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The Formation Control of Multi-agent Systems on a circle

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IEEE/CAA Journal of Automatica Sinica 2018年第1期5卷 148-154页

作者： Qiang Wang Yuzhen Wang Huaxiang Zhang School of Information Science and Engineering Shandong Normal University School of Control Science and Engineering Shandong University

This paper investigates the formation control of a class of multi-agent systems moving on a circle, whose topology is a cyclic graph, and presents several new results for the following two cases: Case I, the agents with single-integrator kinematics,and Case II, the agents with double-integrator kinematics. Firstly,for Case I, two control protocols are proposed under which the multiagent systems keep a uniformly-spaced formation. Secondly,we study Case II, and a control protocol is designed for this case, then the stability of the formation is proved. Finally, three simulations are studied by using our presented results. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the formation control of this class of multi-agent systems.

关键词： circle cyclic graph formation control multiagent systems uniformly spaced

On the Construction of Mohr Stress circle and a Graphic Method in Representing the Stress Components on Different Oblique Planes

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上海交通大学学报 2004年第Z2期38卷 223-228页

作者： Zhubin He Z. R. Wang Kunpeng Kang School of Materials Science and Engineering Harbin Institute of Technology Harbin150001 China School of Materials Science and Engineering Harbin Institute of Technology Harbin150001 China Department of Computer Science Shangqiu Normal University Shangqiu476000 China

The Mohr stress circle for three-dimensional stress is usually determined by equations,which is lack of intuitionistic meanings and difficult to understand. In this paper, the construction of Mohr stress circle is illustrated directly by numerical method. The shortcoming of Mohr stress circle in representing the stress components on different oblique planes for three-dimensional stress is analyzed. A three-dimensional figure is given to describe the variation of normal and shear stress on different oblique planes at one point for the first time.

关键词： Mohr stress circle Graphic method normal stress shear stress

Calculating method of circle radius using genetic algorithms

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中国有色金属学会会刊：英文版 2000年第1期10卷 127-129页

作者：廖平喻寿益钟掘中南工业大学湖南长沙

Some improved methods of the traditional genetic algorithms were proposed and their application in calculating circle radius was discussed. Simulation shows that real number encoding, simulated annealing and saving the best individual into the next generation can effectively improve the accuracy and speed up the searching for global optimization. It is also shown that improved genetic algorithms can effectively calculate the circle radius and be realized easily using computer.

关键词： genetic algorithms circle radius calculating method error analysis

Iterative circle fitting based on circular attracting factor

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Journal of Central South University 2013年第10期20卷 2663-2675页

作者：王恒升张强王福亮 College of Mechanical and Electrical Engineering Central South University State Key Laboratory for High Performance Complex Manufacturing (Central South University)

An intuitive method for circle fitting is proposed. Assuming an approximate circle(CA,n) for the fitting of some scattered points, it can be imagined that every point would apply a force to CA,n, which all together form an overall effect that "draws" CA,n towards best fitting to the group of points. The basic element of the force is called circular attracting factor(CAF) which is defined as a real scalar in a radial direction of CA,n. An iterative algorithm based on this idea is proposed, and the convergence and accuracy are analyzed. The algorithm converges uniformly which is proved by the analysis of Lyapunov function, and the accuracy of the algorithm is in accord with that of geometric least squares of circle fitting. The algorithm is adopted to circle detection in grayscale images, in which the transferring to binary images is not required, and thus the algorithm is less sensitive to lightening and background noise. The main point for the adaption is the calculation of CAF which is extended in radial directions of CA,n for the whole image. All pixels would apply forces to CA,n, and the overall effect of forces would be equivalent to a force from the centroid of pixels to CA,n. The forces from would-be edge pixels would overweigh that from noisy pixels, so the following approximate circle would be of better fitting. To reduce the amount of calculation, pixels are only used in an annular area including the boundary of CA,n just in between for the calculation of CAF. Examples are given, showing the process of circle fitting of scattered points around a circle from an initial assuming circle, comparing the fitting results for scattered points from some related literature, applying the method proposed for circular edge detection in grayscale images with noise, and/or with only partial arc of a circle, and for circle detection in BGA inspection.

关键词： circle detection circle fitting grayscale image iterative algorithm least squares fitting(LSF) circular attracting factor(CAF) BGA inspection

Schwarz’s lemma for the circle packings with the general combinatorics

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Science China Mathematics 2010年第9期53卷 277-290页

作者： XiaoJun Huang JinSong Liu Liang Shen College of Mathematics and Physics Chongqing University Chongqing China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academic of Sciences Beijing China

Rodin (1987) proved the Schwarz’s lemma analog for the circle packings based on the hexagonal combinatorics. In this paper, we prove the Schwarz’s lemma for the circle packings with the general combinatorics and our proof is more simpler than Rodin’s proof. At the same time, we obtain a rigidity property for those packings with the general combinatorics.

关键词： circle packing discrete extremal length the maximum principle hyperbolic geometry

Offset approximation based on reparameterizing the path of a moving point along the base circle

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Applied Mathematics(A Journal of Chinese Universities) 2009年第4期24卷 431-442页

作者： ZHAO Hong-yan Department of Mathematics Zhejiang University Zhejiang 310027 China State Key Laboratory of CAD & CG Zhejiang University Zhejiang 310027 China College of Fundamental Studies Shanghai University of Engineering Science Shanghai 201620 China

This paper presents a novel algorithm for planar curve offsetting. The basic idea is to regard the locus relative to initial base circle, which is formed by moving the unit normal vectors of the base curve, as a unit circular arc first, then accurately to represent it as a rational curve, and finally to reparameterize it in a particular way to approximate the offset. Examples illustrated that the algorithm yields fewer curve segments and control points as well as C^1 continuity, and so has much significance in terms of saving computing time, reducing the data storage and smoothing curves entirely.

关键词： CAD/CAM offset circle convolution Bezier/B-spline curve rational curve

Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on circle Diffeomorphisms

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Acta Mathematica Sinica,English Series 2020年第3期36卷 245-272页

作者： Yun Ping JIANG Department of Mathematics Queens College of the City University of New York FlushingNY 11367-1597USA Department of Mathematics Graduate School of the City University of New York365 Fifth A venueNew YorkNY 10016USA

Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.

关键词： Bers complex manifold structure circle diffeomorphism modulus of continuity quasisymmetric circle homeomorphism Teichmuller space Kobayashi's metric Teichmuller's metric

Influence of Nucleotide-biased Fluorescence Emissions of SYBR Green Ⅱ on the Result Consistence of Rolling circle Amplification

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Chemical Research in Chinese Universities 2019年第6期35卷 1119-1123页

作者： ZHANG Bin JIANG Jiquan YUAN Ying GUAN Yifu Department of Biochemistry and Molecular Biology China Medical UniversityShenyang 110122P.R.China Department of Plastic Surgery School of StomatologyChina Medical UniversityShenyang 110009P.R.China Department of Biochemistry and Molecular Biology College of Medical Laboratory and TechnologyHarbin Medical University(Daqing)Daqing 163000P.R.China

The fluorescence dye SYBR Green Ⅱ(SG Ⅱ)has been frequently used in rolling circle amplification(RCA)based analyses of nucleic acids.However,a good amount of inconsistencies have been reported in regards the quality and reproducibility of RCA reactions.To properly examine this experimental issue,here we utilized a series of synthetic oligonucleotides and circular templates to investigate the impact of SG Ⅱ in RCA reactions.The results indicate that SG Ⅱ enables a strong fluorescence signal only when complexing with guanosine(G)residue.In RCA reactions,long single-stranded RCA products,enriched with G residues,result in higher fluorescence emission when compared with the addition of other nucleotide residues.These results suggest that the nucleotide composition of the reaction can affect the amplification results and,eventually,can lead to inconsistent fluorescence of the RCA products.This work indicates that particular attention should be given when circular templates are designed for the quantitative analysis of nucleic acids,to further allow the signal reproducibility of RCA-based experiments.

关键词： Rolling circle amplification SYBR Green Ⅱ Nucleotide-biased Fluorescence emission

Twistor quantization of the space of half-differentiable vector functions on the circle revisited

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Science China Mathematics 2009年第12期52卷 2714-2729页

作者： SERGEEV Armen Department of Mathematical Physics Steklov Mathematical InstituteMoscow 119991Russia

We discuss the twistor quantization problem for the classical system(Vd,Ad),represented by the phase space Vd,identified with the Sobolev space H 1/2 0 (S1,Rd)of half-differentiable vector functions on the circle,and the algebra of observables Ad,identified with the semi-direct product of the Heisenberg algebra of Vd and the algebra Vect(S1)of tangent vector fields on the circle.

关键词： twistor quantization Sobolev space of half-differentiable functions group of diffeomorphisms of the circle