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Agterberg, F.P. 2013. Fractals and spatial statistics of point patterns. J. Earth Sci. 24: 1–11. Agterberg F.P. Fractals and spatial

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References Falconer , K. 2003 . Fractal Geometry: Mathematical Foundations and Applications , 2 nd edn. Wiley , Chichester

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, depends on the nature of pore size and distribution in a fibrous assembly [ 8 – 10 ]. Therefore, describing the pore structure properties of fibrous assemblies is of great importance. Several researches have discovered the fractal features of porous media

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Abstract  

Self-similarity of Bernstein polynomials, embodied in their subdivision property is used for construction of an Iterative (hyperbolic) Function System (IFS) whose attractor is the graph of a given algebraic polynomial of arbitrary degree. It is shown that such IFS is of just-touching type, and that it is peculiar to algebraic polynomials. Such IFS is then applied to faster evaluation of Bzier curves and to introduce interactive free-form modeling component into fractal sets.

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temperatures, and is source of nonlinearity [ 34 , 35 ]. In this article, we report properties relating to porosity of solids (fractal dimensions, surface roughness parameters) evaluated from atomic force microscopy (AFM) and nitrogen adsorption

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Mandelbrot, B.B. 1983. The Fractal Geometry of Nature. W.H. Freeman, New York. The Fractal Geometry of Nature

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modeling-related research may benefit from it as well. In this study, a fractal geometry-based DFN model was developed, which requires the following input data ( Tóth and Vass 2011 ): • fractal dimension for fracture centers, • parameters ( E and F ) of

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The present paper studies fractal features (such as the fractal dimension) of hypertext systems (such as WWW) and establishes the link with informetric parameters. More concretely, a formula for the fractal dimension in function of the average number of hyperlinks per page is presented and examples are calculated. In general the complexity of these systems is high. This is also expressed by formulae for the total number of hypertext systems that are possible, given a fixed number of documents.

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A new adsorption isotherm equation based on the extension of the potential theory of adsorption on microporous fractal solids and corresponding thermodynamic functions were formulated and applied for description of the experimental data of adsorption on a microporous carbon. The comparison of the obtained results with the original Dubinin-Astakhov equation is presented. In this paper the dependence of thermodynamic functions (the differential molar enthalpy of adsorption ΔH and the differential molar entropy of adsorption ΔS) on the fractal dimension D are discussed, as well.

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F(a) functions (wherea is the rate of conversion), frequently referred to when considering non-isothermal heterogeneous processes, are reconsidered from a fractal viewpoint. This is achieved on the basis of previous studies on the fundamental properties of powders, which show that any powder obtained by mechanical size reduction yields a fractal particle-size distributionP(X,t), whereX is a scaled particle size, with a material-dependent powern asP(X,t)∝X n, and that the obtained powder has a specific surface area,S, expressed with the fractal particle sizex asS∝x D-3 with the fractal dimensionD. This can be interpreted to show that a powder obtained by mechanical grinding has a uniqueD for a specified particle-size range, and, in fact, TA results dependent on thisD were obtained. We also show that a mechanical size reduction process produces fractal surfaces. The phenomenologically known laws which relate input energy and the powder product are theoretically derived by assuming that the energy is consumed in producing fractal surfaces. The well-known reaction functions which relate the conversion rate with the physical and geometrical factors governing a reaction process are reconsidered from a fractal viewpoint. The validity of conventionalF(a) expressions based on integer dimensions are questioned.

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