2 Principles 4 2.1 Fractals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Definition and history . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Fractal dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Hölder exponent and singularity spectrum . . . . . . . . . . . . . 6 2.2 Self-similar random processes . . . . . . . . . . . . . . ....

Using sum-frequency vibrational spectroscopy, we found that water structure at nanoporous silica/water interfaces depended on the nanoporous film structure. For a periodic, self-assembled nanoporous film with monosized 2 nm pores occupying 20% of the top surface area, the surface vibrational spectrum was dominated by water in contact with silica, bare or covered by silane, at the top surface. I...

other fractal-based features as descriptors of the texture of images [2–6]. Applications of the fractal theory in image Fractal dimension has been used for texture analysis as it is highly correlated with the human perception of surface analysis also include image segmentation [2, 6–8], shape roughness. Several methods have been proposed for the estimadescription [9], object characterization [1...

Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of...

In this paper an innovative model that describes the SAR imaging process of natural scenes is presented. It is completely fractal-based. In the hypothesis of small slope regime of the surface, we evaluate here, in closed form, the Power Spectrum Density of the SAR image. The proposed model effectively accounts for the effect of finite sensor resolutions and for the peculiarity of SAR acquisitio...

Gear’s normal contact stiffness played an important role in the mechanical equipment. In this paper, the M-B fractal model is modified and the contact surface coefficient is put forward to set up the fractal model, considering the influence of friction, which could be used to calculate accurately the involute arc cylindrical gears’ normal contact stiffness based on the fractal theory and Hertz ...

The Dehaj area, located in the southern part of the Urumieh-Dokhtar magmatic belt, is a well-endowed terrain hosting a number of world-class porphyry copper deposits. These deposits are all hosted in an acidic to intermediate volcano-plutonic sequence greatly affected by various types of the hydrothermal alterations, whether argillic, phyllic or propylitic. Although there are a handful of hithe...

Temporal blood oxygen level dependent (BOLD) contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD) trends of the form 1/f(alpha). Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise b...

cation exchange capacity and specific surface area are among some of the important soil characteristics the direct measurement of which is laborious, costly and time consuming. therefore, fractal dimension of particle size distribution has been widely studied in relation with many such dynamic and static processes as transmission of water and solutes, water holding capacity, heat storage and co...