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A differential game for cooperative target defense with two slow defenders

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Science China(Information Sciences) 2020年第12期63卷 269-271页

作者： li liANG fang DENG School of Automation Beijing Institute of Technology School of Information Engineering Inner Mongolia University of Science and Technology

Dear editor,Active defense is an effective way to improve battlefield survivability [1]. In the actual battlefield environment, equipment with weaker survivability usually needs a friendly platform to protect it from attacks. For example, important assets need to be protected by armed defense forces in the course of transportation to prevent them from being seized and destroyed by enemy forces.

关键词： Pursuit-evasion game Active defense Target-Attacker-Defender game Barrier Cooperate policy

Numerical Simulation of Bragg Reflection Based on linear Waves Propagation over A Series of Rectangular Seabed

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China Ocean Engineering 2008年第1期22卷 71-86页

作者： Chih-Chung WEN li-hung TSAI Department of Environmental Engineering Hungkuang University Center of Harbor and Marine Technology Institute of TransportationMinistry of Transportation and Communications

A numerical model, Evolution Equation of Mild-Slope Equation （EEMSE） developed by Hsu et al. （2003）, was applied to study the Bragg reflection of water waves over a series of rectangular seabed. Three key parameters of the Bragg reflection including the peak coefficient of primary Bragg reflection, its corresponding relative wavelength, and the bandwidth, have shown to be effective in describing the characteristics of the primary Bragg reflection. The characteristics of the Bragg reflection were investigated under the various conditions comprising number, height, and spacing interval of a series of rectangular seabed. The results reveal that the peak of Bragg reflection increases with the increase of rectangular seabed height and number, the bandwidth and the shift value of the Bragg reflection depend on the increase of the rectangular seabed height as well as the decrease of rectangular seabed number, and the relative rectangular seabed spacing in the rang of 3 and 4 could produce higher Bragg reflection. Finally, a correlative and regressive analysis is performed by use of the calculated data. Based on the results of the analysis, empirical equations were established. Our study results can provide an appropriate choice of a series of rectangular seabed field for a practical design.

关键词： Bragg reflection mild-slope equation rectangular seabed bandwidth of the Bragg reflection rapidly varying component

VARIATIONAL IMAGE FUSION WITH FIRST AND SECOND-ORDER GRADIENT INFORMATION

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Journal of Computational Mathematics 2016年第2期34卷 200-222页

作者： fang li Tieyong Zeng Department of Mathematics East China Normal University and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

Image fusion is important in computer vision where the main goal is to integrate several sources images of the same scene into a more informative image. In this paper, we propose a variational image fusion method based on the first and second-order gradient information. Firstly, we select the target first-order and second-order gradient information from the source images by a new and simple salience criterion. Then we build our model by requiring that the first-order and second-order gradient information of the fused image match with the target gradient information, and meanwhile the fused image is close to the source images. Theoretically, we can prove that our variational model has a unique minimizer. In the numerical implementation, we take use of the split Bregman method to get an efficient algorithm. Moreover, four-direction difference scheme is proposed to discrete gradient operator, which can dramatically enhance the fusion quality. A number of experiments and comparisons with some popular existing methods demonstrate that the proposed model is promising in various image fusion applications.

关键词： Image fusion Feature selection Bounded variation Second bounded variation,Split Bregman

Classification of Bott towers by matrix

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Frontiers of Mathematics in China 2016年第2期11卷 255-268页

作者： Qifeng BAI fang li School of Basic Science Changchun University of Technology Changchun 130012 China School of Mathematics Jilin University Changchun 130012 China

A criterion for the classification of Bott towers is presented, i.e., two Bott towers B,（A） and B,（A＇） are isomorphic if and only if the matrices A and A＇ are equivalent. The equivalence relation is defined by two operations on matrices. And it is based on the observation that any Bott tower B,（A） is uniquely determined by its structure matrix A, which is a strictly upper triangular integer matrix. The classification of Bott towers is closely related to the cohomological rigidity problem for both Bott towers and Bott manifolds.

关键词： Bott manifold Bott tower cohomological rigidity toric manifold

A relation between tilting graphs and cluster-tilting graphs of hereditary algebras

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Frontiers of Mathematics in China 2015年第2期10卷 275-291页

作者： fang li Yichao YANG Department of Mathematics Zhejiang University (Yuquan Campus) Hangzhou 310027 China Department of Mathematics University of Sherbrooke Sherbrooke JIK 2R1 Canada

We give the condition of isomorphisms between tilting graphs and cluster-tilting graphs of hereditary algebras. As a conclusion, it is proved that a graph is a skeleton graph of Stasheff polytope if and only if it is both the tilting graph of a hereditary algebra and also the cluster-tilting graph of another hereditary algebra. At last, when comparing such uniformity, the geometric realizations of simplicial complexes associated with tilting modules and clustertilting objects are discussed respectively.

关键词： Tilting graph cluster-tilting graph cluster category Stasheffpolytope linear quiver

Histone variants: the artists of eukaryotic chromatin

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Science China(life Sciences) 2015年第3期58卷 232-239页

作者： li Min fang YuDa National Key Laboratory of Plant Molecular Genetics Shanghai Institute of Plant Physiology and Ecology Shanghai Institutes for Biological Sciences Chinese Academy of Sciences

The eukaryotic genome is packaged into a complex nucleoprotein structure named chromatin, balancing the compactness of genome and the accessibility of regulatory proteins and RNA polymerases to DNA. The mechanisms of the regulation of chromatin dynamics include the post-translational modification of histones, alteration of nucleosome positions by chromatin remodelers, replacement of canonical histones by histone variants with the aid of histone chaperones, and dynamic organization of the three-dimensional genome in the small nucleus. Histone variants are different from canonical histones by substitution of several amino acid residues or changes in amino acid sequence. Histone variants perform specialized functions such as altering nucleosome stability, dynamics, structure, as well as playing critical roles in a range of biological processes like transcriptional regulation, DNA repair and recombination, development and immune responses. Here we discuss how histone variants, their modification and specific loading to chromatin are involved in transcriptional regulation, DNA repair and plant development.

关键词： histone variants histone modification gene regulation DNA repair stress responsiveness

Differential Graded Structures on Path Categories

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Algebra Colloquium 2015年第4期22卷 677-686页

作者： fang li Dezhan Tan Department of Mathematics Zhejiang University Hangzhou Zhejiang 310027 China

In this paper, we consider the graded path category associated to a quiver. We investigate all n-differentials on such a category, and also study the associated graded lie algebra. Moreover, a necessary and sufficient... 详细信息

关键词： quiver path category graded differential operator graded lie algebra dif-ferential graded category

The (＊＊)-Haagerup Property for C^＊-Algebras

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Chinese Annals of Mathematics,Series B 2016年第3期37卷 367-372页

作者： Changjing li Xiaochun fang School of Mathematical Sciences Shandong Normal University Jinan 250014 China. Department of Mathematics Tongji University Shanghai 200092 China.

Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki's question(2013), and then obtain several results of(**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the(**)-Haagerup property. Some heredity results concerning the(**)-Haagerup property are also proved.

关键词： C^*-algebras Von Neumann algebras Haagerup property

On the First Hochschild Cohomology of Admissible Algebras

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Chinese Annals of Mathematics,Series B 2015年第6期36卷 1027-1042页

作者： fang li Dezhan TAN Department of Mathematics Zhejiang University College of Mathematics and Information Science Shangqiu Normal University

The aim of this paper is to investigate the first Hochschild cohomology of ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, dif- ferential operators from a path algebra to its quotient algebra as an admissible algebra ave discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the k-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field k of characteristic 0.

关键词： Quiver Admissible algebra Differential operators Cohomology