Series: Bolyai Society Mathematical Studies , Vol. 17
2008, Approx. 290 p., Hardcover
ISBN: 978-3-540-77199-9
Due: February 2008
About this book
Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry as well.
The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives a very good overview of recent trends and results in a large part of combinatorics and related topics, and offers an interesting reading for experienced specialists as well as to young researchers and students.
Written for:
Researchers and graduate students in combinatorics, discrete mathematics, set theory, probabilistic methods and stochastic structures
Table of contents
V. Csiszar, L. Rejt and G. Tusnady: Statistical Inference on Random Structures.- L. Addario-Berry, B. A. Reed: Ballot Theorems, Old and New.- R. Graham: Old and New Problems and Results in Ramsey Theory.- A. Seress: Polygonal Graphs.- N. Tokushige: The Random Walk Method for Intersecting Families.- Zs. Tuza and V. Voloshin: Problems and Results on Colorings of Mixed Hypergraphs.- J. Fox and J. Pach: Erd s--Hajnal-type Results on Intersection Patterns of Geometric Objects.- Y. Egawa: Proof Techniques for Factor Theorems.- L. Soukup: Infinite Combinatorics: From Finite to Infinite.- A. Recski: Combinatorial Conditions for the Rigidity of Tensegrity Frameworks.- G. O. H. Katona: Forbidden Intersection Patterns in the Families of Subsets (Introducing a Method).- V. Vu: Random Discrete Matrices.- D. Miklos: Subsums of a finite sum and extremal sets of vertices of the hypercube.
Series: Universitext
5th ed., 2008, XIV, 588 p. 14 illus., 4 in color., Softcover
ISBN: 978-3-540-77340-5
Due: March 5, 2008
About this textbook
Established textbook
Continues to lead its readers to some of the hottest topics of contemporary mathematical research
This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research.This new edition introduces and explains the ideas of the parabolic methods that have recently found such a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.
From the reviews:
"This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. [..] The book is made more interesting by the perspectives in various sections." Mathematical Reviews
Table of contents
Series: The Frontiers Collection
2008, Approx. 320 p. 86 illus., Hardcover
ISBN: 978-3-540-75972-0
Due: March 12, 2008
About this book
When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. In fact, modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. It is shown that the Universe cannot possess exact symmetry, which is a principle of fundamental significance. Curie's principle - which states that the symmetry of the effect is at least that of the cause - features prominently. An introduction to group theory, the mathematical language of symmetry, is included. This book will convince all interested readers of the importance of symmetry in science. Furthermore, it will serve as valuable background reading for all students in the physical sciences.
Table of contents
Series: Publications of the Scuola Normale Superiore
Subseries: Theses (Scuola Normale Superiore) , Vol. 5
2008, Approx. 185 p., Softcover
ISBN: 978-88-7642-319-2
About this book
The experimental achievement of Bose-Einstein condensation (1995) and of Fermi degeneracy (1999) in ultra-cold, dilute gases has opened a new field in atomic physics and condensed matter physics. In this thesis, first we present an overview of theoretical and experimental facts on ultra-cold atomic gases. We then describe a Green's function scheme to study coherent transport by fermions through a one-dimensional array of potential wells. Within this scheme different geometries for the array like single-period, double-period and Fibonacci-ordered quasi-periodic array, are considered. A novel spin-density-functional approach is applied to the study of Fermi gases inside one-dimensional optical lattices.
This approach enables us to investigate both repulsive and attractive Fermi gases within a local-spin-density approximation. We analyze different phases caused by spin-dependent trap for repulsive gas and also by spin-imbalanced population for attractive gas.
Written for:
Graduate students and researchers in condensed matter physics and chemistry
Table of contents
Preface.- 1. Reviews on Ultra-cold quantum gases.- 2. Theory of matter transport in quasi-1D arrays.- 3. Density-functional theory of 1D Fermi gases.- 4. Ultra-cold attractive fermions in 1D optical lattices.
Series: Trends in Logic , Vol. 26
2008, 248 p., Hardcover
ISBN: 978-1-4020-6866-9
Due: March 2008
About this book
This book presents the author’s recent investigations of the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity (L.E.J. Brouwer) and the strong negation (D. Nelson) are studied in the setting of paraconsistent logic.
The paraconsistent logics are those, which admit inconsistent but non-trivial theories, i.e., the logics which allow making inferences in non-trivial fashion from an inconsistent set of hypotheses. Logics in which all inconsistent theories are trivial are called explosive. In the intuitionistic logic Li, the negation is defined as reduction to absurdity. The concept of strong negation is realized in the Nelson logic N3. Both logics are explosive and have paraconsistent analogs: Johansson’s logic Lj and paraconsistent Nelson’s logic N4. It will be shown that refusing the explosion axiom "contradiction implies everything" does not lead to decrease of the expressive power of a logic. To understand, which new expressive possibilities have the logics Lj and N4 as compared to the explosive logics Li and N3, we study the lattices of extensions of the logics Lj and N4. This is the first case when lattices of paraconsistent logics are systematically investigated. The study is based on algebraic methods, demonstrates the remarkable regularity and the similarity of structures of both lattices of logics, and gives essential information on the paraconsistent nature of logics Lj and N4.
The methods developed in this book can be applied for investigation of other classes of paraconsistent logics.
Table of contents
1. Introduction.- Part I. Reductio ad Absurdum.- 2. Minimal Logic. Preliminary Remarks.- 3. Logic of Classical Refutability.- 4. The Class of Extensions of Minimal Logic.- 5. Adequate Algebraic Semantics for Extensions of Minimal Logic.- 6. Negatively Equivalent Logics.- 7. Absurdity as Unary Operator.- Part II. Strong Negation.- 8. Semantical Study of Paraconsistent Nelson's Logic.- 9. N4-Lattices.- 10. The Class of N4-Extensions.- References.- Subject Index.