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The Bargmann Symmetry Constraint and Binary Nonlinearization of the Super Dirac Systems

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Chinese Annals of mathematics,Series B 2010年第3期31卷 361-372页

作者： Jing YU Jingsong HE Wenxiu MA Yi CHENG School of Science Hangzhou Dianzi University Hangzhou 310018 China department of mathematics University of Science and Technology of China Hefei 230026 China department of mathematics University of Science and Technology of China Hefei 230026 China department of mathematics Ningbo University Ningbo 315211 Zhejiang China. department of mathematics and Statistics University of South Florida Florida 33620-5700 USA.

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-diinensional integrable Hamiltonian systems, defined over the super- symmetry manifold R^4N{2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

关键词： Symmetry constraints Binary nonlinearization Super Dirac systems Super finite-dimensional integrable Hamiltonian systems

Effects of water phase concentration on the emulsion polymerization of polyaniline

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Journal of central South university of Technology 2001年第2期8卷 140-142页

作者： PAN Chun yue 1,CHEN Zhen hua 2,HUANG Yong li 1,HUANG Ke long 1 (1.College of Chemistry and Chemical Engineering, central South university, Changsha 410083, China 2.department of Materials Science and Engineering, central South university, Cha 1. College of Chemistry and Chemical Engineering Central South University 410083 Changsha China 2. department of Materials Science and Engineering Central South University 410083 Changsha China

The emulsion polymerization of aniline in three phase system of xylene functionalized protonic acid water was carried out using (NH 4) 2S 2O 4 as oxidant. The influences of water phase concentration on the viscosity, conductivity, transmittance of polyaniline(PAN) latex and its powders were studied. The results show that the properties of PAN prepared through the emulsion polymerization are influenced by the amount of water used in the polymerization. The morphology of PAN varies with the water phase concentration used in the polymerization, which may result in the change of properties of PAN latex and its powders. When the volume fraction of water (φ) is about 20% 30%, the prepared PAN powder has higher conductivity, and the PAN latex has appropriate viscosity and particle size. The consumption of xylene was reduced at high φ value.

关键词： polyaniline emulsion polymerization water concentration property

Decay of geometry for unimodal maps:The C^2 case

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Chinese Science Bulletin 2009年第11期54卷 1859-1862页

作者： SHEN WeiXiao1,2 1 department of mathematics, university of Science and Technology of China, Hefei 230026, China 2.department of mathematics, National university of Singapore, Singapore 117543, Singapore department of mathematics University of Science and Technology of China Hefei 230026 China department of mathematics National University of Singapore Singapore 117543 Singapore

We prove that a C2 unimodal interval map with critical order not greater than 2 has the decay of geometry property, by showing that all the cross-ratio estimates needed in the previous proof for the C3 case remain true.

关键词：衰变几何图案件几何性质比率估计证明

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

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Science China mathematics 2009年第11期52卷 2432-2446页

作者： ZHU YuCan1 & LIU MingSheng2 1 department of mathematics,Fuzhou university,Fuzhou 350002,China 2.department of mathematics,South China Normal university,Guangzhou 510631,China 1. department of mathematics Fuzhou University Fuzhou 350002 China 2. department of mathematics South China Normal University Guangzhou 510631 China

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2,γ2,...,βn+1,γn+1(f)... 详细信息

关键词： Roper-Suffridge extension operator biholomorphic starlike mapping almost spirallike mapping of type β and order α spirallike mapping of type β and order α

OPTIMAL COARSE GRID SIZE IN DOMAIN DECOMPOSITION

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Journal of Computational mathematics 1994年第4期12卷 291-297页

作者： Tony Chan Jian-Ping Shao(department of mathematics, university of Califoruia, Los Angeles, usa) UNIV CALIF LOS ANGELES DEPT MATHLOS ANGELESCA 90024

In most domain decomposition (DD) methods, a coarse grid solve is employed to provide the global coupling required to produce an optimal method. The total cost of a method can depend sensitively on the choice of the coaxse grid size H. In this paper, we give a simple analysis of this phenomenon for a model elliptic problem and a variant of Smith's vertex space domain decomposition method [11, 3]. We derive the optimal value Hopt which asymptotically minimises the total cost of method (number of floating point operations in the sequential case and execution time in the parallel case), for subdomain solvers with different complekities. Using the value of Hopt, we derive the overall complexity of the DD method, which can be significantly lower than that of the subdomain solver

关键词： UCLA OPTIMAL COARSE GRID SIZE IN DOMAIN DECOMPOSITION CAM

A priori estimates for classical solutions of fully nonlinear elliptic equations

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Science China mathematics 2011年第3期54卷 457-462页

作者： CAO Yi1, LI DongSheng1 & WANG LiHe1,2 1College of Science, Xi’an Jiaotong university, Xi’an 710049, China 2department of mathematics, The university of Iowa, Iowa City, IA 52242-1419, usa 1. College of Science Xi’an Jiaotong University Xi’an 710049 China2. Department of Mathematics The University of Iowa Iowa City IA 52242-1419 USA

For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u.

关键词： fully nonlinear classical solutions C2 α estimates

Jackson’s theorem in Q_p spaces

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Science China mathematics 2010年第2期53卷 367-372页

作者： CHEN YingWei 1 & REN GuangBin 1, 2, 1 department of mathematics, university of Science and Technology of China, Hefei 230026, China 2.department of mathematics, university of Aveiro, P-3810-193 Aveiro, Portugal 1. department of mathematics University of Science and Technology of China Hefei 230026 China2. Department of Mathematics University of Aveiro P-3810-193 Aveiro Portugal

A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p 1, and k-1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an absolute const... 详细信息

关键词： Q p space BMOA polynomial approximation

Lipschitz classes on local fields

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Science China mathematics 2007年第7期50卷 1005-1014页

作者： Wei-yi SU~(1+) Guo-xiang CHEN~2 1 department of mathematics,Nanjing university,Nanjing 210093,China 2.department of mathematics,Nanjing Audit university,Nanjing 211815,China 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Nanjing Audit University Nanjing 211815 China

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is ***,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and ***,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).

关键词： local field Holder type space Lipschitz class Cantor type fractal function 11F85 46F05 43A25 28A80 28A78

Gerbes and twisted orbifold quantum cohomology

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Science China mathematics 2008年第6期51卷 995-1016页

作者： PAN JianZhong~1 RUAN YongBin~(2,3) YIN XiaoQin~(1,3+) 1 Institute of mathematics,Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China 2.department of mathematics,university of Wisconsin-Madison,WI 53706,usa 3 department of mathematics,The Hong Kong university of Science and Technology,Hong Kong,China Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China department of mathematics University of Wisconsin-Madison WI 53706 Madison USA department of mathematics The Hong Kong University of Science and Technology Hong Kong China

In this paper,we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.

关键词： gerbe orbifold quantum cohomology 53D45