_b-EQUATION ON COMPLEX MANIFOLDS

By using Koppelman-Leray kernel and under suitable condition the integral representation formula of equation on complex manifolds is obtained.

APPLICATION OF SIMILARITY PRINCIPLE TO STRATIFICATION THEORY STUDY IN GRAVITY CONCENTRATION

The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The approach of the π-equation to predict separating results and to control the separating processes is presented with examples.

HOMOTOPY FORMULA FOR A LOCAL q-CONCAVE WEDGE IN STEIN MANIFOLDS AND IT'S APPLICATIONS

A homotopy formula for a loced q-concave wedge in Stein manifolds is obtained, by using this formula the -equation on local q-concave wedges is solved, and an extension problem on local q-concave wedges is discussed.

Homotopy formulas and ■-equation on local q-convex domains in Stein manifolds

The homotopy formulas of (r,s) differential forms and the solution of equation of type (r,s) on local q-convex domains in Stein manifolds are obtained.The homotopy formulas on local q-convex domains have important applications in uniform estimates of equation and holomorphic extension of CR-manifolds.

█_(b)-Equation on Stein Manifolds

G. M. Khenkin obtained the solution of (p, q)-form ■_b-equation of strictly pseudoconvex complex manifolds. In this note, we study the solution of (p, q)

The Integral Representations and Their Applications on the Analytic Varieties of Bounded Domains in Stein Manifolds

In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.

The Solitary Wave Solutions of Important Model in Particle Physics and Engineering According to Two Different Techniques

In this paper, we utilized the Jaulent-Miodek equation which is one of important models in particle physics and engineering. The exact traveling wave solutions for this equation “involving parameters” according to two different techniques are constructed. When these parameters are taken as special values, the solitary wave solutions are derived from it. A comparison between the obtained results using these two different methods with that obtained by previous authors is demonstrated.

THE EXPLICIT SOLUTIONS OF C_(p,q)^(k+α)-FORM FOR THE -EQUATIONS ON PSEUDOCONVEX OPEN SETS

In this paper, we study the integral solution operators for the -equations on pseudoconvex domains. As a generalization of [1] for the -dequations on pseudoconvex domains with boundary of class C∞, we obtain the explicit integral operator solutions of C -form for the -equations on pseudoconvex open sets with boundary of Ck (k≥0) and the sup-norm estimates of which solutions have similar as that [1] in form.

The Koppelman-Leray formula on complex Finsler manifolds

By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.

Hankel operators on exponential Bergman spaces

We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.

Integral formulas and the Ohsawa-Takegoshi extension theorem

We construct a semiexplicit integral representation of the canonical solution to the (-δ)-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.

Integral formulas for differential forms of type (p,q) on complex Finsler manifolds

Using the invariant integral kernel introduced by Demailly and Laurent-Thiebaut, complex Finsler metric and nonlinear connection associating with Chern-Finsler connection, we research the integral representation theory on complex Finsler manifolds. The Koppelman and Koppelman-Leray formulas are obtained, and the \(\overline \partial \)-equations are solved.

A new technique of integral representations in C^(n)

A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the -equations on strictly pseudoconvex domains in Cn are obtained. These new formulas are simpler than the classical ones, especially the solutions of the -equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in Cn so that all corresponding formulas are simplified.