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From Geometry to quantum mechanics : In Honor of Hideki Omori
This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics that have been arranged in celebration of Hideki Omori's recent retirement from Tokyo University of Science and in honor of his fundamental contributions to these areas.The papers focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, infinite-dimensional Lie group theory, quantizations and noncommutative geometry, as well as applications of partial differential equations and variational methods to geometry.
Frobenius Splitting Methods in Geometry and Representation Theory
The theory of Frobenius splittings has made a significant impact in the study of the geometry of flag varieties and representation theory. This work, unique in book literature, systematically develops the theory and covers all its major developments.
Fracture Mechanics : Inverse Problems and Solutions
This book presents, in a unified manner, a variety of topics in Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems.
Fractals in Biology and Medicine : Beyond Planting Trees
This volume it highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions, including the structural changes that occur in tumours. It helps develop the concepts, questions and methods required in research on fractal biology and natural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine. It discusses present and future applications of fractal geometry, bringing together cellular and molecular biology, engineering, mathematics, physics, medicine and other disciplines and allowing an interdisciplinary vision.
Fractal Geometry, Complex Dimensions and Zeta Functions : Geometry and Spectra of Fractal Strings
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key Features The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra Explicit formulas are extended to apply to the geometric, spectral, and dynamical zeta functions associated with a fractal Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric tube formula The method of Diophantine approximation is used to study self-similar strings and flows Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functions Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts, and discusses several open problems and extensions.
Foundations of information and knowledge systems ; 5th International Symposium, FoIKS 2008, Pisa, Italy, February 11-15, 2008. Proceedings
This book constitutes the refereed proceedings of the 5th International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2008 held in Pisa, Italy, in February 2008. The 13 revised full papers presented together with 9 revised short papers and 3 invited lectures were carefully selected during two rounds of reviewing and improvement from from 79 submissions. The papers deal with any foundational aspect of information and knowledge systems, including submissions from researchers working in fields such as discrete mathematics, logic and algebra, model theory, information theory, complexity theory, algorithmics and computation, geometry, analysis, statistics and optimisation who are interested in applying their ideas, theories and methods to research on information and knowledge systems.
Foundations of Hyperbolic Manifolds
The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow’s rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare«s fundamental polyhedron theorem.
Foundation Mathematics for Computer Science : A Visual Approach
In this second edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the original book and written new chapters on combinatorics, probability, modular arithmetic and complex numbers. These subjects complement the existing chapters on number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers.
Foliations and Geometric Structures
Offers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.
Fluctuations, Information, Gravity and the Quantum Potential
A main theme of the book outlines the role of the quantum potential in quantum mechanics and general relativity and one of its origins via fluctuations formulated in terms of Fisher information. Another theme is the description of various approaches to Bohmian mechanics and their role in quantum mechanics and general relativity. Along the way various approaches to, for instance, the Dirac equation, the Einstein equations, the Klein-Gordon equation, the Maxwell equations and the Schr?dinger equations are described. Statistics and geometry are intertwined in various ways and, among other matters, the aether, cosmology, entropy, fractals, quantum Kaehler geometry, the vacuum and the zero point field are discussed. There is also some speculative material and some original work along with material extracted from over 1000 references and the work is current up to April 2005.
Flow and transport processes with complex obstructions : Applications to cities, vegetative canopies and industry
The NATO Advanced Study Institute “Flow and Transport Processes in Complex - structed Geometries: from cities and vegetative canopies to engineering problems” was held in Kyiv, Ukraine in the period of May 4 - 15, 2004. This book based on the papers presented there provides an overview of this new area in ?uid mechanics and its app- cations that have developed over the past three decades. The subject, whose origins lie both in theory and in practice, is now rapidly developing in many directions. The focus of applied ?uid mechanics research has steadily been shifting from - gineering to environmental applications.
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)?
Fibonacci’s de practica geometrie = Fibonacci’s practice geometry
Practical Geometry is the name of the craft for medieval landmeasurers, otherwise known as surveyors in modern times. Fibonacci wrote De practica geometrie for these artisans, a fitting complement to Liber abbaci. He had been at work on the geometry project for some time when a friend encouraged him to complete the task, which he did, going beyond the merely practical, as he remarked, "Some parts are presented according to geometric demonstrations, other parts in dimensions after a lay fashion, with which they wish to engage according to the more common practice."
Factorization of Matrix and Operator Functions : The State Space Method
The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization.
Face Biometrics for Personal Identification : Multi-Sensory Multi-Modal Systems
This book provides an ample coverage of theoretical and experimental state-of-the-art work as well as new trends and directions in the biometrics field. It offers students and software engineers a thorough understanding of how some core low-level building blocks of a multi-biometric system are implemented. While this book covers a range of biometric traits including facial geometry, 3D ear form, fingerprints, vein structure, voice, and gait, its main emphasis is placed on multi-sensory and multi-modal face biometrics algorithms and systems. "Multi-sensory" refers to combining data from two or more biometric sensors, such as synchronized reflectance-based and temperature-based face images. "Multi-modal" biometrics means fusing two or more biometric modalities, like face images and voice timber. The first part addresses new and emerging face biometrics. Emphasis is placed on biometric systems where single sensor and single modality are employed in challenging imaging conditions. The second part on multi-sensory face biometrics deals with the personal identification task in challenging variable illuminations and outdoor operating scenarios by employing visible and thermal sensors. The third part of the book focuses on multi-modal face biometrics by integrating voice, ear, and gait modalities with facial data. The last part presents generic chapters on multi-biometrics fusion methodologies and performance prediction techniques.
Extremum Problems for Eigenvalues of Elliptic Operators
Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this book, we focus on extremal problems. For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrödinger operator, non homogeneous membranes, or the bi-Laplacian, and we look at optimal composites and optimal insulation problems in terms of eigenvalues.
Explorations in Mathematical Physics : The Concepts Behind an Elegant Language
This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology.
Experimental Algorithms ; 7th International Workshop, WEA 2008 Provincetown, MA, USA, May 30-June 1, 2008 Proceedings
The Workshop on Experimental Algorithms, WEA, is intended to be an international forum for research on the experimental evaluation and engineering of algorithms, as well as in various aspects of computational optimization and its applications. The emphasis of the workshop is the use of experimental me- ods to guide the design, analysis, implementation, and evaluation of algorithms, heuristics, and optimization programs. WEA 2008 was held at the Provincetown Inn, Provincetown, MA, USA, on May 30 – June 1, 2008. This was the seventh workshop of the series.
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.
