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Liouville Quantum Gravity on the unit disk [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2015 Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov ...
Huang, Yichao +2 more
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Covariant integral quantization of the unit disk [PDF]
Journal of Mathematical Physics, 2020 We implement a SU(1, 1) covariant integral quantization of functions on the unit disk. The latter can be viewed as the phase space for the motion of a “massive” test particle on (1+1)-anti-de Sitter space-time, and the relevant unitary irreducible representations of SU(1, 1) corresponding to the quantum version of such motions are found in the discrete
M. A. del Olmo, J. P. Gazeau
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Triangular ratio metric in the unit disk [PDF]
Complex Variables and Elliptic Equations, 2021 The triangular ratio metric is studied in a domain $G\subsetneq\mathbb{R}^n$, $n\geq2$. Several sharp bounds are proven for this metric, especially, in the case where the domain is the unit disk of the complex plane. The results are applied to study the H lder continuity of quasiconformal mappings.
Oona Rainio, Matti Vuorinen
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Routing in Unit Disk Graphs [PDF]
Algorithmica, 2016 Let $S \subset \mathbb{R}^2$ be a set of $n$ sites. The unit disk graph $\text{UD}(S)$ on $S$ has vertex set $S$ and an edge between two distinct sites $s,t \in S$ if and only if $s$ and $t$ have Euclidean distance $|st| \leq 1$. A routing scheme $R$ for $\text{UD}(S)$ assigns to each site $s \in S$ a label $\ell(s)$ and a routing table $ (s)$.
Haim Kaplan +3 more
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Bourgain algebras on the unit disk [PDF]
Pacific Journal of Mathematics, 1993 The Bourgain algebra of H∞(D) relative to L∞(D) is shown to be H∞(D)+ C(D)+ V, where V is an ideal of functions in L∞(D) which vanish in an appropriate sense near the boundary of D.
Cima, Joseph A. +2 more
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Kinetic Connectivity for Unit Disks [PDF]
Discrete & Computational Geometry, 2000 We describe a kinetic data structure (KDS) that maintains the connected components of the union of a set of unit-radius disks moving in the plane. We assume that the motion of each disk can be specified by a low-degree algebraic trajectory; this trajectory, however, can be modified in an on-line fashion.
Li Zhang +3 more
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Unit Disk Visibility Graphs [PDF]
, 2021 We study unit disk visibility graphs, where the visibility relation between a pair of geometric entities is defined by not only obstacles, but also the distance between them. That is, two entities are not mutually visible if they are too far apart, regardless of having an obstacle between them.
Onur Çağırıcı, Deniz Ağaoğlu
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Liar's domination in unit disk graphs [PDF]
Theoretical Computer Science, 2020 In this article, we study a variant of the minimum dominating set problem known as the minimum liar's dominating set (MLDS) problem. We prove that the MLDS problem is NP-hard in unit disk graphs. Next, we show that the recent sub-quadratic time $\frac{11}{2}$-factor approximation algorithm \cite{bhore} for the MLDS problem is erroneous and propose a ...
Ramesh K. Jallu +2 more
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Ritt's theory on the unit disk [PDF]
Forum Mathematicum, 2011 The aim of this paper is to revisit Ritt's theory from a topological perspective by extensively using the concept of fundamental groups. This enables us to regard the theory as an example which illustrates many ideas of a letter of Grothendieck and to put Ritt's theory into a more general analytic setting.
Wang, MX, Ng, TW
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QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs [PDF]
, 2018 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 Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since
Bonnet, E. +4 more
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