Differential calculus and equations Books

The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials...

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of...

This book presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalised functions. Earlier, in part 3 of Oberguggenberger & Rosinger, Lie group...

The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of...

Various applications of the homogenization theory of partial differential equations resulted in the further development of this branch of mathematics, attracting an increasing interest of both mathematicians and experts in...

In t.lw fHll of !!)!)2, Professor Dr. M. Alt.ar, chairman of tIw newly established dppartnwnt or Managenwnt. wit.h Comput.er Science at thp Homanian -American Univprsity in Bucharest (a private univprsil.y), inl.roducod in t.he...

This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we...

. The theory of difference equations, the methods used in their solutions and their wide applications have advanced beyond their adolescent stage to occupy a central position in Applicable Analysis. In fact, in the last five...

At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the...

Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations...

Mathematical modeling plays an essential role in science and engineering. Costly and time consuming experiments (if they can be done at all) are replaced by computational analysis. In industry, commercial codes are widely used...

A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco­ momics and biology, have an irregular structure: classical variational proce­...

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not...

Asymptotic methods of nonlinear mechanics developed by N. M. Krylov and N. N. Bogoliubov originated new trend in perturbation theory. They pene­ trated deep into various applied branches (theoretical physics, mechanics, ap­...

Automorphisms of Affine Spaces describes the latest results concerning several conjectures related to polynomial automorphisms: the Jacobian, real Jacobian, Markus-Yamabe, Linearization and tame generators conjectures. Group...

The analytical basis of Navier-Stokes Equations in Irregular Domains is formed by coercive estimates, which enable proofs to be given of the solvability of the boundary value problems for Stokes and Navier-Stokes equations...

In 1960 the Polish mathematician Zdzidlaw Opial (1930--1974) published an inequality involving integrals of a function and its derivative. This volume offers a systematic and up-to-date account of developments in Opial-type...

Multigrid Methods for Finite Elements combines two rapidly developing fields: finite element methods, and multigrid algorithms. At the theoretical level, Shaidurov justifies the rate of convergence of various multigrid...

Scale is a concept the antiquity of which can hardly be traced. Certainly the familiar phenomena that accompany sc ale changes in optical patterns are mentioned in the earliest written records. The most obvious topological...

This volume contains the proceedings of a NATO Advanced Research Workshop on Periodic Solutions of Hamiltonian Systems held in II Ciocco, Italy on October 13-17, 1986. It also contains some papers that were an outgrowth of the...

Preliminaries.- Sectorial Operators.- Linear Evolution Equations.- Semilinear Evolution Equations.- Quasilinear Evolution Equations.- Dynamical Systems.- Numerical Analysis.- Semiconductor Models.- Activator-Inhibitor Models.- Belousov-Zhabotinskii...

How is free will possible in the light of the physical and chemical underpinnings of brain activity and recent neurobiological experiments? How can the emergence of complexity in hierarchical systems such as the brain, based at...

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all...

By now, most academics have heard something about the new science of complexity. In a manner reminiscent of Einstein and the last hundred years of physics, complexity science has captured the public imagination. ® One can go to...

HR structures.- Solenoid functions.- Self-renormalizable structures.- Rigidity.- Gibbs measures.- Measure scaling functions.- Measure solenoid functions.- Cocycle-gap pairs.- Hausdorff realizations.- Extended Livšic-Sinai eigenvalue formula.- Arc...

When are High Order Methods Effective?.- Well-posedness and Stability.- Order of Accuracy and the Convergence Rate.- Approximation in Space.- Approximation in Time.- Coupled Space-Time Approximations.- Boundary Treatment.- The Box Scheme.- Wave...

Non-scalar variational problems appear in different fields. In geometry, for in­ stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in...

This collection of lectures treats the dynamics of open systems with a strong emphasis on dissipation phenomena related to dynamical chaos. This research area is very broad, covering topics such as nonequilibrium statistical...

In this book, several world experts present (one part of) the mathematical heritage of Kolmogorov. Each chapter treats one of his research themes or a subject invented as a consequence of his discoveries. The authors present...

Basic Principles of Classical Mechanics.- The n-Body Problem.- Symmetry Groups and Order Reduction.- Variational Principles and Methods.- Integrable Systems and Integration Methods.- Perturbation Theory for Integrable Systems.- Non-Integrable Systems.-...

These proceedings are the fifth in the series Traffic and Granular Flow, and we hope they will be as useful a reference as their predecessors. Both the realistic modelling of granular media and traffic flow present important...

Besides turbulence, there is hardly any other scientific topic which has been considered a prominent scientific challenge for such a long time. The special interest in turbulence is not only based on it being a difficult...

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems...

Unique book on Reaction-Advection-Diffusion problems

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the...

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to...

This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory,...

This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission...

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo...

This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the "research project for beginners" proposed at the end of the...

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...

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. Quantum mechanics is supposedly linear, invariant under time-reversal,...

This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts:new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers,...

This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step...

This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher...

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract...