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A note on extremal quasi-conformal mappings

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Science china Mathematics 2010年第1期53卷 63-70页

作者： LI Zhongschool of mathematical sciences,Peking university,Beijing 100871,china 1. school of mathematical sciences Peking University Beijing 100871 China

An extremal quasi-conformal mapping f of a domain D is said to be of non-landslide type if the set Ef(δ):= {z∈D:|μf(z)|≤||μ|| ∞ -δ} has no interior points for any δ > 0. In this paper,we construct a quasi-conformal mapping f of the unit disc D such that its Teichmu¨ller equivalence class [f] contains infinitely many extremal mappings of non-landslide type. The relation between extremal mappings of non-landslide type and locally extremal mappings is also discussed.

关键词： quasi-conformal mappings extremal quasi-conformal mappings locally extremal quasi-conformal mappings

Some basic concepts and problems on the petrogenesis of intra-plate ocean island basalts

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Chinese Science Bulletin 2009年第22期54卷 4148-4160页

作者： NIU Yaoling1,2,3 1 Department of Earth sciences, Durham university, Durham DH1 3LE, UK 2 school of Earth sciences and Resources, china university of Geosciences, Beijing 100083, china 3 school of Earth and Space sciences, Peking university, Beijing 100871, china Department of Earth sciences Durham University Durham DH1 3LE UK school of Earth sciences and Resources China University of Geosciences Beijing 100083 China school of Earth and Space sciences Peking University Beijing 100871 China

Basaltic magmatism that builds intra-plate ocean islands is often considered to be genetically associated with "hotspots" or "mantle plumes". While there have been many discussions on why ocean island basalts (OIB) are geochemically highly enriched as an integral part of the mantle plume hypothesis, our current understanding on the origin of OIB source material remains unsatisfactory, and some prevailing ideas need revision. One of the most popular views states that OIB source material is recycled oceanic crust (ROC). Among many problems with the ROC model, the ocean crust is simply too depleted (e.g., [La/Sm]PM > 1) OIB. Another popular view states that the enriched component of OIB comes from recycled continental crust (RCC, i.e.; terrigenous sediments). While both CC and OIB are enriched in many incompatible elements (e.g., both have [La/Sm]PM >>1), the CC has characteristic enrichment in Pb and deletion in Nb, Ta, P and Ti. Such signature is too strong to be eliminated such that CC is unsuitable as source material for OIB. Plate tectonics and mantle circulation permit the presence of ROC and RCC materials in mantle source regions of basalts, but they must be volumetrically insignificant in contributing to basalt magmatism. The observation that OIB are not only enriched in incompatible elements, but also enriched in the progressively more incompatible elements indicates that the enriched component of OIB is of magmatic origin and most likely associated with low-degree melt metasomatism. H2O and CO2 rich incipient melt may form in the seismic low velocity zone (LVZ). This melt will rise because of buoyancy and concentrate into a melt rich layer atop the LVZ to metasomatize the growing lithosphere, forming the metasomatic vein lithologies. Erupted OIB melts may have three components: (1) fertile OIB source material from depth that is dominant, (2) the melt layer, and (3) assimilation of the metasomatic

关键词：岩石成因论海洋 OIB 矿物学

Global Exact Boundary Controllability for Cubic Semi-linear Wave Equations and Klein-Gordon Equations

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 35-58页

作者： Yi ZHOU Wei XU Zhen LEI Key Laboratory of Mathematics for Nonlinear sciences School of Mathematical Sciences Fudan University Shanghai 200433 China school of mathematical sciences Fudan University Shanghai 200433 China

The authors prove the global exact boundary controllability for the cubic semilinear wave equation in three space dimensions,subject to Dirichlet,Neumann,or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value *** exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method,which reduces the global exact boundary controllability problem to a local *** proof is carried out in line with [2,15].Then a constructive method that has been developed in [13] is used to study the local *** when the region is star-complemented,it is obtained that the control function only need to be applied on a relatively open subset of the *** the cubic Klein-Gordon equation,similar results of the global exact boundary controllability are proved by such an idea.

关键词： Global exact boundary controllability Cubic semi-linear wave equations The exponential decay Star-shaped Star-complemented Cubic Klein- Gordon equations

GLOBAL WELLPOSEDNESS OF MAGNETOHYDRODYNAMICS SYSTEM WITH TEMPERATURE-DEPENDENT VISCOSITY

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Acta Mathematica Scientia 2018年第3期38卷 898-914页

作者： Shibin SU Xiaokui ZHAO school of mathematical sciences Xiamen university school of mathematical sciences Xiamen University

The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.

关键词： MHD system global well-posedness temperature-dependent viscosity

Tubular algebras and affine Kac-Moody algebras

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Science china Mathematics 2007年第4期50卷 521-532页

作者： Zheng-xin CHEN & Ya-nan LIN school of Mathematics and Computer Science, Pujian Normal university, Fuzhou 350007, china school of mathematical sciences, Xiamen university, Xiamen 361005, china 1. school of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China 2. school of mathematical sciences Xiamen University Xiamen 361005 China

The purpose of this paper is to construct quotient algebras L(A) 1 ? /I(A) of complex degenerate composition Lie algebras L(A) 1 ? by some ideals, where L(A 1 ? is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A) 1 ? /I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra L re(A) 1 ? generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A) 1 ? generated by simple A-modules.

关键词： tubular algebras affine Kac-Moody algebras Hall algebras degenerate composition Lie algebras modules with real root 16G70 17B67

Environment and Personal Well-being in Urban china

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Chinese Journal of Population,Resources and Environment 2011年第4期9卷 77-81页

作者： Yang Yuwen 1,2,Yang Wenya 3 1.Research Center for Circular Economy,nankai university,tianjin 300071,china 2.school of Business and Economics,Dalian Nationalities university,Dalian Liaoning116600,china 3.Nottingham university Business school (china),university of Nottingham Ningbo,Ningbo Zhejiang 315100,china Research Center for Circular Economy Nankai University Tianjin 300071 China school of Business and Economics Dalian Nationalities University Dalian Liaoning116600 China Nottingham university Business school (china) University of Nottingham Ningbo Ningbo Zhejiang 315100 China

The aim of this study is to examine the relationship between environment and personal well-being using a sample of 562 urban employees from three cities in Liaoning province in the People's Republic of *** contrast to previous studies,this study controlled positive affectivity (PA),negative affectivity (NA),job satisfaction and Big Five personality *** addition,the research variables of personal well-being index (PWI),positive affectivity,negative affectivity,job satisfaction,Big Five,and environmental satisfaction are measured with multi-item *** research finds that environmental satisfaction is positively related to personal well-being,suggesting that improvement of the natural surroundings in the cities can improve people's well-being.

关键词： environment personal well-being multi-item scales

On the stability of diffusion processes with state-dependent switching

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Science china Mathematics 2006年第9期49卷 1258-1274页

作者： XI Fubao & ZHAO Liqin Department of Mathematics, Beijing Institute of Technology, Beijing 100081, china school of mathematical sciences, Beijing Normal university, Beijing 100875, china Department of Mathematics Beijing Institute of Technology Beijing 100081 China school of mathematical sciences Beijing Normal University Beijing 100875 China

In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes.

关键词： Feller continuity, coupling, strong Feller continuity, exponential ergodicity,state-dependent switching.

On the Distribution of Integral Ideals and Hecke Grssencharacters

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Chinese Annals of Mathematics,Series B 2010年第3期31卷 385-392页

作者： Huixue LAO school of mathematical sciences Shandong Normal University Jinan 250014 China.

The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak＇s results on the distribution of integral ideals, and Chandrasekharan and G... 详细信息

关键词： Dedekind zeta-function Integral ideal Grossencharacters

A new scheme of digital communication using chaotic signals in MIMO channels

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Science china(Information sciences) 2012年第10期55卷 2183-2193页

作者： MA HuanFei 1 & KAN HaiBin 2 1 school of mathematical sciences,Soochow university,Suzhou 215006,china 2 school of Computer Science,Fudan university,Shanghai 200433,china 1. school of mathematical sciences Soochow University Suzhou 215006 China 2. school of Computer Science Fudan University Shanghai 200433 China

This paper proposes a new digital communication scheme,which uses chaotic signals based on the adaptive synchronization and parameter identification technique of chaotic systems reported *** to the multi signal character,this scheme combines the chaotic signal transmission with the MIMO channel technique in a wireless environment,which is different from the traditional chaotic communication *** a practical perspective,an outline of modulation,channel model,demodulation and non-coherent detection is ***,system performance is evaluated by simulations,and improvements on this scheme are also discussed.

关键词： chaotic modulation chaotic digital communication mapping parameters MIMO channel