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Almost periodic solution to singular systems

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Chinese Science Bulletin 1998年第8期43卷 698-700页

作者： Jiarong Liang Yongqing Liu Cunchen Gao S China Univ Technol Dept Automat Canton 510641 Peoples R China

The problems about the almost periodic solution to singular systems are studied. The criterion that the singular systems have almost periodic solutions is obtained. At the same time, the applied example is given.

关键词： singular systems almost periodic solutions boundary.

Quasi-periodic Solutions and Asymptotic Properties for the Isospectral BKP Equation

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Communications in Theoretical Physics 2014年第7期61卷 17-25页

作者：马潘丽田守富 Department of Mathematics China University of Mining and Technology Xuzhou Center of Nonlinear Equations China University of Mining and Technology Xuzhou

In this paper, based on a Riemann theta function and Hirota's bilinear form, a straightforward way is presented to explicitly construct Riemann theta functions periodic waves solutions of the isospectral BKP equation.Once the bilinear form of an equation obtained, its periodic wave solutions can be directly obtained by means of an unified theta function formula and the way of obtaining the bilinear form is given in this paper. Based on this, the Riemann theta function periodic wave solutions and soliton solutions are presented. The relations between the periodic wave solutions and soliton solutions are strictly established and asymptotic behaviors of the Riemann theta function periodic waves are analyzed by a limiting procedure. The N-soliton solutions of isospectral BKP equation are presented with its detailed proof.

关键词： isospectral BKP equation Riemann theta function periodic wave solution soliton solution

Dynamics of Spiral Waves Induced by periodic Mechanical Deformation with Phase Difference

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Communications in Theoretical Physics 2018年第12期69卷 749-752页

作者：李鹏飞乔丽颜赵叶华陈江星马军 Department of Mathematics Hangzhou Dianzi University Department of Physics Hangzhou Dianzi University Department of Physics Lanzhou University of Technology

The dynamics of spiral waves under the influences of periodic mechanical deformation are studied. Here,the mechanical deformation propagating along the medium with phase differences are considered. It is found that weak mechanical deformation may lead to resonant drift of spiral waves. The drift direction and velocity can be changed by the wave length of the deformation. Strong mechanical deformation may result in breakup of spiral waves. The characteristics of breakup are discussed. The critical amplitudes are determined by two factors, i.e. the wave length and frequency of the periodic mechanical deformation. When the wave length of mechanical deformation is comparable to the spiral wave, simulation shows that the critical amplitude is substantially increased. As the frequency of the mechanical deformation is around 1.5 times of the spiral wave, the critical amplitudes are minimal.

关键词： drift breakup of spiral waves periodic mechanical deformation phase difference

Braggs Law with Refractive Correction of Low-angle X-ray Diffraction for periodic Multilayers

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Chinese Physics Letters 1991年第7期8卷 356-359页

作者： JIANG Xiaoming WU Ziqin Synchrotron Radiation Laboratory Institute of High Energy PhysicsAcademia SinicaBeijing 100039 Fundamental Physics Center University of Science and Technology of ChinaHefei 230026

Bragg's law with refractive correction of low-angle X-ray diffraction for periodic multilayers is deduced according to the optical refractive law and interference rules.Variant forms of this law,which accorded with ex... 详细信息

关键词： refractive angle periodic

Spatial dynamics of a nonlocal delayed unstirred chemostat model with periodic input

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International Journal of Biomathematics 2019年第6期12卷 55-72页

作者： Wu-Jun Pu Danhua Jiang Ya Wang Zhanbing Bai Department of Mathematics Longnan Teachers College LongnanGansu 742500P.R.China School of Mathematics and Statistics Lanzhou University LanzhouGansu 730000P.R.China College of Mathematics and System Science Shandong University of Science and Technology Qingdao Shandong 266590P.R.China

In this paper,a nonlocal delayed chernostat model of a single species feeding on a periodically varying input nutrient is proposed.By the theory of semigroup,the existence and uniqueness of solution of the system are obtained.Furthermore,we investigate a threshold result on the global dynamics,and the uniform persistence of the system is established.

关键词： Chernostat nonlocal delay uniform persistence periodic solution

On a new almost periodic type solution of a class of singularly perturbed differential equations with piecewise constant argument

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Science China Mathematics 2002年第4期45卷 484-502页

作者：袁荣 Department of Mathematics Beijing Normal University Beijing China

A new class of ergodic sequences, pseudo almost periodic sequence, is introduced, and the existence of pseudo almost periodic sequence to difference equation is studied. Based on these, we investigate the existence of pseudo almost periodic solutions for a nonautonomous, singularly perturbed differential equations with piecewise constant argument.

关键词： pseudo almost periodic solution, pseudo almost periodic sequence, piecewise constant argument, singular perturbation.

Almost periodic dynamics of delayed prey-predator model with discontinuous harvesting policies and Hassell-Varley type functional response

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International Journal of Biomathematics 2018年第7期11卷 1-36页

作者： Dongxiao Chen Dongshu Wang Fujian Province University Key Laboratory of Computation Science School of Mathematical Sciences Huaqiao University QuanzhouFujian 362021P.R.China

In this study,a class of delayed prey-predator model with Hassell-Varley type functional response is investigated,in which the harvesting policies are modeled by discontinuous functions.Based on functional differential inclusions and set-valued analysis theories,the local and global existence of positive solution in sense of Filippov is given.By employing theory of functional differential inclusions and generalized differential inequalities,some sufficient conditions which guarantee the permanence of the system are obtained.Accord- ing to non-smooth analysis theory with generalized Lyapunov functional approach,a series of useful criteria on existence,uniqueness and global asymptotic stability of the almost positive periodic solution to the system are derived.Some suitable examples together with their numerical simulations are given to illustrate the effectiveness of our results by using MATLAB.

关键词： Discontinuous harvesting policy functional differential inclusions HassellVarley type functional response permanence almost positive periodic solution global attractivity.

Improvement of Camera Calibration Accuracy Based on periodic Arrangement Characteristics of Calibration Target Pattern

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天津大学学报：英文版 2017年第6期23卷 582-590页

作者： Qingguo Tian Yunpeng Li Jinjiang Wang Tianyu Chang School of Precision Instruments and Opto-Electronics Engineering Tianjin UniversityTianjin 300072China Key Laboratory of Opto-Electronics Information Technology of Ministry of Education Tianjin 300072China

Conventional camera calibration that employs calibration targets is a commonly used method to acquire a camera's intrinsic and/or extrinsic parameters. The calibration targets are usually designed as periodic arrays of simple high-contrast patterns that provide highly accurate world coordinate system points and the corresponding image pixel coordinate system points. The existing pixel coordinate extraction algorithms can reach a sub-pixel level; however, they treat each single pattern in one image as an independent individual, which makes it difficult to further improve extraction accuracy. In this paper, a novel method is proposed by utilizing the periodic arrangement characteristics of the calibration target pattern as a global constraint to improve the calibration accuracy. Based on a camera's pinhole model, the intersection point of two fitted curves is used as an optimized pixel point to replace the initial one. Following the pixel coordinate optimization procedures, experiments were performed using real data from a 3D laser line scanner and a dynamic precision calibration target. Our results show that the relative errors of camera homography matrix elements obtained by the proposed optimization method were reduced compared with the commonly used method. The average coordinate measurement accuracy can be improved by nearly 0.05 mm. It is shown that the proposed optimization method can enhance the camera calibration accuracy,especially when the extracted pixels are of poorer precision.

关键词： Camera calibration Pixel coordinate optimization periodic arrangement characteristic Intersection point Concentric circle control point

Uniformly Asymptotic Stability and Existence of periodic Solutions and Almost periodic Solutions

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Science China Mathematics 1994年第8期37卷 933-945页

作者：林发兴 Fuzhou University Fuzhou 350002 PRC

We introduce the concepts of uniformly stable solutions and uniformly-asymptotically stable solutions, and then give the relation between Lyapunov function and those concepts. Furthermore, we establish the theorem that an almost periodic system or periodic system has uniformly-asymptotically stable solutions and Lipschitz’ condition has an almost periodic solution or periodic solution.

关键词： uniformly-asymptotically stable controllable regular almost periodic periodic.