A fractal set which corresponds to the six-vertex model has been obtained and a relationship between the free energy of the six-vertex model and the fractal dimension of the fractal set was established. Notions which correspond to the transfer matrix and the n-equivalence has been found in the area of the fractal geometry. This correspondence can be generalized to the case of the models suitabl...

The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is...

Keywords: Fractal structure Fractal dimension Box-counting dimension Domain of words Language Regular expression Binary-coded decimal Search tree a b s t r a c t A fractal structure is a tool that is used to study the fractal behavior of a space. In this paper, we show how to apply a new concept of fractal dimension for fractal structures, extending the use of the box-counting dimension to new ...

We present measurements of the fractal dimensions associated to the spin clusters for Z4 and Z5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuin Kastelyn (FK) clusters in these models but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in the behavio...

The statistical properties of intra-chromosome maps obtained by a genome-wide chromosome conformation capture method (Hi-C) are described in the framework of the hierarchical crumpling model of heteropolymer chain with quenched disorder in the primary sequence. We conjecture that the observed Hi-C maps are statistical averages over many different ways of hierarchical genome folding, and show th...

This paper reviews the multifractal wavelet model (MWM) and its applications to network traf£c modeling and inference. The discovery of the fractal nature of traf£c has made new models and analysis tools for traf£c essential, since classical Poisson and Markov models do not capture important fractal properties like multiscale variability and burstiness that deleteriously affect performance. Set...

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...

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 diagnosis), measuring additional variables (probing) or executing additional tests (sequential testing/test sequencing). In this paper we combine the above approaches, as well as from Automated Test Pattern Generation (AT...

A fundamental aspect of harmonic analysis on Euclidean spaces deals with various classes of real or complex-valued functions, such as the C classes of functions which are continuous and continuously differentiable up to order k, where k is a nonnegative integer. If k = 0, this simply means that the function is continuous. Of course continuity of a function makes sense on any metric space, or on...

We study a chemical gelation model in two dimensions which includes both monomer aggregations and bond fluctuations. Our numerical simulation shows that a sol-gel transition occurs when an initial monomer concentration is above a critical concentration. Fractal aggregates grow until the sol-gel transition occurs. After the gelation, however, bond fluctuations break the fractal structure and an ...