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Author: Jean-Paul Brasselet Publisher: Springer Science & Business Media ISBN: 3642052045 Category : Mathematics Languages : en Pages : 242
Book Description
Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
Author: Jean-Paul Brasselet Publisher: Springer Science & Business Media ISBN: 3642052045 Category : Mathematics Languages : en Pages : 242
Book Description
Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
Author: Geoffrey R. Grimmett Publisher: Springer Science & Business Media ISBN: 3540328912 Category : Mathematics Languages : en Pages : 392
Book Description
The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Author: Charles Audet Publisher: Springer Science & Business Media ISBN: 0387255702 Category : Business & Economics Languages : en Pages : 294
Book Description
Global optimization aims at solving the most general problems of deterministic mathematical programming: to find the global optimum of a nonlinear, nonconvex, multivariate function of continuous and/or integer variables subject to constraints which may be themselves nonlinear and nonconvex. In addition, once the solutions are found, proof of its optimality is also expected from this methodology. Therefore, with these difficulties in mind, global optimization is becoming an increasingly powerful and important methodology. Essays and Surveys in Global Optimization is the most recent examination of its mathematical capability, power, and wide ranging solutions to many fields in the applied sciences.
Author: Pascal Massart Publisher: Springer ISBN: 3540485031 Category : Mathematics Languages : en Pages : 346
Book Description
Concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn to be essential tools to develop a non asymptotic theory in statistics. This volume provides an overview of a non asymptotic theory for model selection. It also discusses some selected applications to variable selection, change points detection and statistical learning.
Author: Richard Loulou Publisher: Springer Science & Business Media ISBN: 9780387253510 Category : Science Languages : en Pages : 304
Book Description
This new work on energy and environmental modeling describes a broad variety of modeling methodologies, embodied in models of varying scopes and philosophies. Examples range from top-down integrated assessment models to bottom-up partial equilibrium models, to hybrid models.
Author: Joseph P.S. Kung Publisher: Elsevier ISBN: 1483272028 Category : Mathematics Languages : en Pages : 344
Book Description
Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardson rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra.
Author: Herbert Anderson Publisher: Fortress Press ISBN: 1506454801 Category : Religion Languages : en Pages : 236
Book Description
Shaping our journey into the Divine This moving and enlightening book presents us with a compelling vision of what can happen when we take the opportunity to connect stories and rituals--a vision of individuals and communities transformed through a deeper sense of connection to our loved ones, our communities, and God. Herbert Anderson and Edward Foley reveal how when stories and rituals work together, they have the potential to be both mighty and dangerous--mighty in their ability to lift us up and help us make these connections beyond ourselves and dangerous in challenging us to learn to live with complexity and contradiction. They show how much more meaningful a baptism, wedding, or funeral can be when liturgy is made to include and recognize the personal stories of those involved. Suddenly, these familiar life-cycle rituals are infused with new life as participants become connected in a narrative web linking past and present, human and divine. Newly created rituals can also help us connect our stories to the divine story, giving meaning to what we experience and bringing us closer to God. Ministers, worship leaders, and pastoral caregivers can use this approach to storytelling and ritual to find ways to bring together worship and pastoral care.
Author: C. Pozrikidis Publisher: CRC Press ISBN: 1315362082 Category : Mathematics Languages : en Pages : 278
Book Description
The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions. The Fractional Laplacian explores applications of the fractional Laplacian in science, engineering, and other areas where long-range interactions and conceptual or physical particle jumps resulting in an irregular diffusive or conductive flux are encountered. Presents the material at a level suitable for a broad audience of scientists and engineers with rudimentary background in ordinary differential equations and integral calculus Clarifies the concept of the fractional Laplacian for functions in one, two, three, or an arbitrary number of dimensions defined over the entire space, satisfying periodicity conditions, or restricted to a finite domain Covers physical and mathematical concepts as well as detailed mathematical derivations Develops a numerical framework for solving differential equations involving the fractional Laplacian and presents specific algorithms accompanied by numerical results in one, two, and three dimensions Discusses viscous flow and physical examples from scientific and engineering disciplines Written by a prolific author well known for his contributions in fluid mechanics, biomechanics, applied mathematics, scientific computing, and computer science, the book emphasizes fundamental ideas and practical numerical computation. It includes original material and novel numerical methods.
Author: Jean-Paul Brasselet
Author: Jean-Paul Brasselet
Author: Geoffrey R. Grimmett
Author: Charles Audet
Author: Pascal Massart
Author: Thomas Nugent
Author: Richard Loulou
Author: Joseph P.S. Kung
Author: Nationwide Evaluation of X-ray Trends Task Force
Author: Herbert Anderson
Author: C. Pozrikidis