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Abstract  

In the present paper lattice packings of open unit discs are considered in the Euclidean plane. Usually, efficiency of a packing is measured by its density, which in case of lattice packings is the quotient of the area of the discs and the area of the fundamental domain of the packing. In this paper another measure, the expandability radius is introduced and its relation to the density is studied. The expandability radius is the radius of the largest disc which can be used to substitute a disc of the packing without overlapping the rest of the packing. Lower and upper bounds are given for the density of a lattice packing of given expandability radius for any feasible value. The bounds are sharp and the extremal configurations are also presented. This packing problem is related to a covering problem studied by Bezdek and Kuperberg [BK97].

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Abstract  

In sorption measurements, volumetric or gravimetric procedures are commonly used to determine the amount adsorbed. At low pressures, thermomolecular flow and pressure differences according to Knudsen's law disturb measurements. In volumetry, calibration of the dead space is required; in gravimetry, the influence of buoyancy has to be taken into account. In both cases, adsorption of the calibrating gas, usually helium, may disturb the measurements [1]. From the calibration measurements, the density of the sample can in principle be calculated. However, it has been observed in many experiments that its value depends on the calibrating gas.

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Publications, vol. 60, American Mathematical Society , Providence , RI, 2012 . [10] Nagy , D. T. , On the number of 4-edge paths in graphs with given edge density

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Abstract  

Isobaric heat capacities of liquid n-tridecane were measured at temperatures from 313.15 to 373.15 K and at pressures up to 100 MPa using a calorimetric device based on a Calvet calorimeter (Setaram C80). These experimental data combined with the additional knowledge of density data were used to calculate the following properties at pressures up to 100 MPa: isochoric heat capacity, isentropic compressibility and ultrasound velocity.

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curvature and the simplicial density function Journal für reine und angewandte Mathematik 494 189 – 203 10.1515/crll.1998.006 . [5

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References [1] Csörnyei , M. , Grahl , J. and O'Neil , T. C. , Points of middle density in the real line , preprint, available e.g. at http

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, A. Y., Galal, A. H. 1996: Effect of nitrogen fertilization and plant density on yield and quality of sunflower. Assiut J. Agric. Sci. , 27 , 169-177. Effect of nitrogen fertilization and plant density on yield and quality

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S85 S87 Mori, H. and D. A. Chant. 1966. The influence of prey density, relative humidity, and starvation on the predaceous behavior of Phytoseiulus persimilis Athias

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Balaz, V. and Salat, T. , Uniform density u and corresponding I u -convergence, Math. Commun. , 11 (2006), 1–7. Salat T

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