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Diffeomorphisms with the M0-shadowing Property

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1760-1770页

作者： Xu ZHANG Xin Xing WU Department of Mathematics Shandong UniversityWeihai 264209P.R.China School of Sciences Southwest Petroleum UniversityChengdu 610500P.R.China Department of Electronic Engineering City University of Hong KongHong Kong SARP.R.China

This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably M0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.

关键词： Anosov diffeomorphism average shadowing property Mα-shadowing

shadowing Homoclinic Chains to a Symplectic Critical Manifold

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Analysis in Theory and Applications 2021年第1期37卷 1-23页

作者： Sergey Bolotin Moscow Steklov Mathematical Institute Russian Academy of SciencesMoscow119991Russia

We prove the existence of trajectories shadowing chains of heteroclinic or-bits to a sy mplectic normally hyperbolic critical manifold of a Hamiltonian *** results are quite different for real and complex *** results are applied to Hamitonian systems depending on a parameter which slowly changes with rateε.If the frozen autonomous system has a hyperbolic equilibrium possessing trans-verse homoclinic orbits,we construct trajectories shadowing homoclinic chains with energy having quasirandom jumps of orderεand changing with average rate of orderε|lnε|.This provides a partial multidimensional extension of the results of ***-tadt on the destruction of adiabatic invariants for systems with one degree of freedom and a figure 8 separatrix.

关键词： Hamiltonian system homoclinic orbit shadowing

Gluon shadowing,Absorption and Charmonium/Bottonium Suppression in h-A Processe

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Chinese journal of nuclear physics 1994年第3期 189-194页

作者： Chao Wei-qin Liu Bo(Institute of High Energy Physics,Academia Sinica,P.O.Box 918(4),Beijing 100039)(Center of Theoretical Physics,CCAST(World Lab.),Beijing)

The data of charmonium/bottonium suppression in p-A collisions at 800GeV/N are analyzed by considering the shadowing effect of the gluon structure func-tion at small x and the absorption in the target *** empirical parametrization ofthe shadowing effect of the gluon structure function is *** A-and x2-depen-dence of the suppression in p-A collisions is well described based on above physical con-siderations.

关键词： QGP Gluon shadowing Gluon fusion Absorption Suppression

Inverse shadowing and Weak Inverse shadowing Property

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Applied Mathematics 2012年第5期3卷 478-483页

作者： B. Honary Alireza Zamani Bahabadi Department of Mathematics Ferdowsi University of Mashhad Mashhad Iran

In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing property with respect to classes . In addition we study relation between minimality and weak inverse shadowing property with respect to class and relation between expansivity and inverse shadowing property with respect to class .

关键词： Inverse shadowing Property Minimal Homeomorphism δ-Method Positive Expansive

Precise Asymptotic Distribution of the Number of Isolated Nodes in Wireless Networks with Lognormal shadowing

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Applied Mathematics 2014年第15期5卷 2249-2263页

作者： Lixin Wang Alberto Argumedo William Washington Department of Mathematics Sciences and Technology Paine College Augusta USA

In this paper, we study the connectivity of multihop wireless networks under the log-normal shadowing model by investigating the precise distribution of the number of isolated nodes. Under such a realistic shadowing model, all previous known works on the distribution of the number of isolated nodes were obtained only based on simulation studies or by ignoring the important boundary effect to avoid the challenging technical analysis, and thus cannot be applied to any practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic model because the transmission area of each node is an irregular region other than a circular area. Assume that the wireless nodes are represented by a Poisson point process with densitynover a unit-area disk, and that the transmission power is properly chosen so that the expected node degree of the network equals lnn + ξ (n), where ξ (n) approaches to a constant ξ as n →?∞. Under such a shadowing model with the boundary effect taken into consideration, we proved that the total number of isolated nodes is asymptotically Poisson with mean e$ {-ξ}. The Brun’s sieve is utilized to derive the precise asymptotic distribution. Our results can be used as design guidelines for any practical multihop wireless network where both the shadowing and boundary effects must be taken into consideration.

关键词： Connectivity Asymptotic Distribution Random Geometric Graph Isolated Nodes log-Normal shadowing

Topological Stability and Entropy for Certain Set-valued Maps

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Acta Mathematica Sinica,English Series 2024年第4期40卷 962-984页

作者： Yu ZHANG Yu Jun ZHU School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China

In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of *** is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is ***,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered.

关键词： Set-valued map orbit space hyperbolic endomorphism perturbation shadowing expansiveness topological stability entropy

“手机APP+shadowing”学习法对学生自主学习能力的影响

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好家长 2018年第59期 160-160页

作者：胥思名陈丽丽长春光华学院

本论文以韩语专业的大学生为对象,对其运用'手机APP+shadowing'学习方法的影响效果进行统计分析,实践证实大学生在韩语习得过程中使用该方法确实有利于提高韩语听说水平,并能够培养学生对专业学习的兴趣,培养了学生的自主学习能力。期... 详细信息

本论文以韩语专业的大学生为对象,对其运用'手机APP+shadowing'学习方法的影响效果进行统计分析,实践证实大学生在韩语习得过程中使用该方法确实有利于提高韩语听说水平,并能够培养学生对专业学习的兴趣,培养了学生的自主学习能力。期待通过此项研究为中国等其他国家学生的韩语习得提供有益借鉴。

关键词：手机APP shadowing 韩语学习方法

关于“shadowing exercise”方法在日语语法教学中的延伸应用研究

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教师 2014年第29期 56-56页

作者：韦大伟武昌职业学院日韩教研室

在教学过程中发现,很多学生无法摆脱母语迁移的负面影响。学习语法时,习惯将语法的语义高度概括并用汉语记忆,将例句的译文优先记忆,以辅助回忆日语原句。这导致很多学生的学习滞步不前。本文借鉴＂shadowing exercise＂方法,将其应用... 详细信息

在教学过程中发现,很多学生无法摆脱母语迁移的负面影响。学习语法时,习惯将语法的语义高度概括并用汉语记忆,将例句的译文优先记忆,以辅助回忆日语原句。这导致很多学生的学习滞步不前。本文借鉴＂shadowing exercise＂方法,将其应用延伸至日语语法教学中,以期帮助学生摆脱母语迁移的负面影响。

关键词： shadowing exercise 母语迁移延伸应用

J/ψ-N center of mass energy dependence of nuclear absorption effect on J/ψ production

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Chinese Physics C 2010年第1期34卷 22-27页

作者：王宏民侯召宇刘家福孙献静 Physics Department Academy of Armored Forces Engineering of PLA Physics Graduate School Shijiazhuang Railway Institute Institute of High Energy Physics Chinese Academy of Sciences

In this paper, the J/ψ nuclear absorption effect is studied at RHIC and LHC energies with the EKS98 shadowing parameterizations. By assuming that the J/ψ absorption cross section, σ abs , increases with the charmonium-nucleon （J/ψ-N） center of mass energy, s J/ψN , it is found that σ abs should depend on x F （or y） at a certain center of mass energy per nucleon pair,s , especially at LHC energies. The theoretical results with the x F （or y）-dependence of the absorption effect are in good agreement with the experiment data from PHENIX in d-Au collisions and the predicted results will be examined by the forthcoming experimental data from LHC in d-Pb collisions. Finally, we also present baseline calculations of cold nuclear matter effects on J/ψ production in nucleus-nucleus （A-A） collisions and find that the x F （or y）-dependence of absorption effect is very small at both RHIC and LHC energies in A-A collisions.

关键词： x F (or y)-dependence of absorption effect NRQCD model shadowing