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An extended fast algorithm for constructing the Dixon resultant matrix

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Science china Mathematics 2005年第1期48卷 131-143页

作者： ZHAO Shizhong~1 & FU Hongguang~21.Chengdu institute of Computer Applications,Chinese Academy of Sciences,Chengdu 610041,china2.software engineering institute,east china normal university,shanghai 200062,china Chengdu institute of Computer Applications Chinese Academy of Sciences Chengdu China software engineering institute East China Normal University Shanghai China

In recent years,the Dixon resultant matrix has been used widely in the re-sultant elimination to solve nonlinear polynomial equations and many researchers havestudied its efficient *** recursive algorithm is a very efficient algorithm,butwhich deals with the case of three polynomial equations with two variables at *** paper,we extend the algorithm to the general case of n+1 polynomial equations in *** algorithm has been implemented in Maple *** testing the random polyno-mial equations,the results demonstrate that the efficiency of our program is much betterthan the previous methods,and it is exciting that the necessary condition for the existenceof common intersection points on four general surfaces in which the degree with respectto every variable is not greater than 2 is given out in 48×48 Dixon matrix firstly by ourprogram.

关键词： Dixon resultant matrix Sylvester resultant matrix truncated formal power series

The geodetic numbers of graphs and digraphs

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Science china Mathematics 2007年第8期50卷 1163-1172页

作者： Chang-hong LU~(1,2) 1 Department of Mathematics,east china normal university,shanghai 200062,china 2 institute of Theoretical Computing,east china Narnal university,shanghai 200062,china Department of Mathematics East China Normal University Shanghai China institute of Theoretical Computing East China Narnal University Shanghai China

For every two vertices u and v in a graph G, a u-v geodesic is a shortest path between u and v. Let I(u, v) denote the set of all vertices lying on a u-v geodesic. For a vertex subset S, let I(S) denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V (G). For a digraph D, there is analogous terminology for the geodetic number g(D). The geodetic spectrum of a graph G, denoted by S(G), is the set of geodetic numbers of all orientations of graph G. The lower geodetic number is g ?(G) = minS(G) and the upper geodetic number is g +(G) = maxS(G). The main purpose of this paper is to study the relations among g(G), g ?(G) and g +(G) for connected graphs G. In addition, a sufficient and necessary condition for the equality of g(G) and g(G × K 2) is presented, which improves a result of Chartrand, Harary and Zhang.

关键词： convex set digraph distance geodesic geodetic number 05C12 05C20

Computing rarity on uncertain data

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Science china(Information Sciences) 2011年第10期54卷 2028-2039页

作者： JIN CheQing,ZHOU MinQi & ZHOU AoYing shanghai Key Laboratory of Trustworthy Computing,software engineering institute,east china normal university,shanghai 200062,china shanghai Key Laboratory of Trustworthy Computing Software Engineering Institute East China Normal University Shanghai China

The essence of uncertain data management has been well adopted since data uncertainty widely exists in lots of applications,such as Web,sensor networks,*** of the uncertain data models are based on the possible world *** the number of the possible worlds will blowup exponentially with the growth of the data set,it is much more challenging to handle uncertain data than deterministic *** this paper,we take the first attempt to study the rarity,an important statistic that describes the proportion of items with the same frequency,upon uncertain *** have proposed three novel solutions,including an exact method and an approximate method to compute the rarity of a given frequency respectively,and a method to find the frequency of the maximum *** in theorem and extensive experimental results demonstrate the effectiveness and efficiency of the proposed solutions.

关键词： rarity uncertain data possible world

Testing algebraic geometric codes

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Science china Mathematics 2009年第10期52卷 2171-2176页

作者： CHEN Hao software engineering institute, east china normal university, shanghai 200062, china software engineering institute East China Normal University Shanghai China

Property testing was initially studied from various motivations in 1990’s. A code C  GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.

关键词： number theory of finite field property testing algebraic geometric codes 94B35 94B99

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 software engineering institute East China Normal University Shanghai China Department of Computer Science and engineering East China University of Science and Technology Shanghai China Department of Computer Science and engineering Shanghai Jiao Tong University Shanghai 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

WHEN CAN THE STABLE ALGEBRA DETERMINE THE STRUCTURE OF A C-ALGEBRA ?

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 153-156页

作者： WU LIANGSEN (institute of Mathematics, east normal university, shanghai 200062. china) 华东师范大学数学系上海 200062

Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant stable isomorphic to B, then there is a-isomorphism between A and B. An analogous result is obtained by considering On K A in the place of K A, where On is the Cuntz algebra (3≤ n < ∞).

关键词： C-algebra Stable algebra Cuntz algebra α-invariance.

The rule of sediment transport on the Nanhui tidal flat in the Changjiang Estuary

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Acta Oceanologica Sinica 1991年第1期10卷 117-127页

作者： Li Jiufa institute of Estuarine and Coastal Research, east china normal university, shanghai, 200062, china

The Nanhui tidal flat is located in the area of slow current where the ebb currents from the Changjiang Estuaryand the Hangzhou Bay converge and the flood current from the sea diverges into the estuary and the bay. The flat extends seaward in tongue shape and has a wide and gentle surface with a marked difference of tidal levels on its two sides, which results in the sediment longitudinal transport on the flat. The water-sediment conditions are diverse at different locations. The velocity and sediment concentration in intertidal zone are higher during the flood tide than those during the ebb tide. The net sediment transport is landward, resulting in a large amount of deposition of sediments on the shoal. However, the ebb current is the dominant one in deep-water area where the net sediment transport is seaward. There exist two circulation systems in plane view on the shoal and in its adjacent deep-water area, which results in the sediment exchanges between the flat and channel and between the estuary and the bay. The landward storm waves erode shoal face, causing the rise of water level on the flat, originating the formation of the vertical circulation system of the sediment transport, and consequently * accelerating the evolution process of the tidal flat.

关键词： The rule of sediment transport on the Nanhui tidal flat in the Changjiang Estuary

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2008年第2期26卷 123-148页

作者： Yuanming Wang Department of Mathematics,east china normal university,shanghai 200241,china Division of Computational Science,E-institute of shanghai Universities,shanghai normal Benyu Guo Department of Mathematics,shanghai normal university,shanghai 200234,china Division of Computational Science,E-institute of shanghai Universities,shanghai,china Department of Mathematics East China Normal University ShangHai Department of Mathematics Shanghai Normal University ShangHai

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Stearic acid protects primary cultured cortical neurons against oxidative stress

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Acta Pharmacologica Sinica 2007年第3期28卷 315-326页

作者： Ze-jian WANG~2 Cui-ling LIANG~3 Guang-mei LI~2 Cai-yi YU~2 Ming YIN~(2,4)2 School of Pharmacy,shanghai Jiao Tong university,shanghai 200030,china 3 institute of Population Studies,east china normal university,shanghai 200062,china School of Pharmacy Shanghai Jiao Tong University Shanghai China institute of Population Studies East China Normal University Shanghai China

Aim:To observe the effects of stearic acid against oxidative stress in primarycultured cortical ***:Cortical neurons were exposed to glutamate,hydrogen peroxide（H2O2）,or NaN3insult in the presence or absence of *** viability of cortical neurons was determined by MTT assay and *** antioxidant enzymes activity[superoxide dismutases（SOD）,glutathione peroxidase（GSH-Px）,and catalase（CAT）] and lipid peroxidation incultured cortical neurons were evaluated using commercial kits.{3-[l（p-chloro-benzyl）-5-（isopropyl）-3-t-butylthiondol-2-yl]-2,2-dimethylpropanoic acid,Na}[MK886;5 μmol/L;a noncompetitive inhibitor of proliferator-activated receptor（PPAR）α],bisphenol A diglycidyl ether（BADGE;100 μmol/L;an antagonist ofPPARγ）,and cycloheximide（CHX;30 μmol/L,an inhibitor of protein synthesis）were tested for their effects on the neuroprotection afforded by stearic *** blotting was used to determine the PPARγprotein level in cortical ***:Stearic acid dose-dependently protected cortical neurons againstglutamate or H202 injury and increased glutamate uptake in cultured *** protection was concomitant to the inhibition of lipid peroxidation and to thepromotion activity of Cu/Zn SOD and CAT in cultured cortical *** effects were completely blocked by BADGE and *** with H202 for 24 h,the expression of the PPARγprotein decreasedsignificantly（P2O2on the expression of PPARγcan be attenuated by stearic ***:Stearic acid can protect corticalneurons against oxidative stress by boosting the internal antioxidant *** neuroprotective effect may be mainly mediated by the activation of PPARγandnew protein synthesis in cortical neurons.

关键词： oxidative stress receptors peroxisome prolilferator-activated neurons antioxidants