Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimensi...

Recently, self-similarity of complex networks have attracted much attention. Fractal dimension of complex network is an open issue. Hub repulsion plays an important role in fractal topologies. This paper models the repulsion among the nodes in the complex networks in calculation of the fractal dimension of the networks. The Coulomb’s law is adopted to represent the repulse between two nodes of ...

Fractals arise from a variety of sources and have been observed in nature and on computer screens. One of the exceptional characteristics of fractals is that they can be described by a noninteger dimension. The geometry of fractals and the mathematics of fractal dimension have provided useful tools for a variety of scientific disciplines, among which is chaos. Chaotic dynamical systems exhibit ...

There are many research available on the study of a real-valued fractal interpolation function and dimension its graph. In this paper, our main focus is to dimensional results for vector-valued Riemann–Liouville fractional integral. Here, we give some which ensure that functions quite different from functions. We determine interesting bounds Hausdorff graph function. also obtain associated inva...

In this work the existence of a global attractor for the solution semiflow of the coupled two-cell Brusselator model equations is proved. A grouping estimation method and a new decomposition approach are introduced to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of fourvariable reaction-diffusion systems with cubic autocatalytic nonlinear...

Traditional studies of the cranial suture morphology have focused mostly on visual estimation and linear measurements, and thus on evaluating their complexity. This paper presents a new look on cranial sutures as curves, which can be analysed by fractal dimension. This new measure seems to be a much better method of expressing properties of sutural patterns than traditional methods. Our finding...

background: mitral valve prolapse (mvp) is now recognized as the most common cardiovalvular abnormality (cva) in the usa, but there has been much less agreement about other aspects of its epidemiology, diagnosis and clinical features. cva analysis still relies mainly on the visual assessment of echocardiographic imaging and manual measurements by experienced cardiologists. so, automating or sem...