In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map...In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map S(z,ζ) which do not depends holomorphic on z∈D in Koppelman formula is obtained and the L s norm estimates for the solution operators are the same as that [10] in forms.展开更多
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...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.展开更多
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.
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...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.展开更多
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 t...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.展开更多
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 ex...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.展开更多
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 app...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.展开更多
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)
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 the...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.展开更多
We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.
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 construct...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.展开更多
文摘In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map S(z,ζ) which do not depends holomorphic on z∈D in Koppelman formula is obtained and the L s norm estimates for the solution operators are the same as that [10] in forms.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China.
文摘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.
基金Project supported by the National Natural Science Foundation of China
文摘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)
基金This work was supported by the National Natural Science Foundation of China and China Postdoctoral Science Foundation(Grant No.10271097,20040350105)Program for New Century Excellent Talents in Xiamen University.
文摘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.
基金supported by National Natural Science Foundation of China(Grant No.11771139)supported by Ministerio de Educación y Ciencia(Grant No.MTM2017-83499-P)Generalitat de Catalunya(Grant No.2017SGR358)。
文摘We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.
文摘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.
