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Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： wang Hanxing 1.and DAI Yonglong {1.1. department of {{1., Shanghai university, Shanghai {1.1.00, china {1. department of {{1., Zhongshan university, Guangzhou 51.{1.5, china department of {1. Shanghai University Shanghai China department of {1. Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1.as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1. and noncertain extinction (i.e. P(Z n=0 for some n)1. are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

Shape blending of artistic brushstroke represented by disk B-spline curves

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Progress in Natural Science:Materials International 2007年第12期17卷 1501-1507页

作者： Cheng Min1.2.and {1. Guojin1.1. department of {2., Zhejiang university, Hangzhou 31.02., china 2. department of {2., Zhejiang university of Technology, Hangzhou 31.032. china) department of {1. Zhejiang University Hangzhou 310027 China 2. {1. of mathematics Zhejiang University of Technology Hangzhou 310032 China

This paper presents an algorithm for automatically generating in-between frames of two artistic brushstrokes. The basic idea of the algorithm is to represent the two key frames of artistic brushstrokes in disk B-spline curves, and then make blending of their geometric intrinsic variables. Given two key frames of artistic brushstrokes, the skeleton curves can be obtained by certain skeleton-based techniques. After disk B-spline representation of the key frames is generated, interpolation of the intrinsic variables of the initial and the target disk B-spline curves is carried out. Examples show that this method can efficiently create in-between frames of artistic brushstrokes.

关键词： computer aided calligraphy shape blending brushstroke disk B-spline curve skeleton.

Y_CΩ_(2.)are easy terms

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Chinese Science Bulletin 1998年第20期43卷 1707-1709页

作者： ZHAO Xishun 1.and {1. Ju 2.1. {2. of {2., nanjing university, nanjing 2.0093, china 2. Institute of Software, Chinese Academy of Sciences, Beijing 1.0080, china department of {1. Nanjing University Nanjing China Institute of Software Chinese Academy of Sciences Beijing China

For any natural number n≥1. Y CΩ 2. is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2. =M is consistent, where Y C is Curry fixed point combinator, Ω 2. ≡ω 2. ω 2. and ω 2. ≡λ***...x (there are 2. occurrences of x after λx ). This result is a partial solution to Jacopini’s conjecture: Y CΩ n is an easy term for any natural number n≥2.

关键词： λβ-calculus Kuper’s theorem easy term.

Planar cubic hybrid hyperbolic polynomial curve and its shape classification

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Progress in Natural Science:Materials International 2004年第1期14卷 42-47页

作者： wang Guozhao 1.{1. * and YANG Qinmin 1.{1. (1. Institute of Computer Graphics and Image Processing, {1. department of {{1., Zhejiang university, Hangzhou 31.0{1., china) Zhejiang Univ Inst Comp Graph & Image Proc Hangzhou 310027 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The planar cubic hybrid hyperbolic polynomial curves and cubic H Bézier curves are presented. The conditions leading to inflection points and singularities (cusps and loops) are investigated and the shape of these curves is classified. The conclusions enable us to detect inflection points and singularities and get an idea of how to preserve the fair shape when designing such curves.

关键词： hybrid hyperbolic polynomial curve H-Bézier curve shape classification inflection points singularities

Lipschitz continuity of best approximations and Chebyshev centers

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Chinese Science Bulletin 1998年第3期43卷 185-188页

作者： LI Chong 1.and wang Xinghua {1.1. Center for Mathematical Sciences, Zhejiang university, Hangzhou 31.0{1.,{{1. {1. department of mathematics, Hangzhou university, Hangzhou 31.0{1.,{{1. Center for Mathematical Sciences Zhejiang University Hangzhou China department of {1. Hangzhou University Hangzhou China

The Lipschitz continuity results are given for best approximations and Chebyshev centers. Consequently, the open problem presented by Septycki and Vleck is solved completely.

关键词： best approximation Chebyshev center uniform convexity.

Study on lithogeochemistry of Middle Jurassic basalts from southern china represented by the Fankeng basalts from Yongding of Fujian Province

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Science china Earth Sciences 2006年第10期49卷 1020-1031页

作者： ZHOU Jincheng1,2. JIANG Shaoyong1,2. wang Xiaolei1,2. YANG Jinghong 1,2.& ZHANG Mengqun 3 1. State Key Laboratory of Mineral Deposit Research, nanjing university, {2. 2.0093, china 2. department of Earth Sciences, nanjing university, {2. 2.0093, china 3. Modern Analysis Center, nanjing university, {2. 2.0093, china 1. State Key Laboratory of Mineral Deposit Research Nanjing University Nanjing 210093 China 2. {1. of Earth Sciences Nanjing University Nanjing 210093 China 3. Modern Analysis Center Nanjing University Nanjing 210093 China

There exists an E-W trending Middle Jurassic volcanic zone in southern china. The Fankeng basalts in the Yongding basin of Fujian Province are considered to be a typical example. The Fankeng basalts have TiO{1.contents in the range of 1.9{1.-3.{1.%. They are classified as high-Ti basalts. They also have higher total Fe (averaging FeO* = 1..09%). The Middle Jurassic Fankeng basalts from southwestern Fujian have obvious distinctive lithogeochemical features from early Cre- taceous basalts from southeastern coast of china. They have higher HFSE, such as Th, Nb, Ta, Zr and Ti. Their element ratios related with HFSE, such as Zr/Ba, La/Nb, La/Ta ,Zr/Y, Ti/Y, Ba/Nb, K/Ti and Rb/Zr are similar to those of OIB. The most samples have ε Nd(T) of-0.70-0.{1., which are near chondrite. Some samples have higher ε Nd(T) of ***, these basaltic magmas might be derived from depleted asthenospheric mantle. The lithogeochemical characteristics of the Fankeng basalts may be caused by interaction between asthenosphere and lithosphere at the time. The (Early-) Middle Jurassic basalts and gabbros from southeastern Hunan, southern Jiangxi and northern Guangdong provinces show similar geochemical features to those of the Fankeng basalts from the Yongding of Fujian. Occurrence of these OIB-type basalts in the area may be regarded as the petrological mark of upwelling of asthenosphere at the time. Upwelling of asthenosphere has led to tectonic extension and the formation of rifted basin in the area.

关键词： interaction between asthenosphere and lithosphere, lithogeochemistry, basalts, Middle Jurassic, southern china.

Lithology, kinematics and geochronology related to Late Mesozoic basin-mountain evolution in the Nanxiong-Zhuguang area, South china

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Science china Earth Sciences 2004年第8期47卷 673-688页

作者： shu Liangshu1. DENG Ping1.2. {2. Bin1. TAN Zhengzhong2. YU Xinqi1.& SUN Yan1.1. department of Earth Sciences,{2., nanjing 2.0093, china 2. Research Institute No.2.0, CNNC, Shaoguan 51.2}2., china 1. department of Earth Sciences Nanjing University 210093 Nanjing China 2. Research Institute No.2.0 CNNC 512026 Shaoguan China

The Nanxiong red-bed basin and its adjacent Zhuguang granite form a distinctive basin-mountain landform in the Nanling region, South china. Research results suggest that the Zhuguang granite is a polyphase composite pluton developed on the metamorphic basement of the paleo-Tethys-paleo-Asian tectonic regime and possesses geometrical and kinematic features of hot-doming extensional tectonics at the middle-upper crustal level, which is considered as a magmatic complex that resulted from the collision-orogeny during the Indosinian Period, the subduction-consuming during the Early Yanshanian Period and the intra-continental basaltic underplating and deep-seated geodynamics during the Late Yanshanian Period. The Nanxiong basin is a Late Cretaceous-Paleogene asymmetric faulted basin that is characterized by a fault boundary on the northern side and an uncomformable boundary on the southern side, its deposit center was migrated gradually from south to north. Structural kinematic results on the basin-mountain coupled zone demonstrate that the ductile and the brittle rheological layers show a quite coincident sense of shear, implying that it is a continuous process from the ductile extensional deformation followed by locally sinistral strike-slip shear at a middle-crustal level to the brittle tensional deformation at a upper-crustal level during formation of granitic doming extensional tectonics. The Zhuguang granite and the Nanxiong faulted basin constructed a semi-graben tectonic system. Lithological and geochemical results suggest that the Late Triassic to Jurassic granitic bodies in the Zhuguang have some similar features: high SiO{1. Al{1.3, K{1. contents, alkalinity index > {1.8, ANKC value > 1.1. LREE-enriched pattern with high REE contents, marked negative Eu anomalies, enrichment in Rb and Th, depletion in Ba and Nb, showing a K-rich and Al-rich calc-alkaline affinity, which suggest a continuous magmatic evolution from Late Triassic to Jurassic. Formation of Nanxiong ba

关键词： lithology,structural kinematics,basin-mountain evolution,SHRIMP age,Zhuguang granite,Nanxiong basin.

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： wang Huaiyu1.*, HAN Rushan{1.and CHEN Nanxian1.1. department of Physics, Tsinghua {{1., Beijing 1.0084, china {1. department of Physics, Peking {{1., Beijing 1.0871. china) department of Physics Tsinghua University Beijing 100084 China department of Physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

A preliminary study on vegetation-erosion dynamics and its applications

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Science china Earth Sciences 2005年第5期48卷 689-700页

作者： wang Zhaoyin 1.{1., wang Guangqian 1., LI Changzhi 1.& wang Feixin 1.1. department of Hydraulic Engineering, Tsinghua university, Beijing 1.0084, china {1. International Research and Training Center on Erosion and Sedimentation, Beijing 1.0084, china 1. department of Hydraulic Engineering Tsinghua University 100084 Beijing China 2. International Research and Training Center on Erosion and Sedimentation 100084 Beijing China

Vegetation-erosion dynamics is a new interdisciplinary science, studying the laws of evolution of watershed vegetation under the action of various ecological stresses. Introducing a qualitative expression of ecological stresses in this paper, the present authors establish the cou- pled differential equations for the vegetation-erosion process and derive a theoretical solution. The model is applied to the Anjiagou watershed on the Loess Pateau and the Xiaojiang water- shed and its sub-watersheds on the Yunnan Plateau. The calculated results agree well with the vegetation development processes. Abstracted from the differential equations the so-called vegetation-erosion chart is worked out, with which we can predict the development trend of vegetation under no human stresses. It is demonstrated that the erosion control is important for vegetation development and reforestation must be a long-term strategy. On the Yunnan Plateau with relatively high precipitation and temperature, vegetation can be greatly improved if erosion is controlled. On the dry and cold Loess Pateau suffering from high rate of soil erosion, however, vegetation can effectively control erosion but erosion reduction exhibits low effectiveness on vegetation development. Vegetation in the area is not stable and management is always needed to maintain the vegetation.

关键词： vegetation-erosion dynamics, human activities, coupled differential equations, erosion control, vigor ofvegetation.