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Asymptotic Behavior of Some Differential Inequalities with Mixed Delays and Their Applications 具有混合延迟的某些微分不等式的渐近行为及其应用
Axioms Pub Date : 2024-05-02 DOI: 10.3390/axioms13050302
Axiu Shu, Xiaoliang Li, Bo Du
{"title":"Asymptotic Behavior of Some Differential Inequalities with Mixed Delays and Their Applications","authors":"Axiu Shu, Xiaoliang Li, Bo Du","doi":"10.3390/axioms13050302","DOIUrl":"https://doi.org/10.3390/axioms13050302","url":null,"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. 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.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"57 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141019073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Generalized Eta Transformation Formulas as the Hecke Modular Relation 作为赫克模关系的广义埃塔变换公式
Axioms Pub Date : 2024-05-02 DOI: 10.3390/axioms13050304
Nianliang Wang, T. Kuzumaki, Shigeru Kanemitsu
{"title":"The Generalized Eta Transformation Formulas as the Hecke Modular Relation","authors":"Nianliang Wang, T. Kuzumaki, Shigeru Kanemitsu","doi":"10.3390/axioms13050304","DOIUrl":"https://doi.org/10.3390/axioms13050304","url":null,"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 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.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"54 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141022281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimation of Random Coefficient Autoregressive Model with Error in Covariates 带有协变量误差的随机系数自回归模型的估计
Axioms Pub Date : 2024-05-02 DOI: 10.3390/axioms13050303
Xiaolei Zhang, Jin Chen, Qi Li
{"title":"Estimation of Random Coefficient Autoregressive Model with Error in Covariates","authors":"Xiaolei Zhang, Jin Chen, Qi Li","doi":"10.3390/axioms13050303","DOIUrl":"https://doi.org/10.3390/axioms13050303","url":null,"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 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.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"17 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141018500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Nonlinear Integral Inequality with a Tempered Ψ–Hilfer Fractional Integral and Its Application to a Class of Tempered Ψ–Caputo Fractional Differential Equations 一种新的非线性Ψ-希尔费分式积分不等式及其在一类Ψ-卡普托分式微分方程中的应用
Axioms Pub Date : 2024-05-01 DOI: 10.3390/axioms13050301
M. Medved', Michal Pospíšil, Eva Brestovanská
{"title":"A New Nonlinear Integral Inequality with a Tempered Ψ–Hilfer Fractional Integral and Its Application to a Class of Tempered Ψ–Caputo Fractional Differential Equations","authors":"M. Medved', Michal Pospíšil, Eva Brestovanská","doi":"10.3390/axioms13050301","DOIUrl":"https://doi.org/10.3390/axioms13050301","url":null,"abstract":"In this paper, the tempered Ψ–Riemann–Liouville fractional derivative and the tempered Ψ–Caputo fractional derivative of order n−1<α<n∈N are introduced for Cn−1–functions. A nonlinear version of the second Henry–Gronwall inequality for integral inequalities with the tempered Ψ–Hilfer fractional integral is derived. By using this inequality, an existence and uniqueness result and a sufficient condition for the non-existence of blow-up solutions of nonlinear tempered Ψ–Caputo fractional differential equations are proved. Illustrative examples are given.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"497 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141028366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Binary-State Continuous-Time Markov Chain Model for Offshoring and Reshoring 离岸外包和转厂的二元状态连续时间马尔可夫链模型
Axioms Pub Date : 2024-05-01 DOI: 10.3390/axioms13050300
Chiara Brambilla, Luca Grosset, Elena Sartori
{"title":"A Binary-State Continuous-Time Markov Chain Model for Offshoring and Reshoring","authors":"Chiara Brambilla, Luca Grosset, Elena Sartori","doi":"10.3390/axioms13050300","DOIUrl":"https://doi.org/10.3390/axioms13050300","url":null,"abstract":"We present a two-country model (North and South) that describes the phenomenon of offshoring and reshoring. The model is a continuous time-controlled Markov chain with binary states. The main trade-off involves production costs and transaction costs between one country and another. In the first part of this paper, we identify the key parameters of the model: the difference in unit production costs between the two countries considered, the marginal cost of transitioning between countries, and the incentive paid by the North country to all companies that have not relocated at the end of the planning interval. The final goal of our paper is to understand how national tax incentives can influence this process.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"135 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141056989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hyperholomorphicity by Proposing the Corresponding Cauchy–Riemann Equation in the Extended Quaternion Field 通过在扩展四元数场中提出相应的考奇-黎曼方程来实现超全同性
Axioms Pub Date : 2024-04-25 DOI: 10.3390/axioms13050291
Ji-Eun Kim
{"title":"Hyperholomorphicity by Proposing the Corresponding Cauchy–Riemann Equation in the Extended Quaternion Field","authors":"Ji-Eun Kim","doi":"10.3390/axioms13050291","DOIUrl":"https://doi.org/10.3390/axioms13050291","url":null,"abstract":"In algebra, the sedenions, an extension of the octonion system, form a 16-dimensional noncommutative and nonassociative algebra over the real numbers. It can be expressed as two octonions, and a function and differential operator can be defined to treat the sedenion, expressed as two octonions, as a variable. By configuring elements using the structure of complex numbers, the characteristics of octonions, the stage before expansion, can be utilized. The basis of a sedenion can be simplified and used for calculations. We propose a corresponding Cauchy–Riemann equation by defining a regular function for two octonions with a complex structure. Based on this, the integration theorem of regular functions with a sedenion of the complex structure is given. The relationship between regular functions and holomorphy is presented, presenting the basis of function theory for a sedenion of the complex structure.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"23 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140659077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Full Classification of Finite Singleton Local Rings 有限单子局部环的完整分类
Axioms Pub Date : 2024-04-25 DOI: 10.3390/axioms13050290
Sami Alabiad, Yousef Alkhamees
{"title":"Full Classification of Finite Singleton Local Rings","authors":"Sami Alabiad, Yousef Alkhamees","doi":"10.3390/axioms13050290","DOIUrl":"https://doi.org/10.3390/axioms13050290","url":null,"abstract":"The main objective of this article is to classify all finite singleton local rings, which are associative rings characterized by a unique maximal ideal and a distinguished basis consisting of a single element. These rings are associated with four positive integer invariants p,n,s, and t, where p is a prime number. In particular, we aim to classify these rings and count them up to isomorphism while maintaining the same set of invariants. We have found interesting cases of finite singleton local rings with orders of p6 and p7 that hold substantial importance in the field of coding theory.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"42 40","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140656954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Display Conventions for Octagons of Opposition 对角八边形的显示约定
Axioms Pub Date : 2024-04-24 DOI: 10.3390/axioms13050287
David Makinson
{"title":"Display Conventions for Octagons of Opposition","authors":"David Makinson","doi":"10.3390/axioms13050287","DOIUrl":"https://doi.org/10.3390/axioms13050287","url":null,"abstract":"As usually presented, octagons of opposition are rather complex objects and can be difficult to assimilate at a glance. We show how, under suitable conditions that are satisfied by most historical examples, different display conventions can simplify the diagrams, making them easier for readers to grasp without the loss of information. Moreover, those conditions help reveal the conceptual structure behind the visual display.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"118 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140659298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Photon-Added Deformed Peremolov Coherent States and Quantum Entanglement 光子添加的变形佩雷莫洛夫相干态与量子纠缠
Axioms Pub Date : 2024-04-24 DOI: 10.3390/axioms13050289
Kamal Berrada
{"title":"Photon-Added Deformed Peremolov Coherent States and Quantum Entanglement","authors":"Kamal Berrada","doi":"10.3390/axioms13050289","DOIUrl":"https://doi.org/10.3390/axioms13050289","url":null,"abstract":"In the present article, we build the excitedcoherent states associated with deformed su(1,1) algebra (DSUA), called photon-added deformed Perelomov coherent states (PA-DPCSs). The constructed coherent states are obtained by using an alterationof the Holstein–Primakoff realization (HPR) for DSUA. A general method to resolve of the problem of the unitary operator was developed for these kinds of quantum states. The Mandel parameter is considered to examine the statistical properties of PA-DPCSs. Furthermore, we offer a physical method to generate the PA-DPCSs in the framework of interaction among fields and atoms. Finally, we introduce the concept of entangled states for PA-DPCSs and examine the entanglement properties for entangled PA-DPCSs.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140663565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sparse Signal Recovery via Rescaled Matching Pursuit 通过重标度匹配追求实现稀疏信号恢复
Axioms Pub Date : 2024-04-24 DOI: 10.3390/axioms13050288
Wan Li, Peixin Ye
{"title":"Sparse Signal Recovery via Rescaled Matching Pursuit","authors":"Wan Li, Peixin Ye","doi":"10.3390/axioms13050288","DOIUrl":"https://doi.org/10.3390/axioms13050288","url":null,"abstract":"We propose the Rescaled Matching Pursuit (RMP) algorithm to recover sparse signals in high-dimensional Euclidean spaces. The RMP algorithm has less computational complexity than other greedy-type algorithms, such as Orthogonal Matching Pursuit (OMP). We show that if the restricted isometry property is satisfied, then the upper bound of the error between the original signal and its approximation can be derived. Furthermore, we prove that the RMP algorithm can find the correct support of sparse signals from random measurements with a high probability. Our numerical experiments also verify this conclusion and show that RMP is stable with the noise. So, the RMP algorithm is a suitable method for recovering sparse signals.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"17 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140663407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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