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
Quasi-Configurations Derived by Special Arrangements of Lines
Axioms 2024, 13(5), 321; https://doi.org/10.3390/axioms13050321 (registering DOI) - 11 May 2024
Abstract
A quasi-configuration is a point–line incidence structure in which each point is incident with at least three lines and each line is incident with at least three points. We investigate derived quasi-configurations that arise both by duality and intersecting lines of three special
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A quasi-configuration is a point–line incidence structure in which each point is incident with at least three lines and each line is incident with at least three points. We investigate derived quasi-configurations that arise both by duality and intersecting lines of three special arrangements of lines. Sets with few intersection numbers are provided.
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(This article belongs to the Special Issue Theory of Curves and Knots with Applications)
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Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions
by
Meng Qin, Zhuohua Zhang, Rui Luo, Mengjie Ren and Denghui Wu
Axioms 2024, 13(5), 320; https://doi.org/10.3390/axioms13050320 (registering DOI) - 11 May 2024
Abstract
In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the stability of the Borell–Brascamp–Lieb
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In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the stability of the Borell–Brascamp–Lieb inequality for multiple power concave functions via relative asymmetry.
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(This article belongs to the Special Issue Advances in Convex Geometry and Analysis)
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Strategic Behavior and Optimal Inventory Level in a Make-to-Stock Queueing System with Retrial Customers
by
Yuejiao Wang and Chenguang Cai
Axioms 2024, 13(5), 319; https://doi.org/10.3390/axioms13050319 (registering DOI) - 11 May 2024
Abstract
In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they become repeat customers. Each repeat
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In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they become repeat customers. Each repeat customer repeats their demand after an exponential amount of time until they have been successfully served. We explore the equilibrium strategies of customers in both the almost observable and unobservable cases. Furthermore, we also analyze the expected costs of the entire system based on the customers’ behavior in these two cases. Additionally, we determine the optimal inventory levels in both cases through numerical experiments.
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(This article belongs to the Section Mathematical Analysis)
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Quasi-Contraction Maps in Subordinate Semimetric Spaces
by
Areej Alharbi, Hamed Alsulami and Maha Noorwali
Axioms 2024, 13(5), 318; https://doi.org/10.3390/axioms13050318 (registering DOI) - 10 May 2024
Abstract
Throughout this study, we discuss the subordinate Pompeiu–Hausdorff metric (SPHM) in subordinate semimetric spaces. Moreover, we present a well-behaved quasi-contraction (WBQC) to solve quasi-contraction (QC) problems in subordinate semimetric spaces under some local constraints. Furthermore, we provide examples to support our conclusion.
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(This article belongs to the Special Issue Research on Fixed Point Theory and Application)
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A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments
by
Yue-Wu Li and Feng Qi
Axioms 2024, 13(5), 317; https://doi.org/10.3390/axioms13050317 (registering DOI) - 10 May 2024
Abstract
In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some specific arguments, successfully apply a special case
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In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some specific arguments, successfully apply a special case of the newly extended closed-form formula to derive an alternative form for the Maclaurin power series expansion of the Wilf function, and discover two novel increasing rational approximations to a quarter of the circular constant.
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Convergence Results for History-Dependent Variational Inequalities
by
Mircea Sofonea and Domingo A. Tarzia
Axioms 2024, 13(5), 316; https://doi.org/10.3390/axioms13050316 (registering DOI) - 10 May 2024
Abstract
We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove
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We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove that solving these problems is equivalent to solving the original history-dependent variational inequality. Next, we state and prove a convergence criterion, i.e., we provide necessary and sufficient conditions which guarantee the convergence of a sequence of functions to the solution of the considered inequality. Based on the equivalence above, we deduce various consequences that present some interest on their own, and, moreover, we obtain convergence results for the two additional problems considered. Finally, we apply our abstract results to the study of an inequality problem in solid mechanics. It concerns the study of a viscoelastic constitutive law with long memory and unilateral constraints, for which we deduce a convergence result and provide the corresponding mechanical interpretations.
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(This article belongs to the Section Hilbert’s Sixth Problem)
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Parameter Estimation in Spatial Autoregressive Models with Missing Data and Measurement Errors
by
Tengjun Li, Zhikang Zhang and Yunquan Song
Axioms 2024, 13(5), 315; https://doi.org/10.3390/axioms13050315 (registering DOI) - 10 May 2024
Abstract
This study addresses the problem of parameter estimation in spatial autoregressive models with missing data and measurement errors in covariates. Specifically, a corrected likelihood estimation approach is employed to rectify the bias in the log-maximum likelihood function induced by measurement errors. Additionally, a
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This study addresses the problem of parameter estimation in spatial autoregressive models with missing data and measurement errors in covariates. Specifically, a corrected likelihood estimation approach is employed to rectify the bias in the log-maximum likelihood function induced by measurement errors. Additionally, a combination of inverse probability weighting (IPW) and mean imputation is utilized to mitigate the bias caused by missing data. Under several mild conditions, it is demonstrated that the proposed estimators are consistent and possess oracle properties. The efficacy of the proposed parameter estimation process is assessed through Monte Carlo simulation studies. Finally, the applicability of the proposed method is further substantiated using the Boston Housing Dataset.
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(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications)
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Some Results on Zinbiel Algebras and Rota–Baxter Operators
by
Jizhong Gao, Junna Ni and Jianhua Yu
Axioms 2024, 13(5), 314; https://doi.org/10.3390/axioms13050314 (registering DOI) - 10 May 2024
Abstract
Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the RBOs on two and three-dimensional ZAs are presented. Finally,
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Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the RBOs on two and three-dimensional ZAs are presented. Finally, ZAs are also realized in low dimensions of the RBOs of commutative associative algebras. It was found that not all ZAs can be attained in this way.
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Basic Computational Algorithms for Representing an Aircraft Flight (Calculation of 3D Displacement and Displaying)
by
Adan Ramirez-Lopez
Axioms 2024, 13(5), 313; https://doi.org/10.3390/axioms13050313 (registering DOI) - 10 May 2024
Abstract
This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory.
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This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory. Here, the flight is divided into maneuvers and the aircraft conditions are defined as boundary conditions. Then the aircraft position is calculated using nested loops, which execute the calculation procedure at every step time (Δt). The calculation of the aircraft displacement is obtained as a function of the aircraft speed and heading angles. The simulator was created using the C++ programming language, and each part of the algorithm was compiled independently to reduce the source code, allow easy modification, and improve the programming efficiency. Aerial navigation involves very complex phenomena to be considered for an appropriate representation; moreover, in this manuscript, the influence of the mathematical approach to properly represent the aircraft flight is described in detail. The flight simulator was successfully tested by simulating some basic theoretical flights with different maneuvers, which include stationary position, running along the way, take off, and some movements in the airspace. The maximum aircraft speed tested was 120 km/h, the maximum maneuver time was 12 min, and the space for simulation was assumed to be without obstacles. Here, the geometrical description of path and speed is analyzed according to the symmetric and asymmetric results. Finally, an analysis was conducted to evaluate the approach of the numerical methods used; after that, it was possible to confirm that precision increased as the step time was reduced. According to this analysis, no more than 500 steps are required for a good approach in the calculation of the aircraft displacement.
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(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold
by
Shi-Fan Cai, Sudhakar Kumar Chaubey, Xin Xu, Pan Zhang and Zhi-Heng Zhang
Axioms 2024, 13(5), 312; https://doi.org/10.3390/axioms13050312 - 9 May 2024
Abstract
The aim of this paper is to prove a theorem for holomorphic twisted quiver bundles over a special non-compact Gauduchon manifold, connecting the existence of -Hermite–Yang–Mills metric in differential geometry and the analytic
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The aim of this paper is to prove a theorem for holomorphic twisted quiver bundles over a special non-compact Gauduchon manifold, connecting the existence of -Hermite–Yang–Mills metric in differential geometry and the analytic -stability in algebraic geometry. The proof of the theorem relies on the flow method and the Uhlenbeck–Yau’s continuity method.
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(This article belongs to the Special Issue Advances in Differential Geometry and Mathematical Physics)
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Study of the Six-Compartment Nonlinear COVID-19 Model with the Homotopy Perturbation Method
by
Muhammad Rafiullah, Muhammad Asif, Dure Jabeen and Mahmoud A. Ibrahim
Axioms 2024, 13(5), 311; https://doi.org/10.3390/axioms13050311 - 9 May 2024
Abstract
The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method to solve a six-compartment model
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The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method to solve a six-compartment model for the novel coronavirus (COVID-19), which includes susceptible, exposed, asymptomatic infected, symptomatic infected, and recovered individuals, and the concentration of COVID-19 in the environment is indicated by , , , , , and , respectively. We present the series solution of this model by varying the controlling parameters and representing them graphically. Additionally, we verify the accuracy of the series solution (up to the -degree polynomial) that satisfies both the initial conditions and the model, with all coefficients correct at 18 decimal places. Furthermore, we have compared our results with the Runge–Kutta fourth-order method. Based on our findings, we conclude that the homotopy perturbation method is a promising approach to solve nonlinear dynamical models, particularly those associated with pandemics. This method provides valuable insight into how the control of various parameters can affect the model. We suggest that future studies can expand on our work by exploring additional models and assessing the applicability of other analytical methods.
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(This article belongs to the Special Issue Dynamical Systems: Theory and Applications in Mathematical Biology)
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Recent Advances in Fractional Calculus
by
Péter Kórus and Juan Eduardo Nápoles Valdés
Axioms 2024, 13(5), 310; https://doi.org/10.3390/axioms13050310 - 8 May 2024
Abstract
This Special Issue of the scientific journal Axioms, entitled “Recent Advances in Fractional Calculus”, is dedicated to one of the most dynamic areas of mathematical sciences today [...]
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(This article belongs to the Special Issue Recent Advances in Fractional Calculus)
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Study on SEAI Model of COVID-19 Based on Asymptomatic Infection
by
Lidong Huang, Yue Xia and Wenjie Qin
Axioms 2024, 13(5), 309; https://doi.org/10.3390/axioms13050309 - 8 May 2024
Abstract
In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number and calculate the equilibrium point. Secondly, when
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In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number and calculate the equilibrium point. Secondly, when , the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When , the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease.
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(This article belongs to the Special Issue Recent Advances in Mathematical Modeling of COVID-19 and Other Infectious Diseases)
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On Semi-Vector Spaces and Semi-Algebras with Applications in Fuzzy Automata
by
Giuliano G. La Guardia, Jocemar Q. Chagas, Ervin K. Lenzi, Leonardo Pires, Nicolás Zumelzu and Benjamín Bedregal
Axioms 2024, 13(5), 308; https://doi.org/10.3390/axioms13050308 - 8 May 2024
Abstract
In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers . More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues
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In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers . More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing how to compute them. The topological properties of semi-vector spaces, such as completeness and separability, are also investigated here. New families of semi-vector spaces derived from the semi-metric, semi-norm and semi-inner product, among others, are exhibited. Furthermore, we show several new results concerning semi-algebras. After this theoretical approach, we apply such a theory in fuzzy automata. More precisely, we describe the semi-algebra of A-fuzzy regular languages and we apply the theory of fuzzy automata for counting patterns in DNA sequences.
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(This article belongs to the Special Issue Advances in Linear Algebra with Applications)
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A Short Note on Generating a Random Sample from Finite Mixture Distributions
by
Luai Al-Labadi and Anna Ly
Axioms 2024, 13(5), 307; https://doi.org/10.3390/axioms13050307 - 8 May 2024
Abstract
Computational statistics is a critical skill for professionals in fields such as data science, statistics, and related disciplines. One essential aspect of computational statistics is the ability to simulate random variables from specified probability distributions. Commonly employed techniques for sampling random variables include
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Computational statistics is a critical skill for professionals in fields such as data science, statistics, and related disciplines. One essential aspect of computational statistics is the ability to simulate random variables from specified probability distributions. Commonly employed techniques for sampling random variables include the inverse transform method, acceptance–rejection method, and Box–Muller transformation, all of which rely on sampling from the uniform distribution. A significant concept in statistics is the finite mixture model, characterized by a convex combination of multiple probability density functions. In this paper, we introduce a modified version of the composition method, a standard approach for sampling finite mixture models. Our modification offers the advantage of relying on sampling from the uniform distribution, aligning with prevalent methods in computational statistics. This alignment simplifies teaching computational statistics courses, as well as having other benefits. We offer several examples to illustrate the approach.
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(This article belongs to the Special Issue Recent Advances in Statistical Modeling and Simulations with Applications)
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On Conditional Axioms and Associated Inference Rules
by
Joaquín Borrego-Díaz, Andrés Cordón-Franco and Francisco Félix Lara-Martín
Axioms 2024, 13(5), 306; https://doi.org/10.3390/axioms13050306 - 7 May 2024
Abstract
In the present paper, we address the following general question in the framework of classical first-order logic. Assume that a certain mathematical principle can be formalized in a first-order language by a set E of conditional formulas of the form
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In the present paper, we address the following general question in the framework of classical first-order logic. Assume that a certain mathematical principle can be formalized in a first-order language by a set E of conditional formulas of the form . Given a base theory T, we can use the set of conditional formulas E to extend the base theory in two natural ways. Either we add to T each formula in E as a new axiom (thus obtaining a theory denoted by ) or we extend T by using the formulas in E as instances of an inference rule (thus obtaining a theory denoted by ). The theory will be stronger than , but how much stronger can be? More specifically, is conservative over for theorems of some fixed syntactical complexity ? Under very general assumptions on the set of conditional formulas E, we obtain two main conservation results in this regard. Firstly, if the formulas in E have low syntactical complexity with respect to some prescribed class of formulas and in the applications of side formulas from the class and can be eliminated (in a certain precise sense), then is -conservative over . Secondly, if, in addition, E is a finite set with m conditional sentences, then nested applications of of a depth at most of m suffice to obtain conservativity. These conservation results between axioms and inference rules extend well-known conservation theorems for fragments of first-order arithmetics to a general, purely logical framework.
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(This article belongs to the Topic Mathematical Modeling)
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Construction of Fractional Pseudospectral Differentiation Matrices with Applications
by
Wenbin Li, Hongjun Ma and Tinggang Zhao
Axioms 2024, 13(5), 305; https://doi.org/10.3390/axioms13050305 - 4 May 2024
Abstract
Differentiation matrices are an important tool in the implementation of the spectral collocation method to solve various types of problems involving differential operators. Fractional differentiation of Jacobi orthogonal polynomials can be expressed explicitly through Jacobi–Jacobi transformations between two indexes. In the current paper,
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Differentiation matrices are an important tool in the implementation of the spectral collocation method to solve various types of problems involving differential operators. Fractional differentiation of Jacobi orthogonal polynomials can be expressed explicitly through Jacobi–Jacobi transformations between two indexes. In the current paper, an algorithm is presented to construct a fractional differentiation matrix with a matrix representation for Riemann–Liouville, Caputo and Riesz derivatives, which makes the computation stable and efficient. Applications of the fractional differentiation matrix with the spectral collocation method to various problems, including fractional eigenvalue problems and fractional ordinary and partial differential equations, are presented to show the effectiveness of the presented method.
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(This article belongs to the Special Issue Fractional Calculus and the Applied Analysis)
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The Generalized Eta Transformation Formulas as the Hecke Modular Relation
by
Nianliang Wang, Takako Kuzumaki and Shigeru Kanemitsu
Axioms 2024, 13(5), 304; https://doi.org/10.3390/axioms13050304 - 2 May 2024
Abstract
The transformation formula under the action of a general linear fractional transformation for a generalized Dedekind eta function has been the subject of intensive study since the works of Rademacher, Dieter, Meyer, and Schoenberg et al. However, the (Hecke) modular relation structure was
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The transformation formula under the action of a general linear fractional transformation for a generalized Dedekind eta function has been the subject of intensive study since the works of Rademacher, Dieter, Meyer, and Schoenberg et al. However, the (Hecke) modular relation structure was not recognized until the work of Goldstein-de la Torre, where the modular relations mean equivalent assertions to the functional equation for the relevant zeta functions. The Hecke modular relation is a special case of this, with a single gamma factor and the corresponding modular form (or in the form of Lambert series). This has been the strongest motivation for research in the theory of modular forms since Hecke’s work in the 1930s. Our main aim is to restore the fundamental work of Rademacher (1932) by locating the functional equation hidden in the argument and to reveal the Hecke correspondence in all subsequent works (which depend on the method of Rademacher) as well as in the work of Rademacher. By our elucidation many of the subsequent works will be made clear and put in their proper positions.
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(This article belongs to the Section Algebra and Number Theory)
Open AccessArticle
Estimation of Random Coefficient Autoregressive Model with Error in Covariates
by
Xiaolei Zhang, Jin Chen and Qi Li
Axioms 2024, 13(5), 303; https://doi.org/10.3390/axioms13050303 - 2 May 2024
Abstract
Measurement error is common in many statistical problems and has received considerable attention in various regression contexts. In this study, we consider the random coefficient autoregressive model with measurement error possibly present in covariates. The least squares and weighted least squares methods are
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Measurement error is common in many statistical problems and has received considerable attention in various regression contexts. In this study, we consider the random coefficient autoregressive model with measurement error possibly present in covariates. The least squares and weighted least squares methods are used to estimate the model parameters, and the consistency and asymptotic normality of the two kinds of estimators are proved. Furthermore, we propose an empirical likelihood method based on weighted score equations to construct confidence regions for the parameters. The simulation results show that the weighted least squares estimators are superior to the least squares estimators and that the confidence regions have good finite-sample behavior. At last, the model is applied to a real data example.
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(This article belongs to the Special Issue Time Series Analysis: Research on Data Modeling Methods)
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Asymptotic Behavior of Some Differential Inequalities with Mixed Delays and Their Applications
by
Axiu Shu, Xiaoliang Li and Bo Du
Axioms 2024, 13(5), 302; https://doi.org/10.3390/axioms13050302 - 2 May 2024
Abstract
In this paper, we focus on the asymptotic stability of the trajectories governed by the differential inequalities with mixed delays using the fixed-point theorem. It is interesting that the Halanay inequality is a special case of the differential inequality studied in this paper.
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In this paper, we focus on the asymptotic stability of the trajectories governed by the differential inequalities with mixed delays using the fixed-point theorem. It is interesting that the Halanay inequality is a special case of the differential inequality studied in this paper. Our results generalize and improve the existing results on Halanay inequality. Finally, three numerical examples are utilized to illustrate the effectiveness of the obtained results.
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(This article belongs to the Special Issue Research on Fixed Point Theory and Application)
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