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ELECTRICALLY CHARGED SOLITONS IN GAUGE FIELD THEORY

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Acta Mathematica Scientia 2010年第6期30卷 1975-2005页

作者：杨亦松 Department of mathematics Polytechnic Institute of New York University Brooklyn institute of contemporary mathematics Henan University

Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons.

关键词： gauge field theory monopoles vortices dyons calculus of variations topological invariants

UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n

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Acta Mathematica Scientia 2014年第2期34卷 435-443页

作者：冯淑霞刘太顺 institute of contemporary mathematics School of Mathematics and Information ScienceHenan University Department of mathematics Huzhou Teachers College

In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities... 详细信息

关键词： Uniformly starlike mappings uniformly convex mappings the unit ball

ROPER-SUFFRIDGE EXTENSION OPERATOR ON A REINHARDT DOMAIN

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Acta Mathematica Scientia 2014年第6期34卷 1761-1774页

作者：李鸿军冯淑霞 School of mathematics and Information Science Henan University institute of contemporary mathematics School of Mathematics and Information ScienceHenan University

Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =（z1, z′2,…, z′k）′∈ C × C^n2×…× Cnk：｜z1｜^2＋｜｜z2｜｜2^p2＋ … ＋｜｜zk ｜｜k^pk〈 1} given〈1} give by F（z）=（f（z1）＋f＇（z1）∑j=2 kPj（zj,（f＇（z1））1/p2 z2＇,…,（f＇（z1））1/pkzk＇）＇, where f is a normaljized biholomorphic function k（z） =（f（z1）＋ f′（z1）=2 on the unit disc D, and for 2 ≤ j ≤ k, Pj ： C^nj→ C is a homogeneous polynomial of degree pj and zj =（zj1, …, zjnj）′∈ C^nj, nj ≥ 1, pj ≥ 1,｜｜zj｜｜j =（∑l=1 nj｜zjl｜^pj）1/pj. In this paper, some conditions for Pjare found under which the loperator p ｜zjl｜pj=1reserves the properties of almost starlikeness of order α, starlikeness of order αand strongly starlikeness of order α on ΩN, respectively.

关键词： Reinhardt domain Roper-Suffridge operator almost starlike of order α starlike mapping of order α strongly starlike mapping of order α

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

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Acta Mathematica Scientia 2014年第6期34卷 1835-1844页

作者：刘浩夏红川 institute of contemporary mathematics Henan University School of Mathematical Science Xiamen University

In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.

关键词： Roper-Suffridge operator biholomorphic mappings bounded complete Reinhardt domains

SUBCLASSES OF BIHOLOMORPHIC MAPPINGS UNDER THE EXTENSION OPERATORS

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Acta Mathematica Scientia 2019年第1期39卷 297-311页

作者： Chaojun WANG Yanyan CUI Hao LIU College of mathematics and Statistics Zhoukou Normal University College of mathematics and Information Science Hebei Normal University institute of contemporary mathematics Henan University

In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergman-Hartogs domains. Then, by the geometric characteristics of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suff ridge operators preserve the properties of S_Ω~*(β,A, B), parabolic and spirallike mappings of type β and order p, strong and almost spirallike mappings of type 0 and orderα as well as almost starlike mappings of complex order λ on Ω_(p1,…,ps,q)^(B^n) under different conditions, respectively. The conclusions provide new approaches to construct these biholomorphic mappings in several complex variables.

关键词： spirallike mappings Roper-Suffridge operator Bergman-Hartogs domains

THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES

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Acta Mathematica Scientia 2017年第6期37卷 1817-1829页

作者：崔艳艳王朝君刘浩 College of mathematics and Information Science Hebei Normal University College of mathematics and Statistics Zhoukou Normal University institute of contemporary mathematics Henan University

In this paper, we extend the Roper-Suffridge extension operator in complex Ba- nach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit bM1 in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spiraJlike mappings in several complex variables.

关键词： spirallike mappings starlike mappings Roper-Suffridge operator

The Solutions of the Coupled Einstein-Maxwell Equations and Dilaton Equations

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Acta Mathematicae Applicatae Sinica 2018年第3期34卷 485-492页

作者： Rui-feng ZHANG Ya GU institute of contemporary mathematics Henan University Kaifeng 475004 China School of mathematics and Statistics Henan University Kaifeng 475004 China

In this paper, we consider extremely charged static perfect fluid distributions with a dilaton field in the framework of general relativity. By using calculus of variations, we establish the existence theorem for the solutions of this important gravitational system. We show that there is a continuous family of smooth solutions realizing asymptotically flat space metrics.

关键词： nonlinear elliptic equations the variational method the asymptotic estimates.

Biholomorphic Mappings and the Extension Operators on New Hartogs Domains

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Acta Mathematica Sinica,English Series 2019年第5期35卷 671-689页

作者： Yan Yan CUI Chao Jun WANG Hao LIU College of mathematics and Statistics Zhoukou Normal University College of mathematics and Information Science Hebei Normal University institute of contemporary mathematics He’nan University

In this paper, we generalize the Roper–Suffridge operator on the extended Hartogs *** using the geometric properties and the growth theorems of subclasses of biholomorphic mappings,we obtain the generalized operators preserve the properties of parabolic and spirallike mappings of type β and order ρ, S*_Ω(β, A, B), almost starlike mapping of complex order λ on ΩN under different conditions, and thus we get the corresponding results on the unit ball B^n in C^n. The conclusions lead to some known results.

关键词： Biholomorphic mapping Roper-Suffridge operator Hartogs domain

THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

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Acta Mathematica Scientia 2019年第4期39卷 1103-1120页

作者： Yanyan CUI Hao LIU College of mathematics and Statistics Zhoukou Normal University Zhoukou 466001 China institute of contemporary mathematics Henan University Kaifeng 475007 China

We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_?~*(β, A, B), strong and almost spirallike mappings of type βand order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.

关键词： Biholomorphic mappings spirallike mappings Bergman-Hartogs domain Roper-Suffridge operator