منابع مشابه
Ophthalmoscopic-Perspectively Distorted Optic Disc Diameters and Real Disc Diameters.
PURPOSE To investigate the difference between two-dimensionally measured disc diameters (DDs) based on fundus images and three-dimensionally measured DDs based on enhanced depth imaging optical coherence tomography (EDI-OCT). METHODS The DDs were three-dimensionally measured on EDI-OCT images of optic nerve heads and two-dimensionally measured on near-infrared reflectance fundus images in 90 ...
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We show that for integers k ≥ 2 and n ≥ 3, the diameter of the Cayley graph of SLn(Z/kZ) associated to a standard two-element generating set, is at most a constant times n 2 ln k. This answers a question of A. Lubotzky concerning SLn(Fp) and is unexpected because these Cayley graphs do not form an expander family. Our proof amounts to a quick algorithm for finding short words representing eleme...
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We derive a new upper bound for the diameter of a k-regular graphG as a function of the eigenvalues of the adjacency matrix. Namely, supposethe adjacency matrix of G has eigenvalues AI , A2 .••.• An with lAd:::: IA21 ::::... :::: IAnl where AI = k, A = IA21. Then the diameter D(G) must satisfy D(G) :::; rlog(n 1)f1og(k/A)l. We wilJ consider families of graphs whose eigenvalues can b...
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We study the relation between the diameter, the first positive eigenvalue of the discrete p-Laplacian and the `p-distortion of a finite graph. We prove an inequality relating these three quantities and apply it to families of Cayley and Schreier graphs. We also show that the `p-distortion of Pascal graphs, approximating the Sierpinski gasket, is bounded, which allows to obtain estimates for the...
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Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |G which induces a bi-invariant metric dG(x, y) = |Ad(yx−1)|G on G. We prove the existence of a constant β ≈ .23 (independent of G) such that for any closed subgroup H ( G, the diameter of the quotient G/H (in the induced metric) is ≥ β.
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ژورنال
عنوان ژورنال: International Astronomical Union Colloquium
سال: 1983
ISSN: 0252-9211
DOI: 10.1017/s0252921100095488