
Abstract
This paper continues the study of second-order signature properties—the characterization of the extreme 3-uniform hypergraph. Previously, bases were used to count extreme 3-uniform hypergraphs. However, the algorithm using this mechanism is extremely labor-intensive. The structure of the signature allows us to use it
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This paper continues the study of second-order signature properties—the characterization of the extreme 3-uniform hypergraph. Previously, bases were used to count extreme 3-uniform hypergraphs. However, the algorithm using this mechanism is extremely labor-intensive. The structure of the signature allows us to use it as a more efficient basis for the same problem. Here, we establish the nature of the mutual correspondence between the kind of second-order signature and extreme hypergraphs, and we present a new algorithm to find the power of the set of extreme 3-uniform hypergraphs through the set of their characteristic-signatures. New results obtained with the proposed tool are also presented.
Full article
(This article belongs to the Special Issue Advances in Graph Theory and Combinatorial Optimization)
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Perturbed Dirac Operators and Boundary Value Problems
by
Xiaopeng Liu and Yuanyuan Liu
Axioms 2024, 13(6), 363; https://doi.org/10.3390/axioms13060363 - 29 May 2024
Abstract
In this paper, the time-independent Klein-Gordon equation in is treated with a decomposition of the operator by the Clifford algebra . Some properties of integral operators associated the
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In this paper, the time-independent Klein-Gordon equation in is treated with a decomposition of the operator by the Clifford algebra . Some properties of integral operators associated the kind of equations and some Riemann-Hilbert boundary value problems for perturbed Dirac operators are investigated.
Full article
(This article belongs to the Special Issue Differential Equations and Its Application)
Open AccessArticle
Steady Solutions to Equations of Viscous Compressible Multifluids
by
Alexander Mamontov and Dmitriy Prokudin
Axioms 2024, 13(6), 362; https://doi.org/10.3390/axioms13060362 - 28 May 2024
Abstract
For the differential equations of the barotropic dynamics of compressible viscous multifluids in a bounded three-dimensional domain with an immobile rigid boundary, a study of the solvability of the boundary value problem is made. Weak generalized solutions to the boundary value problem are
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For the differential equations of the barotropic dynamics of compressible viscous multifluids in a bounded three-dimensional domain with an immobile rigid boundary, a study of the solvability of the boundary value problem is made. Weak generalized solutions to the boundary value problem are shown to exist with weak constraints on the types of viscosity matrices and constitutive equations for pressure and momentum exchange.
Full article
(This article belongs to the Special Issue Fluid Dynamics: Mathematics and Numerical Experiment)
Open AccessArticle
Multi-Strategy-Improved Growth Optimizer and Its Applications
by
Rongxiang Xie, Liya Yu, Shaobo Li, Fengbin Wu, Tao Zhang and Panliang Yuan
Axioms 2024, 13(6), 361; https://doi.org/10.3390/axioms13060361 - 28 May 2024
Abstract
The growth optimizer (GO) is a novel metaheuristic algorithm designed to tackle complex optimization problems. Despite its advantages of simplicity and high efficiency, GO often encounters localized stagnation when dealing with discretized, high-dimensional, and multi-constraint problems. To address these issues, this paper proposes
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The growth optimizer (GO) is a novel metaheuristic algorithm designed to tackle complex optimization problems. Despite its advantages of simplicity and high efficiency, GO often encounters localized stagnation when dealing with discretized, high-dimensional, and multi-constraint problems. To address these issues, this paper proposes an enhanced version of GO called CODGBGO. This algorithm incorporates three strategies to enhance its performance. Firstly, the Circle-OBL initialization strategy is employed to enhance the quality of the initial population. Secondly, an exploration strategy is implemented to improve population diversity and the algorithm’s ability to escape local optimum traps. Finally, the exploitation strategy is utilized to enhance the convergence speed and accuracy of the algorithm. To validate the performance of CODGBGO, it is applied to solve the CEC2017, CEC2020, 18 feature selection problems, and 4 real engineering optimization problems. The experiments demonstrate that the novel CODGBGO algorithm effectively addresses the challenges posed by complex optimization problems, offering a promising approach.
Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
Open AccessArticle
Skew Cyclic and Skew Constacyclic Codes over a Mixed Alphabet
by
Karthick Gowdhaman, Cruz Mohan, Chinnapillai Durairajan, Selda Çalkavur and Patrick Solé
Axioms 2024, 13(6), 360; https://doi.org/10.3390/axioms13060360 - 28 May 2024
Abstract
In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet , where p is an odd prime with m odd and
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In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet , where p is an odd prime with m odd and with , and with Such codes consist of the juxtaposition of three codes of the same size over and , respectively. We investigate the generator polynomial for skew cyclic codes over . Furthermore, we discuss the structural properties of the skew cyclic and skew constacyclic codes over We also study their q-ary images under suitable Gray maps.
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Open AccessArticle
Generalized Bounded Turning Functions Connected with Gregory Coefficients
by
Huo Tang, Zeeshan Mujahid, Nazar Khan, Fairouz Tchier and Muhammad Ghaffar Khan
Axioms 2024, 13(6), 359; https://doi.org/10.3390/axioms13060359 - 28 May 2024
Abstract
In this research article, we introduce new family of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for
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In this research article, we introduce new family of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for the functions belonging to this newly defined family, demonstrating their sharpness. Furthermore, we find the third Hankel determinant for functions in the class . Moreover, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the under-considered class are estimated.
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(This article belongs to the Special Issue New Developments in Geometric Function Theory III)
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On the Kantorovich Theory for Nonsingular and Singular Equations
by
Ioannis K. Argyros, Santhosh George, Samundra Regmi and Michael I. Argyros
Axioms 2024, 13(6), 358; https://doi.org/10.3390/axioms13060358 - 28 May 2024
Abstract
We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the implementation of these methods easier than in
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We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the implementation of these methods easier than in earlier studies. The analysis uses relaxed generalized continuity of the derivatives of operators involved required to control the derivative and on real majorizing sequences. The same approach can also be implemented on other iterative methods with inverses. The examples complement the theory by verifying the convergence conditions and demonstrating the performance of the methods.
Full article
(This article belongs to the Special Issue Differential Equations and Inverse Problems)
Open AccessArticle
An Intuitionistic Fuzzy Multi-Criteria Approach for Prioritizing Failures That Cause Overproduction: A Case Study in Process Manufacturing
by
Ranka Sudžum, Snežana Nestić, Nikola Komatina and Milija Kraišnik
Axioms 2024, 13(6), 357; https://doi.org/10.3390/axioms13060357 - 27 May 2024
Abstract
Overproduction is one of the most significant wastes of Lean that can occur in any manufacturing company. Identifying and prioritizing failures that lead to overproduction are crucial tasks for operational managers and engineers. Therefore, this paper presents a new approach for determining the
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Overproduction is one of the most significant wastes of Lean that can occur in any manufacturing company. Identifying and prioritizing failures that lead to overproduction are crucial tasks for operational managers and engineers. Therefore, this paper presents a new approach for determining the priority of failures that cause overproduction, based on an intuitionistic fuzzy Multi-Criteria Optimization model and the Failure Mode and Effects Analysis framework. The existing vagueness in the relative importance of risk factors and their values is described using natural language words, which are modeled with trapezoidal intuitionistic fuzzy numbers. Determining the relative importance of risk factors is defined as a fuzzy group decision-making problem, and the weight vector is obtained by applying the proposed Analytical Hierarchy Process with trapezoidal intuitionistic fuzzy numbers. The compromise solution, as well as the stability check of the obtained compromise solution, is achieved using the proposed Multi-Criteria Optimization and Compromise Solution with trapezoidal intuitionistic fuzzy numbers. The proposed model was applied to data collected from a process manufacturing company.
Full article
(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Fuzzy Modeling, Optimization and Computational Intelligence)
Open AccessArticle
New Nonlinear Retarded Integral Inequalities and Their Applications to Nonlinear Retarded Integro-Differential Equations
by
Mahvish Samar, Xinzhong Zhu, Abdul Shakoor and Mawia Osman
Axioms 2024, 13(6), 356; https://doi.org/10.3390/axioms13060356 - 27 May 2024
Abstract
The purpose of this article is to present some new nonlinear retarded integral inequalities which can be utilized to study the existence, stability, boundedness, uniqueness, and asymptotic behavior of solutions of nonlinear retarded integro-differential equations, and these inequalities can be used in the
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The purpose of this article is to present some new nonlinear retarded integral inequalities which can be utilized to study the existence, stability, boundedness, uniqueness, and asymptotic behavior of solutions of nonlinear retarded integro-differential equations, and these inequalities can be used in the symmetrical properties of functions. These inequalities also generalize some former famous inequalities in the literature. Two examples as applications will be provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problems for nonlinear integro-differential equations and differential equations which can be seen in graphs. This research work will ensure opening new opportunities for studying nonlinear dynamic inequalities on a time-scale structure of a varying nature.
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(This article belongs to the Special Issue Advances in Difference Equations)
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Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions
by
Remigijus Leipus, Jonas Šiaulys, Svetlana Danilenko and Jūratė Karasevičienė
Axioms 2024, 13(6), 355; https://doi.org/10.3390/axioms13060355 - 25 May 2024
Abstract
This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped
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This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided.
Full article
(This article belongs to the Special Issue Stochastic Modeling and Optimization Techniques)
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One-Dimensional BSDEs with Jumps and Logarithmic Growth
by
El Mountasar Billah Bouhadjar, Nabil Khelfallah and Mhamed Eddahbi
Axioms 2024, 13(6), 354; https://doi.org/10.3390/axioms13060354 - 24 May 2024
Abstract
In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with
[...] Read more.
In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with respect to the jump component. Our study rigorously establishes the existence and uniqueness of solutions within suitable functional spaces. Additionally, we relax the Lipschitz condition on the Poisson component, permitting the generator to exhibit logarithmic growth with respect to all variables. Taking a step further, we employ an exponential transformation to establish an equivalence between a solution of a BSDEJ exhibiting quadratic growth in the z-variable and a BSDEJ showing a logarithmic growth with respect to y and z.
Full article
(This article belongs to the Special Issue Stochastic Modeling and Its Analysis)
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Dynamical Behaviors of Stochastic SIS Epidemic Model with Ornstein–Uhlenbeck Process
by
Huina Zhang, Jianguo Sun, Peng Yu and Daqing Jiang
Axioms 2024, 13(6), 353; https://doi.org/10.3390/axioms13060353 - 24 May 2024
Abstract
Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact
[...] Read more.
Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact that it has long been assumed that the immune system produces corresponding antibodies after vaccination, but usually does not achieve the level of complete protection for undergoing environmental fluctuations. In this paper, we investigate a stochastic SIS epidemic model with incomplete inoculation, which is perturbed by the Ornstein–Uhlenbeck process and Brownian motion. We determine the existence of a unique global solution for the stochastic SIS epidemic model and derive control conditions for the extinction. By constructing two suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process, we establish sufficient conditions for the existence of stationary distribution, which means the disease will prevail. Furthermore, we obtain the exact expression of the probability density function near the pseudo-equilibrium point of the stochastic model while addressing the four-dimensional Fokker–Planck equation under the same conditions. Finally, we conduct several numerical simulations to validate the theoretical results.
Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
Open AccessArticle
An Introduction to Extended Gevrey Regularity
by
Nenad Teofanov, Filip Tomić and Milica Žigić
Axioms 2024, 13(6), 352; https://doi.org/10.3390/axioms13060352 - 24 May 2024
Abstract
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in
[...] Read more.
Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in Gevrey settings. In this paper, we consider a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview of extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultra distributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic.
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(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)
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