Series: Springer Proceedings in Mathematics & Statistics, Vol. 43
2013, X, 340 p. 7 illus.
Hardcover
ISBN 978-1-4614-6641-3
Due: May 31, 2013
Collects contributions based on the proceedings of "International Number Theory Conference in Memory of Alf van der Poorten"
These proceedings will presents high quality research articles and comprehensive surveys from distinguished mathematicians in order to promote number theory and related topics
The subjects of these articles and surveys are inspired by Alf van der Poorten's wide area of research interests, including number theory, continued fractions, elliptic curves and more
Number Theory and Related Fields collects contributions based on the proceedings of the “International Number Theory Conference in Memory of Alf van der Poorten,” hosted by CARMA and held March 12?16, 2012, at the University of Newcastle, Australia. The purpose of the conference was to commemorate the research and influence of Alf van der Poorten in number theory and in general mathematics and presented an exciting venue for promoting number-theoretic research and graduate study in Australia. Comprehensive accounts of recent achievements in theoretical and computational number theory and its applications to cryptography and theoretical computer science were also paramount to the conference.
The volume begins with a detailed academic appreciation of van der Poorten’s life and work, and includes research articles written by some of the most distinguished mathematicians in the field of number theory. Contributions also include related topics that focus on the various research interests of van der Poorten, such as continued fractions and elliptic curves. Researchers in number theory and its applications will find this Proceedings of great interest.
Preface.- Life and Mathematics of Alfred Jacobus van der Poorten (D. Hunt).- Ramanujan-Sato-Like Series (G. Almkvist, J. Guillera).- On the Sign of the Real Part of the Riemann Zeta Function (J. Arias de Reyna, R.P. Brent, J. van de Lune).- Additive Combinatorics with a View Toward Computer Science and Cryptography (K. Bibak).- Transcendence of Stammering Continued Fractions (Y. Bugeaud).- Algebraic Independence of Infinite Products and Their Derivatives (P. Bundschuh).- Small Representations by Indefinite Ternary Quadratic Forms (J.B. Friedlander, H. Iwaniec).- Congruences for Andrews' SPT-Function Modulo 32760 and Extension of Atkin's Hecke-Type Partition Congruences (F.G. Garvan).- Continued Fractions and Dedekind Sums for Function Fields (Y. Hamahata).- Burgess's Bounds for Character Sums (D.R. Heath-Brown).-Structured Hadamard Conjecture (I.S. Kotsireas).- Families of Cubic Thue Equations with Effective Bounds for the Solutions (C. Levesque, M. Waldschmidt).- Consequences of a Factorization Theorem for Generalized Exponential Polynomials with Infinitely Many Integer Zeros (V. Laohakosol, O. Phuksuwan).- On Balanced Subgroups of the Multiplicative Group (C. Pomerance, D. Ulmer).- Some Extensions of the Lucas Functions (E.L. Roettger, H.C. Williams, R.K. Guy).- The Impact of Number Theory and Computer-Aided Mathematics on Solving the Hadamard Matrix Conjecture (J. Seberry).- Description of Generalized Continued Fractions by Finite Automata (J. Shallit).- Some Notes on Weighted Sum Formulae for Double Zeta Values (J. Wan).- Period(d)ness of L-Values (W. Zudilin).
Series: Springer Series in Computational Mathematics, Vol. 44
2013, XIII, 673 p. 67 illus., 8 in color.
Hardcover
ISBN 978-3-642-36518-8
Due: May 31, 2013
.A self contained presentation of the mathematical theory of mixed FEM
Applications to elliptic problems, elasticity, electromagnetism, Stokes' problem
An augmented version of a classical book?
Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
Preface.- Variational Formulations and Finite Element Methods.- Function Spaces and Finite Element Approximations.- Algebraic Aspects of Saddle Point Problems.- Saddle Point Problems in Hilbert spaces.- Approximation of Saddle Point Problems.- Complements: Stabilisation Methods, Eigenvalue Problems.- Mixed Methods for Elliptic Problems.- Incompressible Materials and Flow Problems.- Complements on Elasticity Problems.- Complements on Plate Problems.- Mixed Finite Elements for Electromagnetic Problems.- Index.
Series: Springer Proceedings in Mathematics & Statistics, Vol. 45
2013, XII, 350 p. 30 illus.
Hardcover
ISBN 978-1-4614-7171-4
Due: May 31, 2013
Provides a broad spectrum of numerical techniques and real life applications of these techniques
All fundamentally important aspects of numerical modeling of physical phenomena described by partial differential equations are covered
Additionally, some state-of-the-art numerical multiscale discretization and solution techniques are presented ?
One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time-dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles, and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability, and robustness of the algorithms in porous media, structural mechanics, and electromagnetism are presented.
Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.
Improving Conservation for First-Order System Least Squares Finite-Element Methods, James Adler, Panayot Vassilevski.- Multiscale Coarsening for Linear Elasticity by Energy Minimization, Heiko Andrae, Marco Buck, Oleg Iliev.- Preconditioners for some matrices of two-by-two block form, with applications, I, Owe Axelsson.- A multigrid algorithm for an elliptic problem with a perturbed boundary condition, Andrea Bonito, Joe Pasciak.- Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs, James Brannick, Yao Chen, Xiaozhe Hu, Ludmil Zikatanov.- Aspects of Guaranteed Error Control in Computational Partial Differential Equations, Carsten Carstensen, Christian Merdon, Johannes Neumann.- A Finite Volume Element Method for a Nonlinear Parabolic Problem, Panagiotis Chatzipantelidis, Victor Ginting.- Multidimensional Sensitivity Analysis of Large-scale Mathematical Models, Ivan Dimov, Rayna Georgieva.- Structures and waves in a nonlinear heat-conducting medium, Stefka Dimova, Milena Dimova, Daniela Vasileva.- Efficient parallel algorithms for unsteady incompressible flows, Jean-Luc Guermond, Peter Minev.- Efficient solvers for some classes of time-periodic eddy current optimal control problems.- Michael Kolmbauer, Ulrich Langer.- Robust Algebraic Multilevel Preconditioners for Anisotropic Problems, Johannes Kraus, Maria Lymbery, Svetozar Margenov.- A weak Galerkin mixed finite element method for biharmonic equations, Lin Mu, Junping Wang, Yanqiu Wang, Xiu Ye.- Domain decomposition scheme for first order evolution equations with nonselfadjoint operators, Petr Vabishchevich, Petr Zakharov.- Spectral coarse spaces in robust two-level methods, Joerg Willems.
Series: Texts in Applied Mathematics, Vol. 58
2013, XVIII, 186 p. 13 illus., 1 in color.
Hardcover
ISBN 978-1-4614-6979-7
Due: May 31, 2013
.Exercises are included at the end of each chapter
An unusual feature of the book is its treatment of the effect of temporal correlations
Ideas are presented within a clean, clear, and systematic framework
"Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization, basic statistical mechanics, and generalized Langevin equations and the Mori-Zwanzig formalism. The applications include sampling algorithms, data assimilation, prediction from partial data, spectral analysis, and turbulence.
The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications.
For this new edition the material has been thoroughly reorganized and updated, and new sections on scaling, sampling, filtering and data assimilation, based on recent research, have been added. There are additional figures and exercises.
Preliminary.- Probability.- Brownian Motion.- Stationary Stochastic Processes.- Statistical Mechanics.- Index.- Time-Dependent Statistical Mechanics.
Series: Applied Mathematical Sciences, Vol. 184
2013, X, 290 p. 18 illus., 11 in color.
Hardcover
ISBN 978-1-4614-6991-9
Due: May 31, 2013
Authored by two leading active researchers
Self-contained and with most recent results on state-dependent delay equations and global bifurcations
Contains theory and some related applications
This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters. The book aims to be self-contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).
Content Level ≫ Research
Keywords ≫ Bifurcation Systems with Delay - Bifurcation Theory in ODE - Functional Differential Equations - Lyapunov-Schmidt Reduction
Related subjects ≫ Dynamical Systems & Differential Equations
Introduction to Dynamic Bifurcation Theory.- Introduction to Functional Differential Equations.-Center Manifold Reduction.- Normal form theory.- Lyapunov-Schmidt Reduction.- Degree theory.- Bifurcation in Symmetric FDEs?.