Arnold Neumaier - Böcker

Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

This monograph introduces mathematicians, physicists, and engineers to the ideas relating quantum mechanics and symmetries - both described in terms of Lie algebras and Lie groups. The exposition of quantum mechanics from this point of view reveals that classical mechanics and quantum mechanics are very much alike. Written by a mathematician and a physicist, this book is (like a math book) about precise concepts and exact results in classical mechanics and quantum mechanics, but motivated and discussed (like a physics book) in terms of their physical meaning. The reader can focus on the simplicity and beauty of theoretical physics, without getting lost in a jungle of techniques for estimating or calculating quantities of interest.

This book introduces mathematicians, physicists, and philosophers to a new, coherent approach to theory and interpretation of quantum physics, in which classical and quantum thinking live peacefully side by side and jointly fertilize the intuition. The formal, mathematical core of quantum physics is cleanly separated from the interpretation issues. The book demonstrates that the universe can be rationally and objectively understood from the smallest to the largest levels of modeling. The thermal interpretation featured in this book succeeds without any change in the theory. It involves one radical step, the reinterpretation of an assumption that was virtually never questioned before - the traditional eigenvalue link between theory and observation is replaced by a q-expectation link: Objective properties are given by q-expectations of products of quantum fields and what is computable from these. Averaging over macroscopic spacetime regions produces macroscopic quantities with negligible uncertainty, and leads to classical physics. - Reflects the actual practice of quantum physics. - Models the quantum-classical interface through coherent spaces. - Interprets both quantum mechanics and quantum field theory. - Eliminates probability and measurement from the foundations. - Proposes a novel solution of the measurement problem.

This book constitutes the thoroughly refereed post-proceedings of the First International Workshop on Global Constraints Optimization and Costraint Satisfaction, COCOS 2002, held in Valbonne-Sophia Antipolis, France in October 2002.The 15 revised full papers presented together with 2 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address current issues in global optimization, mathematical programming, and constraint programming; they are grouped in topical sections on optimization, constraint satisfaction, and benchmarking.

Theformulationofmanypracticalproblemsnaturallyinvolvesconstraintsonthe variables entering the mathematical model of a real-life situation to be analyzed. It is of great interest to ?nd the possible scenarios satisfying all constraints, and, iftherearemanyofthem,eitherto?ndthebestsolution,ortoobtainacompact, explicit representation of the whole feasible set. The 2nd Workshop on Global Constrained Optimization and Constraint S- isfaction, COCOS 2003, which took place during November 18–21, 2003 in L- sanne, Switzerland, was dedicated to theoretical, algorithmic, and application oriented advances in answering these questions. Here global optimization refers to ?nding the absolutely best feasible point, while constraint satisfaction refers to?ndingallpossiblefeasiblepoints.AsinCOCOS2002,the?rstsuchworkshop (see the proceeedings [1]), the emphasis was on complete solving techniques for problems involving continuous variables that provide all solutions with full rigor, and on applications which, however, were allowed to have relaxed standards of rigor. The participants used the opportunity to meet experts from global optimi- tion, mathematical programming, constraint programming, and applications, and to present and discuss ongoing work and new directions in the ?eld. Four invited lectures and 20 contributed talks were presented at the workshop. The invited lectures were given by John Hooker (Logic-Based Methods for Global Optimization), Jean-Pierre Merlet (Usual and Unusual Applications of Interval Analysis), Hermann Schichl (The COCONUT Optimization Environment), and Jorge Mor´ e (Global Optimization Computational Servers). This volume contains the text of Hooker’s invited lecture and of 12 c- tributed talks. Copies of the slides for most presentations canbe found at [2]. Constraintsatisfactionproblems.Threepapersfocusonalgorithmicaspects of constraint satisfaction problems.