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Existence of Invariant Tori for Certain Weakly Reversible Mappings

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Acta Mathematica Sinica,English Series 2002年第4期18卷 701-718页

作者： Bao She wei department of mathematics, nanjing university. nanjing 210093. P. R. china department of mathematics Nanjing University Nanjing 210093 P. R. China

In this paper, we consider certain mappings. M, sufficiently close to an integrable one, which is weakly reversible with respect to the mappings G sufficiently close to an involution of type (m.n). where m, n∈Z_+ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for proving the existence of a Cantor family of m-tori invariant under the reversible mappings M and the reversing mapping G.

关键词： Weakly reversible mappings Weakly undegenerate condition Invariant tori

Lipschitz classes on local fields

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Science china mathematics 2007年第7期50卷 1005-1014页

作者： wei-yi SU~(1+) Guo-xiang CHEN~2 1 department of mathematics,nanjing university,nanjing 210093,china 2 department of mathematics,nanjing Audit university,nanjing 211815,china 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Nanjing Audit University Nanjing 211815 China

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is ***,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and ***,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).

关键词： local field Holder type space Lipschitz class Cantor type fractal function 11F85 46F05 43A25 28A80 28A78

On the Conditions of a Center and General Integrals of Quadratic Differential Systems

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Acta Mathematica Sinica,English Series 2001年第2期17卷 229-236页

作者： wei Yin YE department of mathematics. nanjing Normal university. nanjing 210097, P. R. china Yan Qian YE department of mathematics. nanjing university, nanjing 210093, P. R. china department of mathematics Nanjing Normal University Nanjing 210097 P. R. China department of mathematics Nanjing University Nanjing 210093 P. R. China

We give the general integral of quadratic differential system with center in two cases under the Chinese classification.

关键词： Quadratic differential system Center General integral

Completely regular paracompact reflection of locales

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Science china mathematics 2006年第6期49卷 820-826页

作者： HE wei & LUO Maokang department of mathematics, nanjing Normal university, nanjing 210097, china department of mathematics, Sichuan university, chengdu 610064, china department of mathematics Nanjing Normal University Nanjing 210097 China department of mathematics Sichuan University Chengdu 610064 China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

The Blow-up of Solutions for Two-Dimensional Irrotational Compressible Euler Equations

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Acta Mathematica Sinica,English Series 2001年第2期17卷 217-228页

作者： Hui cheng YIN Qin ZHENG Shu Ze JIN department of mathematics, nanjing university. nanjing 210093, P. R. china department of mathematics Nanjing University Nanjing 210093 P. R. China

For two-dimensional irrotational compressible Euler equations with initial data where that is a small perturbation from a constant state, we prove that the first-order derivatives of ρ, υ blow-up at the blow-up time... 详细信息

关键词： Lifespan Commutator method Nash-Moser iteration.

Variational construction of unbounded orbits in Lagrangian systems

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Science china mathematics 2010年第3期53卷 617-624页

作者： cheng Chong-Qing 1, & LI Xia 2 1 department of mathematics, nanjing university, nanjing 210093, china 2 department of mathematics, Suzhou university of Science and Technology, Suzhou 215001, china 1. department of mathematics Nanjing University Nanjing 210093 China2. Department of Mathematics Suzhou University of Science and Technology Suzhou 215001 China

We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2 by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtain... 详细信息

关键词： positive definite Lagrangian variational method unbounded orbit

Surface Billiards and Nonvanishing Lyapunov Exponents

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Acta Mathematica Sinica,English Series 1997年第1期13卷 21-34页

作者： cheng Jian (department of mathematics,nanjing university,nanjing 210008,china) department of mathematics Nanjing University 210008 Nanjing China

We study in this paper the billiards on surfaces with mix-valued Gaussian curvature and the condition which gives nonvanishing Lyapunov exponents of the *** introduce a criterion upon which a small perturbation of the... 详细信息

关键词： Billiards Lyapunov exponents Curvature

A NEW CLASS OF UNIFORMLY SECOND ORDERACCURATE DIFFRENCE SCHEMES FOR 2D SCALAR CONSERVATION LAWS

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Journal of Computational mathematics 1997年第4期15卷 311-318页

作者： Juan cheng(department of Aerodynamics, nanjing university of Aeronautics & Astronautics,nanjing, china)Jia-zun Dai (department of mathematics, Physics and Mechanics, nanjing university of Aeronautics & Astronautics, nanjing, china) 南京航空航天大学空气动力学系江苏南京南京航空航天大学数学系江苏南京

In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws,we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the conver gence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak L∞-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2D Burgers equation are given and the relatively satisfied result is obtained.

关键词： Math A NEW CLASS OF UNIFORMLY SECOND ORDERACCURATE DIFFRENCE SCHEMES FOR 2D SCALAR CONSERVATION LAWS high Ph

Nutrient transport following water transfer through the world's largest water diversion channel

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Journal of Environmental Sciences 2024年第1期135卷 703-714页

作者： Yuanhui cheng Hong Zhang wei Yin State Key Laboratory of Environmental Aquatic Chemistry Research Center for Eco-Environmental SciencesChinese Academy of SciencesBeijing 100085 China Changjiang Water Resources Protection Institute Wuhan 430051China university of Chinese Academy of Sciences Beijing 100049China

Nutrient levels in the artificial channel constructed for the Middle Route Project are significant indicators of water quality safety and aquatic ecological integrity for this large,interbasin ***,the distribution and transport of nutrients along the channel were poorly *** on a time-series dataset as well as mass balance and material flow analysis methods,the water and nutrient transport fluxes in the Middle Route of the South-to-North Water Diversion Project were identified in this *** results indicate that the nutrient concentrations varied considerably with time,but there was no significant difference among the 30 stations of the main *** temperature difference was the major factor in the large fluctuations of water quality indicators over *** nutrient loadings varied with the water volume outputs from the main channel to the waterreceiving *** deposition was an important source of nutrients in the main channel,accounting for 9.13%,20.6%,and 0.635%of the nitrogen,phosphorus,and sulfur input from the Danjiangkou Reservoir,*** 2021,a net accumulation of 988 tons of N,29 tons of P,and 2,540 tons of S,respectively,were present in the main *** increase of these external and internal nutrient loadings would cause water quality fluctuation and deterioration in some local sections of the main *** study quantified the spatial and temporal patterns of nutrient transport in the Middle Route and revealed the ecological effects on the aquatic environment,assisting authorities on the project to develop effective water conservation strategies.

关键词： Nutrient transport Spatiotemporal patterns The Middle Route The South-to-North Diversion Project Hydro-ecological effects Water-receiving cities