While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of…
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of comple…
When close to a continuous phase transition, many physical systems can usefully be mapped to ensembles of fluctuating loops, which might represent for example polymer rings, or line defects in a lattice magnet, or worldlines of quantum particles. 'Loop models' provide a unifying…
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects…
This book provides a perspective on a number of approaches to financial modelling and risk management. It examines both theoretical and practical issues. Theoretically, financial risks models are models of a real and a financial "uncertainty", based on both common and private in…
The work developed in this thesis addresses very important and relevant issues of accretion processes around black holes. Beginning by studying the time variation of the evolution of inviscid accretion discs around black holes, and their properties, the author investigates the c…