Lie group theory was originally created more than 100 years ago as a tool for solving
ordinary and partial differential equations. In this article we review the results of a much …

Up to now we have introduced a fractional derivative definition for special simple function
classes. In the following section we will present common generalizations for arbitrary …

Since the first edition of this book was published several new developments have been
made in the field of the moiré theory. The most important of these concern new results that …

This book provides a self-contained and accessible introduction to linear and multilinear
algebra. Besides the standard techniques for linear and multilinear algebra many advanced …

Developmental systems theory provides powerful tools for predicting complex, dynamic
interactions among biological and environmental processes in human behavior and health …

The Kronecker product of matrices plays a central role in mathematics and in applications
found in engineering and theoretical physics. These applications are signal processing …

A single qubit is a two-state system, such as a two-level atom. The states (kets)| h> and| v> of
the horizontal and vertical polarization of a photon can also be considered as a two-state …

We present the theory of double reductions of PDEs with two independent variables that
admit a Lie point symmetry and a conserved vector invariant under the symmetry. The theory …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

We present the package SADE (Symmetry Analysis of Differential Equations) for the
determination of symmetries and related properties of systems of differential equations. The …