By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s （Ω） of nonlinear boundary value probl...By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s （Ω） of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈＋∞, and 2N/N＋1 〈 p ≤ 2 for N（≥ 1） which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.展开更多
We establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit polydisk Dnin Cn. By using the Carath′eodory metric and Kobayashi metric of Dn, we obtain some properties of t...We establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit polydisk Dnin Cn. By using the Carath′eodory metric and Kobayashi metric of Dn, we obtain some properties of the complex Jacobian matrix Jf(p) at a boundary point p of Dnfor a holomorphic self-mapping f of Dn. Our results extend the classical Schwarz lemma at the boundary to high dimensions.展开更多
The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the...The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the calculation domain. The mapping method deals with the irregular surface and the low-velocity layer underneath it using a fine grid. For the deeper high-velocity layers, the use of a fine grid causes local oversampling. In addition, when the irregular surface is transformed to horizontal, the flattened interface below the surface is transformed to curved, which produces inaccurate modeling results because of the presence of ladder-like burrs in the simulated seismic wave. Thus, we propose the mapping method based on the dual-variable finite-difference staggered grid. The proposed method uses different size grid spacings in different regions and locally variable time steps to match the size variability of grid spacings. Numerical examples suggest that the proposed method requires less memory storage capacity and improves the computational efficiency compared with forward modeling methods based on the conventional grid.展开更多
In this paper, a new volume rendering method with boundary enhancement is presented. The boundary is extracted and represented by surfaces explicitly. Then, using 3D texture mapping and graphics acceleration hardware,...In this paper, a new volume rendering method with boundary enhancement is presented. The boundary is extracted and represented by surfaces explicitly. Then, using 3D texture mapping and graphics acceleration hardware, the volume data can be rendered with controllable boundary shading effect almost in real time. Test shows that this method is 4-5 times faster than the previous methods. Moreover, it can also be extended to render the surfaces and the volumetric data together interactively.展开更多
Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a doubl...Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a double pole or (ii)(?) has no pole of order exceeding two on (?)△. The 'if' part of the conjecture had been solved by himself. We will give the affirmative answer to the 'only if' part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper, which generalizes the 'if' part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990.展开更多
基金This research is supported by the National Natural Science Foundation of China(No. 10471033).
文摘By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s （Ω） of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈＋∞, and 2N/N＋1 〈 p ≤ 2 for N（≥ 1） which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.
基金supported by National Natural Science Foundation of China(Grant Nos.11101139,11271124 and 11301136)Natural Science Foundation of Zhejiang Province(Grant No.LY14A010017)Natural Science Foundation of Hebei Province(Grant No.A2014205069)
文摘We establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit polydisk Dnin Cn. By using the Carath′eodory metric and Kobayashi metric of Dn, we obtain some properties of the complex Jacobian matrix Jf(p) at a boundary point p of Dnfor a holomorphic self-mapping f of Dn. Our results extend the classical Schwarz lemma at the boundary to high dimensions.
基金financially supported by the National Natural Science Foundation of China(Nos.41104069 and 41274124)the National 973 Project(Nos.2014CB239006 and 2011CB202402)+1 种基金the Shandong Natural Science Foundation of China(No.ZR2011DQ016)Fundamental Research Funds for Central Universities(No.R1401005A)
文摘The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the calculation domain. The mapping method deals with the irregular surface and the low-velocity layer underneath it using a fine grid. For the deeper high-velocity layers, the use of a fine grid causes local oversampling. In addition, when the irregular surface is transformed to horizontal, the flattened interface below the surface is transformed to curved, which produces inaccurate modeling results because of the presence of ladder-like burrs in the simulated seismic wave. Thus, we propose the mapping method based on the dual-variable finite-difference staggered grid. The proposed method uses different size grid spacings in different regions and locally variable time steps to match the size variability of grid spacings. Numerical examples suggest that the proposed method requires less memory storage capacity and improves the computational efficiency compared with forward modeling methods based on the conventional grid.
文摘In this paper, a new volume rendering method with boundary enhancement is presented. The boundary is extracted and represented by surfaces explicitly. Then, using 3D texture mapping and graphics acceleration hardware, the volume data can be rendered with controllable boundary shading effect almost in real time. Test shows that this method is 4-5 times faster than the previous methods. Moreover, it can also be extended to render the surfaces and the volumetric data together interactively.
文摘Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a double pole or (ii)(?) has no pole of order exceeding two on (?)△. The 'if' part of the conjecture had been solved by himself. We will give the affirmative answer to the 'only if' part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper, which generalizes the 'if' part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990.
