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Solute channels of the outer membrane: from bacteria to chloroplasts [PDF]
, 2007 Chloroplasts, unique organelles of plants, originated from endosymbiosis of an ancestor of today's cyanobacteria with a mitochondria-containing host cell. It is assumed that the outer envelope membrane, which delimits the chloroplast from the surrounding
Philippar, Katrin +2 more
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Hausdorff measures in topological spaces
, 1965 Given a non-negative set function τ on a family ɑ of subsets of a metric space X, an outer measure ν can be generated on X as follows: for B⊂X and δ > 0, [Equations omitted] The Hausdorff s-dimensional and h-measures are special cases of this measure.
Willmott, Richard C.
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On the Computation of the Hausdorff Dimension of the Walrasian Economy: Addendum [PDF]
In a recent paper, Dominique (2009) argues that for a Walrasian economy with m consumers and n goods, the equilibrium set of prices becomes a fractal attractor due to continuous destructions and creations of excess demands. The paper also posits that the
Dominique, C-Rene
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Generalized energy inequalities and higher multifractal moments [PDF]
, 2014 We present a class of generalized energy inequalities and indicate their use in investigating higher multifractal moments, in particular Lq-dimensions of images of measures under Brownian processes, Lq-dimensions of almost self-affine measures, and moments
Falconer, Kenneth John, Kenneth Falconer
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Positive-measure self-similar sets without interior [PDF]
, 2006 We recall the problem posed by Peres and Solomyak in Problems on self-similar and self-affine sets; an update. Progr. Prob. 46 (2000), 95–106: can one find examples of self-similar sets with positive Lebesgue measure, but with no interior?
Solomyak, B +9 more
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On comparable and non-comparable Hausdorff measures [PDF]
, 2014 Розвиток загальних методiв обчислення розмiрностi Хаусдорфа–Безиковича — одна з центральних проблем теорiї фракталiв. Дослiджено тривiальнiсть (нетривiальнiсть) мережевих мiр Хаусдорфа.
Торбін, Г.М. +1 more
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On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes [PDF]
: In a recent paper, Dominique (2009) argues that for a Walrasian economy with m consumers and n goods, the equilibrium set of prices becomes a fractal attractor due to continuous destructions and creations of excess demands.
Dominique, C-Rene
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ON HAUSDORFF MEASURES AND SBR MEASURES FOR PARABOLIC RATIONAL MAPS
, 1999 If J is the Julia set of a parabolic rational map having Hausdorff dimension h<1, we show that Sullivan's h-conformal measure on J is either absolutely continuous or orthogonal with respect to the Hausdorff measures defined by the function [Formula ...
S. ROHDE, M. DENKER
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Survey of Lebesgue and Hausdorff Measures [PDF]
, 2019 Measure theory is fundamental in the study of real analysis and serves as the basis for more robust integration methods than the classical Riemann integrals.
Oliver, Jacob N
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The Hausdorff Dimension Distribution of Finite Measures in Euclidean Space
, 1986 Let E be a Borel set of RN. The α-outer Hausdorff measure of E has been defined to bewhereand each Bi is a closed ball. d(Bi) denotes the diameter of Bi.It is easily seen that the same value Hα(E) is obtained if we consider coverings of E by open balls ...
Colleen D. Cutler
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