Results 1 to 10 of about 686,674 (292)
The Calabi invariant for Hamiltonian diffeomorphisms of the unit disk [PDF]
arXiv, 2021 In this article, we study the Calabi invariant on the unit disk usually defined on compactly supported Hamiltonian diffeomorphisms of the open disk. In particular we extend the Calabi invariant to the group of $C^1$ diffeomorphisms of the closed disk which preserves the standard symplectic form.
Benoit Joly
arxiv +3 more sources
EPTAS and Subexponential Algorithm for Maximum Clique on Disk and Unit Ball Graphs [PDF]
J. ACM 68(2): 9:1-9:38 (2021), 2021 A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for \textsc{Maximum Clique} on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90].
Marthe Bonamy +8 more
arxiv +3 more sources
Characterization of the asymptotic Teichmüller space of the open unit disk through shears [PDF]
Pure and Applied Mathematics Quarterly, 2014 We give a parametrization to the asymptotic Teichmuller space of the open unit disk through equivalent classes of shear functions induced by quasisymmetric homeomorphisms on the Farey tesselation of the unit disk. Then using the parametrization, we define a new metric on the asymptotic Teichmuller space. Two other related metrics are also introduced on
Jinhua Fan, Jun Hu
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Analytic maps of the open unit disk onto a Gleason part [PDF]
Pacific Journal of Mathematics, 1976 where [|/(j = sup {\f(x)\: x e X), and we write φ ~ θ when G(φ, θ) < 2 (or, equivalently, σ(φ9 θ) < 1). Then ~ is an equivalence relation in ^(A), and an equivalence class P(m) = {φ: φ e ^€(A), φ ~ m}(Ξ2 {m}) is called the (nontrivial) Gleason part of m ...
K. Kishi
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Geometric Inequalities via a Symmetric Differential Operator Defined by Quantum Calculus in the Open Unit Disk [PDF]
Journal of Function Spaces, 2020 The present investigation covenants with the concept of quantum calculus besides the convolution operation to impose a comprehensive symmetric q-differential operator defining new classes of analytic functions. We study the geometric representations with applications.
Rabha W. Ibrahim +2 more
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Homeomorphism between the open unit disk and a Gleason part [PDF]
Journal of the Mathematical Society of Japan, 1975 $\tau$ is not necessarily a homeomorphism. Such examples are found in Wermer [10], p. 443, Hoffman [6], p. 109 and others. The purpose of this paper is to establish some conditions for $\tau$ to be a homeomorphism.
K. Kishi
openaire +3 more sources
Classes and Boundary Properties of Functions in the Open Unit Disk
Proceedings of the Bulgarian Academy of Sciences, 2022 Let \(\psi\) be a Blaschke product and \(d\theta(\mathop{\rm supp}\psi)=0\). In this paper we prove that the functions of Bourgain algebra \( (\psi H^\infty (D), L^\infty (D))_b \) have essential non-tangential limit at almost every point of \(T=\{z:\mid z\mid = 1\}\).
Miroslav Hristov
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Finding a Maximum Clique in a Disk Graph [PDF]
arXiv, 2023 A disk graph is an intersection graph of disks in the Euclidean plane, where the disks correspond to the vertices of the graph and a pair of vertices are adjacent if and only if their corresponding disks intersect. The problem of determining the time complexity of computing a maximum clique in a disk graph is a long-standing open question.
Jared Espenant +2 more
arxiv +3 more sources
A PTAS for the Weighted Unit Disk Cover Problem [PDF]
arXiv, 2015 We are given a set of weighted unit disks and a set of points in Euclidean plane. The minimum weight unit disk cover (\UDC) problem asks for a subset of disks of minimum total weight that covers all given points. \UDC\ is one of the geometric set cover problems, which have been studied extensively for the past two decades (for many different geometric ...
J. Li, Yifei Jin
arxiv +3 more sources
Thin sets in an open unit disk
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1973 =inf sup k(z) (k-=l, 2, ...). If lim 1 , 2(b--a)(1--ab) xeE zeF, Izl=x lm(n 0, then F is not thin at z--1. Notation and terminology. Let C be a complex plane. For a subset A of C, we denote by 3A the boundary of A in C. Let U be an open unit disk {[z[
Masayuki Osada
openaire +4 more sources