It is well-known that the curvature tensor is an isometric invariant of C(2) Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C(1). This unexpected flexibility has many paradoxical consequences, one of them is the existence ...

Fractal-rate behavior is a ubiquitous and important aspect of normal mammalian cochlear-nerve activity, which may well be absent in nerve bers excited by present cochlear prostheses. We propose simple methods for introducing fractal uctuations into a cochlear prosthesis, thus providing the natural statistical character of eighth-nerve ber spike trains. Fractal behavior is ubiquitous in mammalia...

in the classification of traditional domes, they are divided into two main categories: “roc” (cone-shaped) and “nār” (hemisphere-like) domes. urchīn domes are a sub-category of cone-shaped domes which were common in the past in the region of mesopotamia and southwest of iran. the fractal geometry is the best way to describe the geometrical structure of these domes, because the existence of self...

Gear’s normal contact stiffness played an important role in the mechanical equipment. In this paper, the M-B fractal model is modified and the contact surface coefficient is put forward to set up the fractal model, considering the influence of friction, which could be used to calculate accurately the involute arc cylindrical gears’ normal contact stiffness based on the fractal theory and Hertz ...

in this article we introduce the notion of textit{fractal $omega$-operad} emerging from  a natural $omega$-operad associated to any coglobular object in the category of higher operads in batanin's sense, which in fact is a coendomorphism $omega$-operads. we have in mind coglobular object of higher operads which algebras are kind of higher transformations. it follows that this natural $omega$-op...

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...