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Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
Introduction to Geometric Computing
The geometric ideas in computer science, mathematics, engineering, and physics have considerable overlap and students in each of these disciplines will eventually encounter geometric computing problems. The topic is traditionally taught in mathematics departments via geometry courses, and in computer science through computer graphics modules. This text isolates the fundamental topics affecting these disciplines and lies at the intersection of classical geometry and modern computing.
Introduction to Classical Geometries
This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions.
Introduction à la résolution des systèmes polynomiaux = Introduction to solving polynomial systems
This book is an introduction to algebraic methods for solving this type of equations. We show how the geometry of algebraic varieties defined by these equations, their dimension, their degree, or their components can be deduced from the properties of the corresponding quotient algebras. For this, we approach methods of effective algebraic geometry, such as Grobner bases, resolution by eigenvalues and vectors, resultants, bezoutians, duality, Gorenstein algebras and algebraic residues.
Interactive Curve Modeling : With Applications to Computer Graphics, Vision and Image Processing
Interactive curve modeling techniques and their applications are extremely useful in a number of academic and industrial settings, and specifically play a significant role in multidisciplinary problem solving, such as in font design, designing objects, CAD/CAM, medical operations, scientific data visualization, virtual reality, character recognition, and object recognition, etc. Various problems such as iris, fingerprint, and signature recognition, can also be intelligently solved and automated using curve techniques.
Integrated Graphic and Computer Modelling
Full colour throughout, the book explores programming language developments from machine code to more natural language forms, and the basic display operations and commands needed to create effective computer graphic systems. As the visual presentation of real and virtual environments becomes more and more the norm in application systems, a clear understanding of the theory that underpins these techniques is required of all students and practitioners studying and working on large computer systems.
Integral closure : Rees algebras, multiplicities, algorithms
Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.
Integrable Hamiltonian Hierarchies : Spectral and Geometric Methods
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students.
Integer programming and combinatorial optimization ; 9th International IPCO Conference, Cambridge, MA, USA, May 27-29, 2002. Proceedings
This volume contains the papers selected for presentation at IPCO 2002, the NinthInternationalConferenceonIntegerProgrammingandCombinatorial- timization, Cambridge, MA (USA), May 27–29, 2002. The IPCO series of c- ferences highlights recent developments in theory, computation, and application of integer programming and combinatorial optimization. IPCO was established in 1988 when the ?rst IPCO program committee was formed. IPCO is held every year in which no International Symposium on Ma- ematical Programming (ISMP) takes places. The ISMP is triennial, so IPCO conferences are held twice in every three-year period. The eight previous IPCO conferences were held in Waterloo (Canada) 1990, Pittsburgh (USA) 1992, Erice (Italy) 1993, Copenhagen (Denmark) 1995, Vancouver (Canada) 1996, Houston (USA) 1998, Graz (Austria) 1999, and Utrecht (The Netherlands) 2001. In response to the call for papers for IPCO 2002, the program committee received 110 submissions, a record number for IPCO. The program committee met on January 7 and 8, 2002, in Aussois (France), and selected 33 papers for inclusion in the scienti?c program of IPCO 2002. The selection was based on originality and quality, and re?ects many of the current directions in integer programming and combinatorial optimization research.
Integer programming and combinatorial optimization ; 13th International Conference, IPCO 2008 Bertinoro, Italy, May 26-28, 2008 Proceedings
The volume contains the papers selected for presentation at IPCO 2008, the 13th International Conference on Integer Programming and Combinatorial - timization that was held in Bertinoro (Italy), May 26–28, 2008. The IPCO series of conferences, sponsored by the Mathematical Progr- ming Society, highlights recent developments in theory, computation, and app- cation of integer programming and combinatorial optimization. The frst conf- ence took place in 1990; starting from IPCO 1995, the proceedings are published in the Lecture Notes in Computer Science series. The 12 previous IPCO conferences were held in Waterloo (Canada) 1990.
Integer programming and combinatorial optimization ; 12th International IPCO Conference, Ithaca, NY, USA, June 25-27, 2007, Proceedings
Constitutes the refereed proceedings of the 12th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2007, held in Ithaca, NY, USA, in June 2007. This book presents 36 revised full papers that were reviewed and selected from over 120 submissions.
Integer Programming and Combinatorial Optimization ; 11th International IPCO Conference, Berlin, Germany, June 8-10, 2005, Proceedings
Since its start in 1990, the IPCO conference series (held under the auspices of theMathematicalProgrammingSociety)hasbecomeanimportantforumforthe presentation of recent results in Integer Programming and Combinatorial Op- mization. This volume compiles the papers presented at IPCO XI, the eleventh conference in this series, held June 8–10, 2005, at the Technische Universit¨ at Berlin. The high interest in this conference series is evident in the large number of submissions. For IPCO XI, 119 extended abstracts of up to 10 pages were submitted. During its meeting on January 29–30, 2005, the Program Committee carefully selected 34 contributions for presentation in non-parallel sessions at the conference. The ?nal choices were not easy at all, since, due to the limited number of time slots, many very good papers could not be accepted. During the selection process the contributions were refereed according to the standards of refereed conferences. As a result of this procedure, you have in your hands a volume that contains papers describing high-quality research e?orts. The page limit for contributions to this proceedings volume was set to 15. You may ?nd full versions of the papers in scienti?c journals in the near future. We thank all the authors who submitted papers. Furthermore, the Program Committee is indebted to the many reviewers who, with their speci?c expertise, helped a lot in making the decisions.
Instability in Models Connected with Fluid Flows I
Instability in Models Connected with Fluid Flows I presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics. Fields covered include: controllability and accessibility properties of the Navier- Stokes and Euler systems, nonlinear dynamics of particle-like wavepackets, attractors of nonautonomous Navier-Stokes systems, large amplitude monophase nonlinear geometric optics, existence results for 3D Navier-Stokes equations and smoothness results for 2D Boussinesq equations, instability of incompressible Euler equations, increased stability in the Cauchy problem for elliptic equations.
Innovative Superhard Materials and Sustainable Coatings for Advanced Manufacturing ; Proceedings of the NATO Advanced Research Workshop on Innovative Superhard Materials and Sustainable Coating, Kiev, Ukraine,12 - 15 May 2004.
Modern industry imposes ever increasing requirements upon tools and tool materials as to the provision for performance under the conditions of high cutting speeds and dynamic loads as well as under intensive thermal and chemical interactions with workpiece materials. The industry demands a higher productivity in combination with the accuracy of geometry and dimensions of workpieces and quality of working surfaces of the machined pieces. These requirements are best met by the tool superhard materials (diamond and diamond-like cubic boron nitride). Ceramics based on silicon carbide, aluminum and boron oxides as well as on titanium, silicon and aluminum nitrides offer promise as tool materials. Tungsten-containing cemented carbides are still considered as suitable tool materials. Hi- hardness and high strength composites based on the above materials fit all the requirements imposed by machining jobs when manufacturing elements of machinery, in particular those operating under the extreme conditions of high temperatures and loads.
Information Geometry : Near Randomness and Near Independence
This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.
Infinite groups : geometric, combinatorial and dynamical aspects
This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others.
Index and Stability in Bimatrix Games : A Geometric-Combinatorial Approach
The contribution of this thesis can be divided into two parts. The first part concerns methods and techniques. By introducing a new geometriccombinatorial construction for bimatrix games, this thesis gives a new, intuitive re-interpretation of the index. This re-interpretation is to a large extent self-contained and does not require a background in algebraic topology. The second part of this thesis concerns the relationship between the index and strategic properties. In this context, the thesis provides two new results, both of which are obtained by means of the new construction and are explained in further detail below. The first result shows that, in non-degenerate bimatrix games, the index can fully be described by a simple strategic property.
Imagination and Rigor : Essays on Eduardo R. Caianiello's Scientific Heritage
The aim of this Volume of scientific essays is twofold. From one side, by remembering the scientific figure of Eduardo R. Caianiello, it aims at focusing his outstanding contributions - from theoretical physics to cybernetics - which after so many years still represent occasion of innovative paths to be fruitfully followed. It must be stressed the contribution that his interdisciplinary methodology can still be of great help in affording and solving present day complex problems. On the other side, it aims at pinpointing with the help of the scientists contributing to the Volume - some crucial problems in present day research in the fields of interest of Eduardo Caianiello and which are still among the main lines of investigation of some of the Istitutes founded by Eduardo (Istituto di Cibernetica del CNR, IIAS, etc).
Il senso e la narrazione = The sense and the narration
Humans are creatures of narration: infinitely they narrate and narrate themselves, intertwine dialogues, light up stories to illuminate the dark caves of the heart and the world, recover and transmute memories. We live between a firm and rough, unknowable reality, an enormous furnace of perturbations and calls and colors, and an elusive, delicate and ephemeral interiority: and between the two, between the world and us, we weave with thought and with words a fragile ponte, a bridge called sense. Swing this bridge at the unequal breath of a cosmic wind, dropping phosphoric fragments: sudden hourglasses, anonymous centaurs, sleepless geometers, distant syllogisms, vanished lineages, black basalts, crazy anchorites, silent plesiosaurs, flutes and bagpipes ... and they recompose figures, and we ask ourselves questions about those figures and tell stories. Only the vertigo of asking and narrating can give meaning to a life that some say is interwoven with pure chance. Forever detached from the flourishing matrix of the world, tormented by thought, prisoners of words, slaves of interpretation, lost in a long corridor of facing mirrors: we are at the center of a great, incomprehensible rumble.
Idempotent matrices over complex group algebras
The study of idempotent elements in the group algebras originates from geometric and analytic considerations. … This book provides an introduction to the study of these problems.It collects and presents in a systematic way basic techniques and important results that have been obtained during the past few decades.The book is suitable for independent study. Moreover, all chapters and appendices finish with a sufficient number of exercises that also increase the quality of the book.
