Differential calculus and equations

This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics.

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics.

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions.

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics.

Abstract models for many problems in science and engineering take the form of an operator equation.

Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces.

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years.

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator.

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics.

This book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory.

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives.

These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas.

The main aim of this book is to present recent results concerning inequalities of the Jensen, Cebysev and Gruss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S.

This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES.

This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par- tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech- nical Research Council of Turkey and the Middle East Technical University.

This volume of the Proceedings of the congress ISAAC '97 collects the con- tributions of the four sections 1.

There was a time, not long ago, when the only treatment options considered to be worthwhile for patients requiring psychiatric care were the 50-minute hour on the one hand, or full-time hospitalization on the other.

Many problems arising in the physical sciences, engineering, biology and ap- plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces.

This volume consists of papers presented in the special sessions on "e;Complex and Numerical Analysis"e;, "e;Value Distribution Theory and Complex Domains"e;, and "e;Use of Symbolic Computation in Mathematics Education"e; of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997.

There is almost no field in Mathematics which does not use Mathe- matical Analysis.

IMA Volumes 135: Transport in Transition Regimes and 136: Dispersive Transport Equations and Multiscale Models focus on the modeling of processes for which transport is one of the most complicated components.

The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans- formations.

This is a textbook for a one semester course on numerical analysis for senior undergraduate or beginning graduate students with no previous knowledge of the subject.

The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999.

This book is the Proceedings of the Second ISAAC Congress.

Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed.

1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics.

During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions.

In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly.

The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati- cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications.

This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October.

Since the seminal work of P.

Harmonic maps are solutions to a natural geometrical variational prob- lem.

Overview Many problems in mathematical physics and applied mathematics can be reduced to boundary value problems for differential, and in some cases, inte- grodifferential equations.

Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994.

Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical analysis, approximation theory, partial differential equations, integral equations, harmonic analysis, etc.

The main goal of this work is to revisit the proof of the global stability of Minkowski space by D.

We deal in this work with quantitative results in the pointwise approximation of func- tions by positive linear functionals and operators.

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects.

common feature is that these evolution problems can be formulated as asymptoti- cally small perturbations of certain dynamical systems with better-known behaviour.

Equations of the Ginzburg-Landau vortices have particular applications to a number of problems in physics, including phase transition phenomena in superconductors, superfluids, and liquid crystals.

Differential equations is a subject of wide applicability, and knowledge of dif- Differential equations is a subject of wide applicability, and knowledge of dif- ferential ferential equations equations topics topics permeates permeates all all areas areas of of study study in in engineering engineering and and applied applied mathematics.

We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties.