Displaying similar documents to “Centered densities and fractal measures.”

Hausdorff and packing measure for thick solenoids

Michał Rams (2004)

Studia Mathematica

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For a linear solenoid with two different contraction coefficients and box dimension greater than 2, we give precise formulas for the Hausdorff and packing dimensions. We prove that the packing measure is infinite and give a condition necessary and sufficient for the Hausdorff measure to be positive, finite and equivalent to the SBR measure. We also give analogous results, generalizing [P], for affine IFS in ℝ².

Universal container for packing rectangles

Janusz Januszewski (2002)

Colloquium Mathematicae

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The aim of the paper is to find a rectangle with the least area into which each sequence of rectangles of sides not greater than 1 with total area 1 can be packed.

Packing spectra for Bernoulli measures supported on Bedford-McMullen carpets

Thomas Jordan, Michał Rams (2015)

Fundamenta Mathematicae

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We consider the packing spectra for the local dimension of Bernoulli measures supported on Bedford-McMullen carpets. We show that typically the packing dimension of the regular set is smaller than the packing dimension of the attractor. We also consider a specific class of measures for which we are able to calculate the packing spectrum exactly, and we show that the packing spectrum is discontinuous as a function on the space of Bernoulli measures.

Packing Parameters in Graphs

I. Sahul Hamid, S. Saravanakumar (2015)

Discussiones Mathematicae Graph Theory

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In a graph G = (V,E), a non-empty set S ⊆ V is said to be an open packing set if no two vertices of S have a common neighbour in G. An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The minimum and maximum cardinalities of a maximal open packing set are respectively called the lower open packing number and the open packing number and are denoted by ρoL and ρo. In this paper, we present some bounds on these parameters. ...