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71.
Baris Coskunuzer 《Mathematische Zeitschrift》2006,252(4):811-824
We show that for any extreme curve in a 3-manifold M, there exist a canonical mean convex hull containing all least area disks spanning the curve. Similar result is true for
asymptotic case in such that for any asymptotic curve , there is a canonical mean convex hull containing all minimal planes spanning Γ. Applying this to quasi-Fuchsian manifolds,
we show that for any quasi-Fuchsian manifold, there exist a canonical mean convex core capturing all essential minimal surfaces.
On the other hand, we also show that for a generic C3-smooth curve in the boundary of C3-smooth mean convex domain in ℝ3, there exist a unique least area disk spanning the curve. 相似文献
72.
J.P. Nayak 《Applied Surface Science》2010,257(2):458-462
Bioglass-ceramics with SiO2-Na2O-CaO composition was prepared by sol-gel method using rice husk ash as a silica source. Material was sintered at different temperatures ranging from 900 to 1050 °C for 2 h. Phase-formation behaviour, densification characteristics, and mechanical strength of glass-ceramics were investigated. The material sintered at 1000 °C showed a good mechanical strength. Mechanical properties were correlated with microstructural features. Both in vitro bioactivity and biodegradability of sintered material were investigated by incubating in simulated body fluid and Tris buffer solution, respectively. Scanning electron microscopy, energy dispersive spectroscopy and X-ray diffraction were used to investigate the surface deposition during body fluid incubation. Both bioactivity and degradability decreased with increase in sintering temperature. 相似文献
73.
74.
Mitre C. Dourado 《Discrete Mathematics》2010,310(4):832-1977
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between two not necessarily distinct vertices in D. The geodetic number of G is the minimum cardinality of a geodetic set of G.We prove that it is NP-complete to decide for a given chordal or chordal bipartite graph G and a given integer k whether G has a geodetic set of cardinality at most k. Furthermore, we prove an upper bound on the geodetic number of graphs without short cycles and study the geodetic number of cographs, split graphs, and unit interval graphs. 相似文献
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78.
H. X. Phu 《Numerical Functional Analysis & Optimization》2013,34(7-8):915-920
H. Minkowski proved C= convext C whenever C is a compact convex subset of a finite-dimensional linear space. If C is bounded but not closed, this representation does not hold anymore. In this case, we introduce the set of so-called γ-extreme points extγC of C and show C = convext γ C = raco extγ C, where raco M denotes the rational convex hull of M. 相似文献
79.
Tin-Yau Tam 《Linear and Multilinear Algebra》2013,61(1-3):87-113
The relationship between the classical Schur-Horn's theorem on the diagonal elements of a Hermitian matrix with prescribed eigenvalues and Kostant's convexity theorem in the context of Lie groups. By using Kostant's convexity theorem, we work out the statements on the special orthogonal group and the symplectic group explicitly. Schur-Horn's result can be stated in terms of a set of inequalities. The counterpart in the Lie-theoretic context is related to a partial ordering, introduced by Atiyah and Bott, defined on the closed fundamental Weyl chamber. Some results of Thompson on the diagonal elements of a matrix with prescribed singular values are recovered. Thompson-Poon's theorem on the convex hull of Hermitian matrices with prescribed eigenvalues is also generalized. Then a result of Atiyah-Bott is recovered. 相似文献
80.
A. Nezakati 《随机分析与应用》2013,31(3):558-564
The expected number of real zeros of polynomials a 0 + a 1 x + a 2 x 2 +…+a n?1 x n?1 with random coefficients is well studied. For n large and for the normal zero mean independent coefficients, irrespective of the distribution of coefficients, this expected number is known to be asymptotic to (2/π)log n. For the dependent cases studied so far it is shown that this asymptotic value remains O(log n). In this article, we show that when cov(a i , a j ) = 1 ? |i ? j|/n, for i = 0,…, n ? 1 and j = 0,…, n ? 1, the above expected number of real zeros reduces significantly to O(log n)1/2. 相似文献