AIMS Mathematics最新文献_第2页

Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations 具有随机波动的时变SIS流行病模型的hamilton系统的精确解和叠加规则

IF 2.2 3区数学

AIMS Mathematics Pub Date : 2023-04-18 DOI: 10.3934/math.20231225

R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz

{"title":"Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations","authors":"R. Campoamor-Stursberg, Eduardo Fernández-Saiz, F. J. Herranz","doi":"10.3934/math.20231225","DOIUrl":"https://doi.org/10.3934/math.20231225","url":null,"abstract":"Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ mathfrak{b}_2 $ and $ mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ mathfrak{h}_6 $, according to the embedding chain $ mathfrak{b}_2subset mathfrak{h}_4subset mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43783486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Further characterizations and representations of the Minkowski inverse in Minkowski space 闵可夫斯基逆在闵可夫斯基空间中的进一步表征与表示

IF 2.2 3区数学

AIMS Mathematics Pub Date : 2023-03-24 DOI: 10.3934/math.20231189

Jiale Gao, Qingwen Wang, Kezheng Zuo, Jiabao Wu

引用次数: 0

Some identities on degenerate hyperbolic functions arising from $ p $-adic integrals on $ mathbb{Z}_p $ $mathbb上$p$-dic积分引起的退化双曲函数的一些恒等式{Z}_p$

IF 2.2 3区数学

AIMS Mathematics Pub Date : 2023-03-04 DOI: 10.3934/math.20231298

Taekyun Kim, Dae San Kim, H. Kim

引用次数: 0

On common fixed point results in bicomplex valued metric spaces with application 二复值度量空间中的公共不动点结果及其应用

IF 2.2 3区数学

AIMS Mathematics Pub Date : 2023-03-01 DOI: 10.3934/math.2023278

Asifa Tassaddiq, Jamshaid Ahmad, A. Al-Mazrooei, Durdana Lateef, F. Lakhani

引用次数: 2

Unsteady-state turbulent flow field predictions with a convolutional autoencoder architecture 用卷积自编码器结构预测非定常湍流流场

3区数学

AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231522

Álvaro Abucide, Koldo Portal, Unai Fernandez-Gamiz, Ekaitz Zulueta, Iker Azurmendi

{"title":"Unsteady-state turbulent flow field predictions with a convolutional autoencoder architecture","authors":"Álvaro Abucide, Koldo Portal, Unai Fernandez-Gamiz, Ekaitz Zulueta, Iker Azurmendi","doi":"10.3934/math.20231522","DOIUrl":"https://doi.org/10.3934/math.20231522","url":null,"abstract":"<abstract> Traditional numerical methods, such as computational fluid dynamics (CFD), demand large computational resources and memory for modeling fluid dynamic systems. Hence, deep learning (DL) and, specifically Convolutional Neural Networks (CNN) autoencoders have resulted in accurate tools to obtain approximations of the streamwise and vertical velocities and pressure fields, when stationary flows are considered. The novelty of this paper consists of predicting the future instants from an initial one with a CNN autoencoder architecture when an unsteady flow is considered. Two neural models are proposed: The former predicts the future instants on the basis of an initial sample and the latter approximates the initial sample. The inputs of the CNNs take the signed distance function (SDF) and the flow region channel (FRC), and, for the representation of the temporal evolution, the previous CFD sample is added. To increment the amount of training data of the second neural model, a data augmentation technique based on the similarity principle for fluid dynamics is implemented. As a result, low absolute error rates are obtained in the prediction of the first samples near the shapes surfaces. Even in the most advanced time instants, the prediction of the vortices zone is quite reliable. 62.12 and 9000 speed-up ratios are achieved by the predictions of the first and second neural models, respectively, compared to the computational cost regarded by the CFD simulations. </abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134889360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations 二维非线性分数阶Hadamard积分方程的高阶均匀精确数值格式

3区数学

AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231523

Ziqiang Wang, Kaihao Shi, Xingyang Ye, Junying Cao

引用次数: 0

Theoretical and numerical aspects of the Malaria transmission model with piecewise technique 分段技术的疟疾传播模型的理论和数值方面

3区数学

AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231451

Shakeel Muhammad, Obaid J. Algahtani, Sayed Saifullah, Amir Ali

引用次数: 0

Rich and complex dynamics of a time-switched differential equation model for wild mosquito population suppression with Ricker-type density-dependent survival probability 具有riker型密度依赖生存概率的野生蚊子种群抑制的时间切换微分方程模型的丰富和复杂动力学

3区数学

AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231467

Zhongcai Zhu, Xue He

{"title":"Rich and complex dynamics of a time-switched differential equation model for wild mosquito population suppression with Ricker-type density-dependent survival probability","authors":"Zhongcai Zhu, Xue He","doi":"10.3934/math.20231467","DOIUrl":"https://doi.org/10.3934/math.20231467","url":null,"abstract":"<abstract>Dengue presents over 390 million cases worldwide yearly. Releasing <italic>Wolbachia</italic>-infected male mosquitoes to suppress wild mosquitoes via cytoplasmic incompatibility has proven to be a promising method for combating the disease. As cytoplasmic incompatibility causes early developmental arrest of the embryo during the larval stage, we introduce the Ricker-type survival probability to assess the resulting effects. For periodic and impulsive release strategies, our model switches between two ordinary differential equations. Owing to a Poincaré map and rigorous dynamical analyses, we give thresholds $ T^*, c^* $ and $ c^{**} (&gt;c^*) $ for the release period $ T $ and the release amount $ c $. Then, we assume $ c &gt; c^* $ and prove that our model admits a globally asymptotically stable periodic solution, provided $ T &gt; T^* $, and it admits at most two periodic solutions when $ T &lt; T^* $. Moreover, for the latter case, we assert that the origin is globally asymptotically stable if $ cge c^{**} $, and there exist two positive numbers such that whenever there is a periodic solution, it must initiate in an interval composed of the aforementioned two numbers, once $ c^* &lt; c &lt; c^{**} $. We also offer numerical examples to support the results. Finally, a brief discussion is given to evoke deeper insights into the Ricker-type model and to present our next research directions.</abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135102808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computing mod $ ell $ Galois representations associated to modular forms for small primes 计算与小素数模形式相关的模伽罗瓦表示

3区数学

AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231473

Peng Tian, Ha Thanh Nguyen Tran, Dung Hoang Duong

引用次数: 0

The effects of fear and delay on a predator-prey model with Crowley-Martin functional response and stage structure for predator 恐惧和延迟对具有Crowley-Martin功能反应和捕食者阶段结构的捕食者-猎物模型的影响

3区数学

AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231498

Weili Kong, Yuanfu Shao

{"title":"The effects of fear and delay on a predator-prey model with Crowley-Martin functional response and stage structure for predator","authors":"Weili Kong, Yuanfu Shao","doi":"10.3934/math.20231498","DOIUrl":"https://doi.org/10.3934/math.20231498","url":null,"abstract":"<abstract>Taking into account the delayed fear induced by predators on the birth rate of prey, the counter-predation sensitiveness of prey, and the direct consumption by predators with stage structure and interference impacts, we proposed a prey-predator model with fear, Crowley-Martin functional response, stage structure and time delays. By use of the functional differential equation theory and Sotomayor's bifurcation theorem, we established some criteria of the local asymptotical stability and bifurcations of the system equilibrium points. Numerically, we validated the theoretical findings and explored the effects of fear, counter-predation sensitivity, direct predation rate and the transversion rate of the immature predator. We found that the functional response as well as the stage structure of predators affected the system stability. The fear and anti-predation sensitivity have positive and negative impacts to the system stability. Low fear level and high anti-predation sensitivity are beneficial to the system stability and the survival of prey. Meanwhile, low anti-predation sensitivity can make the system jump from one equilibrium point to another or make it oscillate between stability and instability frequently, leading to such phenomena as the bubble, or bistability. The fear and mature delays can make the system change from unstable to stable and cause chaos if they are too large. Finally, some ecological suggestions were given to overcome the negative effect induced by fear on the system stability.</abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"123 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135212340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0