We introduce two classes of egg type domains, built on general boundedsymmetric domains, for which we obtain the Bergman kernel inexplicit formulas. As an auxiliary tool, we compute the integralof complex powers of th...We introduce two classes of egg type domains, built on general boundedsymmetric domains, for which we obtain the Bergman kernel inexplicit formulas. As an auxiliary tool, we compute the integralof complex powers of the generic norm on a bounded symmetricdomains using the well-known integral of Selberg. Thisgeneralizes matrix integrals of Hua and leads to a specialpolynomial with integer or half-integer coefficients attached toeach irreducible bounded symmetric domain.展开更多
In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions ...In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.展开更多
This paper presents a novel approach called the boundary integrated neural networks(BINNs)for analyzing acoustic radiation and scattering.The method introduces fundamental solutions of the time-harmonic wave equation ...This paper presents a novel approach called the boundary integrated neural networks(BINNs)for analyzing acoustic radiation and scattering.The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations(BIEs)within the neural networks,replacing the conventional use of the governing equation in physics-informed neural networks(PINNs).This approach offers several advantages.First,the input data for the neural networks in the BINNs only require the coordinates of“boundary”collocation points,making it highly suitable for analyzing acoustic fields in unbounded domains.Second,the loss function of the BINNs is not a composite form and has a fast convergence.Third,the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons.Finally,the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs.Numerical examples are presented to demonstrate the performance of the proposed method,and a MATLAB code implementation is provided as supplementary material.展开更多
This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integr...This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given.展开更多
In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second funda...In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain （unit disk） and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.展开更多
文摘We introduce two classes of egg type domains, built on general boundedsymmetric domains, for which we obtain the Bergman kernel inexplicit formulas. As an auxiliary tool, we compute the integralof complex powers of the generic norm on a bounded symmetricdomains using the well-known integral of Selberg. Thisgeneralizes matrix integrals of Hua and leads to a specialpolynomial with integer or half-integer coefficients attached toeach irreducible bounded symmetric domain.
基金Supported by the NSF of China (G10571122) the NFS of Fujian Province of China (Z0511004)
文摘In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.
基金Natural Science Foundation of Shandong Province of China,Grant/Award Numbers:ZR2022YQ06,ZR2021JQ02Development Plan of Youth Innovation Team in Colleges and Universities of Shandong Province,Grant/Award Number:2022KJ140+2 种基金National Natural Science Foundation of China,Grant/Award Number:12372199Fund of the Key Laboratory of Road Construction Technology and Equipment,Chang'an University,Grant/Award Number:300102253502Water Affairs Technology Project of Nanjing,Grant/Award Number:202203。
文摘This paper presents a novel approach called the boundary integrated neural networks(BINNs)for analyzing acoustic radiation and scattering.The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations(BIEs)within the neural networks,replacing the conventional use of the governing equation in physics-informed neural networks(PINNs).This approach offers several advantages.First,the input data for the neural networks in the BINNs only require the coordinates of“boundary”collocation points,making it highly suitable for analyzing acoustic fields in unbounded domains.Second,the loss function of the BINNs is not a composite form and has a fast convergence.Third,the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons.Finally,the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs.Numerical examples are presented to demonstrate the performance of the proposed method,and a MATLAB code implementation is provided as supplementary material.
文摘This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given.
基金supported by NNSF of China(11171260)RFDP of Higher Education of China(20100141110054)+3 种基金NSF of Fujian ProvinceChina(2008J0187)STF of Education Department of Fujian ProvinceChina(JA11341)
文摘In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density happen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain （unit disk） and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained.
