A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing ...A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.展开更多
We study the number of zeros of Abelian integrals for the quadratic centers having almost all their orbits formed by cubics, when we perturb such systems inside the class of all polynomial systems of degree n.
We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn...We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn） =μ^-∑i=1^n α≥1 k（x, ξ）, αi≥ 1 and μ 〉 0. The continuity of this operator in L^（^＇＇） is well studied by Fabes and Rivière. Our goal is to extend their result to generalized Morrey spaces L^p,ω（R^n）, p ∈ （1, ∞） with a weight w satisfying suitable dabbling and integral conditions. A special attention is paid to the commutator C[α, k]=Kα- αK with the operator of multiplication by BMO functions.展开更多
Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded...Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.展开更多
In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.
The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian...The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally, this paper proposes several sufficient conditions for feedback dissipative realization.展开更多
In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 【 p 【 ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and exte...In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 【 p 【 ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and extension of some known results.展开更多
In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our...In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.展开更多
It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of s...It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO.展开更多
Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the...Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon＇s identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe＇s covering lemma in multiparameter setting.展开更多
We prove weighted q-variation inequalities with 2<q<∞for sharp truncations of singular integral operators in higher dimensions.The vector-valued extensions of these inequalities are also given.Parallel results ...We prove weighted q-variation inequalities with 2<q<∞for sharp truncations of singular integral operators in higher dimensions.The vector-valued extensions of these inequalities are also given.Parallel results are proven for differential operators.展开更多
文摘A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.
基金This work was supported by theNational Natural Science Foundation of China (Grant No. 10101031) Guangdong Natural Science Foundations (Grant No. 001289) Natural Science Foundation of Zhongshan University for young teachers.
文摘We study the number of zeros of Abelian integrals for the quadratic centers having almost all their orbits formed by cubics, when we perturb such systems inside the class of all polynomial systems of degree n.
文摘We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn） =μ^-∑i=1^n α≥1 k（x, ξ）, αi≥ 1 and μ 〉 0. The continuity of this operator in L^（^＇＇） is well studied by Fabes and Rivière. Our goal is to extend their result to generalized Morrey spaces L^p,ω（R^n）, p ∈ （1, ∞） with a weight w satisfying suitable dabbling and integral conditions. A special attention is paid to the commutator C[α, k]=Kα- αK with the operator of multiplication by BMO functions.
文摘Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.
基金supported by the Natural Science Foundation of China(61673169,11401191,11371125)the Tianyuan Special Funds of the Natural Science Foundation of China(11626101)the Natural Science Foundation of the Department of Education of Zhejiang Province(201635325)
文摘In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.
基金This work was supported by Project 973 of China(Grant Nos.G1998020307,G1998020308)China Postdoctoral Science Foundation.
文摘The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally, this paper proposes several sufficient conditions for feedback dissipative realization.
基金supported by National Natural Science Foundation of China (Grant Nos.10931001,10901017)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20090003110018)Natural Science Foundation of Zhejiang Province (Grant No.Y7080325)
文摘In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 【 p 【 ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and extension of some known results.
基金Supported by RFDP of China (Grant No. 20050027025)NSF of China (Grant No. 10571014, 10571015)
文摘In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.
文摘It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO.
基金supported by the NSF of USA(Grant No.DMS0901761)supported by NNSF of China(Grant Nos.10971228and11271209)Natural Science Foundation of Nantong University(Grant No.11ZY002)
文摘Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon＇s identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe＇s covering lemma in multiparameter setting.
基金supported by National Natural Science Foundation of China(Grant Nos.11671308 and 11431011)Ministerio de Economia y Competitividad/al Fondo Europeo de Desarrollo Regional(Grant No.MTM2015-66157-C2-1-P)
文摘We prove weighted q-variation inequalities with 2<q<∞for sharp truncations of singular integral operators in higher dimensions.The vector-valued extensions of these inequalities are also given.Parallel results are proven for differential operators.
