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15 papers · 1 filter
From fractal R-L ladder networks to the diffusion equation
Jacky Cresson, Anna Szafranska
We give a self-contained presentation of fractal R-L ladder networks as well as a detailed computation of the admittance of these systems. We also discuss the conditions under whic…
Generally covariant -particle dynamics
Tomasz Miller, Michał Eckstein, Paweł Horodecki +1
A simultaneous description of the dynamics of multiple particles requires a configuration space approach with an external time parameter. This is in stark contrast with the relativ…
Equiangular tight frames and unistochastic matrices
Dardo Goyeneche, Ondrej Turek
In this work, we show that a complex equiangular tight frame (ETF) composed by vectors in dimension exists if and only if a certain bistochastic matrix, univocally determin…
Dark energy as a manifestation of nontrivial arithmetic
Marek Czachor
Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, $\mathbb{R}_+^…
Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
Diederik Aerts, Marek Czachor, Maciej Kuna
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier tra…
Relativity of arithmetic as a fundamental symmetry of physics
Marek Czachor
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with…