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About Some Monge–Kantovorich Type Norm and Their Applications to the Theory of Fractals
If X is a Hilbert space, one can consider the space cabv(X) of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich type norm.
Ion Mierluș-Mazilu, Lucian Niță
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SCALE-INVARIANT AND WAVE NATURE OF THE HUBBLE PARAMETER
The value of the global Hubble parameter corresponding to astrophysical observations was determined theoretically without using ʌСDM models. A nonlinear fractal model of the connection between the distance to the observed galaxy and its coordinate is ...
Z.Zh. Zhanabaev +2 more
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Fractal Dimension Analysis to Detect the Progress of Cancer Using Transmission Optical Microscopy
Fractal dimension, a measure of self-similarity in a structure, is a powerful physical parameter for the characterization of structural property of many partially filled disordered materials.
Liam Elkington +2 more
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On fractal measures and diophantine approximation [PDF]
The paper under review is concerned with an extension of Mahler's problem in metric number theory, originally resolved by \textit{V. G. Sprindzuk} [''Mahler's problem in metric number theory,'' Nauka i Teknika, Minsk (1967; Zbl 0168.29504)]. Mahler conjectured that almost no points with respect to the natural measure on the curve \((x, x^2, \dots, x^n)\
Kleinbock, Dmitry +2 more
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WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied?
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Harmonic analysis of fractal measures [PDF]
38 pages, AMS-TeX ("amsppt" document style)
Jørgensen, Palle E. T., Pedersen, Steen
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Psychedelic drugs, such as psilocybin and LSD, represent unique tools for researchers investigating the neural origins of consciousness. Currently, the most compelling theories of how psychedelics exert their effects is by increasing the complexity of ...
Thomas F. Varley +4 more
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Fractal Singularities in a Measure and How to Measure Singularities on a Fractal [PDF]
This is a preliminary report upon a piece of research being carried out by T. C. Halsey, Mogens Jensen, Leo Kadanoff, Itamar Procaccia and Boris Shraiman. It is an outgrowth of the thinking reflected in the work of Hentschel and Procaccia1 and of Halsey, Meakin and Procaccia.2 A fuller report on this work will appear later.
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Triangular constellations in fractal measures [PDF]
4 pages, 1 ...
Wilkinson, Michael, Grant, John
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FRACTAL STRUCTURE AND FRACTAL MEASUREMENT
. This article is devoted to the study of fractal structure and fractal dimensions. The article explains the concept of fractals, the ability to determine the fractal sizes of parts of the human body based on fractals and, based on these data, determine or predict what disease a person suffers from.
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