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Unit-Disk Range Searching and Applications [PDF]
Scandinavian Workshop on Algorithm Theory, 2022 Given a set $P$ of $n$ points in the plane, we consider the problem of computing the number of points of $P$ in a query unit disk (i.e., all query disks have the same radius).
Haitao Wang
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Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete [PDF]
, 2013 We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges.
J. Díaz, P. Bose, R. Tamassia
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Liouville Quantum Gravity on the unit disk [PDF]
Annales De L Institut Henri Poincare-probabilites 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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Inner composition of analytic mappings on the unit disk
International Journal of Mathematics and Mathematical Sciences, 1991 A basic theorem of iteration theory (Henrici [6]) states that f analytic on the interior of the closed unit disk D and continuous on D with Int(D)f(D) carries any point z ϵ D to the unique fixed point α ϵ D of f. That is to say, fn(z)→α as n→∞.
John Gill
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Hardness of the maximum-independent-set problem on unit-disk graphs and prospects for quantum speedups [PDF]
Physical Review Research, 2023 Rydberg atom arrays are among the leading contenders for the demonstration of quantum speedups. Motivated by recent experiments with up to 289 qubits [Ebadi et al., Science 376, 1209 (2022)] we study the maximum independent set problem on unit-disk ...
Ruben S. Andrist +11 more
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Sub-Bergman Hilbert spaces on the unit disk III [PDF]
Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2023 For a bounded analytic function $\varphi $ on the unit disk $\mathbb {D}$ with $\|\varphi \|_\infty \le 1$ , we consider the defect operators $D_\varphi $ and $D_{\overline \varphi }$ of the Toeplitz operators $T_{\overline \varphi }$ and ...
S. Luo, Kehe Zhu
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Triangular ratio metric in the unit disk [PDF]
Complex Variables and Elliptic Equations, 2020 The triangular ratio metric is studied in a domain , . Several sharp bounds are proven for this metric, especially in the case where the domain is the unit disk of the complex plane.
O. Rainio, M. Vuorinen
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AIMS Mathematics, 2023 The boundedness and compactness of weighted composition operators have been extensively investigated on various analytic function spaces. In this paper, we study the boundedness and compactness of two several variables differences weighted composition ...
Aydah Mohammed Ayed Al-Ahmadi
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Sparse Hop Spanners for Unit Disk Graphs [PDF]
International Symposium on Algorithms and Computation, 2020 A unit disk graph $G$ on a given set of points $P$ in the plane is a geometric graph where an edge exists between two points $p,q \in P$ if and only if $|pq| \leq 1$.
A. Dumitrescu +2 more
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On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk
Mathematics, 2023 The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk
Astamur Bagapsh, Alexandre Soldatov
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