In this paper,we first establish the sharp growth theorem and the distortion theorem of the Frechet derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n...In this paper,we first establish the sharp growth theorem and the distortion theorem of the Frechet derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some restricted conditions.We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of C^(n) with an arbitrary norm and the unit polydisk in C^(n) under certain restricted assumptions.Finally we obtain the sharp Goluzin type distortion theorem for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some additional conditions.The results derived all reduce to the corresponding classical results in one complex variable,and include some known results from the prior literature.展开更多
In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm reli...In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.展开更多
In this paper,we give a number of characterizations for a Banach space X which is isometric to a subspace of c_(0),or,c_(0)(Г),successively,in terms of extreme points of its dual unit ball Bx*,Frechet and Gateaux der...In this paper,we give a number of characterizations for a Banach space X which is isometric to a subspace of c_(0),or,c_(0)(Г),successively,in terms of extreme points of its dual unit ball Bx*,Frechet and Gateaux derivatives of its norm,or,in terms ofω^(*)-strongly exposed points andω^(*)-exposed points of Bx*.展开更多
基金Supported by National Natural Science Foundation of China(11871257,12071130)。
文摘In this paper,we first establish the sharp growth theorem and the distortion theorem of the Frechet derivative for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some restricted conditions.We next give the distortion theorem of the Jacobi determinant for biholomorphic mappings defined on the unit ball of C^(n) with an arbitrary norm and the unit polydisk in C^(n) under certain restricted assumptions.Finally we obtain the sharp Goluzin type distortion theorem for biholomorphic mappings defined on the unit ball of complex Banach spaces and the unit polydisk in C^(n) with some additional conditions.The results derived all reduce to the corresponding classical results in one complex variable,and include some known results from the prior literature.
文摘In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.
基金Supported by National Natural Science Foundation of China(Grant No.11731010)。
文摘In this paper,we give a number of characterizations for a Banach space X which is isometric to a subspace of c_(0),or,c_(0)(Г),successively,in terms of extreme points of its dual unit ball Bx*,Frechet and Gateaux derivatives of its norm,or,in terms ofω^(*)-strongly exposed points andω^(*)-exposed points of Bx*.
