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排序方式: 共有192条查询结果,搜索用时 15 毫秒
1.
Paul C. YANG 《数学年刊B辑(英文版)》2017,38(2):695-710
CR geometry studies the boundary of pseudo-convex manifolds.By concentrating on a choice of a contact form,the local geometry bears strong resemblence to conformal geometry.This paper deals with the role conformally invariant operators such as the Paneitz operator plays in the CR geometry in dimension three.While the sign of this operator is important in the embedding problem,the kernel of this operator is also closely connected with the stability of CR structures.The positivity of the CR-mass under the natural sign conditions of the Paneitz operator and the CR Yamabe operator is discussed.The CR positive mass theorem has a consequence for the existence of minimizer of the CR Yamabe problem.The pseudo-Einstein condition studied by Lee has a natural analogue in this dimension,and it is closely connected with the pluriharmonic functions.The author discusses the introduction of new conformally covariant operator P-prime and its associated Q-prime curvature and gives another natural way to find a canonical contact form among the class of pseudo-Einstein contact forms.Finally,an isoperimetric constant determined by the Q-prime curvature integral is discussed. 相似文献
2.
We introduce the notion of sofic measurable equivalence relations. Using them we prove that Connes' Embedding Conjecture as well as the Measurable Determinant Conjecture of Lück, Sauer and Wegner hold for treeable equivalence relations. 相似文献
3.
Ming-Chien Yang 《Applied mathematics and computation》2010,216(12):3754-3760
The n-dimensional star graph Sn is an attractive alternative to the hypercube graph and is a bipartite graph with two partite sets of equal size. Let Fv and Fe be the sets of faulty vertices and faulty edges of Sn, respectively. We prove that Sn − Fv − Fe contains a fault-free cycle of every even length from 6 to n! − 2∣Fv∣ with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. We also show that Sn − Fv − Fe contains a fault-free path of length n! − 2∣Fv∣ − 1 (respectively, n! − 2∣Fv∣ − 2) between two arbitrary vertices of Sn in different partite sets (respectively, the same partite set) with ∣Fv∣ + ∣Fe∣ ? n − 3 for every n ? 4. 相似文献
4.
《Wave Motion》2017
The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is considered in the parabolic approximation. Using the embedding formula approach, the reflection and transmission coefficients are expressed through the directivities of the edge Green’s function of the propagation problem. The asymptotics of the directivities of the edge Green’s functions are constructed for the case of small gaps between the screen and the walls of the waveguide. As the result, the reflection and transmission coefficients are found. The validity of known asymptotics of these coefficients is studied. 相似文献
5.
Fábio Dahia Carlos Romero Lúcio F. P. da Silva Reza Tavakol 《General Relativity and Gravitation》2008,40(6):1341-1351
We study the classical geodesic motions of nonzero rest mass test particles and photons in (3 + 1 + n)- dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between
the motions in the (3 + 1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles
and photons to the (3 + 1)- spacetime submanifold. In addition to providing information regarding the motion of photons, we
also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions
for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the
stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces
with codimension one. 相似文献
6.
We consider the problem of diffraction of a plane wave by a quarter-plane (a flat cone) with Dirichlet boundary conditions. The most efficient approach to this problem is the technique of Smyshlyaev’s formulae or a modified Smyshlyaev’s formula, both of which are representations of the diffraction coefficient as contour integrals over a complex parameter. These representations have been proven independently. Here we are demonstrating a link between these classes of formulae. The link is established by developing an embedding procedure (in the very special sense of diffraction theory) on the unit sphere. 相似文献
7.
The proposed all-optical 2-D switching networks are (i) M×N-gon prism switches (M2, N3) and (ii) 3-D grids of any geometry N3. For the routing we assume (1) the projection of the spatial architectures onto plane graphs (2) the embedding of the latter guest graphs into (in)complete host hypercubes (N=4) and generally, into N-cube networks (N3) and (3) routing by means of the cube algorithms of the host. By the embedding mainly faulty cubes (synonyms: injured cubes, incomplete cubes) arise which complicate the routing and analysis. The application of N-cube networks (i) extend the hypercube principles to any N3 (ii) increase the number of plane host graphs and (iii) reduce the incompleteness of the host cubes. Several different embeddings of the intersection graphs (IGs) of 2-D switching networks and several different routings are explained for N=4 and 6 by various examples. By the expansion of the grids (enlargement) internal waveguides (WGs) and internal switches are introduced which interact with the switches of the original 3-D grid without increasing the number of stages (NS). The embeddings by expansion apply to interconnection networks whereas dilation-2 embeddings (dilation ≡ distance of the nearest-neighbour nodes of the guest graph at the host) are rather suitable for the emulation of algorithms. Concepts for fault-tolerant routing and algorithm mapping are briefly explained. 相似文献
8.
Andrea Cianchi 《Potential Analysis》2008,28(4):379-388
The Orlicz-Sobolev spaces that are multiplicative Banach algebras are characterized.
相似文献
9.
引入了强smooth格的概念,讨论了smooth格与强smooth格的一些基本性质,证明了强smooth格可用保任意交和Scott闭集之并的映射嵌入到某方体[0,1]X之中. 相似文献
10.
在Fuzzifying(模糊化)数学的框架下,建立了Fuzzifying闭包系统和Birkhoff型Fuzzifying闭包算子的概念; 引入了Fuzzifying闭包空间范畴和Fuzzifying闭包系统空间范畴,并从范畴论的角度证明Birkhoff型Fuzzifying闭包算子与Fuzzifying闭包系统是协调的.最后文中还得到Fuzzifying闭包空间范畴和Fuzzifying闭包系统空间范畴可以嵌入到Birkhoff型L-闭包空间范畴这一重要结果. 相似文献