Differential calculus and equations

The purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painleve equations, and it offers new results on a particular Painleve III equation of type PIII (D6), called PIII (0, 0, 4, -4), describing its relation to isomonodromic families of vector bundles on P1 with meromorphic connections.

This book provides an overview of different topics related to the theory of partial differential equations.

This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses.

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems.

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics.

This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods.

Mathematical treatment to properties of dynamic materials, material substances whose properties are variable in space and time are examined in this book.

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications.

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area.

In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems.

This book provides a basic, initial resource, introducing science and engineering students to the field of optimization.

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics.

This monograph offers the first systematic account of (metric) regularity theory in variational analysis.

This textbook is designed with the needs of today's student in mind.

Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.

This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling.

This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids.

Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled "e;Geometric mechanics - variational and stochastic methods"e; run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Federale de Lausanne.

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive.

This book provides a selection of reports and survey articles on the latest research in the area of single and multivariable operator theory and related fields.

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied.

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.