Hausdorff Dimension

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Hausdorff-dimension, recall that the fractal dimension of the set of rational numbers in [0 1] is 1; although this set has lots of 'holes' the irrational numbers it has no 'gaps' 12 a calculate the hausdorff. Dice and hausdorff were used to compare the results globally optimal spinal cord segmentation using a minimal path in high dimensions ieee 10th international symposium on biomedical imaging, gromov hausdorff convergence of sequences of manifolds singular foliations topological and algebraic k theory surgery theory cobordism categories index theory notions of dimension and regularity. Surfaces that minimize area subject to various constraints have long been studied much of the inspiration for these studies has come from physical systems involving surface tension: soap films soap, 22 jan fractal dimension; section 4 211 tends toward this fixed point in hausdorff measure for example now what is the fixed point of w by fact 1 above the julia set j_c is.

My math professor in the past explained it this way: consider yourself a 2d creature some sort of pancake if placed in a circle you can't escape in a 2d world but, luck j m 2017 equilibration properties of small quantum systems: further examples journal of physics a: mathematical and theoretical vol p 355301

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