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THE GENERALIZED ROPER-SUFFRIDGE EXTENSION OPERATOR

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Acta Mathematica Scientia 2008年第1期28卷 63-80页

作者：冯淑霞刘太顺 college of mathematics and Information Science Henan University Department of mathematics Huzhou Teachers College

This note induces some generalized Roper-Suffridge extension operators such that they are used to construct some almost starlike mappings of order α and starlike mappings of order a on different domains.

关键词： Roper-Suffridge operator almost starlike mapping of order a starlike mappings of order

On Hamiltonian Property of Cayley Digraphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 547-556页

作者： Fang DUAN Qiong-xiang HUANG School of mathematics Science Xinjiang Normal UniversityUrumqi 830017China college of mathematics and Systems Science Xinjiang UniversityUrumqi 830017China

Let G be a finite group generated by S and C(G,S) the Cayley digraphs of G with connection set S.In this paper,we give some sufficient conditions for the existence of hamiltonian circuit in C(G,S),where G=Zm×H is a semiproduct of Zmby a subgroup H of G.In particular,if m is a prime,then the Cayley digraph of G has a hamiltonian circuit unless G=Zm×H.In addition,we introduce a new digraph operation,called φ-semiproduct of Γ1by Γ2and denoted by Γ1×Γ_φΓ2,in terms of mapping φ:V(Γ2)→{1,-1}.Furthermore we prove that C(Zm,{a})×_φ C(H,S) is also a Cayley digraph if φ is a homomorphism from H to{1,-1} ≤ Zm~*,which produces some classes of Cayley digraphs that have hamiltonian circuits.

关键词： Cayley digraphs hamiltonian circuit external semidirect product

Empirical likelihood for spatial cross-sectional data models with matrix exponential spatial specification

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Applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 125-139页

作者： LIU Yan RONG Jian-rong QIN Yong-song Nanning University Nanning 530200China Center for Applied mathematics of Guangxi and college of mathematics and Statistics Guangxi Normal UniversityGuilin 541004China

In this paper,we study spatial cross-sectional data models in the form of matrix exponential spatial specification(MESS),where MESS appears in both dependent and error terms.The empirical likelihood(EL)ratio statistics are established for the parameters of the MESS model.It is shown that the limiting distributions of EL ratio statistics follow chi-square distributions,which are used to construct the confidence regions of model parameters.Simulation experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method.

关键词： MESS empirical likelihood con dence region

Critical observability of partially observed discrete event systems under cyber attacks

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Science China(Information Sciences) 2024年第2期67卷 333-334页

作者： Liyun TONG Jinling LIANG Yang LIU Department of mathematics School of SciencesHangzhou Dianzi University School of mathematics Southeast University college of mathematics and Computer Science Zhejiang Normal University

The discrete event system(DES) is a dynamic system driven by asynchronous/sudden events and has been widely used in many critical infrastructures, such as electric transportation networks and intelligent transportatio...

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GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX

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Acta Mathematica Scientia 2011年第2期31卷 681-693页

作者：陈波涛米永生穆春来 college of mathematics and Computer Sciences Yangtze Normal University college of mathematics and Statistics Chongqing University

This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel＇dovich-Kompaneetz-Barenblatt profile

关键词： Critical global existence curve degenerate parabolic systems critical Fujitacurve nonlinear boundary flux blow-up

Physical informed memory networks for solving PDEs:implementation and applications

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Communications in Theoretical Physics 2024年第2期76卷 51-61页

作者： Jiuyun Sun Huanhe Dong Yong Fang college of mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

With the advent of physics informed neural networks(PINNs),deep learning has gained interest for solving nonlinear partial differential equations(PDEs)in recent years.In this paper,physics informed memory networks(PIMNs)are proposed as a new approach to solving PDEs by using physical laws and dynamic behavior of PDEs.Unlike the fully connected structure of the PINNs,the PIMNs construct the long-term dependence of the dynamics behavior with the help of the long short-term memory network.Meanwhile,the PDEs residuals are approximated using difference schemes in the form of convolution filter,which avoids information loss at the neighborhood of the sampling points.Finally,the performance of the PIMNs is assessed by solving the Kd V equation and the nonlinear Schr?dinger equation,and the effects of difference schemes,boundary conditions,network structure and mesh size on the solutions are discussed.Experiments show that the PIMNs are insensitive to boundary conditions and have excellent solution accuracy even with only the initial conditions.

关键词： nonlinear partial differential equations physics informed memory networks physics informed neural networks numerical solution

A Minimum Residual Based Gradient Iterative Method for a Class of Matrix Equations

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 17-34页

作者： Qing-qing Zheng Department of mathematics College of ScienceChina University of Petroleum-BeijingBeijing102249China

In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results.

关键词： Sylvester matrix equation coupled matrix equation minimum residual gradient descent convergence analysis

CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY

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Acta Mathematica Scientia 2024年第1期44卷 1-36页

作者： Thomas E.CECIL Department of mathematics and Computer Science College of the Holy CrossWorcesterMA01610USA

This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.

关键词： Dupin hypersurfaces isoparametric hypersurfaces Lie sphere geometry Lie sphere transformations Lie curvatures

On limit fractional Volterra hierarchies

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Communications in Theoretical Physics 2024年第1期76卷 7-16页

作者： Lixiang Zhang Chuanzhong Li School of mathematics and Statistics Ningbo UniversityNingbo315211China college of mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.

关键词： limit fractional Volterra hierarchy noncommutative limit fractional Volterra hierarchy Darboux transformation soliton solution quasi determinant solution