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• "unit disk"
Clear All  # Double-saturated packing of unit disks

Periodica Mathematica Hungarica
Author: A. Bezdek

## Abstract

A set of closed unit disks in the Euclidean plane is said to be double-saturated packing if no two disks have inner points in common and any closed unit disk intersects at least two disks of the set. We prove that the density of a double saturated packing of unit disks is ≥

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\geqslant \pi /\sqrt {27}$$ \end{document}
and the lower bound is attained by the family of disks inscribed into the faces of the regular triangular tiling.

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# Large transversals to small families of unit disks

Acta Mathematica Hungarica
Authors: T. Bisztriczky, F. Fodor and D. Oliveros
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# Paths on the doubly covered region of a covering of the plane by unit discs

Studia Scientiarum Mathematicarum Hungarica

Given a covering of the plane by closed unit discs

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{F}$$ \end{document}
and two points A and B in the region doubly covered by
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{F}$$ \end{document}
, what is the length of the shortest path connecting them that stays within the doubly covered region? This is a problem of G. Fejes-Tóth and he conjectured that if the distance between A and B is d, then the length of this path is at most
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sqrt {2d} + O(1)$$ \end{document}
. In this paper we give a bound of 2.78d + O(1).

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# Morera type theorems on the unit disc

Analysis Mathematica
Author: V. V. Volchkov

Получен ряд теорем об аналитичности функц ии, непрерывной в единич ном круге и имеющей нулев ые интегралы по некот орым окружностям. Ранее по добные результаты были изве стны лишь на всей комп лексной плоскости. Решена задача Фаркаша: доказ ано, что непрерывная в единичном круге функция, имеюща я нулевые интегралы по всем окружностям, кас ающимся границы этого круга, является аналитичес кой.

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# On the convergence of Kergin and Hakopian interpolants at Leja sequences for the disk

Acta Mathematica Hungarica
Author: Van Manh Phung

.1007/BF02843159 .  Calvi , J.-P. and Phung , V. M. , Lagrange interpolation at real projections of Leja sequences for the unit disk , Proc. Amer. Math. Soc. (accepted

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# Some subclasses of analytic functions with bounded Mocanu variation

Acta Mathematica Hungarica
Authors: S. Bukhari and K. Noor

## Abstract

Analytic functions with bounded Mocanu variation generalize the concept of α-convexity in the unit disc. We introduce and study certain classes of such functions. Inclusion results are obtained and a sharp radius problem is solved.

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# Lemniscate and exponential starlikeness of regular Coulomb wave functions

Studia Scientiarum Mathematicarum Hungarica
Author: İbrahim Aktaş

## Abstract

In this study, a normalized form of regular Coulomb wave function is considered. By using the differential subordinations method due to Miller and Mocanu, we determine some conditions on the parameters such that the normalized regular Coulomb wave function is lemniscate starlike and exponential starlike in the open unit disk, respectively. In additon, by using the relationship between the regular Coulomb wave function and the Bessel function of the first kind we give some conditions for which the classical Bessel function of the first kind is lemniscate and exponential starlike in the unit disk 𝔻.

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# Generalized q-starlike functions

Studia Scientiarum Mathematicarum Hungarica
Authors: Khalida Inayat Noor and Sadia Riaz

In this paper, we introduce a new concept of q-bounded radius rotation and define the class R*m(q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S*q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.

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# Approximation by complex modified Szász-Mirakjan operators

Studia Scientiarum Mathematicarum Hungarica
Authors: Nursel Çetin and Nurhayat İspir

In this study, we investigate approximation properties and obtain Voronovskaja type results for complex modified Szász-Mirakjan operators. Also, we estimate the exact orders of approximation in compact disks and prove that the complex modified Szász-Mirakjan operators attached to an analytic function preserve the univalence, starlikeness, convexity and spirallikeness in the unit disk.

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# The Spectrum of Annihilation Plus Orthogonal Creation

Acta Mathematica Hungarica
Author: B. Bodenstorfer

## Abstract

Let ℌ be a Hilbert space and F(ℌ) be the full Fock space generated by ℌ. For v ∈ ℌ, the (left) creation operator l(v) : F(ℌ) → F(ℌ),f↦ v ⊗ f, and its adjoint, the (left) annihilation operator l(v)*, are defined. If v, w ∈ℌ are orthonormal, it is proved that the spectrum of the operator l(v) + l(w)* is purely continuous and conincides with the closed unit disk.

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