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Maschke-type theorem and Morita context over weak Hopf algebras

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Science china Mathematics 2006年第5期49卷 587-598页

作者： ZHANG Liangyun College of Science, nanjing Agricultural university, nanjing 2.0095, china department of Mathematics, nanjing university, nanjing 2.0008, china 1. College of Science Nanjing Agricultural University Nanjing 210095 China 2. department of Mathematics Nanjing University Nanjing 210008 China

This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.

关键词： weak Hopf algebra, smash product, Maschke-type theorem, Morita context.

Extension of isometries on the unit sphere of l^p (Γ) space

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Science china Mathematics 2010年第4期53卷 1085-1096页

作者： FANG XiNian 1,& WANG JianHua 2.1 School of Mathematics and Statistics,nanjing Audit university,nanjing 2.002.,china 2.department of Mathematics,Anhui Normal university,Wuhu 2.1000,china 1. School of Mathematics and Statistics Nanjing Audit University Nanjing 210029 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 < p < ∞,p≠2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto ... 详细信息

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley’s problem.

关键词： isometric extension l p (Γ) space isometry 1-Lipschitz mapping

The developmental trend of labrum and median eyes of Orsten-type preserved Phosphatocopina (Crustacea)

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Science china Earth sciences 2010年第1期53卷 18-26页

作者： LIU Zheng 1,2.& DONG XiPing 1,2.1 School of Earth and Space sciences,Peking university,Beijing 100871,{2. 2.State Key Laboratory of Palaeobiology and Stratigraphy,nanjing Institute of Geology and Palaeontology,Chinese Academy of sciences,nanjing 2.0008,{2. 1. School of Earth and Space sciences Peking University Beijing 100871 China2. State Key Laboratory of Palaeobiology and Stratigraphy Nanjing Institute of Geology and Palaeontology Chinese Academy of Sciences Nanjing 210008 China

The Phosphatocopina (Crustacea,Arthropoda) is an important group of 'Orsten-type' preserved *** is resolved as the sister-group of *** we study the labrum,the median eyes,and the inner lamella of Phosphatocopina based on the selected specimens respectively from western Hunan,South china,and *** labrum characters of different species exhibit interspecific *** ratio of labrum length/shield length is significant to the reconstruction of the ontogeny of *** labrum characters should be introduced to the diagnosis of *** the earliest growth stage,the median eyes were inconspicuous,almost as flat as the other area of the ***,with the growth of the individuals they became *** were two obviously concave structures on the ventral side of the hypostome in later stages,which were the positions where the median eyes should have been *** addition,the two modes of preservation of the inner lamella,i.e.,that of shrinking and that of bulging up,are interpreted as the preservational artifact herein.

关键词： Phosphatocopina Crustacea Orsten-type preservation morphology ontogeny Cambrian South china Sweden

Automorphisms with order three of affine Lie algebras

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Chinese Science Bulletin 1998年第21期43卷 1793-1798页

作者： JIN Quanqin 1,2.and HOU Zixin 2.1. department of Mathematics, Hebei university, Baoding 071002. {2. 2. department of Mathematics, Nankai university, Tianjin 300071, {2. department of Mathematics Hebei University Baoding China department of Mathematics Nankai University Tianjin China

Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two... 详细信息

关键词： affine Lie algebra automorphism of order three first (second) kind of automorphism.

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2.GUO Yuqi 2.and CEN Jiaping (Shum Kar-ping) 31. department of Mathematics, Xi’an university of Architecture & Technology, Xi’an 710055, {2. 2. department of Mathematics, Yunnan university, Kunming 650091, {2. 3. department of department of Mathematics Xi’an University of Architecture & Technology Xi’an China department of Mathematics Yunnan University Kunming China department of Mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

Depth zonation of Arenigian acritarchs in South china

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Chinese Science Bulletin 1997年第3期42卷 248-251页

作者： XU Wanhongdepartment of Earth sciences,{2., nanjing 2.0093. china department of Earth sciences Nanjing University Nanjing China

STAPLIN revealed that palaeoenvironment changes seem to control acritarch distribution patterns. However, scientists have been puzzled by the fact that characteristic offshore acritarchs occur with nearshore ones. This note demonstrates depth zonation of Arenigian acritarchs in South china and reveals the variation of water depth in South china during the Arenig Age.

关键词： South china Arenigian acritarch depth zonation.

Probing proton halo of the exotic nucleus ^(2.)S by elastic electron scattering

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Science china(Physics,Mechanics & Astronomy) 2004年第1期47卷 42-51页

作者： WANG Zaijun1 & REN Zhongzhou1’2.1. department of Physics, nanjing university, {2. 2.0008, china 2. Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator at Lanzhou, Lanzhou 730000, china Correspondence should be addressed to Ren Zhongzhou (email: zren@*** zren99@***) Received June 16, 2.03 1. department of Physics Nanjing University 210008 Nanjing China 2. Center of Theoretical Nuclear Physics National Laboratory of Heavy-Ion Accelerator at Lanzhou 730000 Lanzhou China

Elastic electron scattering on the exotic light nucleus 2.S is investigated in the plane wave Born approximation. The variation of the squared form factors of 2.S with momentum transfer is compared with that of 32.. It is found that the behavior of the form factors near the second minimum (with a moderate momentum transfer) is sensitive to the alteration of the charge density distribution of halo protons in 2.S. This indicates that elastic electron scattering can be a good probe of the structure of proton-halo nuclei.

关键词： elastic electron scattering, cross section, form factor, proton-halo nucleus.

Study on Theory and Application of the Energy Method used for Analyzing Compressive Instability in Sheet Forming

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厦门大学学报（自然科学版） 2002年第S1期41卷 126-127页

作者： XIONG Zhi-qing 1, XIE Lan-sheng 2.(1. department of Mechanical Engineering, nanjing Institute of Techno logy, nanjing 2.0013, china 2. College of Mechanical and Electrical Engineering, nanjing university of Aer onautics and Astronautics, nanjing 2.0016, china)

It is pointed out that there was serious weakness w he n using the energy method for studying compressive plastic instability in sheet forming in the past. Where applying the deduced instability strengths to relativ e engineering analysis, theoretical solutions were away from practices. Its basi c reason is that simplified process in mathematical analysis of elastic bending energy was completely applied to that of plastic bending energy. Where the cambe r expressed by function of displacement normal to a plate was approximated to re alistic deflective camber, the displacement of deflected plate to compressed dir ection was neglected. With the aid of the improved instability strengths, the pr edictions on both critical buckling dimension of blank in cup deep-drawing with out blankholder through cylindrical die or conical die and the minimum blankhold er pressure to prevent buckling under constant load are universally in agreement with both experimental results and experiential data. On the bases of above-mentioned improvement, the approximate expressions for bo th the curvature and the twist used in equation of the energy of elastic bending are also ameliorated. Thus the obtained general equations for both the energy a nd the work done by internal force in plastic bending of a plate are more precis e than before. In the analyses of plastic buckling of shell with bending moment, the effect of bending moment is considered through the work done by simulative bending for ce. The method proposed in this paper can not only simplify analyses but also ge t practical result.

关键词： sheet forming deep-drawing buckling energy me thod

Study on growth and properties of novel γ-LiAlO_2.substrate

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Science china(Technological sciences) 2006年第2期49卷 188-193页

作者： ZOU Jun1,2. ZHOU Shengming1, XU Jun1 & ZHANG Rong3 1. Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of sciences, Shanghai 2.1800, china 2. Graduate School of Chinese Academy of sciences, Beijing 100039, china 3. Laboratory of Solid State Microstructures and department of Physics, nanjing university, nanjing 2.0093. china 1. Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Shanghai 201800 China 2. Graduate School of Chinese Academy of sciences Beijing 100039 China 3. Laboratory of Solid State Microstructures and department of Physics Nanjing University Nanjing 210093 China

Transparent γ-LiAlO2.single crystal has been grown by Temperature Gradient technique. The surface of the wafer annealed in O2.atmosphere at 1100°C for 70 h became opaque and Li-poor phase (LiAl5O8); while, that annealed in Li-rich atmosphere kept transparent and smooth. The full-width at half maximum value dropped to 30 arcsecs when the wafer was annealed in Li-rich atmosphere. That annealed in O2.atmosphere increased to 78 arcsec. Compared with absorption spectra, we can conclude that the 196 nm absorption peak was caused by Li vacancies and the 736 nm peak was caused by O vacancies.

关键词： γ-LiAlO2 crystal, scanning electron micrograph (SEM), absorption spectra.