Omega

Summary

Omega (oʊˈmiːɡə,_oʊˈmɛɡə,_oʊˈmeɪɡə,_əˈmiːɡə; capital: Ω, lowercase: ω; Ancient Greek ὦ, later ὦ μέγα, Modern Greek ωμέγα) is the twenty-fourth and final letter in the Greek alphabet. In the Greek numeric system/isopsephy (gematria), it has a value of 800. The word literally means "great O" (ō mega, mega meaning "great"), as opposed to omicron, which means "little O" (o mikron, micron meaning "little"). In phonetic terms, the Ancient Greek Ω represented a long open-mid back rounded vowel ɔː, comparable to the "aw" of the English word raw in dialects without the cot–caught merger, in contrast to omicron which represented the close-mid back rounded vowel o , and the digraph ου which represented the long close-mid back rounded vowel oː. In Modern Greek, both omega and omicron represent the mid back rounded vowel o̞ or ɔ̝. The letter omega is transliterated into a Latin-script alphabet as ō or simply o. As the final letter in the Greek alphabet, omega is often used to denote the

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L'objectif de ce cours est d'acquérir les connaissances de base liées aux machines électriques (conversion électromécanique). Le cours porte sur le circuit magnétique, le transformateur, les machines synchrones, asynchrones, à courant continu et les moteurs pas à pas.

Cours introductif à la commande des systèmes dynamiques. On part de quatre exemples concrets et on introduit au fur et à mesure un haut niveau d'abstraction permettant de résoudre de manière unifiée les problèmes d'asservissement et de régulation, en particulier les questions de stabilité.

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Orlicz regularity of the gradient of solutions to quasilinear elliptic equations in the plane

Linda Maria De Cave

Given a planar domain Omega, we study the Dirichlet problem {-divA(x, del v) = f in Omega, v = 0 on partial derivative Omega, where the higher-order term is a quasilinear elliptic operator, and f belongs to the Zygmund space L(log L)delta(log log log L)(beta/2) (Omega) with beta >= 0 and delta >= 1/2. We prove that the gradient of the variational solution v is an element of W-0(1,2) (Omega) belongs to the space L-2(log L)(2 delta-1)(log log log L)(beta)(Omega).

Springer International Publishing Ag2016

In this paper we study a nonlinear elliptic boundary value problem with a general singular lower order term, whose model is {-Delta u = H(u)mu, in Omega, u = 0 on partial derivative Omega, u > 0 on Omega, where Omega is an open bounded subset of R-N, mu is a nonnegative bounded Radon measure on Omega and H is a continuous positive function outside the origin such that lim H(s) = +infinity. We do not require any monotonicity property on the singular s -> 0(+) function H. (c) 2015 Elsevier Ltd. All rights reserved.

Pergamon-Elsevier Science Ltd2015

Tight Bounds for Online Edge Coloring

David Wajc

Vizing's celebrated theorem asserts that any graph of maximum degree Delta admits an edge coloring using at most Delta + 1 colors. In contrast, Bar-Noy, Motwani and Naor showed over a quarter century ago that the trivial greedy algorithm, which uses 2 Delta - 1 colors, is optimal among online algorithms. Their lower bound has a caveat, however: it only applies to low-degree graphs, with Delta = O(log n), and they conjectured the existence of online algorithms using Delta (1+o(1)) colors for Delta = omega(log n). Progress towards resolving this conjecture was only made under stochastic arrivals (Aggarwal et al., FOCS'03 and Bahmani et al., SODA'10). We resolve the above conjecture for adversarial vertex arrivals in bipartite graphs, for which we present a (1+o(1))Delta-edge-coloring algorithm for Delta = omega(log n) known a priori. Surprisingly, if Delta is not known ahead of time, we show that no (e/e-1 - Omega(1)) Delta-edge-coloring algorithm exists. We then provide an optimal, (e/e-1 + o(1))Delta-edge-coloring algorithm for unknown Delta = omega(log n). To obtain our results, we study a nonstandard fractional relaxation for edge coloring, for which we present optimal fractional online algorithms and a near-lossless online rounding scheme, yielding our optimal randomized algorithms.

IEEE COMPUTER SOC2019