The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical ...

Infinity is where things happen that don't. — S. Knight Ever since Benoit Mandelbrot published his book on fractals [1], we've become accustomed to seeing fantastic and beautiful fractal images such as the ones at the bottom of the pages of this article. A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale. If you zoom in on an image of a fractal, yo...

In his groundbreaking work, ‘The Fractal Geometry of Nature’ (Mandelbrot, 1982), Benoit Mandelbrot described how fractals could account for a long list of natural forms ranging from trees to coastlines. Two recent studies in Science and The EMBO Journal have suggested that chromatin and the nucleoplasmic space surrounding it should be added to the fractal list. Fractals are ‘self-similar’, mean...

The purpose of this work is to compare the linear and non-linear kriging methods in the mineral resource estimation of the Qolqoleh gold deposit in Saqqez, NW Iran. Considering the fact that the gold distribution is positively skewed and has a significant difference with a normal curve, a geostatistical estimation is complicated in these cases. Linear kriging, as a resource estimation method, c...

The convection-diffusion process in porous electrodes depends greatly upon the structure. A fractal model for catalyst a thin-zone bed reactor is established using He?s derivative, and variational principle also space, an approximate solution obtained. Additionally ancient Chinese algorithm adopted to solve algebraic equation.

Purpose – Fractal geometry can be used to model natural objects which cannot be easily represented by the euclidean geometry. However, contemporary computer-aided design (CAD) and computer-aided manufacturing (CAM) systems cannot be used to model a fractal object efficiently. In a general layer manufacturing (LM) workflow, a model described by the euclidean geometry is required in order to gene...

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive monitoring), measuring additional variables (probing) or executing additional tests (sequential diagnosis/test sequencing). In this paper we combine the above approaches with techniques from Automated Test Pattern Generat...

The fractal interpolation theory was used to the research of road surface roughness, and its simulating method was proposed through the piecewise fractal model. The fractal interpolation model was established for the actual road surface roughness, its influential factors and their laws of influencing were also analyzed, and then the model accuracy was confirmed by the fractal parameters and the...

This thesis comprises analytic and numerical studies of static, geometrical properties of fractals and dynamical processes in them. First, we have numerically estimated the subset fractal dimensions DS describing the scaling of some subsets S of the fractal cluster with the linear cluster size R in the q-state Potts models. These subsets include the total mass of the cluster, the hull, the exte...