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Chinese Science Bulletin 1997年第3期42卷 259-260页

作者： MAI Jiehua and GU Rongbao1.Institute of mathematics, shantou university, shantou 515063, china 2. Department of mathematics, Anhui university, Hefei 230039, china Institute of mathematics Shantou University Shantou China Department of mathematics Anhui University Hefei China

IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2) flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2) flows.

关键词： Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

An adaptive control with optimal disturbances rejection

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Science china(Information Sciences) 2012年第7期55卷 1704-1714页

作者： LI ShengPing & FAN YingHui Department of Mechantronics Engineering,shantou university,shantou 515063,china Department of Mechantronics Engineering Shantou University Shantou China

This paper provides a way to optimize the overall disturbances rejection performance of the adaptive control system in the presence of unknown external ***,the updatable non-empty admissible model set,which is consistent to the a priori knowledge of the plant parameter and the online measurements,is *** the overall system performance as the criteria,the nominal model is optimally chosen within the admissible model *** optimal nominal model is subsequently used to synthesize the optimal closed-loop controller based on the 1 design *** the above two aspects,an optimal adaptive control scheme is *** of the consistency of the identification criteria and control object,the adaptive control scheme proposed in this paper can achieve the overall optimal disturbances rejection performance,and the effect of the interplay between the identification and control of the adaptive system can be handled *** addition,the computable optimal performance is also provided.

关键词： unknown external disturbances adaptive control optimal performance

Effects of Chronic Stress and Phenytoin on the Long-term Potentiation (LTP) in Rat Hippocampal CA1 Region

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Acta Biochimica et Biophysica Sinica 2004年第5期36卷 375-378页

作者： Hui ZHENG*, Quan YANG, and Chong-Tao XU Mental Health Center, shantou university Medical College, shantou 515063, china Mental Health Center Shantou University Medical College Shantou 515063 China

To investigate the changes of LTP in hippocampal CA1 region induced by chronic stress and the effect of phenytoin on them, thirty-two adult male Sprague-Dawley rats were randomly divided equally into four groups: control group, control-phenytoin group, stress-saline group and stress-phenytoin group. Isolated hippocampal slices of rats were used to observe the changes of long-term potentiation (LTP) in hippocampal CA1 field using electrophysiological technique. Amplitude of population spike (PS) and field excitatory postsynaptic potentials (fEPSPs) slope were used to indicate the changes of LTP. High-frequency stimulation (HFS) was applied to Schaffer collaterals of hippocampal CA3 field, and the changes of PS amplitude and fEPSPs slope in CA1 field were observed. The results showed that the LTP induction rate, the increases of PS amplitude and fEPSPs slope after HFS in control and stress-phenytoin groups were significantly greater than those in stress-saline group (P0.05). It is suggested that chronic stress can damage the development of LTP in hippocampal CA1 field, while phenytoin can protect the LTP of stressed hippocampal slices in normal state.

关键词： phenytoin long-term potentiation hippocampus stress

Global smooth solution of multi-dimensional non-homogeneous conservation laws

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Progress in Natural Science:Materials International 2004年第10期14卷 15-22页

作者： YANG Xiaozhou 1 and ZHANG Tong 2 (1.Department of mathematics,shantou university,shantou515063,china 2.Institute of mathematics,Chinese Academy of Sci-ences,Beijing100080,china) Dept. of Math. Shantou Univ. Shantou 515063 China Inst. of Math. Chinese Acad. of Sci. Beijing 100080 China

The initial value problem of multi-dimensional non-homogeneous conservation laws is studied and a sufficient condition of the existence of its global smooth solution is ***,three equivalent propositions of the existence of global smooth solution for multi-dimensional homogeneous scalar conservation laws are also *** global smooth solution is uniquely expressed by the global implicit function that is determined by a scalar equation,not by a system as usual methods do.

关键词： conservation laws global smooth solution global implicit function diffeomorphism

A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in H-spaces

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 425-430页

作者： Ji-cheng HouDepartment of mathematics, shantou university, shantou 515063, chinaCorrespondence address: Department of mathematics and Information Science, Yantai university, Yantai264005, china Department of mathematics Shantou University Shantou China

In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibr... 详细信息

关键词： H-space fixed points abstract economy non-compact domain Nash equilibria compactly open lower sections

Multiwavelet sampling theorem in Sobolev spaces

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Science china mathematics 2010年第12期53卷 3197-3214页

作者： LI YouFa 1,2 & YANG ShouZhi 1, 1 Department of mathematics, shantou university, shantou 515063, china 2 College of mathematics and Information Sciences, Guangxi university, Nanning 530004, china Department of mathematics Shantou University Shantou China College of mathematics and Information Sciences Guangxi University Nanning China

This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.

关键词： Sobolev spaces refinable function vectors dual multiwavelet frames delta function sampling theorem

The nonexistence of sensitive commutative group actions on graphs

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Science china mathematics 2007年第8期50卷 1197-1204页

作者： Jie-hua MAI~1 En-hui SHI~(2+) 1 Institute of mathematics,shantou university,shantou 515063,china 2 School of Mathematical Sciences,Suzhou university,Suzhou 215006,china Institute of mathematics Shantou University Shantou China School of Mathematical Sciences Suzhou University Suzhou China

In this paper,we observe a special kind of continuous functions on *** estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on ***,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.

关键词： homeomorphism commutative group action graph map sensitivity expansiveness infinite spiral curve

Non-wandering points and the depth for graph maps

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Science china mathematics 2007年第12期50卷 1818-1824页

作者： Jie-hua MAI~1 Tai-xiang SUN~(2+) ~1 Institute of mathematics,shantou university,shantou 515063,china ~2 College of mathematics and Information Sciences,Guangxi university,Nanning 530004,china Institute of mathematics Shantou University Shantou China College of mathematics and Information Sciences Guangxi University Nanning China

Let G be a graph and f: G → G be continuous. Denote by R(f) and Ω(f) the set of recurrent points and the set of non-wandering points of f respectively. Let Ω0 (f) = G and Ωn (f) =Ω(f|Ωn-1(f)) for all n ∈ N. The minimal m ∈ NU {∞} such that Ωm(f) = Ωm+1(f) is called the depth of f. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2. Furthermore, we obtain some properties of non-wandering points of f.

关键词： graph map, non-wandering point, the depth of a graph map

A LIMIT THEOREM FOR INTERACTING MEASURE-VALUED BRANCHING PROCESSES

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Acta Mathematica Scientia 1997年第3期17卷 241-249页

作者：赵学雷杨敏 Institute of mathematics Shantou University Shantou 515063 China The State Information Center Beijing 100045 China

It is well known that Fleming-Viot superprocesses can be obtained from the Dawson-Watanabe superprocesses by conditioning the latter to have constant total mass. The same question is investigated for measure-valued branching processes with interacting intensity independent of the geographical position. It is showed that a sequence of conditioned probability laws of this kind of interacting measure-valued branching processes also approximates to the probability law of Fleming-Viot superprocesses.

关键词： interacting measure-valued Branching processes DW-superprocesses FV-superprocesses conditioned probability law

Anisotropic effect on the vibronic reduction factors

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Chinese Science Bulletin 2006年第21期51卷 2553-2558页

作者： QIU Qing-chun1,2 & QIAO Fen1,2 1. Department of Physics and IT, Medical College, shantou university,shantou 515041, china 2. Department of Physics, shantou university, shantou 515063, china Department of Physics and IT Medical College Shantou University Shantou China Department of Physics Shantou University Shantou China

The reduction factors p and q defined by Ham in the Ee JT system and their relation 2q-p=1 have been well accepted and the concept of reduction factors is widely used in the studies of vibronic coupling. However, when the system is under the anisotropic conditions, the reduction factors and their relation will change accordingly. The first-order reduction factors p and q of Ee system were further studied using the method of unitary transformation here. The relation between p and q proposed by Ham was investigated under both conditions of the linear coupling and the anisotropic effects. The result demonstrated that the relation of 2q-p=1 was only correct for the linear vibronic coupling, but not correct when the anisotropic effect was considered. This result suggested that the anisotropic effect influence considerably the reduction factors, and hence the physical properties of materials. Our method could be also applied to other JT systems, especially the highly symmetric JT systems involving C60 molecules.

关键词：电子振动耦合声子交迭 Jahn-Teller效应各向异性