This book deals at some length with the question: Since there are many more poor than rich, why don’t the poor just tax the rich heavily and reduce the inequality? In the 19th century and the first half of the 20th century, the topic of inequality was discussed widely. Ending or reducing inequality was a prime motivating factor in the emergence of communism and socialism. The book discusses w…
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Ma…
This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bel…
This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic. These are devoted to the theoretical and/or numerical analysis of problems involving boundary and interior layers and methods for solving these problems numerically. The a…
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the applicati…
The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers. Around the middle …
Computer simulation-based education and training is a multi-billion dollar industry. With the increased complexity of organizational decision making, projected demand for computer simulation-based decisional aids is on the rise. The objective of this book is to enhance systematically our understanding of and gain insights into the general process by which human facilitated ILEs are effectively …
Il libro ha origine dall'attività svolta durante il progetto "BetOnMath", un'esperienza di Matematica Civile finalizzata alla prevenzione dell'abuso di gioco d'azzardo tra gli studenti della scuola secondaria di secondo grado attraverso un insegnamento innovativo della matematica. In particolare, durante il progetto gli autori del libro hanno sviluppato un percorso didattico modulare sulla mat…
The purpose of this book is to introduce two recent topics in mathematical physics and probability theory: the Schramm–Loewner evolution (SLE) and interacting particle systems related to random matrix theory. A typical example of the latter systems is Dyson's Brownian motion (BM) model. The SLE and Dyson's BM model may be considered as "children" of the Bessel process with parameter D, BES(D)…
Penulis menunjukkan bahwa beberapa komitmen metodologis untuk objek matematika dibuat berdasarkan praktik matematika; beberapa dibuat berdasarkan pertimbangan mendasar; dan beberapa dibuat dalam metode hipotesis penerapan matematika.