Asterisque, Volume: 376
2016; 340 pp; Softcover
MSC: Primary 53; 14; 37;
Print ISBN: 978-2-85629-825-1
In this volume, the authors study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. They construct a natural isomorphism between the Frobenius manifold structures of the (big) quantum cohomology of the toric manifold and of Saito's theory of singularities of the potential function constructed in [Fukaya, Tohoku Math. J. 63 (2011)] via the Floer cohomology deformed by ambient cycles. Their proof of the isomorphism involves the open-closed Gromov?Witten theory of one-loop.
A publication of the Societe Mathematique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in the Lagrangian Floer theory and mirror symmetry.
Research and Exposition in Mathematics -- Volume 35
ii+204 pages, soft cover, ISBN 978-3-88538-235-5,
Propositional logics, both classical and non-classical, usually do not incorporate the dimension of time. However, even Aristotle already mentioned that time plays an important role in the evaluation of truth values of propositions. His well-known example was the statement ?There will be a sea battle tomorrowg. Certainly, tomorrow it will be clear if this proposition is true or false, but today we cannot assign one of these values. Therefore, he accepted that two-valued logic cannot capture the entire human thinking.
After Aristotle's time, a lot was created by men and, nowadays, logic is not an exceptional area for human reasoning. From the 1940's on, computers were built and the era of the Artificial Intelligence gently started. Nowadays, practically any more advanced product contains some kind of processor which decides situations in a way similar to that of a human being. However, for such technical devices the forecast for truth values of propositions in the future is not only a speculation. Due to the constructions and the technical possibilities, we can often compute these values, and propositions concerning the near future are of great importance for the control of these systems. This has motivated many authors to investigate the so-called temporal logic, i.e., the logic where time is considered as a variable of the propositional formula.
Tense logic was introduced by Arthur Prior in the late 1950's as a result of his interest in the relationship between tense and modality. The logical language of tense logic contains, in addition to the ususal truth-functional operators, four the so-called modal operators.
The aim of this monograph is not to present tense logic in full detail. As Aristotle's logic was useful for two millennia in science, but for computer programming only its formalization via Boolean algebras is applied, we will present only an algebraic axiomatization of tense logic and tense operators here. Classical propositional logic was axiomatized by George Boole via Boolean algebras, but this was only a starting point for the formalization of logic. In 1930 intuitionistic logic was formalized by the use of Heyting algebras, in the late 1950's the many-valued Lukasiewicz logic was axiomatized by C. C. Chang by the so-called MV-algebras, many-valued Post logic by Post algebras and in recent decades fuzzy logic, relevance logic, Hajek's basic logic and linear logic by residuated lattices. Hence, we will use algebraic tools for the axiomatization of tense operators. Using the fact that these are modal operators, we will axiomatize also modal operators in this way. Since all of these operators can be considered as quantifiers, we will start with the axiomatization of quantifiers developed by P. Halmos and J. D. Rutledge. Our algebraic methods and tools will be described in full detail, without taking into account whether the reader is or is not a specialist in lattice theory.
The authors hope that their monograph will not be the final attempt at the field of modal and tense operators and the development of corresponding algebraic tools and methods but, on the contrary, it will serve as a compendium and, possibly, a motivation for the readers for their future research.
Advanced Lectures in Mathematics, Volume 34
Published: 14 March 2016
ISBN-13,9781571463159
Paperback
462 pages
This volume describes some recent developments in harmonic analysis and its applications to partial differential equations and geometric analysis. Subjects covered include: local Tb theorems in non-homogeneous or vector-valued setting, multilinear embedding theorems, norm estimates of quasi-modes on Riemannian manifolds, Calderon?Zygmund singular integral operators and commutators, Dirichlet-to-Neumann maps, multilinear and multi-parameter Fourier multipliers, weighted normed inequalities, nonlinear Schrodinger equations, function space theory, etc.
Some Topics in Harmonic Analysis and Applications makes an excellent reference for mathematicians, and graduate students, and post-doctorals working in analysis, PDEs, and related areas.
This volume is part of the Advanced Lectures in Mathematics book series.
ISBN: 978-1-84821-818-5
232 pages
May 2016, Wiley-ISTE
This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system.
The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications.
This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.
PART 1. INTRODUCTION AND EXAMPLES
Chapter 1. Introduction
Chapter 2. Examples of Inverse Problems
PART 2. LINEAR INVERSE PROBLEMS
Chapter 3. Integral operators and equations
Chapter 4. Linear Least Squares Problems Singular Value Decomposition
Chapter 5. Linear Inverse Problems
PART 3. NONLINEAR INVERSE PROBLEMS
Chapter 6. Nonlinear Inverse Problems General Aspects
Chapter 7. Examples of Parameter Estimation
See More
Hardback
Published: 09 June 2016 (Estimated)
288 Pages
234x156mm
ISBN: 9780198759591
The contributions in this volume have been written by world leading experts in the field.
Cutting edge research on scope and limits of mathematical knowledge.
Extended introduction to key problems, arguments, and positions.
Clear structure through the whole collection of articles.
The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
Algorithm, consistency and epistemic randomness
1: Dean: ALGORITHMS AND THE MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
2: Visser: THE SECOND INCOMPLETENESS THEOREM REFLECTIONS AND RUMINATIONS
3: Moschovakis: ITERATED DEFINABILITY, LAWLESS SEQUENCES AND BROUWER'S CONTINUUM
4: Achourioti: A SEMANTICS FOR IN PRINCIPLE PROVABILITY
Mind and Machines
5: Carlson: Collapsing Knowledge and Epistemic Church's Thesis
6: Koellner: G odel's Disjunction
7: Shapiro: Idealization, mechanism, and knowability
Absolute Undecidability
8: Leach-Krouse: PROVABILITY, MECHANISM AND THE DIAGONAL PROBLEM
9: Williamson: Absolute Provability and Safe Knowledge of Axioms
10: Antonutti, Horsten: Epistemic Church's Thesis and Absolute Undecidability