Integral formulas and the Ohsawa-Takegoshi extension theorem

We construct a semiexplicit integral representation of the canonical solution to the (?)-equation with respect to a plurisubharmonic weight function in a pseudoconvex domain. The construction is based on a construction related to the Ohsawa-Takegoshi extension theorem combined with a method to construct weighted integral representations due to M. Andersson.     

State Model and the Link Polynomial with Two Variables

State representation is used to discuss the link with two variables, and the estimation of breadth of the two variables(say l and m) is given for 5-links.     

Regularity Theorems for Elliptic and Hypoelliptic Operators via the Global Relation

In this paper we give a new proof regarding the regularity of solutions to hypoelliptic partial differential equations with constant coefficients. On the assumption of existence, we provide a spectral representation for the solution and use this spectral representation to deduce regularity results. By exploiting analyticity properties of the terms within the spectral representation, we are able to give simple estimates for the size of the derivatives of the solutions and interpret them in terms of Gevrey classes.     

本刊英文版Vol.32(2016),No.8论文摘要（英文）

正A New Functor from D_5-Mod to E_6-Mod Xiao Ping XU Abstract We find a new representation of the simple Lie algebra of type E_6 on the polynomial algebra in 16 variables,which gives a fractional representation of the corresponding Lie group on 16-dimensional space.Using this representation and Shen's idea of mixed product,we construct a new functor from D_5-Mod to E_6-Mod.A condition for the functor to map a     

The Mehler Formula for the Generalized Clifford-Hermite Polynomials

The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional Fractional Fourier transform. In this paper, we introduce a multi-dimensional Fractional Fourier transform in the framework of Clifford analysis. By showing that it coincides with the classical tensorial approach we are able to prove Mehler＇s formula for the generalized Clifford-Hermite polynomials of Clifford analysis.     

BCKLUND TRANSFORMATION AND LAX REPRESENTATION FOR A NONLINEAR DIFFERENTIAL EQUATION

In this paper, the Hirota bilinear method is applied to a nonlinear equation which is a deformation to a KdV equation with a source. Using the Hirota’s bilinear operator, we obtain its bilinear form and construct its bilinear Bcklund transformation. And then we obtain the Lax representation for the equation from the bilinear Bcklund transformation and testify the Lax representation by the compatibility condition.     

A Numerical Calculation Algorithm of the Inclination Function Based on the Representation of SO(3) Group

In the determination of the Earth gravity field in satellite geodesy, the inclination functions represent the projection of data observed along the orbital plane of a satellite orbit into the sphere in the terrestial reference frame. The inclination functions in this work is studied from a group theoretical perspective. The inclination functions are proved to generate a representation of the SO(3) group. An orthogonal relation of the inclination functions is derived and some recurrence relations...     

The Presentation Problem of the Conjugate Cone of the Hardy Space Hp (0 < p ≤ 1)

The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).     

Representation Theorem for Mild C-existence Families

As we know,the representation theorem is one of the most important theorems foroperator semigroup theory.The representation theorem for exponentially bounded C-semigroup with dense range R(C) was given in [1 ] ,which was generalized to the casethat C does notnecessarily have dense range(see[2 ] ) .In this paper,more general caseis considered.We get a representation theorem for exponentially bounded mild C-exis-tence families.According to this,a simple proof of a construction theorem for C-s…     

The Hypoellipticity for a Class of Nonhomogeneous Convolution Operator on the Nilpotent Lie Group H~n×R~k

In this paper,we use the method of representation of Lie group to study a class of nonhomoge-neous convolution operator on the nilpotent Lie group H~M×R~k,and give a criteerion of their hypoellipticity.     

关于Γ-半环的Jacobson根

The purpose of this paper is to consider the Jacobson radical of a Γ-hemi-ring from the point of view of the representation theory in the ring theory. We will define the irreducible representation semimodule and the radical of a Γ-hemiring, and prove some fundamental properties of the radical which correspond to those in the ring theory. The external notion of the radical will be related to internal one, at the same time, we shall see that the radical defined in this paper coincides with the Jacobson radical and with the semiradical of the Γ-hemiring.     

SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN

The object of this paper is to study the non-tangential increasing properties of positiveharmonic function u in Lipschitz domain by means of Martin representation theory. A necessaryand sufficient condition of the control of growth of u near any fixed boundary point is obtained.It is shown that the non-tangential increasing degree of u near a boundary point is exactlythe local degree of its representation measure with respect to the harmonic measure. Someexamples are given.     

QUANTUM MECHANICAL SOLUTION OF A DAMPED HARMONIC OSCILLATOR WITH TIME-DEPENDENT PARAMETERS

By means of a time-dependent canonical transformation, the time evolution operator and the wave function of a damped harmonic oscillator with time-dependent parameters are explicitly constructed in the occupation number representation. The expectation values of mechanical variables are then shown to obey the classical equation of motion. Finally, the wave function in the coordinate representation is also derived.     

Modular Lie Superalgebras of H-type

In this article the Z-graded transitive modular Lie superalgebra О i≥-1 Li, whose representation of Lo in L-1 is isomorphic to the natural representation of osp(L-1), is determined.     

The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l∞-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear isometries.     

A SYSTEM OF BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS FOR HARMONIC ELASTIC WAVES IN R3

Here we derive a new representation of the derivative of the double-layer potential for harmonic elastic waves in R3.Based on this new representation,the Neumann internal problem and the Neumann external problem of harmonic elastic waves are reduced to a system of boundary integro-differential equations,which is convenient for numerical approximation.     

An integral representation for the weighted geometric mean and its applications

By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.     

SOME SHAPE-PRESERVING QUASI-INTERPOLANTS TO NON-UNIFORMLY DISTRIBUTED DATABY MQ-B-SPLINES

Based on the definition of MQ-B-Splines, this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details. And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.     

The isometric extension problem in the unit spheres of l~p(Г)(p >1) type spaces

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of lp(Г)(p > 1,p ≠ 2) type spaces, and then we conclude that such mappings can be extended to the whole space as real linear isometries by using the previous result of the author.     

On Geometric Realization of the General Manakov System

It is well-known that the general Manakov system is a 2-components nonlinear Schr¨odinger equation with 4 nonzero real parameters. The analytic property of the general Manakov system has been well-understood though it looks complicated. This paper devotes to exploring geometric properties of this system via the prescribed curvature representation in the category of Yang-Mills’ theory. Three models of moving curves evolving in the symmetric Lie algebras u(2, 1) = k_α ⊕ m_α(α =...