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1.
凸体的曲率映象与仿射表面积 总被引:4,自引:0,他引:4
本文研究了一些特殊凸体与其极体的曲率仿射表面积乘积的下界.对任意两个凸体,建立了它们的投影体的混合体积与其仿射表面积的一个不等式(见文[1-15]). 相似文献
2.
Jean-Pierre Dedieu Gregorio Malajovich Mike Shub 《Foundations of Computational Mathematics》2005,5(2):145-171
We prove a linear bound on the average total curvature of the
central path of linear programming theory in terms of the number
of independent variables of the primal problem, and independent of
the number of constraints. 相似文献
3.
Jian Zhong PAN Shao Bing WU 《数学学报(英文版)》2006,22(1):23-26
in this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact non-negative curved manifolds admit (complete) metrics with non-negative curvature. 相似文献
4.
Friedbert Prü fer Franco Tricerri Lieven Vanhecke 《Transactions of the American Mathematical Society》1996,348(11):4643-4652
We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.
5.
6.
Li-Yang Shao Albane Laronche Predrag Mikulic Jacques Albert 《Optics Communications》2010,283(13):2690-2694
We demonstrate a new type of fiber optic bend sensor with a hybrid structure made up of a long period grating (LPG) and a tilted fiber Bragg grating (TFBG). The sensing mechanism is based on the spectrum of power transfers between the core and cladding modes from a TFBG located downstream from a LPG. We show that the curvature of a beam can be determined by the reflected power difference between the core mode and the recoupled cladding modes. We further provide design rules for the LPG and TFBG to optimize and linearize the sensor response. In addition, the temperature cross-sensitivities of this configuration are also investigated for two different types of fiber. 相似文献
8.
《力学快报》2020,10(6):412-418
Curvature is one of the most important features of lipid membranes in living cells, which significantly influences the structure of lipid membranes and their interaction with proteins. Taken the human islet amyloid polypeptide (hIAPP), an important protein related to the pathogenesis of type II diabetes, as an example, we performed molecular dynamics (MD) simulations to study the interaction between the protein and the lipid structures with varied curvatures. We found that the lipids in the high curvature membrane pack loosely with high mobility. The hIAPP initially forms H-bonds with the membrane surface that anchored the protein, and then inserts into the membrane through the hydrophobic interactions between the residues and the hydrophobic tails of the lipids. hIAPP can insert into the membrane more deeply with a larger curvature and with a stronger binding strength. Our result provided important insights into the mechanism of the membrane curvature-dependent property of proteins with molecular details. 相似文献
9.
We consider embedded compact hypersurfacesM in a halfspace of hyperbolic space with boundaryM in the boundary geodesic hyperplaneP of the halfspace and with non-zero constant mean curvature. We prove the following. Let {M
n
} be a sequence of such hypersurfaces withM
n
contained in a disk of radiusr
n
centered at a point P such thatr
n
0 and that eachM
n
is a large. H-hypersurface,H > 1. Then there exists a subsequence of {M
n
} converging to the sphere of mean curvatureH tangent toP at. In the case of smallH-hypersurfaces orH 1, if we add a condition on the curvature of the boundary, there exists a subsequence of {M
n
} which are graphs. The convergence is smooth on compact subset of 3
. 相似文献
10.
Kayll Lake 《General Relativity and Gravitation》2003,35(12):2271-2277
The Kerr vacuum has two independent invariants derivable from the Riemann tensor without differentiation. Both of these invariants must be examined in order to avoid an erroneous conclusion that the ring singularity of this spacetime is directional. 相似文献