Axioms Pub Date : 2024-05-10 DOI: 10.3390/axioms13050314

Jizhong Gao, Junna Ni, Jianhua Yu

引用次数: 0

Parameter Estimation in Spatial Autoregressive Models with Missing Data and Measurement Errors 有缺失数据和测量误差的空间自回归模型的参数估计

Axioms Pub Date : 2024-05-10 DOI: 10.3390/axioms13050315

Tengjun Li, Zhikang Zhang, Yunquan Song

引用次数: 0

Study of the Six-Compartment Nonlinear COVID-19 Model with the Homotopy Perturbation Method 用同调扰动法研究六室非线性 COVID-19 模型

Axioms Pub Date : 2024-05-09 DOI: 10.3390/axioms13050311

M. Rafiullah, Muhammad Asif, Dure Jabeen, M. A. Ibrahim

{"title":"Study of the Six-Compartment Nonlinear COVID-19 Model with the Homotopy Perturbation Method","authors":"M. Rafiullah, Muhammad Asif, Dure Jabeen, M. A. Ibrahim","doi":"10.3390/axioms13050311","DOIUrl":"https://doi.org/10.3390/axioms13050311","url":null,"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 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 S(t), E(t), A(t), I(t), R(t), and B(t), 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 (n−1)th-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.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140997508","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

Canonical Metrics on Twisted Quiver Bundles over a Class of Non-Compact Gauduchon Manifold 一类非紧凑高杜洪流形上的扭转曲束上的典范度量

Axioms Pub Date : 2024-05-09 DOI: 10.3390/axioms13050312

Shi-Fan Cai, S. Chaubey, Xin Xu, Pan Zhang, Zhi-Heng Zhang

引用次数: 0

A Short Note on Generating a Random Sample from Finite Mixture Distributions 关于从有限混合分布生成随机样本的简短说明

Axioms Pub Date : 2024-05-08 DOI: 10.3390/axioms13050307

L. Al-Labadi, Anna Ly

引用次数: 0

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection 基于无症状感染的 COVID-19 SEAI 模型研究

Axioms Pub Date : 2024-05-08 DOI: 10.3390/axioms13050309

Lidong Huang, Yue Xia, Wenjie Qin

{"title":"Study on SEAI Model of COVID-19 Based on Asymptomatic Infection","authors":"Lidong Huang, Yue Xia, Wenjie Qin","doi":"10.3390/axioms13050309","DOIUrl":"https://doi.org/10.3390/axioms13050309","url":null,"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 R0 and calculate the equilibrium point. Secondly, when R0<1, 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 R0>1, 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 R0 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.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 45","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141000169","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

Recent Advances in Fractional Calculus 分数微积分的最新进展

Axioms Pub Date : 2024-05-08 DOI: 10.3390/axioms13050310

Péter Kórus, J. N. Nápoles Valdés

引用次数: 0

On Semi-Vector Spaces and Semi-Algebras with Applications in Fuzzy Automata 论半向量空间和半代数及其在模糊自动机中的应用

Axioms Pub Date : 2024-05-08 DOI: 10.3390/axioms13050308

G. G. La Guardia, J. Chagas, E. Lenzi, L. Pires, Nicolás Zumelzu, Benjamín R. C. Bedregal

引用次数: 0

On Conditional Axioms and Associated Inference Rules 论条件公理和相关推理规则

Axioms Pub Date : 2024-05-07 DOI: 10.3390/axioms13050306

Joaquín Borrego-Díaz, Andrés Cordón-Franco, Francisco Félix Lara-Martín

{"title":"On Conditional Axioms and Associated Inference Rules","authors":"Joaquín Borrego-Díaz, Andrés Cordón-Franco, Francisco Félix Lara-Martín","doi":"10.3390/axioms13050306","DOIUrl":"https://doi.org/10.3390/axioms13050306","url":null,"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 α(v)→β(v). 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 T+E) or we extend T by using the formulas in E as instances of an inference rule (thus obtaining a theory denoted by T+E–Rule). The theory T+E will be stronger than T+E–Rule, but how much stronger can T+E be? More specifically, is T+E conservative over T+E–Rule for theorems of some fixed syntactical complexity Γ? 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 Π and in the applications of E–Rule side formulas from the class Π and can be eliminated (in a certain precise sense), then T+E is ∀B(Π)-conservative over T+E–Rule. Secondly, if, in addition, E is a finite set with m conditional sentences, then nested applications of E–Rule of a depth at most of m suffice to obtain ∀B(Π) 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.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"99 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141003890","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

Construction of Fractional Pseudospectral Differentiation Matrices with Applications 构建分数伪谱微分矩阵及其应用

Axioms Pub Date : 2024-05-04 DOI: 10.3390/axioms13050305

Wenbin Li, Hongjun Ma, Tinggang Zhao

引用次数: 0

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