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On two transverse nonlinear models of axially moving beams

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Science china(Technological Sciences) 2009年第3期52卷 743-751页

作者： DING Hu1 & CHEN LiQun1,2 1 shanghai Institute of Applied mathematics and Mechanics, shanghai university, shanghai 200072, china 2 department of Mechanics, shanghai university, shanghai 200444, china 1. shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China 2. department of Mechanics Shanghai University Shanghai 200444 China

Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.

关键词： axially moving beam nonlinearity transverse vibration finite difference method differential quadrature method

Bounded Projections and Duality on Spaces of Holomorphic Functions in the Unit Ball of (?)~n

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Acta Mathematica Sinica,English Series 1995年第1期11卷 29-36页

作者： Ren Fuyao department of mathematics Fudan university shanghai,200433 china Xiao Jianbin department of mathematics Hunan normal university Changsha,410081 china harm.showa-u.ac.jp

In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are *** exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).... 详细信息

关键词： Bounded Projections and Duality on Spaces of Holomorphic Functions in the Unit Ball of Math Ball

An improved approach to the efficient construction of and search operations in motion graphs

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Science china(Information Sciences) 2012年第5期55卷 1042-1051页

作者： GAO Yan 1,CHEN ZhiHua 2,CHEN MinGang 3 & SHEN Yang 3 1 Software Engineering Institute,east china normal university,shanghai 200062,china 2 department of Computer Science and Engineering,east china university of Science and Technology,shanghai 200237,china 3 department of Computer Science and Engineering,shanghai Jiao Tong university,shanghai 200240,china 1. Software Engineering Institute East China Normal University Shanghai 200062 China2. Department of Computer Science and Engineering East China University of Science and Technology Shanghai 200237 China3. Department of Computer Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China

Motion graphs have been widely used as an effective technique in the synthesis of human *** synthesize well-formed motions,motion graphs require smooth transitions and good ***,the time and costs grow quadratically as the graph size *** this paper,we present a method to set up a hierarchical structure,called a structure *** coarse level of this graph models different motion categories and their transitions,and the fine level mainly captures different motion *** interpolation space method is used to improve the graph connectivity at the fine *** structure guides the establishment of a faster and more realistic graphical *** the building process,this structure also helps with searching the motion graph,by performing a traverse search and placing the findings into a direct look-up table or local search ***,when there is no direct link between the different motions,a navigation map is introduced to conduct an appropriate search path via a series of transition motion *** experimental results indicate that our approach could lower the computation time in construction and searching,while simultaneously providing a richer variety of motion styles.

关键词： motion graph structure table registration curve motion interpolation

A family of transitive modular Lie superalgebras with depth one

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Science china mathematics 2007年第10期50卷 1451-1466页

作者： Wen-de LIU~(1+) Yong-zheng ZHANG~2 ~1 department of mathematics,Harbin normal university,Harbin 150080,china ~2 department of mathematics,Northeast normal university,Changchun 130024,china 1. department of mathematics Harbin Normal University Harbin 150080 China 2. department of mathematics Northeast Normal University Changchun 130024 China

The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian *** restricted Lie superalgebras are also considered.

关键词： flag, divided power algebra, modular Lie superalgebra, embedding theorem

MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

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Chinese Annals of mathematics,Series B 2000年第4期21卷 479-488页

作者： WANG ZAIHONG (department of mathematics, Capital normal university, Beijing 100037, china.) department of mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem

DECOMPOSITIONS OF BOSONIC MODULES OF LIE ALGEBRAS W_(1+∞) AND W_(1+∞)(gl_N)

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Chinese Annals of mathematics,Series B 2005年第4期26卷 633-642页

作者： HU NAIHONG LIU DONG department of mathematics East China Normal University Shanghai 200062 China. department of mathematics Changzhou Institute of Technology Changzhou 213002 Jiangsu China.

A bosonic construction (with central charge c = 2) of Lie algebras W1+∞ and W1+∞ (glN), as well as the decompositions into irreducible modules are described. And for W1+∞, when restricted to its Virasoro subalgebra... 详细信息

关键词： Bosonic representation Virasoro algebra

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Science china mathematics 2004年第5期47卷 659-674页

作者： SHI Peihu & WANG Mingxindepartment of mathematics, Southeast university, Nanjing 210018, china department of mathematics, Xuzhou normal university, Xuzhou 221116, china 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p 2, and in case of existence, such solution is unique. Form > 1, it is shown that very singular self-similar solutions exist if and only if 1 2 andnq + (n + 1)p 2 +mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.

关键词： quasilinear parabolic equations, self-similar solutions, very singular solution, classification.

THE TOPOLOGICAL AND DYNAMICAL PROPERTIES OF NONORIENTABLE SURFACES

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Chinese Annals of mathematics 1988年第2期9卷 197-206页

作者：朱德明 department of mathematics east china normal university shanghai china.

Four topological and dynamical properties of nonorientable surfaces are *** is that for every continuous flow defined on any nonorientable closed surface,thereexist periodic or singular closed *** the case of the projective plane,it confirms aconjecture of professor Ye Yian-qian in his lecture notes“dynamical systems on surfaces”.Secondly,the author gives an exact upper bound of the number of closed curves onnonorientable surfaces,which do not intersect each other and the complement of their sumis still *** third is concerned with the upper and lower bound of the number ofthe periodic or singular closed orbits with certain *** last is related to theconnectedness of the complement of a lifting curve on two-fold covering *** firstproperty may be considered as a generalization of Kneser theorem from Klein bottle togeneral nonorientable surfaces and the second as a generalization of[4]Theorem 9.3.6from orientable surfaces to nonorientable surfaces.

关键词： Th THE TOPOLOGICAL AND DYNAMICAL PROPERTIES OF NONORIENTABLE SURFACES PCO

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2(1. department of mathematics, Hangzhou normal university, Hangzhou 310036, china 2. department of Applied mathematics, School of Mathematical Sciences, South china university of Technology, Guangzhou 510640, china) department of mathematics Hangzhou Normal University Hangzhou 310036 China department of Applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.