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The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks 水平分区西尔平斯基垫片网络的平均吸收时间
IF 0.6
Analysis in Theory and Applications Pub Date : 2024-04-01 DOI: 10.4208/ata.oa-2021-0014
Zhizhuo Zhang,Bo Wu, Zuguo Yu
{"title":"The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks","authors":"Zhizhuo Zhang,Bo Wu, Zuguo Yu","doi":"10.4208/ata.oa-2021-0014","DOIUrl":"https://doi.org/10.4208/ata.oa-2021-0014","url":null,"abstract":"The random walk is one of the most basic dynamic properties of complex\u0000networks, which has gradually become a research hotspot in recent years due to its\u0000many applications in actual networks. An important characteristic of the random walk\u0000is the mean time to absorption, which plays an extremely important role in the study\u0000of topology, dynamics and practical application of complex networks. Analyzing the\u0000mean time to absorption on the regular iterative self-similar network models is an important way to explore the influence of self-similarity on the properties of random\u0000walks on the network. The existing literatures have proved that even local self-similar\u0000structures can greatly affect the properties of random walks on the global network,\u0000but they have failed to prove whether these effects are related to the scale of these\u0000self-similar structures. In this article, we construct and study a class of Horizontal Partitioned Sierpinski Gasket network model based on the classic Sierpinski gasket network, which is composed of local self-similar structures, and the scale of these structures will be controlled by the partition coefficient $k.$ Then, the analytical expressions\u0000and approximate expressions of the mean time to absorption on the network model\u0000are obtained, which prove that the size of the self-similar structure in the network will\u0000directly restrict the influence of the self-similar structure on the properties of random\u0000walks on the network. Finally, we also analyzed the mean time to absorption of different absorption nodes on the network to find the location of the node with the highest\u0000absorption efficiency.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"27 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140581170","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
Dynamics Analysis for a Hierarchical System with Nonlinear Cut-Off Interaction and Free Will 具有非线性切断交互作用和自由意志的分层系统动力学分析
IF 0.6
Analysis in Theory and Applications Pub Date : 2024-04-01 DOI: 10.4208/ata.oa-2021-0004
Ziyu Zhao,Yicheng Liu, Xiao Wang
{"title":"Dynamics Analysis for a Hierarchical System with Nonlinear Cut-Off Interaction and Free Will","authors":"Ziyu Zhao,Yicheng Liu, Xiao Wang","doi":"10.4208/ata.oa-2021-0004","DOIUrl":"https://doi.org/10.4208/ata.oa-2021-0004","url":null,"abstract":"Noting that the particles communicate with each other within a finite distance, in the paper, we investigate the hierarchical model with free will and cut-off\u0000function (linear or nonlinear). As our observation, the cut-off size $r$ is a sensitive coefficient to achieve the flocking behavior. Besides we will use energy function to achieve\u0000some sufficient conditions to achieve a flock. The free-will represents the tendency of\u0000the particle itself to move. It will either facilitate or prevent cluster generation. Some\u0000numerical simulations will validate our conclusions.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"319 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140581027","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 Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential 关于具有软势能的线性朗道方程时间解析性的备注
IF 0.6
Analysis in Theory and Applications Pub Date : 2024-04-01 DOI: 10.4208/ata.oa-2022-0029
Chaojiang Xu, Yan Xu
{"title":"A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential","authors":"Chaojiang Xu, Yan Xu","doi":"10.4208/ata.oa-2022-0029","DOIUrl":"https://doi.org/10.4208/ata.oa-2022-0029","url":null,"abstract":"In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. We prove that the solution to the Cauchy\u0000problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial\u0000datum for positive time. So that the smoothing effect of Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat\u0000equation.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"103 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140581160","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
Variable Exponent Herz-Morrey-Hardy Spaces Characterized by Wavelets and Its Application 用小波表征的变指数赫兹-莫雷-哈代空间及其应用
IF 0.6
Analysis in Theory and Applications Pub Date : 2023-12-01 DOI: 10.4208/ata.oa-2017-0026
Demin Yao, Kai Zhao
{"title":"Variable Exponent Herz-Morrey-Hardy Spaces Characterized by Wavelets and Its Application","authors":"Demin Yao, Kai Zhao","doi":"10.4208/ata.oa-2017-0026","DOIUrl":"https://doi.org/10.4208/ata.oa-2017-0026","url":null,"abstract":"In this paper, using the atomic decomposition of the Herz-Morrey-Hardy\u0000spaces with variable exponent, the wavelet characterization by means of a local version\u0000of the discrete tent spaces with variable exponent is established. As an application, the\u0000boundedness of the fractional integral operators from variable exponent Herz-Morrey-Hardy spaces into variable exponent Herz-Morrey spaces is obtained.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"51 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066782","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
Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities 具有电位和一般非线性的分数薛定谔方程的驻波
IF 0.6
Analysis in Theory and Applications Pub Date : 2023-12-01 DOI: 10.4208/ata.oa-2022-0012
Zaizheng Li,Qidi Zhang, Zhitao Zhang
{"title":"Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities","authors":"Zaizheng Li,Qidi Zhang, Zhitao Zhang","doi":"10.4208/ata.oa-2022-0012","DOIUrl":"https://doi.org/10.4208/ata.oa-2022-0012","url":null,"abstract":"We study the existence of standing waves of fractional Schrödinger equations with a potential term and a general nonlinear term: $$iu_t − (−∆) ^su − V(x)u + f(u) = 0, (t, x) ∈ mathbb{R}_+ × mathbb{R}^N,$$ where $s ∈ (0, 1),$ $N > 2s$ is an integer and $V(x) ≤ 0$ is radial. More precisely, we\u0000investigate the minimizing problem with $L^2$-constraint: $$E(alpha)={rm inf}left{frac{1}{2}int_{mathbb{R}^N}|(-Delta)^{frac{s}{2}}u|^2+V(x)|u|^2-2F(|u|)mid uin H^s(mathbb{R}^N),||u||^2_{L^2(mathbb{R}^N)}=alpharight}.$$ Under general assumptions on the nonlinearity term $f(u)$ and the potential term $V(x),$ we prove that there exists a constant $α_0 ≥ 0$ such that $E(α)$ can be achieved for all $α > α_0,$ and there is no global minimizer with respect to $E(α)$ for all $0 < α < α_0.$ Moreover, we propose some criteria determining $α_0 = 0$ or $α_0 > 0.$","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"33 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139057550","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
Approximation Properties of Newman Type Interpolation Rational Functions with Fewer Nodes 节点更少的纽曼型插值有理函数的逼近特性
IF 0.6
Analysis in Theory and Applications Pub Date : 2023-12-01 DOI: 10.4208/ata.oa-2020-0048
Laiyi Zhu, Xingjun Zhao
{"title":"Approximation Properties of Newman Type Interpolation Rational Functions with Fewer Nodes","authors":"Laiyi Zhu, Xingjun Zhao","doi":"10.4208/ata.oa-2020-0048","DOIUrl":"https://doi.org/10.4208/ata.oa-2020-0048","url":null,"abstract":"In the present note, we consider the problem: how many interpolation nodes\u0000can be deleted from the Newman-type rational function such that the convergence rate\u0000still achieve.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"19 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066778","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
Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator 广义$m$-线性$n$-维Hardy-Littlewood-Pόlya算子的锐利界
IF 0.6
Analysis in Theory and Applications Pub Date : 2023-06-01 DOI: 10.4208/ata.oa-2020-0039
Qianjun He, Mingquan Wei null, Dunyan Yan
{"title":"Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator","authors":"Qianjun He, Mingquan Wei null, Dunyan Yan","doi":"10.4208/ata.oa-2020-0039","DOIUrl":"https://doi.org/10.4208/ata.oa-2020-0039","url":null,"abstract":"In this paper, we calculate the sharp bound for the generalized m-linear ndimensional Hardy-Littlewood-Pólya operator on power weighted central and noncentral homogeneous Morrey spaces. As an application, the sharp bound for the Hardy-Littlewood-Pólya operator on power weighted central and noncentral homogeneous Morrey spaces is obtained. Finally, we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces, which generalizes the previous results.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"15 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80457796","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: 3
Null-Controllability of a Diffusion Equation with Fractional Integro-Differential Expressions 具有分数阶积分微分表达式的扩散方程的零可控性
Analysis in Theory and Applications Pub Date : 2023-06-01 DOI: 10.4208/ata.oa-2018-0020
Xiangdong Yang
{"title":"Null-Controllability of a Diffusion Equation with Fractional Integro-Differential Expressions","authors":"Xiangdong Yang","doi":"10.4208/ata.oa-2018-0020","DOIUrl":"https://doi.org/10.4208/ata.oa-2018-0020","url":null,"abstract":". The article considers the controllability of a diffusion equation with fractional integro-differential expressions. We prove that the resulting equation is null-controllable in arbitrary small time. Our method reduces essentially to the study of classical moment problems.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135142855","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
Multiple Integral Inequalities for Schur Convex Functions on Symmetric and Convex Bodies 对称和凸体上Schur凸函数的多重积分不等式
IF 0.6
Analysis in Theory and Applications Pub Date : 2023-06-01 DOI: 10.4208/ata.oa-2019-0023
S. Dragomir
{"title":"Multiple Integral Inequalities for Schur Convex Functions on Symmetric and Convex Bodies","authors":"S. Dragomir","doi":"10.4208/ata.oa-2019-0023","DOIUrl":"https://doi.org/10.4208/ata.oa-2019-0023","url":null,"abstract":". In this paper, by making use of Divergence theorem for multiple integrals, we establish some integral inequalities for Schur convex functions de(cid:133)ned on bodies B (cid:26) R n that are symmetric, convex and have nonempty interiors. Examples for three dimensional balls are also provided.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"25 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81504663","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
Strong $T$-Stability of Picard Iteration in a Non-Normal Cone Metric Space 非正态锥度量空间中Picard迭代的强$T$-稳定性
IF 0.6
Analysis in Theory and Applications Pub Date : 2023-06-01 DOI: 10.4208/ata.oa-2018-0022
Shaoyuan Xu, Suyu Cheng null, Yanying Han
{"title":"Strong $T$-Stability of Picard Iteration in a Non-Normal Cone Metric Space","authors":"Shaoyuan Xu, Suyu Cheng null, Yanying Han","doi":"10.4208/ata.oa-2018-0022","DOIUrl":"https://doi.org/10.4208/ata.oa-2018-0022","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"477 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91205346","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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