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曲面四角化上的直差分方程 被引量:1
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作者 刘彦佩 《昆明理工大学学报(自然科学版)》 CAS 北大核心 2012年第3期78-84,共7页
本文旨在讨论由球面(或平面)近四角化以度和根面次为参数根同构类引出的函数方程.论证了在整域扩张中解的存在性和唯一性.而且,也导出了这个解的正项和表示式.在此基础上,引进欠-1面四角化,通过讨论以度、欠面次和根面次为参数根同构类... 本文旨在讨论由球面(或平面)近四角化以度和根面次为参数根同构类引出的函数方程.论证了在整域扩张中解的存在性和唯一性.而且,也导出了这个解的正项和表示式.在此基础上,引进欠-1面四角化,通过讨论以度、欠面次和根面次为参数根同构类,得到一个三变元函数的直差分方程,进而导致在泛柱面上的情形,也求出解的正项和表示式. 展开更多
关键词 曲面 四角化 整域扩张 直差分方程 LAURENT级数
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曲面四角化偏微分方程
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作者 刘彦佩 《昆明理工大学学报(自然科学版)》 CAS 北大核心 2012年第5期79-87,94,共10页
本文旨在以球面(或平面,可定向亏格0曲面)为基础,讨论通过数射影面(不可定向亏格1曲面)、环面(可定向亏格1曲面)和Klein瓶(不可定向亏格2曲面)上的四角化所导出的偏微分方程组,建立了这些方程组在一个整域扩张上的定性理论和求解方法.并... 本文旨在以球面(或平面,可定向亏格0曲面)为基础,讨论通过数射影面(不可定向亏格1曲面)、环面(可定向亏格1曲面)和Klein瓶(不可定向亏格2曲面)上的四角化所导出的偏微分方程组,建立了这些方程组在一个整域扩张上的定性理论和求解方法.并且,导出了所有这些解使得任何项系数皆正项和的显式.由此启示,一般高亏格曲面的情形,完全可以在球面的基础上,由较小亏格曲面通过一个偏微分方程组所确定. 展开更多
关键词 曲面 四角化 整域扩张 偏微分方程 LAURENT级数
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内无叶的可平面近四角化计数(英文)
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作者 龙述德 蔡俊亮 《数学进展》 CSCD 北大核心 2017年第4期498-506,共9页
所有悬挂点都在根面边界的可平面近四角化称为内无叶的.本文研究了内无叶的可平面近四角化的计数并给出了以其根面次、非根点数和内面数为三个参数的一些计数公式.
关键词 四角化 计数函数 函数方程 拉格朗日反演
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Simultaneous diagonalization of two quaternion matrices
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作者 周建华 《Journal of Southeast University(English Edition)》 EI CAS 2003年第2期178-181,共4页
The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each q... The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence. 展开更多
关键词 semi-positive definite matrix quaternion matrix adjoint matrix CONGRUENCE
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Synthesis of hexagonal and triangular Fe3O4 nanosheets via seed-mediated solvothermal growth 被引量:2
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作者 Chunhui Li Ruixue Wei Yanmin Xu Ailing Sun Liuhe Wei 《Nano Research》 SCIE EI CAS CSCD 2014年第4期536-543,共8页
Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocr... Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocrystals are dispersed in a uniform microemulsion environment as "seeds" for further re-growth through a secondary solvothermal process. The growth of anisotropic morphologies has been explained by the presence and orientation of twin planes in the face-centered cubic Fe3O4 which direct the shape of the growing particles. In particular, reentrant grooves resulting from twin planes are favorable sites for the addition of adatoms, leading to anisotropic growth. Triangular nanosheets are believed to contain one twin face which directs the growth of the primary particles in two dimensions. Hexagonal nanosheets are believed to contain two parallel planes that allow the growth edges to regenerate one another. The growth mechanism is evidenced by the analysis of high-resolution transmission electron microscopy (HRTEM) results and the as-prepared Fe3O4 nanoparticles have been shown to be an effective catalyst in the synthesis of quinoxaline. 展开更多
关键词 Fe3O4 nanocrystal solvothermal synthesis anisotropic growth twin plane
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Monopole and Coulomb Field as Duals within the Unifying Reissner–Nordstrm Geometry
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作者 Alcides Garat 《Communications in Theoretical Physics》 SCIE CAS CSCD 2014年第6期699-702,共4页
We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce t... We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner–Nordstr¨om geometry. 展开更多
关键词 Einstein-Maxwell spacetime classical general relativity gauge field theories symmetry and con-servation laws
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