Differential calculus and equations

This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation.

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems.

This textbook, now in its second edition, provides a broad introduction to the theory and practice of both continuous and discrete dynamical systems with the aid of the Mathematica software suite.

This book discusses the state-of-the-art and open problems in computational finance.

Presenting some recent results on the construction and the moments of Levy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction.

This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory.

This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time.

This book aims to face particles in flows from many different, but essentially interconnected sides and points of view.

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22-25, 2016 in San Antonio, Texas.

Written by leading experts in an emerging field, this book offers a unique view of the theory of stochastic partial differential equations, with lectures on the stationary KPZ equation, fully nonlinear SPDEs, and random data wave equations.

This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations.

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior.

The articles in this collection are a sampling of some of the research presented during the conference "e;Stochastic Analysis and Related Topics"e;, held in May of 2015 at Purdue University in honor of the 60th birthday of Rodrigo Banuelos.

This monograph contains expert knowledge on complex fluid-flows in microfluidic devices.

This book provides an introduction to PDE-constrained optimisation using finite elements and the adjoint approach.

This contributed volume contains a collection of articles on the most recent advances in integral methods.

This contributed volume contains a collection of articles on the most recent advances in integral methods.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications.

This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation.

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems.

Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs.

This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory.

This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems.

This volume collects the edited and reviewed contribution presented in the 7th iTi Conference in Bertinoro, covering fundamental and applied aspects in turbulence.

This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincare and Darboux to basic tools of modern mathematics.

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation.

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch.

Written by leading experts, this book provides a clear and comprehensive survey of the "e;status quo"e; of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy.

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.

There are several physico-chemical processes that determine the behavior of multiphase fluid systems - e.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications.

This thesis presents a rigorous, abstract analysis of multigrid methods for positive nonsymmetric problems, particularly suited to algebraic multigrid, with a completely new approach to nonsymmetry which is based on a new concept of absolute value for nonsymmetric operators.

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "e;Intensive Research Program on Advances in Nonsmooth Dynamics 2016"e;, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 1st to April 29th, 2016.

Das vorliegende Lehrbuch enthält eine kompakte, in Vorlesungen erprobte Einführung in diese moderne Sichtweise der GDGn, wobei der klassische Stoff nicht vernachlässigt wird.

This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date.

This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers.

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini.

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge-Ampere and linearized Monge-Ampere equations.

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2016.

Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications.

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems.

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Bedlewo, Poland in September 2015.

This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L.

This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand.

The book collects the most relevant results from the INdAM Workshop "e;Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics"e; held in Rome, September 14-18, 2015.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial  structure of complicated systems.

This book is divided into two parts, the first of which seeks to connect the phase transitions of various disciplines, including game theory, and to explore the synergies between statistical physics and combinatorics.

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds.