Related papers: Mathematical Encounters
Based on a variety of philosophical approaches and my own work for decades in pure and applied mathematics teaching and research, I explain my view upon the basic difficulties of acquiring the Mathematical Experience (in the sense of P.J.…
The present notes summarise the oligopoly dynamics lectures professor Lu\'is Cabral gave at the Bank of Portugal in September and October 2017. The lectures discuss a set industrial organisation problems in a dynamic environment, namely…
Optimization and Stochastic Processes Applied to Economy and Finance -- is the name of this book translated to English; It has been used at the IME-USP - The Institute of Mathematics and Statistics of the University of Sao Paulo, since…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
These are the lecture notes of a course given by the first author on December 27, 2012 - January 4, 2013, held at the Academy of Mathematics and Systems Science Chinese Academy of Sciences in Beijing.
During the past few years the development of experimental techniques has allowed the quantitative analysis of biological systems ranging from neurobiology and molecular biology. This work focuses on the quantitative description of these…
Opening Lecture at the Second Rencontres du Vietnam, October 21-28, 1995.
These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in December~1992. They constitute a brief and elementary introduction to…
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
These are notes from my mini-course at ICRA13, Sao Paulo, 2008
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second…
These are lecture notes of a course that I gave to people doing research for their Ph.D. thesis in theoretical chemistry or spectroscopy. The course was given on December 9-13, 2002, in Han-sur-Lesse, Belgium. The lecture notes start with…
These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is…
This is basically a review of the field of Quasi-Monte Carlo intended for computational physicists and other potential users of quasi-random numbers. As such, much of the material is not new, but is presented here in a style hopefully more…
These notes are the outgrowth of a series of lectures given at MSRI in January 1995 at the beginning of the special semester in complex dynamics and hyperbolic geometry. In these notes, the primary aim is to motivate the study of complex…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics…
Path integral Monte Carlo (PIMC) simulations have become an important tool for the investigation of the statistical mechanics of quantum systems. I discuss some of the history of applying the Monte Carlo method to non-relativistic quantum…
These notes originated in a series of lectures I gave in Marseille in May, 2013. I was invited to give an introduction to the isomorphism theorems, originating with Dynkin, which connect Markov local times and Gaussian processes. This is an…
The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts [64-66] that reflect a certain range of developments, but even in their totality they cannot be taken as a…