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On U(n)-invariant strongly convex complex Finsler metrics

Science China Mathematics 2021年第11期64卷 2461-2478页

作者： Kun Wang Hongchuan Xia Chunping Zhong School of Mathematical Sciences Xiamen UniversityXiamen 361005China College of Mathematics and Statistics Xinyang Normal UniversityXinyang 464000China

In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) to be strongly convex,which also makes it possible to investigate the relationship between real and complex Finsler geometries via concrete and computable *** prove a rigid theorem which states that a U(n)-invariant strongly convex complex Finsler metric F is a real Berwald metric if and only if F comes from a U(n)-invariant Hermitian *** give a characterization of U(n)-invariant weakly complex Berwald metrics with vanishing holomorphic sectional curvature and obtain an explicit formula for holomorphic curvature of the U(n)-invariant strongly pseudoconvex complex Finsler ***,we prove that the real geodesics of some U(n)-invariant complex Finsler metric restricted on the unit sphere S^(2n-1)■C^(n) share a specific property as that of the complex Wrona metric on C^(n).

关键词： U(n)-invariant complex Finsler metric strongly convex real Berwald metric holomorphic curvature

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Iterative parameter estimate with batched binary-valued observations

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Science China(Information Sciences) 2016年第5期59卷 158-175页

作者： Yanlong ZHAO Wenjian BI Ting WANG Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences

In this paper, we consider linear system identification with batched binary-valued *** constructed an iterative parameter estimate algorithm to achieve the maximum likelihood(ML) *** first interesting result was that there exists at most one finite ML solution for this specific maximum likelihood problem, which was induced by the fact that the Hessian matrix of the log-likelihood function was negative definite under binary data and Gaussian system noises. The global concave property and local strongly concave property of the log-likelihood function were obtained. Under mild conditions on the system input, we proved that the ML function has a unique maximum point. The second main result was that the ML estimate was consistent under persistent excitation inputs, which infers the effectiveness of ML estimate. Finally, the proposed iterative estimate algorithm converged to a fixed vector with an exponential rate that was proved by constructing a Lyapunov function. A more interesting result was that the limit of the iterative algorithm achieved the maximization of the ML function. Numerical simulations are illustrated to support the theoretical results obtained in this paper well.

关键词： Binary-valued observation maximum likelihood estimate strongly convex system identification exponential rate

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A REMARK ON GENERAL COMPLEX(α,β)METRICS

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Acta Mathematica Scientia 2021年第3期41卷 670-678页

作者： Hongchuan XIA Chunping ZHONG School of Mathematics and Statistics Xinyang Normal UniversityXinyang 464000China School of Mathematical Sciences Xiamen UniversityXiamen 361005China

In this paper,we give a characterization for the general complex(α,β)metrics to be strongly *** an application,we show that the well-known complex Randers metrics are strongly convex complex Finsler metrics,whereas ... 详细信息

关键词： strongly convex strongly pseudoconvex general complex(α β)metrics

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