This paper deals with some multidimensional integral operators involving the Gauss hypergeometric function in the kernel and generating the multidimensional modified fractional calculus operators introduced in [8]. Some mapping properties, weighted inequalities, a formula of integration by parts and index laws are obtained.

A class of multidimensional greatest common divisor algorithms is studied. Their connection with the Jacobi algorithm is established and used to obtain theoretical properties such as the existence of digit frequencies. A technique of D. H. Lehmer's for Euclid's algorithm is generalized for efficient computation of the multidimensional algorithms. For triples of integers, two algorithms of inter...

While the reversibility of multidimensional cellular automata is undecidable and there exists a criterion for determining if a multidimensional linear cellular automaton is reversible, there are only a few results about the reversibility problem of multidimensional linear cellular automata under boundary conditions. This work proposes a criterion for testing the reversibility of a multidimensio...

Multidimensional databases is a key technology in the enabling of interactive analyses of large amounts of data for decision-making purposes. Multidimensional databases differ from previous technologies by viewing data specifically as multidimensional cubes, which have proven to be particularly well suited for data analyses. Multidimensional models more specifically categorize data as either fa...

Thanks to the explosive growth of sensing devices and capabilities, multidimensional (MD) signals — such as images, videos, multispectral images, light fields, and biomedical data volumes — have become ubiquitous. Multidimensional filter banks and the associated constructions provide a unified framework and an efficient computational tool in the formation, representation, and processing of thes...

The aim of this work is to identify the properties that a universal multidimensional input device should have in order to optimally function with 3D applications, including Web browsers, window managers, digital content creation software, and computer games. Such applications have become increasingly effective due to the rapid development of computer graphics. This situation has generated a gre...

The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of multidimensional persistence have been proved to hold when topological spaces are filtered by continuous functions, i.e. for continuous data. This paper aims to provide a b...

In this chapter, we illustrate the properties of the continuous shearlet transform with respect to its ability to describe the set of singularities of multidimensional functions and distributions. This is of particular interest since singularities and other irregular structures typically carry the most essential information in multidimensional phenomena. Consider, for example, the edges of natu...