Fractal geometry has been applied widely in the analysis of medical images to characterize the irregular complex tissue structures that do not lend themselves to straightforward analysis with traditional Euclidean geometry. In this study, we treat the nonfractal behaviour of medical images over large-scale ranges by considering their box-counting fractal dimension as a scale-dependent parameter...

The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form s = 1/2+iλn. Hilbert-Polya argued that if a Hermitian operator exists whose eigenvalues are the imaginary parts of the zeta zeros, λn’s, then the RH is true. In this paper a fractal supersymmetric quantum mechanical (SUSY-QM) model is proposed to prove the RH. It is based on a quantum inv...

There were great expectations in the 1980s in connection with the practical applications of mathematical processes which were built mainly upon Fractal Dimension (FD) mathematical basis. Significant results were achieved in the 1990s in practical applications in the fields of information technology, certain image processing areas, data compression, and computer classification. In the present pu...

Measures of many geophysical phenomena are fractal. One of these is fracture spacing along a rock face. For the most part, the only parameter that has been extracted from such a fractal data set is its dimension. However, fractals which are strictly self-similar can be succinctly described mathematically as an Iterated Function System (IFS). In this case the parameters of the functions of an IF...

Most fractal image coding methods rely upon collage coding , that is, nding a fractal transform operator Tc that sends a target image u as close as possible to itself. The xed point attractor uc of Tc is generally a good approximation to u. However, it is well known that collage coding does not necessarily yield an optimal attractor, i.e., one for which the approximation error jju ? ucjj is min...

It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric ...

The topic of the specific surface area (SSA) of powders is not sufficiently described in the literature in spite of its nontrivial contribution to adsorption and dissolution processes. Fractal geometry provides a way to determine this parameter via relation SSA ~ x(D ́ 3)s(2 ́ D), where x (m) is the particle size and s (m) is a scale. Such a relation respects nano-, micro-, or macro-topography on...

In this work, variety of complex dynamics are found in a fractional-order antimicrobial resistance (AMR) model based on the generalized Gamma function. Firstly, extended left and right Caputo fractional differential operators, respectively, ELCFDO ERCFDO introduced. The basic features outlined. is shown to have new parameter that affects occurrence AMR system. Secondly, discretization studied u...

A geometrically symmetrical fractal structure is presented in this paper to provide an alternative approach for the miniaturization design of microstrip bandpass filters (BPFs). The generation process of the geometric geometry is described in detail, and a new fractal resonator called Greek-cross fractal resonator (GCFR) is produced by etching the proposed fractal configuration on the surface o...

Properties of Tolman-Bondi (TB) model produced by two set of initial conditions, 1) fractal density and simultaneous bang time and 2) fractal density and linear Hubble law, are studied. It is shown for the first set that for some physical resonable values of parameters of the model, the central density and the cosmological density parameter Ω0, an area of compatibility of initial conditions has...