Related papers: Mathematics and map drawing in the eighteenth cent…

In this survey we present a generalization of the notion of metric space and some applications to discrete structures as graphs, ordered sets and transition systems. Results in that direction started in the middle eighties based on the…

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

Generalized Lagrangian mean theories are used to analyze the interactions between mean flows and fluctuations, where the decomposition is based on a Lagrangian description of the flow. A systematic geometric framework was recently developed…

We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces…

We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…

In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…

For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With…

The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…

Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…

Lagrangian averaging theories, most notably the Generalised Lagrangian Mean (GLM) theory of Andrews & McIntyre (1978), have been primarily developed in Euclidean space and Cartesian coordinates. We re-interpret these theories using a…

This report is an introduction to mathematical map colouring and the problems posed by Heawood in his paper of 1890. There will be a brief discussion of the Map Colour Theorem; then we will move towards investigating empire maps in the…

In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a…

The early Renaissance artist Albrecht Durer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and mathematical tools for their trade. In the…

We present some episodes from the history of interactions between geometry and physics over the past century.

A map is discussed that connects, in 1+1 dimensions, Galilei's relativity to Einstein's special relativity. By means of this map it is possible to derive special-relativistic formulas from the corresponding Galilean ones. Beyond being…

This paper studies the magnitude homology of graphs focusing mainly on the relationship between its diagonality and the girth. Magnitude and magnitude homology are formulations of the Euler characteristic and the corresponding homology,…

The notion of quadratic maps between arbitrary groups appeared at several places in the literature on quadratic algebra. Here a unified extensive treatment of their properties is given; the relation with a relative version of Passi's…

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where…

In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…