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Complete Study on a Bi-Center Problem for the z2-Equivariant Cubic Vector Fields

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Acta Mathematica Sinica,English Series 2011年第7期27卷 1379-1394页

作者： yi Rong LIU ji Bin LI Department ofMathematics Zhejiang Normal University Jinhua 321004 P. R. China Department of Mathematics Zhejiang Normal University Jinhua 321004 P. R. China School of Science Kunming University of Science and Technology Kunming 650093 P. R. China

For the planar z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.

关键词： Center problem Liapunov constant focal value integral factor invariant integral cubic polynomial system

Decomposition Theorems and Conjugate Pair in D_K Spaces

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1513-1525页

作者： ji zhen zHOU yu Tian WU School of Sciences Anhui University of Science and Technology School of Mathematics and Information Sciences Zhaoqing University

Let K be a right-continuous and nondecreasing function. A function f analytic in the unit disk D belongs to the space OK if ∫D｜f＇（z）｜2K（1 - ｜z｜2）dA（z）〈 ∞. Decomposition theorems for OK spaces are established in this paper. As an application, we obtain a characterization of interpolation by functions in DK spaces. Furthermore, we characterize functions in DK spaces by conjugate pairs.

关键词： DK spaces decomposition theorem conjugate pair

A Note on a Subclass of Cowen–Douglas Operators

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1795-1806页

作者： Liang TIAN Wei GUO Kui ji College of Mathematics and Information Science Hebei Normal University

In this note, we study a rich operator class denoted by PB_n(Ω) which includes all homogeneous operators and quasi-homogeneous operators in the Cowen–Douglas class. A complete unitarily classification theorem is giv... 详细信息

关键词： Cowen–Douglas operator curvature similarity classification unitary classification

3-restricted connectivity of graphs with given girth

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Applied Mathematics(A Journal of Chinese Universities) 2008年第3期23卷 351-358页

作者： GUO Li-tao MENG ji-xiang College of Math. and Sys. Sci. Xinjiang Univ. Xinjiang 830046 China

Let G = （V, E） be a connected graph. X belong to V（G） is a vertex set. X is a 3-restricted cut of G, if G- X is not connected and every component of G- X has at least three vertices. The 3-restricted connectivity κ3（G）（in short κ3） of G is the cardinality of a minimum 3-restricted cut of G. X is called κ3-cut, if ｜X｜ = κ3. A graph G is κ3-connected, if a 3-restricted cut exists. Let G be a graph girth g ≥ 4, κ3（G） is min{d（x）＋ d（y）＋ d（z） - 4 ： xyz is a 2-path of G}. It will be shown that κ3（G） = ξ3（G） under the condition of girth.

关键词： 3-restricted cut 3-restricted connectivity girth

z_2-Equivariant Cubic System Which yields 13 Limit Cycles

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 781-800页

作者： yi-rong LIU ji-bin LI School of Mathematics Central South University Department of Mathematics Zhejiang Normal University School of Science Kunming University of Science and Technology

For the planar z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.

关键词： planar dynamical system limit cycles bifurcations Lyapnov constant weak focus

Spectral Studies on the Conformational Transitions of Bovine Insulin During Denaturant-induced Unfolding

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Chemical Research in Chinese Universities 2014年第2期30卷 222-227页

作者： ji Xu MA Xiaojuan BIAN Liujiao College of Life Science Northwest University Xi@@an 710069 P.R.China

Transitions among various molecule states and conformational changes of bovine insulin were investigated under different denaturing conditions by means of fluorescence phase diagrams,fluorescence quenching,1-anilinonaphthalene-8-sulfonate（ANS） binding assay and circular dichroism（CD） *** both guanidine hydrochloride（GuHCl）-and urea-denatured procedures,the spatial structure of insulin molecules changed from ordered states to relative unordered ones with the increasing of denaturant *** GuHCl-denatured process followed a four-state model,for there were two intermediates existed in 2.0 and 6.0 mol/L GuHC1,*** I1 is more compact than the normal *** intermediate I2 has lost most of the secondary *** GuHCl concentration was above 6.0 mol/L,the fluorophores originally existed in the internal of insulin molecules would expose to the ***,the urea-denatured process followed a three-state model,only one intermediate existed in 2.5 mol/L *** the urea-denatured procedure,the fluorophores originally existed in theinternal of insulin molecules didn＇t expose to the surface.

关键词： Bovine insulin Unfolding Intermediate Guanidine hydrochloride Urea

The relations between the metallicity and orbital parameters of Galactic disk stars

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Science China(Physics,Mechanics & Astronomy) 2010年第7期53卷 1348-1356页

作者： LI ji SUN jianAn FU RuiJuan College of Physics Science&Information Engineering Hebei Normal UniversityShijiazhuang 050016China

The iron abundance gradient in the Galactic disk provides fundamental constraints on the chemical evolution of this important component of the ***,there are still some arguments about the shape of the iron abundance gradient across the Galactic stellar *** provide quantitative constraints on these trends,we constructed an unbiased stellar sample from the common objects of two large *** sample consists of 4004 disk stars in the solar neighborhood with the range of metallicity [Fe/H] from ^-1.0 to ~0.5,including 3855 thin disk stars and 146 thick disk *** range of their mean Galactocentric distances R m is from ~4 to ~11 kpc,and the range of their maximum vertical distance from the Galactic Plane z max is from 0 to ~3.5 *** relations of the stellar metallicity [Fe/H] with the orbital eccentricity e,and [Fe/H] with R m,as well as [Fe/H] with z max are investigated in *** results showed that:(1) The orbital eccentricity of disk stars decreases with increasing metallicity,while this trend becomes flat for stars with [Fe/H]>-0.2.(2) For thin disk,there is a clear radial iron gradient of-0.051±0.005 dex/***,this metallicity gradient is discontinuous once we split the sample into the inner(Rm<8kpc) and outer disk(Rm≥8 kpc):a slope of about 0 dex/kpc is present in the inner disk and a slope of-0.12 dex/kpc is in the outer *** the thick disk,there is no trend of [Fe/H] with R m.(3) The vertical gradient of iron abundance is-0.146 dex/kpc and-0.251 dex/kpc for the thick and thin disks,***,the vertical abundance gradient shows a steeper trend with the evolution of the *** results confirm the collapse mechanism associated with the formation and evolution of the Galactic disk.

关键词： Galaxy Galactic disk star orbital eccentricity abundance gradient

Thermodynamic and Optical Properties of CuAlO_2 under Pressure from First Principle

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Journal of Wuhan University of Technology(Materials Science) 2015年第6期30卷 1338-1344页

作者：张丽琴程艳 ji Guangfu College of Physics and Electronic Information Huaibei Normal University College of Physical Science and Technology Sichuan University Laboratory for Shock Wave and Detonation Physics Research Institute of Fluid Physics Chinese Academy of Engineering Physics

The structural stability, thermodynamic and optical properties of delafossite CuAlO2 were investigated using the norm-conserving pseudopotential technique based on the fi rst-principle density-functional theory. The ground-state properties obtained by minimizing the total energy were in favorable agreement with previous works. By using the quasi-harmonic Debye model, the thermodynamic properties including the Debye temperature QD, heat capacity CV, thermal expansion coeffi cient a, and Grüneisen parameter g were successfully obtained in the temperature range from 0 to 1 000 K and pressure range from 0 to 80 GPa, respectively. The optical properties including dielectric function e（v）, absorption coeffi cient a（v）, refl ectivity coeffi cient R（v）, and refractive index n（v） were also calculated and analyzed.

关键词： first principle CuAlO2 thermodynamic properties optical properties

Methodology of non-equilibrium thermodynamics for kinetics research of CO_2 capture by ionic liquids

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Science China Chemistry 2012年第6期55卷 1079-1091页

作者： LU XiaoHua ji yuanHui FENG Xin ji Xiaoyan State Key Laboratory of Materials-Oriented Chemical Engineering Nanjing University of Technology Nanjing 210009 China Division of Energy Science Energy Engineering Lulea University of Technology SE-97187 Lule& Sweden

In this paper, the methodology of non-equilibrium thermodynamics is introduced for kinetics research of CO2 capture by ionic liquids, and the following three key scientific problems are proposed to apply the methodology in kinetics research of CO2 capture by ionic liquids: reliable thermodynamic models, interfacial transport rate description and accurate experimental flux. The obtaining of accurate experimental flux requires reliable experimental kinetics data and the effective transport area in the CO2 capture process by ionic liquids. Research advances in the three key scientific problems are reviewed systematically and further work is analyzed. Finally, perspectives of non-equilibrium thermodynamic research of the kinetics of CO2 capture by ionic liquids are proposed.

关键词： ionic liquids CO2 capture non-equilibrium thermodynamics hlterfacial transport rate nanobubble statistical rate theory