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Two-dimensional Riemann problems of simplified Euler equation

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Chinese Science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2.and HUANG Feimin+1 1. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, china {2., Shantou university, Guangdong 515063, china Institute of Applied mathematics Chinese Academy of Sciences Beijing China department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.

On the Cayley-Bacharach property and the construction of vector bundles

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Science china mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2.1 department of mathematics and Statistics,Huazhong Normal {2.,Wuhan 430079,china 2.department of mathematics,East china Normal {2.,Shanghai 2.02.1,china department of mathematics and Statistics Huazhong Normal University Wuhan China department of mathematics East China Normal University Shanghai China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2.for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

A New Cyclopeptide from Polycarpon prostratum

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Chinese Chemical Letters 2000年第7期11卷 593-594页

作者： Zhong Tao DING Jun ZHOU Yong Xian CHENG Ning Hua TAN(Laboratory of Phytochemistry kunming Institute of Botany, Academia Sinica, kunming 6502.4{2. of Chemistry, yunnan university, kunming 650091) department of Chemistry Yunnan University Kunming 650091 China Laboratory of Phytochemistry Kunming Institute of Botany Academia Sinica Kunming 650204 China

A new cyclic peptide named polycarponin A, was isolated from the whole plants of Polycarpon prostratum. Its structure was determined by detailed spectroscopic analysis.

关键词： Polycarpon prostratum Caryophyllaceae cyclopeptide polycarponin A

Minimal systems of generators for central division algebra and semi-simple algebra

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Chinese Science Bulletin 1998年第21期43卷 1777-1780页

作者： QIU Qizhang 1 and SUN Ling 2.1. department of mathematics, Wuhan {2., Wuhan 430072. china 2. department of Information science, Wuhan {2., Wuhan 430072. china. department of mathematics Wuhan University Wuhan China department of Information science Wuhan University Wuhan China

Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A ... 详细信息

关键词： central division algebra semi-simple algebra generator minimal system of generators.

Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2.& YAN LiTan 3 1 department of mathematics,East{2. university of Science and Technology,Shanghai 2.02.7,china 2.department of mathematics,Anhui Normal university,Wuhu 2.1000,china 3 department of mathematics,Donghua university,Shanghai 2.162.,china department of mathematics East China University of Science and Technology Shanghai China department of mathematics Anhui Normal University Wuhu China department of mathematics Donghua University Shanghai China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2.be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2.09, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2.2. 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

Analysis on cohesive crack opening displacement considering the strain softening effect

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Science china(Physics,Mechanics & Astronomy) 2006年第1期49卷 88-101页

作者： WANG Limin1, XU Shilang2.& ZHAO Xiqiang3 1. Mechanics department, Shandong university of Technology, Zibo 2.5049,{2. 2. Civil Engineering department, Dalian university of Technology, Dalian 11602.,{2. 3. mathematics department, Ocean university of{2., Qingdao 2.6071,{2. Mechanics department Shandong University of Technology Zibo China Civil Engineering department Dalian University of Technology Dalian China mathematics department Ocean University of China Qingdao China

In order to investigate the crack propagation in quasi-brittle materials like rock, ceramic and concrete, Hillerborg and his co-researchers abstracted the fracture process zone in front of a stress free crack in terms of a “fictitious crack zone”. On the fictitious crack zone, cohesive stresses distribute following a given softening relationship of stress vs. crack opening. Based on the polynomial or power series expression of cohesive crack opening displacement, the relationship of the cohesive stress vs. the crack opening displacement is established using elastic theory and integral equation, and some unknown physics variables are obtained using variation approach. The calculation results gained in this paper are close to the experimentally test ones.

关键词： cohesive crack, softening, dissipation work, variation approach.

Direction Fuzzy Measures

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Direction Fuzzy Measures

L-R smash products for bimodule algebras

第六届中国不确定系统年会

作者： Jixing Wang department of mathematics,{2. university,kunming 650091,china

＜正＞In order to solve a great number of direc- tion fuzzy problems,which can not be solved well by classical fuzzy sets,the direction fuzzy set theory was introduced by Wang[11].The purpose of this paper is to perfect the direction fuzzy theory by introducing direction fuzzy *** order to obtain them, first of all,a relative direction fuzzy a-algebras is pre- ***,some direction fuzzy measures on the basis of it are ***,the important outer and inner direction fuzzy measures are proposed in a new way,and their elementary properties are dis- cussed.

关键词： Fuzzy measure Direction fuzzy measure Relative direction fuzzy measure Set-cut direction fuzzy set Direction fuzzy σ-algebra

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of mathematics, Nanjing Agricultural {2., Nanjing 2.0095, china department of mathematics, Nanjing {2., Nanjing 2.0008, china) department of mathematics Nanjing Agricultural University Nanjing 210095 China department of mathematics Nanjing U-niversity Nanjing 210008 China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

Checking for normality in linear mixed models

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Science china mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,ZHU LiXing 2.3 & FANG Yun 4 1 School of Finance and Statistics,East china Normal university,Shanghai 2.02.1,{2. 2.School of Statistics and mathematics,yunnan university of Finance and Economics,yunnan 6502.1,{2. 3 The department of mathematics,Hong Kong Baptist university,Hong Kong 999077,{2. 4 mathematics and Science College,Shanghai Normal university,Shanghai 2.02.4,{2. School of Finance and Statistics East China Normal University Shanghai China School of Statistics and mathematics Yunnan University of Finance and Economics Yunnan China The department of mathematics Hong Kong Baptist University Hong Kong China mathematics and Science College Shanghai Normal University Shanghai China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test