Our main goal in this long survey article is to provide an overview of the theory of complex
fractal dimensions and of the associated geometric or fractal zeta functions, first in the case …

The present research monograph is a testimony to the fact that Fractal Analysis is deeply
connected to numerous areas of contemporary Mathematics. Here, we have in mind, in …

If you cleave the hearth of one drop of water a hundred pure oceans emerge from
it.(Mahmud Shabistari, Gulshan-i-raz) We have decided to contribute to the volume of the …

In this work, a simulation model of a vibratory conveying system is presented. The simulation
model is based on a continuous contact formulation in vertical direction which is extended …

The theory of fractal strings and their complex dimensions investigates the geometric,
spectral and physical properties of fractals and precisely describes the oscillations in the …

Noncommutative Riemannian geometry and diffusion on ultrametric Cantor sets Page 1 J.
Noncommut. Geom. 3 (2009), 447–480 Journal of Noncommutative Geometry © European …

In the context of metric geometry, we introduce a new necessary and sufficient condition for
the convergence of an inductive sequence of quantum compact metric spaces for the …

In this paper we define (local) Dirac operators and magnetic Schrödinger Hamiltonians on
fractals and prove their (essential) self-adjointness. To do so we use the concept of 1-forms …

We study derivations and Fredholm modules on metric spaces with a local regular
conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a …

Let (A, H, D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A
acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A …