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ON THE VARIATIONS OF G_2

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 387-394页

作者： LIU DONG LIN LEI Department of Mathematics, east china normal university, shanghai 200062, china. Department of Mathematics, east china normal university, shanghai 200062, china. Department of Mathematics East China Normal University Shanghai 200062 China

In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic2, which are called the variations of G2. In this paper, the authors investigate their derivationalgebras. It is shown that G2 and its variations all possess unique nondegenerate associativeforms. The authors also find some nonsingular derivations of ViG for i = 3, 4, 5, 6, and therebyconstruct some left-symmetric structures on ViG for i = 3,4,5,6. Some errors about thevariations of si(3, F) in [1] are corrected.

关键词：变分导子代数结合型左对称结构 Lie代数特征

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

Algebraic Surfaces of General Type with K^2 = 2p_g-1, p_g■5

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Acta Mathematica Sinica,English Series 1996年第3期12卷 234-243页

作者： Liu Xianfang, Department of Mathematics east china normal university shanghai, 200062 china.urrent address: institute of systems science Beijing, 100080 china Department of Mathematics East China Normal University Shanghai China

This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g 13 all these surfaces are simply-connected.

关键词： Double cover Canonical resolution Fibration Singular fiber Ramification divisor Branch locus

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.

THE PROJECTIVE PLANE CROSSING NUMBERS OF CIRCULAR GRAPHS

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Journal of systems science & Complexity 2008年第2期21卷 316-322页

作者： Dengju MA Han REN School of science Nantong University Nantong 226007 China Department of Mathematics East China Normal University Shanghai 200062 China

作者为一张圆形的图的射影的飞机十字路口数字给上面的界限。另外，作者证明圆形的图 C (8,3 ) 和 C (9,3 ) 的射影的飞机十字路口数字分别地是 2 和 1。

关键词：射影平面图论相交数数学理论

Tolerance of Physocypria kraepelini (Crustacean, Ostracoda) to water-borne ammonia, phosphate and pH value

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Journal of Environmental sciences 2009年第11期21卷 1575-1580页

作者： YU Na, CHEN Shimei, LI Erchao, CHEN Jiayan, CHEN Liqiao School of Life science, east china normal university, shanghai 200062, china School of Life science East China Normal University Shanghai 200062 China

This study evaluated the median lethal concentration （LC50） and safe concentration of water-borne ammonia, phosphate and pH value on Physocypria kraepelini, a freshwater Ostracoda with a static renewal test system. The results indicated that the LC50 values of ammonia for P. kraepelini were 1026.71, 859.98, 771.79 and 583.82 mg/L at 24, 48, 72 and 96 h exposure, respectively, and the safe concentration range of ammonia for the long-term survival of P. kraepelini was less than 58.38 mg/L. The safe range of pH value for the survival of P. kraepelini was from 6.59 to 7.61. P. kraepelini has a high tolerance to ammonia, phosphate and pH value which are the main environmental factors in the serious eutrophication water.

关键词： ammonium phosphate Physocypria kraepelini

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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science china.Mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of Mathematics, east china normal university, shanghai 200062, china.College of Mathematics & Information science, Northwest normal university, Lanzhou 730070, china Department of Mathematics East China Normal University Shanghai China College of Mathematics & Information science Northwest Normal University Lanzhou China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

Variation of peroxidase isoenzyme and biofilm of Phanerochaete chrysosporium in continuous membrane bioreactor for Reactive Brilliant Red X3-B treatment

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Journal of Environmental sciences 2009年第7期21卷 940-947页

作者： GAO Shang, CHEN Cheng, TAO Fang, HUANG Minsheng, MA Lihua, WANG Zhonghua, WU Linhui School of Resource and Environment science, east china normal university, shanghai 200062, china. School of Resource and Environment science East China Normal University Shanghai 200062 China

The influence of a Reactive Brilliant Red X-3B （RBR X-3B） dye on the peroxidase isoenzyme ofPhanerochaete chrysosporium was determined, and the biofilm structure in a white rot fungal continuous membrane bioreactor （MBR） was also investigated by scanning electron microscope （SEM）. The variation of peroxidase isoenzyme and the decolorization rate in the continuous MBR were evaluated. The results showed that the 100 mg/L RBR X-3B could stimulate the production of the peroxidase isoenzyme in the shaking-flask culture. In addition, two new peroxidase isoenzyme bands with relative mobility （Rf） value of 0.27 and 0.28 appeared, but the activity was lower than the blank control of 11 d. In the continuous MBR, the system worked stably during the first 60 d, the main peroxidase isoenzyme bands existed and three new bands with Rf value of 0.10, 0.27, and 0.28 appeared. Meanwhile, the biofilm grew well and the average decolorization rate could reach 90.6%. But the bands of peroxidase isoenzyme decreased rapidly at day 65, only two bands with Rf value 0.24 and 0.26 existed, and the decolorization rate decreased to 78.3%. Therefore, 5 bottles of P. chrysosporium mycelial pellet were added into the MBR, and then the activity of the peroxidase isoenzyme and the decolorization rate had a slight recovery. Finally, the decolorization rate finally decreased to 75.2%. These results contribute to a comprehensive understanding of the variation of peroxidase isoenzyme and biofilm in continuous MBR by white rot fungi.

关键词： Phanerochaete chrysosporium continuous membrane bioreactor Reactive Brilliant Red X3-B peroxidase isoenzyme pattern

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

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关键词：稳定代数昆兹代数不变量群序列