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...

Motivated by the interplay of Bethe-Ansatz integrability and localization in Richardson model superconductivity, we consider a time-reversal symmetry breaking deformation this model, known as Russian Doll Model (RDM), implement diagonal on-site disorder. The ergodicity-breaking properties single-particle spectrum are analyzed using large-energy renormalization group (RG) over momentum-space spe...

This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequ...

Detection of deep and hidden mineralization using the surface geochemical data is a challenging subject in the mineral exploration. In this work, a novel scenario based on the spectrum–area fractal analysis (SAFA) and the principal component analysis (PCA) has been applied to distinguish and delineate the blind and deep Mo anomaly in the Dalli Cu–Au porphyry mineralization area. The Dalli miner...

we introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. these kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. we construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...

Self-similar fractals are useful models of the soil solid and pore sets along lines, across areas and inside volumes. The scaling properties of these sets, analysed by the divider method within the known scale range over which the fractal extends, were described by three parameters, the solid (Ds) and pore (Dp) linear box or capacity empirical fractal dimensions, and the total number of rulers ...