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| Author | : Jean-Pierre Serre |
| Publisher | : CRC Press |
| Total Pages | : 169 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 1466501936 |
Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in
| Author | : Pierre Gilles Lemarie-Rieusset |
| Publisher | : CRC Press |
| Total Pages | : 412 |
| Release | : 2002-04-26 |
| Genre | : Mathematics |
| ISBN | : 9781420035674 |
The Navier-Stokes equations: fascinating, fundamentally important, and challenging,. Although many questions remain open, progress has been made in recent years. The regularity criterion of Caffarelli, Kohn, and Nirenberg led to many new results on existence and non-existence of solutions, and the very active search for mild solutions in the 1990's culminated in the theorem of Koch and Tataru that, in some ways, provides a definitive answer. Recent Developments in the Navier-Stokes Problem brings these and other advances together in a self-contained exposition presented from the perspective of real harmonic analysis. The author first builds a careful foundation in real harmonic analysis, introducing all the material needed for his later discussions. He then studies the Navier-Stokes equations on the whole space, exploring previously scattered results such as the decay of solutions in space and in time, uniqueness, self-similar solutions, the decay of Lebesgue or Besov norms of solutions, and the existence of solutions for a uniformly locally square integrable initial value. Many of the proofs and statements are original and, to the extent possible, presented in the context of real harmonic analysis. Although the existence, regularity, and uniqueness of solutions to the Navier-Stokes equations continue to be a challenge, this book is a welcome opportunity for mathematicians and physicists alike to explore the problem's intricacies from a new and enlightening perspective.
| Author | : Pierre-Louis Lions |
| Publisher | : Pitman Publishing |
| Total Pages | : 332 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : |
This volume contains a complete and self-contained treatment of Hamilton-Jacobi equations. The author gives a new presentation of classical methods and of the relations between Hamilton-Jacobi equations and other fields. This complete treatment of both classical and recent aspects of the subject is presented in such a way that it requires only elementary notions of analysis and partial differential equations.
| Author | : Sergio Blanes |
| Publisher | : CRC Press |
| Total Pages | : 287 |
| Release | : 2017-11-22 |
| Genre | : Mathematics |
| ISBN | : 1315354861 |
Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.
| Author | : Scott Corry |
| Publisher | : CRC Press |
| Total Pages | : 246 |
| Release | : 2016-11-25 |
| Genre | : Mathematics |
| ISBN | : 1315354608 |
Structured as a dialogue between a mathematician and a physicist, Symmetry and Quantum Mechanics unites the mathematical topics of this field into a compelling and physically-motivated narrative that focuses on the central role of symmetry. Aimed at advanced undergraduate and beginning graduate students in mathematics with only a minimal background in physics, this title is also useful to physicists seeking a mathematical introduction to the subject. Part I focuses on spin, and covers such topics as Lie groups and algebras, while part II offers an account of position and momentum in the context of the representation theory of the Heisenberg group, along the way providing an informal discussion of fundamental concepts from analysis such as self-adjoint operators on Hilbert space and the Stone-von Neumann Theorem. Mathematical theory is applied to physical examples such as spin-precession in a magnetic field, the harmonic oscillator, the infinite spherical well, and the hydrogen atom.
| Author | : Martin Hanke |
| Publisher | : CRC Press |
| Total Pages | : 148 |
| Release | : 1995-04-26 |
| Genre | : Mathematics |
| ISBN | : 9780582273702 |
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
| Author | : Richard Melrose |
| Publisher | : CRC Press |
| Total Pages | : 392 |
| Release | : 1993-03-31 |
| Genre | : Mathematics |
| ISBN | : 1439864608 |
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
| Author | : Ali Pourhashemi |
| Publisher | : CRC Press |
| Total Pages | : 291 |
| Release | : 2015-01-28 |
| Genre | : Medical |
| ISBN | : 1482252430 |
This book facilitates the study of problematic chemicals in such applications as chemical fate modeling, chemical process design, and experimental design. This volume provides comprehensive coverage of modern biochemical engineering, detailing the basic concepts underlying the behavior of bioprocesses as well as advances in bioprocess and biochemic
| Author | : Magdalena D. Toda |
| Publisher | : CRC Press |
| Total Pages | : 157 |
| Release | : 2017-10-30 |
| Genre | : Mathematics |
| ISBN | : 1498744648 |
This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry. While it focuses on Willmore energy and related conjectures, it also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry. Rather than reproducing published results, it presents new directions, developments and open problems. It addresses questions like: What is new in Willmore theory? Are there any new Willmore conjectures and open problems? What are the contemporary applications of Willmore surfaces? As well as mathematicians and physicists, this book is a useful tool for postdoctoral researchers and advanced graduate students working in this area.
