Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach

This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical moments of the kinetic distribution function, it is finally possible to recover macroscopic relationships between the average risk and the road congestion, which show an interesting and reasonable correlation with the well-known free and congested phases of the flow of vehicles.Comment: 23 pages, 3 figures, Commun. Math. Sci., 201

Histoire des sciences exactes

Jean Dhombres, directeur d’études avec Jean Bricmont, professeur à l’Université catholique de Louvain Critiques des philosophies des sciences actuelles et essai de refondation La philosophie des sciences se développa au XXe siècle en réaction à la perception d’une double crise, celle de la philosophie critique ou de la métaphysique, et celle de la science classique bouleversée par les découvertes de la relativité et de la mécanique quantique. Durant la première moitié du XXe siècle, cette phi..

Gli studi sui fondamenti della geometria nella seconda metà dell'ottocento con particolare riferimento alla situazione italiana

Appare immediato a chi si soffermi sulla storia della matematica della seconda metà dell'ottocento che lo studio della geometria ebbe in quel periodo notevoli sviluppi

Peano and the Debate on Infinitesimals

The main aim of this paper is to put Peano’s opinion about the unacceptability of the actual infinitesimal notion into evidence. First we briefly focus on the cultural environment where Peano’s considerations originated and developed. Then we examine Peano’s article of 1892, “Dimostrazione dell’impossibilità di segmenti infinitesimi costanti” [Peano 1892]

About individuation of standard-representative elements for cognitive process

This paper is a development of the epistemological analysis based on the assumption that the cognitive-inductive structure is a starting point of a particular kind of cognitive process. We will assume this process to be a cognitive transformation from one state to another of a dynamic countable system. Our purpose is to determine some elements (standard-representative) aimed at deepening the knowledge of the system mentioned above

Measures relating to cognitive syntactic power and to informative content of the cognitive-inductive structures

In this paper the A. proposes and studies the measure of cognitive syntactic power and the measure of informative content of a cognitive-inductive structure (it is a particular relational-structure).The A. observes that the examined measures are measures of informarion according to Kampé de Ferie-Forte's axiomatic theory (Inf case and hyperbolic case)

The early period of the calculus of variations

This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s δ-calculus, including: • The isoperimetrical problems • Shortest lines and geodesics • Euler’s Methodus Inveniendi and the two Additamenta Finally, the authors give the readers a sense of how vast the calculus of variations has become in centuries hence, providing some idea of what lies outside the scope of the book as well as the current state of affairs in the field. This book will be of interest to anyone studying the calculus of variations who wants a deeper intuition for the techniques and ideas that are used, as well as historians of science and mathematics interested in the development and evolution of modern calculus and analysis.

Dall'eredita' Grassmanniana alla teorie delle omografie nella scuola di Peano

A survey on the influence of Grassmann\u2019s theories on the school of Peano. In section 3 we explain the modern point of view of Peano\u2019s ideas related to homography theory

The geometric side for an axiomatic theory of Evolution

Starting from an idea of G. V. Schiaparelli (1898), we introduce a geometric model for an axiomatic theory of Evolution and use it to introduce some results on speciation events