Physicists become acquainted with special functions early in their studies. Consider our
perennial model, the harmonic oscillator, for which we need Hermite functions, or the …

Feynman path integrals have been introduced by Feynman in his formulation of quantum
mechanics [1]. 1 Since their inception they have occupied a somewhat ambiguous position …

This paper has two parts. The first part surveys Euler's work on the constant $\gamma=
0.57721\cdots $ bearing his name, together with some of his related work on the gamma …

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 …

We derive several new algorithms for particle flow with non-zero diffusion corresponding to
Bayes' rule. This is unlike all of our previous particle flows, which assumed zero diffusion for …

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 …

In a domain RN we consider compact, Birman–Schwinger type operators of the form TP; A
DA PA with P being a Borel measure in; containing a singular part, and A being an order N …

In laboratory and numerical experiments, physical quantities are known with a finite
precision and described by rational numbers. Based on this, we deduce that quantum …

Fractal tube Formulas for compact sets and relative fractal drums Page 1 J. Fractal Geom. 5 (2018),
1–119 DOI 10.4171/JFG/57 Journal of Fractal Geometry © European Mathematical Society …