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A locking-free anisotropic nonconforming rectangular finite element approximation for the planar elasticity problem

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Applied Mathematics(A Journal of Chinese Universities) 2008年第1期23卷 9-18页

作者： SHi Dong-yang WANG cai-xia Dept. of Math. Zhengzhou Univ. Zhengzhou 450052 China. Faculty of Math. and inform. Sci. North China Univ. of Water Conservancy and Electric PowerZhengzhou 450011 China.

This paper deals with a new nonconforming anisotropic rectangular finite element approximation for the planar elasticity problem with pure displacement boundary condition. By use of the special properties of this element, and by introducing the complementary space and a series of novel techniques, the optimal error estimates of the energy norm and the l^2-norm are obtained. The restrictions of regularity assumption and quasi-uniform assumption or the inverse assumption on the meshes required in the conventional finite element methods analysis are to be got rid of and the applicable scope of the nonconforming finite elements is extended.

关键词： anisotropic mesh locking-free nonconforming finite element optimal error estimate complementary space.

Synthesis and Crystal Structure of 1,4-Bis-(benztriazol-1-ylmethyl)-2,3,5,6-tetramethylbenzene

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Chinese Journal of Structural Chemistry 2005年第3期24卷 279-282页

作者： cai Yue-Peng HE Guang-Ping cai Yi ZHANG Chi SU Cheng-Yong KANG Bei-Sheng Dearment of Chemistr South China Normal UniversiyGuanzhou 510631China School of Chemisiry and Chemical Engineering Sun Yer-sen UniversitGuangzhou 510275China School of Pharmacaceutical Sciences Anhui Collegeof Traditional Chinese MedicineHefei 230038China

The title compound 1,4-bis(benztriazol-1-ylmethyl)-2,4,5,6-trimethylbenzene crys- tal.izes in the monoclinic system, space group Pbca with a = 9.842(5), b = 9.455(5), c = 22.165(12) ?, V = 2062.6(18) ?3, Dc = 1.277 g/cm3, Z = 4, C24H24N6, Mr = 396.49, μ(MoKa) = 0.079 mm-1 and F(000) = 840. The structure was refined to R = 0.0662 and wR = 0.1891 for 1163 observed reflections (i > 2σ(i)). The title molecule has trans-conformation about the central phenyl ring. The zigzag-like molecules are connected by face-to-face π…π stacking to form an infinite 2D layer.

关键词： bis(benztriazol-1-ylmethyl)-2 4 5 6-trimethylbenzene synthesis crystal structure face-to-faceπ…πinteraction 2D layer

l^q interior Estimates of the Gradient for Weak Solutions of Quasilinear El.iptic Equations

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Acta Mathematica Sinica,English Series 2007年第12期23卷 2225-2234页

作者： Feng Ping YAO Yong Yong cai lMAM School of Mathematical Sciences Peking University Bering 100871 P. R. China

The authors present a new proof of l^q interior estimates of the gradient for weak solutions of a quasilinear el.iptic equation of p-laplacian type.

关键词： l^q interior estimates weak solutions quasilinear el.iptic maximal function

OD-characterization of Almost Simple Groups Related to U_3(5)

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Acta Mathematica Sinica,English Series 2010年第1期26卷 161-168页

作者： liang cai ZHANG Wu Jie SHi School of Mathematical Sciences Suzhou University Suzhou 215006 P. R. China College of Mathematics and Physics Chongqing University Shapingba 400044 P. R. China

let G be a finite group with order ｜G｜=p1^α1p2^α2……pk^αk, where p1 〈 p2 〈……〈 Pk are prime numbers. One of the well-known simple graphs associated with G is the prime graph （or Gruenberg- Kegel graph） denoted .by г（G）（or GK（G））. This graph is constructed as follows： The vertex set of it is π（G） = {p1,p2,…,pk} and two vertices pi, pj with i≠j are adjacent by an edge （and we write pi - pj） if and only if G contains an element of order pipj. The degree deg（pi） of a vertex pj ∈π（G） is the number of edges incident on pi. We define D（G）：= （deg（p1）, deg（p2）,..., deg（pk））, which is called the degree pattern of G. A group G is called k-fold OD-characterizable if there exist exactly k non- isomorphic groups H such that ｜H｜ = ｜G｜ and D（H） = D（G）. Moreover, a 1-fold OD-characterizable group is simply called OD-characterizable. let l ：= U3（5） be the projective special unitary group. in this paper, we classify groups with the same order and degree pattern as an almost simple group related to l. in fact, we obtain that l and l.2 are OD-characterizable; l.3 is 3-fold OD-characterizable; l.S3 is 6-fold OD-characterizable.

关键词： almost simple group prime graph degree of a vertex degree pattern

Allometric models for leaf area and leaf mass predictions across different growing seasons of elm tree(Ulmus japonica)

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Journal of Forestry Research 2017年第5期28卷 975-982页

作者： Huiying cai Xueying Di Guangze Jin Center for Ecological Research Northeast Forestry University School of Forestry Northeast Forestry University

Convenient and effective methods to determine seasonal changes in individual leaf area (lA) and leaf mass (lM) of plants are useful.in research on plant physiology and forest ecology. However, practical methods for estimating lA and lM of elm (Ulmus japonica) leaves in different periods have rarely been reported. We collected sample elm leaves in June, July and September. Then, we developed allometric models relating lA, lM and leaf parameters, such as leaf length (l) and width (W) or the product of l and W (lW). Our objective was to find optimal allometric models for conveniently and effectively estimating lA and lM of elm leaves in different periods. lA and lM were significantly correlated with leaf parameters (P llometric models with lW as an independent variable were best for estimating lA and lM in each period. A linear model was separately developed to predict lA of elm leaves in June, July and September, and it yielded high accuracies of 93, 96 and 96%, respectively. Similarly, a specific allometric model for predicting lM was developed separately in three periods, and the optimal model form in both June and July was a power model, but the linear model was optimal for September. The accuracies of the allometric models in predicting lM were 88, 83 and 84% for June, July and September, respectively. The error caused by ignoring seasonal variation of allometric models in predicting lA and lM in the three periods were 1-4 and 16-59%, respectively.

关键词： leaf length leaf width linear model Power model Non-destructive method

Non-lie Symmetry Groups of （2＋1）-Dimensional Nonlinear Systems

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Communications in Theoretical Physics 2006年第6X期46卷 1005-1010页

作者： MA Hong-cai lOU Sen-Yue Department of Mathematics Donghua University Shanghai 200051 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Center of Nonlinear Science Ningbo University Ningbo 315211 China

A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Appl.ing the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the lie point symmetry groups and the non-lie symmetry groups are obtained. The lie symmetry groups obtained via traditional lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the lie groups are much simpler than those obtained via the standard approaches.

关键词： symmetry groups CK direct method symmetries exact solution

ACTiVE CONTROl OF A FlEXiBlE CANTilEVER PlATE WiTH MUl.iPlE TiME DElAYS

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Acta Mechanica Solida Sinica 2008年第3期21卷 257-266页

作者： longxiang Chen Ji Pan Guoping cai Department of Engineering Mechanics Shanghai Jiaotong University Shanghai 200240 China

Active control of a flexible cantilever plate with mul.iple time delays is investigated using the discrete optimal control method. A controller with mul.iple time delays is presented. in this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.

关键词： flexible cantilever plate mul.iple time delays discrete optima l control

Polyethylene glycol (PEG) as a benign solvent for Knoevenagel condensation

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Chinese Chemical letters 2008年第9期19卷 1043-1046页

作者： Yang liu Jun liang Xiu Hong liu Ji cai Fan Zhi cai Shang Department of Chemistry Zhejiang University Hangzhou 310027 China

The Knoevenagel condensation of aromatic aldehydes with active methylene compound proceeded efficiently in polyethylene glycol at room temperature with l-proline as catalyst. The yield is high and the products had E-isomer dominantly. Polyethylene glycol containing l-proline could be recycled and reused for several times without noticeably decreasing in productivity.

关键词： Polyethylene glycol l-Proline Knoevenagel condensation

Synthesis and Crystal Structure of an infinite 1D Zigzag Chain Compound (dimbH^+)(ClO_4^-) and its Comparison with (dimb)2H_2O (dimb = 1,3-Di(imidazol-1-ylmethyl)-5-methylbenzene)

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Chinese Journal of Structural Chemistry 2003年第4期22卷 439-443页

作者： YAOJing-cai MAYong-lin HUANGWei GOUShao-Hua DepartmentofChemistry LuoyangTeachersCollegeLuoyang471022China；CoordinationChemistryInstituteStateKeyLaboratoryofCoordinationChemistryNanjingUniversityNanjing210093China CoordinationChemistryinstitute StateKeyLaboratoryofCoordinationChemistryNanjingUniversityNanjing210093China

A new imidazolium compound, C15H17N4ClO4, was prepared from a flexible bidentate ligand of 1,3-di(imidazol-1-ylmethyl)-5-methylbenzene, and characterized by X-ray analysis. it is of orthorhombic, space group Pnma with a = 8.182(2), b = 12.874(3), c = 15.611(4) ? V = 1644.4(7) 3, Dc = 1.425 g/cm3, Z = 4, Mr = 352.78, m(MoKa) = 0.944 mm-1, F(000) = 736, S = 1.036, the final R = 0.0521 and wR = 0.1187 for 1128 observed reflections (i > 2s(i)). An infinite one-dimensional zigzag chain is formed by NH…N hydrogen bonding interactions between the imidazolium salt cations.

关键词： di(imidazol-1-ylmethyl)-5-methylbenzene imidazolium salt hydrogen bonding interactions zigzag chain crystal structure