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G-type dispersion equation under suppressed rigid boundary:analytic approach

Applied Mathematics and Mechanics(English Edition) 2016年第4期37卷 501-512页

作者： S.K.VISHWAKARMA Runzhang XU College of Automation Harbin Engineering University Department of Mathematics Birla Institute of Technology and Science (BITS)Pilani Hyderabad Campus College of Science Harbin Engineering University

This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentially and periodically along the depth. The displacements of the wave are found in the individual medium followed by a dispersion equation using a suitable analytic approach and a boundary condition. The prominent effect of inhomogeneity contained in the media, the rigid boundary plane, and the initial stress on the phase and group velocities is shown graphically.

关键词： G-type wave analytic approach dispersion equation group velocity rigid boundary

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Neuronal population dynamic model: An analytic approach

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Progress in Natural Science:Materials International 2009年第9期19卷 1159-1163页

作者： Wentao Huang a, Licheng Jiao a, Yuelei Xub, Shiping Ma b, Jianhua Jia a a Institute of Intelligent Information Processing, Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, P.O. Box 224, Xi’an 710071, China b Department of Avionics Engineering, Engineering College of Air Force Engineering University, Xi’an 710038, China Institute of Intelligent Information Processing Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education Xidian University P.O. Box 224 Xi’an 710071 China Department of Avionics Engineering Engineering College of Air Force Engineering University Xi’an 710038 China

A novel analytic approach is presented to study the population of excitatory and inhibitory spiking neurons in this paper. The evolution in time of the population dynamic equation is determined by a partial differential equation. A new function is proposed to characterize the population of excitatory and inhibitory spiking neurons, which is different from the population density function discussed by most researchers. And a novel evolution equation, which is a nonhomogeneous parabolic type equation, is derived. From this, the stationary solution and the firing rate of the stationary states are given. Last, by the Fourier transform, the time dependent solution is also obtained. This method can be used to analyze the various dynamic behaviors of neuronal populations.

关键词： analytic approach Neuronal population Dynamic model Fourier transform

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Exponential Convergence Rates of Markov Chains under a Weaken Minorization Condition

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1829-1836页

作者： Shu Lan HU Xin Yu WANG School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan 430073 P. R. China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 P. R. China

In this paper, we obtain the quantitative bound of the exponential convergence rates of Markov chains under a weaken minorization condition, using the coupling method and the analytic approach. And also, we obtain the... 详细信息

关键词： Convergence rates Markov chains coupling method analytic approach

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