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# Covering a planar domain with sets of small diameter

Author: A. Heppes

## Summary

The problem of covering a circle, a square or a regular triangle with \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} $n$ \end{document} congruent circles of minimum diameter (the {\it circle covering} problem) has been investigated by a number of authors and the smallest diameter has been found for several values of \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} $n$ \end{document}. This paper is devoted to the study of an analogous problem, the {\it diameter covering} problem, in which the shape and congruence of the covering pieces is relaxed and -- invariably -- the maximal diameter of the pieces is minimized. All cases are considered when the solution of the first problem is known and in all but one case the diameter covering problem is solved.

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# Minimal Translation Covers For Sets of Diameter 1

Authors: Károly Bezdek and Robert Connelly
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# Does glaucoma medication influence the diameter of the retinal arteriole in the human eye?

Authors: Péter Kóthy and G. Holló

diameter of the isolated porcine short posterior ciliary artery. Invest Ophthalmol. Vis. Sci. 40, 370-377 (1999) Effects of topical β-Blockers on the diameter of the isolated porcine short posterior ciliary artery

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# Well function curves for different geometric situations in a large-diameter well

Authors: M. Banerjee, P. Chandra, D. Shanker, H. Singh and V. Singh

Banerjee M 1997: On the studies of parameters of aquifers having large diameter wells. Report of Minor Research UGC (India) funded Project No. R/Dev/Scheme No. 805(D)/95-96/18590, 1

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# Applicability of fetal thoracic aortic diameter measurement in the prediction of birth weight in Holstein-Friesian cows — Short communication

Authors: Boglárka Vincze, András Gáspárdy, Levente Kovács, Ervin Albert, Luca Kézér, Ferenc Baska and Ottó Szenci

. , Xu , X. P. , Guo , W. and Huo , Y. ( 2015 ): Association of resting heart rate with infrarenal aortic diameter: a cross sectional study in Chinese hypertensive adults . Eur. J. Vasc. Endovasc. Surg. 50 , 714 – 721 .

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# On multiple Borsuk numbers in normed spaces

Authors: Zsolt Lángi and Márton Naszódi

References [1] Boltyanski , V. G. , On the partition of plane figures into pieces of smaller diameters (in Russian

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# A gap phenomenon on Riemannian manifolds with reverse volume pinching

Author: P. Wang

## Abstract

Let M n be an n(≧ 3)-dimensional compact, simply connected Riemannian manifold without boundary and S n be the unit sphere of the Euclidean space R n+1. By two different means we derive an estimate of the diameter whenever the manifold considered satisfies that the sectional curvature K M ≦ 1, while Ric (M) ≧

\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} $$\tfrac{{n + 2}}{4}$$ \end{document}
and the volume V (M) ≦
\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} $$\tfrac{3}{2}$$ \end{document}
(1 + η)V (S n) for some positive number η depending only on n. Consequently, a gap phenomenon of the manifold will be given according to the estimate of the diameter.

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# Correlation between age basal diameter of Fraxinus Ornus L. in three ecologically contrasting habitats

Authors: P. Csontos, J. Tamás and Tibor Kalapos

Manna ash (Fraxinus ornus L.) is a typical deciduous tree of South European distributioin reaching the northern border of its range in the Carpathian Basin. The correlation between age and basal diameter of this tree was analysed in three ecologically contrasting habitats, as follows. (1) Succesional habitat. Abandonedframland with scattered occurrence of manna ash as a colonisong tree of this area. (2) Austrian pine plantation, where manna ash often forms a spontaneous subordinate tree or shrub layer. (3) Cotino-Quercetum pubescentis, the naturla vegetation on south facing calcareous hillslopes in Hungary, where Quercus pubescenes Willd. and Fraxinus ornus codominate in the low canopy. At each sampling site 21 individuals were selected with an even distribution within circumference categories ranging  from 6cm to 60cm. Circumference measurements were made at the base of the trunk, or cores were taken by a driller. Linear regression analysis was applied to test the correlation between age and diameter.

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# A tube-excited X-ray fluorescence spectrometer for use in small-diameter boreholes

Authors: J. Reeves, R. Arthur, R. Brodzinski and C. Shepard

## Abstract

A portable in-situ x-ray fluorescence analytical system that uses an x-ray tube excitation source and a cooled Si(Li) spectrometer for detecting characteristic emission x rays has been developed for use in small-diameter wells and boreholes. The 15-watt, iron-anode x-ray tube operates up to 30 kV. Three wells at the Sandia National Laboratory Chemical Waste Landfill, lined with 76 thick polyethylene, were logged specifically for Cr contamination. Detection limits below 50 ppm were achieved with counting intervals of 600 seconds and with the Si(Li) detector operating at 450-eV resolution (full width at half maximum [FWHM] for the Mn K-alpha x ray).

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# Diameters and best approximation of the classes B p,θ r of periodic functions of several variables

Author: А. Романюк

## Резуме

Получены точные по порядку оценки ортопроекционных и линейных поперечников классов B p,θ r периодических функций многих переменных в пространстве L q, 1 ≤ p, q, ≤ ∞. Установлен порядок наилучшего приближения в пространстве L классов B ∞,θ r периодических функций двух переменных тригонометрическими полиномами с «номерами» гармоник иэ гиперболического креста.

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