SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS IN COMPLEX CLIFFORD ANALYSIS

In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cn+1, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△mf=0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cn+1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.     

UNIQUENESS PROBLEM FOR MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES INTO P^N（C） WITH TRUNCATED MULTIPLICITIES

This paper proves some uniqueness theorems for meromorphic mappings in several complex variables into the complex projective space P N(C) with truncated multiplicities,and our results improve some earlier work.     

On almost complex curves and Hopf hypersurfaces in the nearly Khler six-sphere

We study the almost complex curves and Hopf hypersurfaces in the nearly Khler S6(1),and their relations.For Hopf hypersurfaces,we give a classification theorem under some additional conditions.For compact almost complex curves,we obtain some interesting global results with respect to Gaussian curvature,area and the genus.     

All Meromorphic Solutions of Some Algebraic Differential Equations

In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.     

Admissible solutions of systems of complex partial difference equations on Cn

In a recent papers,some authors applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. We will mainly investigate Malmquist theorem of a type of systems of complex partial difference equations on Cn,improvements and extensions of such results are presented in this paper.     

The Meromorphic Solutions of the Zakharov-Kuznetsov Modified Equal Width Equation

In this paper,we use the complex method to obtain all meromorphic solutions of the complex Zakharov-Kuznetsov modified equal width equation,then find the exact traveling wave solutions of the Zakharov-Kuznetsov modified equal width equation.At last,we give some computer simulations to illustrate our main results.     

A RESULT OF SYSTEMS OF NONLINEAR COMPLEX ALGEBRAIC DIFFERENTIAL EQUATIONS

In this article, we mainly investigate the behavior of systems of complex differential equations when we add some condition to the quality of the solutions, and obtain an interesting result, which extends Gaekstatter and Laine＇s result concerning complex differential equations to the systems of algebraic differential equations.     

Isolated complex singularities and their CR links Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued.     

On Meromorphic Solutions of Nonlinear Complex Differential Equations

Applying the Nevanlinna theory of meromorphic function,we investigate the non-admissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result.Meanwhile,we prove that the meromorphic solutions of some types of the systems of nonlinear complex differential equations are non-admissible.Moreover,the form of the systems of equations with admissible solutions is discussed.     

关于复阶k一致α-凸p叶函数类的新积分算子的凸性（英文）

In this paper,we obtain the convexity of new general integral operator on some classes of fc-uniformly p-valentα-convex functions of complex order.These results extend some known theorems.     

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.     

OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE

The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.     

COMPLEX POWER OF HERMITE OPERATOR

In this paper the authors define complex power of Hermite operator and give some applications in Riemann Zeta function.     

HOLOMORPHIC HARMONIC ANALYSIS ON COMPLEX REDUCTIVE GROUPS

The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures.     

ON THE ZEROS OF A CLASS OF POLYNOMIALS AND RELATED ANALYTIC FUNCTIONS

In this paper we prove some interesting extensions and generalizations of Enestrom- Kakeya Theorem concerning the location of the zeros of a polynomial in a complex plane. We also obtain some zero-free regions for a class of related analytic functions. Our results not only contain some known results as a special case but also a variety of interesting results can be deduced in a unified way by various choices of the parameters.     

ZEROS OF ENTIRE SOLUTIONS TO COMPLEX LINEAR DIFFERENCE EQUATIONS＊

In this article,we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations,and obtain some relations of the exponent of convergence of z...     

Higher Singular Integral and Its Application

In this paper,the definition of higher Hadamard integral on complex ball is given,and some results are obtained.     

The truncated Second Main Theorem and uniqueness theorems

In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.     

OSCILLATION THEORY TO SOME COMPLEX LINEAR LARGE DIFFERENTIAL EQUATIONS

In this paper, some complex linear differential equations are investigated. Many results on the relation between solutions and their derivatives are obtained.     

Painlevé Property and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlev′e property, then it admits certain class of first integrals. We also present some relationships between the Painlev′e property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.