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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 1. Department of Mathematics East China Normal University Shanghai 200062 China 2. Institute of Theoretical Computing East China Narnal University Shanghai 200062 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

The Tracial Rokhlin Property for Automorphisms on Non-simple C~*-Algebras

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Chinese Annals of Mathematics,Series B 2010年第2期31卷 191-200页

作者： Jiajie HUA Department of Mathematics East China Normal University Shanghai 200241 China.

Let A be a unital AF-algebra （simple or non-simple） and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that J α＊... 详细信息

关键词： Rokhlin property Tracial rank zero AF-algebra

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (Department of Mathematics, shanghai normal university, shanghai 20023{4. {{4.) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

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 [a]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. 4., 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

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational Mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (Department of Mathematics, shanghai normal university, shanghai 20023{4. {{4.) Department of Mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

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

Periodic Solutions of Schrdinger Flow from S^3 to S^2

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Chinese Annals of Mathematics,Series B 2006年第4期27卷 401-410页

作者： Hao YIN Department of Mathematics East-China Normal University Shanghai 200062 China.

This paper deals with the periodic solutions of Schrǒdinger flow from S^3 to S^2. It is shown that the periodic solution is related to the variation of some functional and there exist S^1-invariant critical points to... 详细信息

关键词： Schrǒdinger flow Periodic solution Variational method

Enhancing Positive Citizenship Ideals on Students Through Bibliotherapy and Cognitive Counseling

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心理科学 2002年第1期25卷 47-52页

作者： Ismail Hussein Hashim (east china normal university Department of Psychology,shanghai,200062) eastchinanormaluniversityDepartmentofPsychology Shanghai200062

The paper views feelings touching as very important in cultivating positive citizenship ideals amongst the *** main preoccupation of the study was to provide relevant information concerning the efficacy of bibliotherapy and cognitive counseling as two methods that could be applied by counselors in school field to promote positive citizenship ideals in the *** study was carried out in Alfashir principality (Sudan)in April *** of one hundred and twenty five secondary school students were touched with regards to what they regarded as citizenship *** control and experimental measures approach,the two groups of the subjects were treated to bibliotherapy and cognitive counseling, while the third group was left as control *** indicated significant differences in the efficacy of the two methods for positively fostering citizenship ideals among the youth in favor of *** results have demonstrated that bibliotherapy can be effectively applied in school setting through the school curriculum to positively foster citizenship ideals among the youth.

关键词：学生心理学读书疗法认知咨询服务心理研究教育心理学

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. {{4.) 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.