الصفحة 4
الصفحة 4
Formal Methods in Software and Systems Modeling : Essays Dedicated to Hartmut Ehrig on the Occasion of His 60th Birthday
By presenting state-of-the-art research results on various aspects of formal and visual modeling of software and systems, this book commemorates the 60th birthday of Hartmut Ehrig. The 24 invited reviewed papers are written by students and collaborators of Hartmut Ehrig who are established researchers in their fields. Reflecting the scientific interest and work of Hartmut Ehrig, the papers fall into three main parts on graph transformation, algebraic specification and logic, and formal and visual modeling.
Formal Methods for Open Object-Based Distributed Systems ; 9th IFIP WG 6.1 International Conference, FMOODS 2007, Paphos, Cyprus, June 6-8, 2007, Proceedings
This book constitutes the refereed proceedings of the 9th IFIP WG 6.1 International Conference on Formal Methods for Open Object-Based Distributed Systems, FMOODS 2007, held in Paphos, Cyprus in June 2007. The papers are organized in topcical sections on model checking rewriting logic components and services algebraic calculi specification, verification and refinenment, and quality of service.
Formal Methods and Testing : An Outcome of the FORTEST Network, Revised Selected Papers
This book constitutes the thoroughly refereed and peer-reviewed outcome of the Formal Methods and Testing (FORTEST) network - formed as a network established under UK EPSRC funding that investigated the relationships between formal (and semi-formal) methods and software testing - now being a subject group of two BCS Special Interest Groups: Formal Aspects of Computing Science (BCS FACS) and Special Interest Group in Software Testing (BCS SIGIST).
Formal Concept Analysis ; 6th International Conference, ICFCA 2008, Montreal, Canada, February 25-28, 2008. Proceedings
Formal Concept Analysis (FCA) is a mathematical theory of concepts and c- ceptual hierarchyleadingto methods for conceptually analyzing data and kno- edge. The theory itselfstronglyreliesonorder and lattice theory,whichhasbeen studied by mathematicians over decades. FCA proved itself highly relevant in several applications from the beginning , and, over the last years, the range of application shaskept growing. The mainreasonfor this comesfromthe fact that our modern society has turned into an “information” society. After years and years of using computers, companies realized they had stored gigantic amounts of data.
FM 2006: Formal Methods ; 14th International Symposium on Formal Methods, Hamilton, Canada, August 21-27, 2006, Proceedings
This book presents the refereed proceedings of the 14th International Symposium on Formal Methods, FM 2006, held in Hamilton, Canada, August 2006. The book presents 36 revised full papers together with 2 invited contributions and extended abstracts of 7 invited industrial presentations, organized in topical sections on interactive verification, formal modelling of systems, real time, industrial experience, specification and refinement, programming languages, algebra, formal modelling of systems, and more.
Field Arithmetic ; 3rd ed.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.
Field Arithmetic ; 2nd ed.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Evolutionary Equations : Picard's Theorem for Partial Differential Equations, and Applications
This book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner.
Evolution Algebras and their Applications
Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.
Essential Topology
Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated ""Hairy Ball theorem"" and on to homotopy and homology: the cornerstones of contemporary algebraic topology. While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student, reflecting the fact that these are often the key examples behind current research.
Essays in Constructive Mathematics
This book aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it, by basing all definitions and proofs on finite algorithms. The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving integrals and differentials as it does, might seem to call for infinite processes. In this case too, however, finite algorithms suffice to define the genus of an algebraic curve, to prove that birationally equivalent curves have the same genus, and to prove the Riemann-Roch theorem. The main algorithm in this case is Newton's polygon, which is given a full treatment. Other topics covered include the fundamental theorem of algebra, the factorization of polynomials over an algebraic number field, and the spectral theorem for symmetric matrices.
Error-Correcting Linear Codes : Classification by Isometry and Applications
This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players. The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes.
Equidistribution in Number Theory, An Introduction
This volume presents details of the lecture series that were given at the school. Across the broad panorama of topics that constitute modern number t- ory one nds shifts of attention and focus as more is understood and better questions are formulated. Over the last decade or so we have noticed incre- ing interest being paid to distribution problems, whether of rational points, of zeros of zeta functions, of eigenvalues, etc. Although these problems have been motivated from very di?erent perspectives, one nds that there is much in common, and presumably it is healthy to try to view such questions as part of a bigger subject.
Enumerative Invariants in Algebraic Geometry and String Theory : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 6–11, 2005
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Dynamic brain : From neural spikes to behaviors ; 12th International Summer School on Neural Networks, Erice, Italy, December 5-12, 2007, Revised Lectures
The volume presents 12 thoroughly revised tutorial papers based on lectures given by leading researchers at the 12th International Summer School on Neural Networks in Erice, Italy, in December 2007.
D-Modules, Perverse Sheaves, and Representation Theory
D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. Significant concepts and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using D-module theory.
Discovering Mathematics with Magma : Reducing the Abstract to the Concrete
This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. The book range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.
Digital self-tuning controllers : Algorithms, implementation and applications
Digital Self-tuning Controllers presents you with a complete course in self-tuning control, beginning with a survey of adaptive control and the formulation of adaptive control problems. Modelling and identification are dealt with before passing on to algebraic design methods and particular PID and linear-quadratic forms of self-tuning control. Finally, laboratory verification and experimentation will show you how to ground your theoretical knowledge in real plant control.
Differential Analysis on Complex Manifolds
In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.
Difference Algebra
This book reflects the contemporary level of difference algebra; it contains a systematic study of partial difference algebraic structures and their applications, as well as the coverage of the classical theory of ordinary difference rings and field extensions. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. It will be also of interest to researchers in computer algebra, theory of difference equations and equations of mathematical physics. The book is self-contained; it requires no prerequisites other than knowledge of basic algebraic concepts and mathematical maturity of an advanced undergraduate.
