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projective and indecomposable S-acts

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Science China Mathematics 1999年第6期42卷 593-599页

作者：陈裕群岑嘉评 Department of Mathematics South China Normal University Guangzhou China Department of Mathematics the Chinese University of Hong Kong Hong Kong China

Let S be a semigroup and E the set of all idempotents in S. Let S-Act be the category of all S-acts. Let (?) be a full subcategory of S-Act which contains _sS and is closed under coproducts and summands. It is proved that, in (?), an S-act P is projective and unitary if and only if P (?) Ц_i∈1 Se_i, e_i∈E. In particular, P is a projective, indecomposable and unitary object if and only if P (?) Se for some e∈E. These generalize some results obtained by Knauer and Talwar.

关键词： S-acts projective acts indecomposable acts

Function projective Lag Synchronization of Chaotic Systems with Certain Parameters via Adaptive-impulsive Control

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International Journal of Automation and computing 2019年第2期16卷 238-247页

作者： Xiu-Li Chai Zhi-Hua Gan Institute of Image Processing and Pattern Recognition Henan University Institute of Intelligent Network System School of SoftwareHenan University

A new method is presented to study the function projective lag synchronization(FPLS) of chaotic systems via adaptive-impulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are designed. Based on the Lyapunov stability theory and the impulsive control technology, some effective sufficient conditions are derived to ensure the drive system and the response system can be rapidly lag synchronized up to the given scaling function matrix. Numerical simulations are presented to verify the effectiveness and the feasibility of the analytical results.

关键词： Function projective lag synchronization (FPLS) adaptive-impulsive chaotic systems numerical simulation Lyapunov stability theory

Grobner-Shirshov Basis and Minimal projective Resolution of Uq^+(B2)

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Algebra Colloquium 2018年第4期25卷 713-720页

作者： Lingling Mao Jingqian Wang Department of Basic Education Xi'an Traffic Engineering University Xi'an 710300China College of Electrical & Information Engineering Shaanxi University of Science & Technology Xi'an 710021China

In this paper,by using the Anick resolution and Grobner-Shirshov basis for quantized enveloping algebra of type B2,we compute the minimal projective resolution of the trivial module of Uq^+(B2),and as an application w... 详细信息

关键词： Anick resolution minimal projective resolution Grobner-Shirshov basis

Adaptive Generalized projective Synchronization of Takagi-Sugeno Fuzzy Drive-response Dynamical Networks with Time Delay

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Chinese Physics Letters 2012年第2期29卷 33-36页

作者：郑永爱 College of Information Engineering Yangzhou UniversityYangzhou 225127

Time-delay Takagi-Sugeno fuzzy drive-response dynamical networks (TD-TSFDRDNs) are defined by extending the drive-response dynamical networks.Based on the LaSalle invariant principle,a simple and systematic adaptive control scheme is proposed to synchronize the TD-TSFDRDNs with a desired scalar factor.A sufficient condition for the generalized projective synchronization in TD-TSFDRDNs is derived.Moreover,numerical simulations are provided to verify the correctness and effectiveness of the scheme.

关键词： dynamical invariant projective

Generalized projective Synchronization of Fractional Order Chaotic Systems with Different Dimensions

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Chinese Physics Letters 2012年第2期29卷 44-46页

作者：王莎于永光 Department of Mathematics Beijing Jiaotong UniversityBeijing 100044

The generalized projective synchronization of different dimensional fractional order chaotic systems is investigated.According to the stability theory of linear fractional order systems,a sufficient condition to realize synchronization is obtained.The fractional order chaotic and hyperchaotic systems are applied to achieve synchronization in both reduced and increased dimensions.The corresponding numerical results coincide with theoretical analysis.

关键词： chaotic fractional projective

Vanishing Ideals of projective Spaces over Finite Fields and a projective Footprint Bound

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Acta Mathematica Sinica,English Series 2019年第1期35卷 47-63页

作者： Peter BEELEN Mrinmoy DATTA Sudhir R.GHORPADE Department of Applied Mathematics and Computer Science Technical University of DenmarkDK 2800.Kgs.LyngbyDenmark Department of Applied Mathematics and Computer Science Technical University of DenmarkDK 2800Kgs.LyngbyDenmark Current address:Department of Mathematics and StatisticsUiT-The Arctic Unwersity ofNorwayN-9037TromsφNorway Department of Mathematics Indian Institute of Technology BombayPowaiMumbai 400076India

We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre’s inequality for the number of points of projective hypersurfaces over finite fields is included.

关键词： Finite field projective space algebraic variety vanishing ideal Grobner basis footprint bound projective hypersurface

The arithmetic genus and extrinsic geometry of smooth projective variety

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Science China Mathematics 1998年第7期41卷 729-735页

作者：陈志华姚勤 Department of Applied Mathematics Tongji University Shanghai China

Some theorems concerning the projective normality and extrinsic geometry on the smooth variety are proved under some supposed conditions related to the arithmetic genus of the smooth variety.

关键词： subvariety arithmetic genus projective normality.

Function projective Synchronization for Two Gyroscopes under Specific Constraints

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Chinese Physics Letters 2013年第7期30卷 38-42页

作者：闵富红 School of Electrical and Automation Engineering Nanjing Normal UniversityNanjing 210042

The function projective synchronization between two coupled gyroscope systems is investigated under the sinusoidal constraints.From the theory of discontinuous dynamical systems,the necessary and sufficient conditions of such synchronization are given,and the parameter map is developed.Numerical simulations for the function synchronization of two coupled gyroscopes are illustrated to verify the effectiveness of this method.

关键词： method. function projective

Modified projective Synchronization of Fractional-order Chaotic Systems with Different Dimensions

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 527-538页

作者： Xi ZHANG Ran-chao WU School of Mathematics Anhui UniversityHefei 230601China Nanchang No.1 Secondary Vocational School Nanchang330013China

In this paper,the modified projective synchronization between two fractional-order chaotic systems with different dimensions is investigated.The added-order scheme and the reduced-order scheme are proposed,respectively.Based on the Laplace transformation and feedback control theory,controllers are designed such that two chaotic systems with different dimensions could be synchronized asymptotically under the presented schemes.Corresponding numerical simulations are given to show the effectiveness of the proposed schemes.

关键词： Modified projective synchronization Fractional-order chaotic systems Laplace transformation