Related papers: Some questions related to fractals
This encyclopedia article addresses questions like the following. How does the Sun shine? Does the neutrino have a mass? Are there weak interactions beyond those described by the standard model of particle physics?
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
A review is given of the key works relevant to the problem of dynamical fluctuation-electromagnetic interaction, a problem of topical interest over a period of several decades. We discuss controversies and present day progress in this…
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
Neutrino oscillations appear to be a simple quantum mechanical phenomenon. However, a closer look at them reveals a number of subtle points and apparent paradoxes. Some of the basic issues of the theory of neutrino oscillations are still…
Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual…
We give a review of classical, thermodynamic and quantum properties of black holes relevant to fundamental physics.
Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along…
The thesis focuses on different aspects of radio pulsars: on the one hand it describes research on the pulsar emission mechanism (nulling, drifting subpulses, single-pulse polarisation and their mutual interaction). On the other it gives an…
We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct unit fractions, a practice rooted in ancient Egyptian…
These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.
An overview of the current data and phenomenology on the structure of the photon and an outline of some opportunities available in the medium term future.
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with…
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…