الصفحة 4
الصفحة 4
The Art of Random Walks
Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity.
The Algorithm Design Manual
The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography.
Teoria delle Equazioni e Teoria di Galois = Equation Theory and Galois Theory
Algebra was born as the study of the solvability of polynomial equations and essentially remained so until in 1830 Evariste Galois - a brilliant mathematician with a short and adventurous life - definitively solved this problem, at the same time laying the foundations for the birth of modern algebra understood as the study of algebraic structures. Classical Galois Theory is now taught at various levels within the degree courses in Mathematics. This textbook was accordingly written to be used flexibly. Some parts - such as the one on Field Theory - can also be used for more advanced courses in Algebra, Geometry and Number Theory. Other topics - such as the study of the solubility by radicals of low degree equations or of the constructability with ruler and compass of plane figures - can be carried out in Complementary Mathematics courses for the didactic address. The volume also contains historical notes, many detailed examples and exercises.
Technologies for E-Learning and Digital Entertainment: Third International Conference, Edutainment 2008 Nanjing, China, June 25-27, 2008 Proceedings
Includes e-learning platforms and tools, e-learning system for education, application of e-learning systems, e-learning resource management, interaction in game and education, integration of game and education, game design and development, virtual characters, animation and navigation, graphics rendering and digital media, as well as geometric modeling in games and virtual reality.
Technologies for E-Learning and Digital Entertainment ; 2nd International Conference, Edutainment 2007, Hong Kong, China, June 11-13, 2007, Proceedings
A total of 90 papers were selected, after peer review, for this volume. Topics of these papers fall into six diff- ent areas ranging from fundamental issues in geometry and imaging to virtual reality systems and their applications in entertainment and education. These topics include Virtual Reality in Games and Education, Virtual Characters in Games and Education, E-learning Platforms and Tools, Geometry in Games and Virtual Reality, Vision, Imaging and Video Technology, and Collaborative and Distributed Environments. We are grateful to the International Program Committee and the reviewers for their effort to get all the papers reviewed in a short period of time. We would also like to thank everyone who contributed to organizing the conference.
Tata Lectures on Theta I
The first of a series of three volumes surveying the theory of theta functions and its significance in the fields of representation theory and algebraic geometry, this volume deals with the basic theory of theta functions in one and several variables, and some of its number theoretic applications.Requiring no background in advanced algebraic geometry, the text serves as a modern introduction to the subject.
Tales of Mathematicians and Physicists
Contains a wealth of new information about the lives and accomplishments of more than a dozen scientists throughout five centuries of history: from the first steps in algebra up to new achievements in geometry in connection with physics. The heroes of the book are renowned figures from early eras, such as Cardano, Galileo, Huygens, Leibniz, Pascal, Euler, Lagrange, and Laplace, as well some scientists of the last century: Klein, Poincaré, and Ramanujan.
Symplectic Geometry and Quantum Mechanics
Devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a rigorous presentation of the basics of symplectic geometry and of its multiply-oriented extension. Further chapters concentrate on Lagrangian manifolds, Weyl operators and the Wigner-Moyal transform as well as on metaplectic groups and Maslov indices.
Symplectic 4-Manifolds and Algebraic Surfaces : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy September 2–10, 2003
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics.
Symmetry : Cultural-historical and ontological aspects of science-arts relations The natural and man-made world in an interdisciplinary approach
Symmetry used to be a fundamental phenomenon in crystallography, where its basic concept was elaborated, in morphological biology, and of course in mathematics, which provided its exact description. In the last half century symmetry (and symmetry breaking) has become a leading principle in physics, in all sciences that deal with the structure of matter, as well as in the biochemistry of proteins, the study of the genetic code, brain research (where functional asymmetries have been revealed), psychology, and in developing architectural structures and in business decision-making, to name but a few examples. This book seeks to find common regularities among these apparently disparate phenomena. It covers most of the achievements reached in the sciences in recent decades that have been given new impetus by the mutual influences of art and science related to symmetry (or the lack of it).
Symmetries and Overdetermined Systems of Partial Differential Equations
Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogenous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too. This three-week summer program considered the symmetries preserving various natural geometric structures. Often these structures are themselves derived from partial differential equations whilst their symmetries turn out to be contrained by overdetermined systems. This leads to further topics including separation of variables, conserved quantities, superintegrability, parabolic geometry, represantation theory, the Bernstein-Gelfand-Gelfand complex, finite element schemes, exterior differential systems and moving frames.
Symbolic-Numeric Computation
The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations, two types of computation coexisting in mathematics yet separated in traditional research of mathematical computation. This book with 23 chapters presents original research and tutorial survey on the integration and interaction of symbolic and numeric computations. It represents the current state of the art and will serve as a valuable reference on the development of algorithms and software packages for hybrid symbolic-numeric computation.
Surface Evolution Equations : A Level Set Approach
This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense.
Supermanifolds and Supergroups : Basic Theory
Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections.
Sturm-Liouville Theory and its Applications
Undergraduate textbooks on Fourier series which follow a pointwise approach to convergence miss the rich geometric content which comes with treating the subject within the inner product space L2. This book, developed from a course taught to senior undergraduates, provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The basic results of this theory, namely the orthogonality and completeness of its eigenfunctions, are established in Chapter 2; the remaining chapters present examples and applications. The last two chapters, on Fourier and Laplace transformations, while not part of the Sturm-Liouville theory, extend the Fourier series method for representing functions to integral representations.
Structural mechanics : Analytical and numerical approaches for structural analysis
Covers both standard and advanced topics of structural mechanics. Standard subjects covered include geometric stability, forces and displacements of statically determinate structures, force and displacement method, and influence lines. Advanced topics include matrix displacement method, dynamics of structures, and limit loading.
Structural analysis of multi-storey buildings
Relies on creating continuum models approach and presents the theoretical background and the governing differential equations (for researchers) and simple closed-form solutions (for practicing structural engineers). The continuum models also help to understand how the stiffness and geometrical characteristics influence the three-dimensional behaviour of complex bracing systems. The back-of-the-envelop formulae for the maximum deflection and rotation, load shares, fundamental frequency and critical load facilitate quick global structural analysis for even large buildings. It is shown how the global critical load ratio can be used for monitoring the "health" of the structure acting as a performance indicator and "safety factor".
String Theory : from Gauge Interactions to Cosmology ; Proceedings of the NATO Advanced Study Institute on String Theory: From Gauge Interactions to Cosmology, Cargèse, France, from 7 to 19 June 2004
String Theory is our current best candidate for the unification of all fundamental forces, including gravity, in a consistent quantum framework. In this collection of lectures delivered at the Cargèse Summer School "String Theory: from Gauge Interactions to Cosmology'', world leading experts provide an up-to-date survey of the latest developments in this topic, including the gauge/gravity correspondence, superstring cosmology and cosmic strings, topological string theory and matrix models, physics beyond the standard model and the landscape of vacua of string theory, conformal field theory and critical phenomena in statistical mechanics.
Strength Analysis in Geomechanics
The book presents a new approach for the solution of geomechanical problems - it explicitly takes into account deformation and fracture in time, which are neglected in classical methods although these properties create important effects. The method reveals the influence of the form of a structure on its ultimate state. It uses the rheological law which accounts for large strains at a non-linear unsteady creep, an influence of a stress state type, an initial anisotropy and damage. The whole approach takes into account five types of non-linearity (physical as well as geometrical ones) and contains several new ideas. For example, it considers the fracture as a process, the difference between the body and an element of the material which only deforms and fails because it is in the structure, the simplicity of some non-linear computations against the consequent linear ones, the dependence of the maximum strain in dangerous poins of the body only on the material.
Stochastic Geometry : Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 13-18, 2004
Contains the lectures given at the CIME summer school in Martina Franca in September 1974. The four main lecturers covered the areas of Spatial Statistics, Random Points, Integral Geometry and Random Sets, they are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents an up-to-date description of important parts of Stochastic Geometry.
