The singular integration occurred in sound field calculation with BEM is discussed in this article. The method to deal with 1st and higher order singular integration is given. The numerical results show that this meth...The singular integration occurred in sound field calculation with BEM is discussed in this article. The method to deal with 1st and higher order singular integration is given. The numerical results show that this method can simplify the program and improve the precision.展开更多
The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes ...The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.展开更多
Given f being Holder continuous in a region GC. For the Cauchy principal integral where G is a smooth closed contour,lt is established that,if a sequence or smooth closed contours G(n ∈N ) smoothly convergent top,the...Given f being Holder continuous in a region GC. For the Cauchy principal integral where G is a smooth closed contour,lt is established that,if a sequence or smooth closed contours G(n ∈N ) smoothly convergent top,then the corresponding sequence I(Γm,f)is convergent to I (,f). Furthermore,when Γ is approximated by a sequence of complex cubic splines(Γ)interpolatory to Γ,the error is estimated.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,...In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.展开更多
The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic sol...The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.展开更多
This work presents some numerical aspects of isogeometric boundary element methods(IGABEM).The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface.Several numeri...This work presents some numerical aspects of isogeometric boundary element methods(IGABEM).The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface.Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis.Then a numerical implementation of IGABEM on the trimmed NURBS is detailed.Based on this idea,the surface crack problem is modeled incorporation with the phantom element method.The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.展开更多
Understanding the fracture behavior of vertical cracks in piezoelectric semiconductor(PS)structures is vital due to their impacts on device reliability.This study establishes a model for a PS strip with a vertical cra...Understanding the fracture behavior of vertical cracks in piezoelectric semiconductor(PS)structures is vital due to their impacts on device reliability.This study establishes a model for a PS strip with a vertical crack under combined mechanical and electric loading,considering both central and edge cracks.Using Fourier transforms and dislocation density functions,the Mode-Ⅲproblem is converted to Cauchy-type singular integral equations.The crack surface fields,intensity factors,and energy release rate are derived.The accuracy of the proposed model is verified through the finite element(FE)simulation via COMSOL Multiphysics.The results for low electron concentrations align with those of the intrinsic piezoelectric materials,validating the correctness of the present model as well.The combined effects of crack position,applied electric loading,and initial carrier concentration on the crack propagation are analyzed.The normalized electric displacement factor shows heightened sensitivity to crack size,electromechanical loading,and carrier concentration.The crack position significantly influences the crack surface fields and normalized intensity factors due to the boundary proximity effect.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
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
It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ...It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).展开更多
In this paper,the author discusses some singular integral operators,singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels,and obtain some useful prop...In this paper,the author discusses some singular integral operators,singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels,and obtain some useful properties for them.These results improve both the classical theory of singular integral equation and the classical theory of singular quadrature.展开更多
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and th...In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.展开更多
On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operat...On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Holder continuous property on the boundary.展开更多
The solutions of the nonlinear singular integral equation,t 6 L,are considered,where L is a closed contour in the complex plane,b≠0 is a constant and f(t)is a polynomial.It is an extension of the results obtained in[...The solutions of the nonlinear singular integral equation,t 6 L,are considered,where L is a closed contour in the complex plane,b≠0 is a constant and f(t)is a polynomial.It is an extension of the results obtained in[1]when f(t)is a constant.Certain special cases are illustrated.展开更多
In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the...In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the authors also consider the extreme cases.展开更多
A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integr...A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.展开更多
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also gi...Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.展开更多
文摘The singular integration occurred in sound field calculation with BEM is discussed in this article. The method to deal with 1st and higher order singular integration is given. The numerical results show that this method can simplify the program and improve the precision.
基金Work sponsored by"Ministero dell' University"CNR of Italy
文摘The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.
文摘Given f being Holder continuous in a region GC. For the Cauchy principal integral where G is a smooth closed contour,lt is established that,if a sequence or smooth closed contours G(n ∈N ) smoothly convergent top,then the corresponding sequence I(Γm,f)is convergent to I (,f). Furthermore,when Γ is approximated by a sequence of complex cubic splines(Γ)interpolatory to Γ,the error is estimated.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
基金Supported by the National Natural Science Foundation of China(11671397,11571160,12071052)the Yue Qi Young Scholar of China University of Mining and Technology(Beijing)。
文摘In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.
基金Supported by National Natural Science Foundation of China(Grant No.11971015).
文摘The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.
基金National Natural Science Foundation of China(NSFC)under Grant(No.51904202).
文摘This work presents some numerical aspects of isogeometric boundary element methods(IGABEM).The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface.Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis.Then a numerical implementation of IGABEM on the trimmed NURBS is detailed.Based on this idea,the surface crack problem is modeled incorporation with the phantom element method.The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.
基金Project supported by the Guangdong Basic and Applied Basic Research Foundation of China(Nos.2022B1515020099 and 2024A1515240026)the National Natural Science Foundation of China(No.12372147)the Fundamental Research Funds for the Central Universities of China(No.HIT.OCEF.2024019)。
文摘Understanding the fracture behavior of vertical cracks in piezoelectric semiconductor(PS)structures is vital due to their impacts on device reliability.This study establishes a model for a PS strip with a vertical crack under combined mechanical and electric loading,considering both central and edge cracks.Using Fourier transforms and dislocation density functions,the Mode-Ⅲproblem is converted to Cauchy-type singular integral equations.The crack surface fields,intensity factors,and energy release rate are derived.The accuracy of the proposed model is verified through the finite element(FE)simulation via COMSOL Multiphysics.The results for low electron concentrations align with those of the intrinsic piezoelectric materials,validating the correctness of the present model as well.The combined effects of crack position,applied electric loading,and initial carrier concentration on the crack propagation are analyzed.The normalized electric displacement factor shows heightened sensitivity to crack size,electromechanical loading,and carrier concentration.The crack position significantly influences the crack surface fields and normalized intensity factors due to the boundary proximity effect.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
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.
文摘It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).
基金Supported by the Netional Natural Science Foundation of China and the Foundation of the State Education Commission of China.
文摘In this paper,the author discusses some singular integral operators,singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels,and obtain some useful properties for them.These results improve both the classical theory of singular integral equation and the classical theory of singular quadrature.
基金Foundation item is supported by the NNSF of China(19971064)
文摘In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
基金Supported by the National Natural Science Foundation of China (10771049, 10801043)the Hebei Natural Science Foundation (A2007000225, A2010000346)
文摘On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Holder continuous property on the boundary.
文摘The solutions of the nonlinear singular integral equation,t 6 L,are considered,where L is a closed contour in the complex plane,b≠0 is a constant and f(t)is a polynomial.It is an extension of the results obtained in[1]when f(t)is a constant.Certain special cases are illustrated.
基金This project is supported by the National 973Project(G199907510)the SEDF of China(20010027002)
文摘In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the authors also consider the extreme cases.
基金supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206)Innovation Foundation of Xiamen University(XDKJCX20063019),the National Science Foundation of China (10771174)
文摘A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
基金Supported by NNSF and RFDP of Higher Education of China.
文摘Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given.
