Lecture Notes

This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface ge

Climate change is mainly caused by emissions of CO2 from burning fossil fuels, which provides over 85% of the world’s energy. Strategies for mitigating climate change are connected with handling econo

Kinetic Monte Carlo (kMC) simulations still represent a quite new area of research, with a rapidly growing number of publications. Broadly speaking, kMC can be applied to any system describable as a s

As usual, some of the contributions to this 44th Seminaire de Probabilites were presented during the Journees de Probabilites held in Dijon in June 2010. The remainder were spontaneous submissions or

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolutio

Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens ou

The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet

Stochastic Energetics by now commonly designates the emerging field that bridges the gap between stochastic dynamical processes and thermodynamics.Triggered by the vast improvements in spatio-temporal

The basic idea, simple and revolutionary at the same time, to replace the concept of a point particle with a one-dimensional string, has opened up a whole new field of research. Even today, four decad

Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning at an introductory level suitable for student

In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.

The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful

Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary parti

Over the years enormous effort was invested in proving ergodicity, but for a number of reasons, con?dence in the fruitfulness of this approach has waned. — Y. Ben-Menahem and I. Pitowsky [1] Abstract

Not only does this monograph provide a general analysis of random effects in mechanical (engineering) systems, but it addresses deep questions concerning the nature of randomness, and gives potentiall

The lattice formulation is at present the most successful approach to Quantum Chromodynamics - the theory of quarks and gluons. This book is intended for newcomers to the field and presents a clear an

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well asan overview of classical and recent results on some aspects of the approximation of functio

Following the pioneering discovery of alpha clustering and of molecular resonances, the field of nuclear clustering is today one of those domains of heavy-ion nuclear physics that faces the greatest c

There have been many significant advances in time-dependent density functional theory over recent years, both in enlightening the fundamental theoretical basis of the theory, as well as in computation

The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009.Complex systems arise in sever

This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting

Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective

Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analy

In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic

Der Weg von der Inbetriebnahme eines Prozessorsystems bis zur Implementierung einer Human Machine Interface (HMI) bildet den Schwerpunkt dieses Werks. Der Autor erlautert, wie Treiber und Betriebssyst

Condensed matter systems where interactions are strong are inherently difficult to analyze theoretically. The situation is particularly interesting in low-dimensional systems, where quantum fluctuatio

This book arises as the natural continuation of the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place in Toledo (Spain) in March 2010. T

In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of sever

The measurement of spin-polarization observables in reactions of nuclei and particles is of great utility and advantage when the effects of single-spin sub-states are to be investigated. Indeed, the

This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972–1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy o

Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical

The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory pla

This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and

This volume deals with the theory of finite topological spaces and itsrelationship with the homotopy and simple homotopy theory of polyhedra.The interaction between their intrinsic combinatorial and t

Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognize