• Mathematics

## The Goodwillie Tower and the EHP Sequence

Author: Mark Behrens
Publisher: American Mathematical Soc.
ISBN: 0821869027
Category: Mathematics
Page: 90
View: 3230
The author studies the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime $2$. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. He relates the Goodwillie filtration to the $P$ map, and the Goodwillie differentials to the $H$ map. Furthermore, he studies an iterated Atiyah-Hirzebruch spectral sequence approach to the homotopy of the layers of the Goodwillie tower of the identity on spheres. He shows that differentials in these spectral sequences give rise to differentials in the EHP spectral sequence. He uses his theory to recompute the $2$-primary unstable stems through the Toda range (up to the $19$-stem). He also studies the homological behavior of the interaction between the EHP sequence and the Goodwillie tower of the identity. This homological analysis involves the introduction of Dyer-Lashof-like operations associated to M. Ching's operad structure on the derivatives of the identity. These operations act on the mod $2$ stable homology of the Goodwillie layers of any functor from spaces to spaces.

• Mathematics

## Issues in General and Specialized Mathematics Research: 2013 Edition

Author: N.A
Publisher: ScholarlyEditions
ISBN: 1490106928
Category: Mathematics
Page: 1215
View: 7223
Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

• Mathematics

## Hopf Algebras and Congruence Subgroups

Author: Yorck Sommerhäuser,Yongchang Zhu
Publisher: American Mathematical Soc.
ISBN: 0821869132
Category: Mathematics
Page: 134
View: 7959
The authors prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, they show that the projective kernel is a congruence subgroup. To do this, they introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.

• Mathematics

## Elements of Homotopy Theory

Publisher: Springer Science & Business Media
ISBN: 1461263182
Category: Mathematics
Page: 746
View: 3870
As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.

• Mathematics

## Theory of Algebraic Functions of One Variable

Author: Richard Dedekind,Heinrich Weber
Publisher: American Mathematical Soc.
ISBN: 0821890344
Category: Mathematics
Page: 152
View: 7420
This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veranderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in 1882. The translation has been enriched by a Translator's Introduction that includes historical background, and also by extensive commentary embedded in the translation itself. The translation, introduction, and commentary provide the first easy access to this important paper for a wide mathematical audience: students, historians of mathematics, and professional mathematicians. Why is the Dedekind-Weber paper important? In the 1850s, Riemann initiated a revolution in algebraic geometry by interpreting algebraic curves as surfaces covering the sphere. He obtained deep and striking results in pure algebra by intuitive arguments about surfaces and their topology. However, Riemann's arguments were not rigorous, and they remained in limbo until 1882, when Dedekind and Weber put them on a sound foundation. The key to this breakthrough was to develop the theory of algebraic functions in analogy with Dedekind's theory of algebraic numbers, where the concept of ideal plays a central role. By introducing such concepts into the theory of algebraic curves, Dedekind and Weber paved the way for modern algebraic geometry.

• Mathematics

## Recent Advances in Homotopy Theory

Publisher: Amer Mathematical Society
ISBN: 9780821841587
Category: Mathematics
Page: 82
View: 422

• Mathematics

## Modern Classical Homotopy Theory

Author: Jeffrey Strom
Publisher: American Mathematical Soc.
ISBN: 0821852868
Category: Mathematics
Page: 835
View: 7573
The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.

## The Future of Electricity Demand

Author: Tooraj Jamasb,Michael G. Pollitt
Publisher: Cambridge University Press
ISBN: 1107008506
Page: 478
View: 3311
This book is a comprehensive and analytical perspective on the future of electricity demand in a low-carbon world.

• Mathematics

## The Lin-Ni's Problem for Mean Convex Domains

Author: Olivier Druet,Frédéric Robert,Juncheng Wei
Publisher: American Mathematical Soc.
ISBN: 0821869094
Category: Mathematics
Page: 105
View: 3422
The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.

• Science

## Valuing Ecosystem Services:

Toward Better Environmental Decision-Making
Author: Committee on Assessing and Valuing the the Services of Aquatic and Related Terrestrial Ecosystems,Water Science and Technology Board,Division on Earth and Life Studies,National Research Council
ISBN: 030909318X
Category: Science
Page: 290
View: 3492
Nutrient recycling, habitat for plants and animals, flood control, and water supply are among the many beneficial services provided by aquatic ecosystems. In making decisions about human activities, such as draining a wetland for a housing development, it is essential to consider both the value of the development and the value of the ecosystem services that could be lost. Despite a growing recognition of the importance of ecosystem services, their value is often overlooked in environmental decision-making. This report identifies methods for assigning economic value to ecosystem services-even intangible ones-and calls for greater collaboration between ecologists and economists in such efforts.

• Mathematics

## Elliptic Curves, Hilbert Modular Forms and Galois Deformations

Author: Laurent Berger,Gebhard Böckle,Lassina Dembélé,Mladen Dimitrov,Tim Dokchitser,John Voight
Publisher: Springer Science & Business Media
ISBN: 3034806183
Category: Mathematics
Page: 249
View: 1253
The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ≠ p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.

• Science

## Electron Transport in Quantum Dots

Author: Jonathan P. Bird
Publisher: Springer Science & Business Media
ISBN: 1461504376
Category: Science
Page: 472
View: 5385
When I was contacted by Kluwer Academic Publishers in the Fall of 200 I, inviting me to edit a volume of papers on the issue of electron transport in quantum dots, I was excited by what I saw as an ideal opportunity to provide an overview of a field of research that has made significant contributions in recent years, both to our understanding of fundamental physics, and to the development of novel nanoelectronic technologies. The need for such a volume seemed to be made more pressing by the fact that few comprehensive reviews of this topic have appeared in the literature, in spite of the vast activity in this area over the course of the last decade or so. With this motivation, I set out to try to compile a volume that would fairly reflect the wide range of opinions that has emerged in the study of electron transport in quantum dots. Indeed, there has been no effort on my part to ensure any consistency between the different chapters, since I would prefer that this volume instead serve as a useful forum for the debate of critical issues in this still developing field. In this matter, I have been assisted greatly by the excellent series of articles provided by the different authors, who are widely recognized as some of the leaders in this vital area of research.

• Nature

## Global Birding

Traveling the World in Search of Birds
Author: Les Beletsky
Publisher: National Geographic Books
ISBN: 9781426206405
Category: Nature
Page: 319
View: 8815
Explains why birders take their hobby to other countries and where they like to go, in a continent-by-continent overview of which birds are most highly sought that includes color photos, maps, and birding contacts.

• Health & Fitness

## Beyond the Black Box

The Forensics of Airplane Crashes
Author: George Bibel
Publisher: JHU Press
ISBN: 9780801886317
Category: Health & Fitness
Page: 393
View: 7412
Beyond the Black Box shows how crash investigators use physics, aerodynamics, and mechanical engineering to determine the probable cause of a crash and how resulting safety recommendations are incorporated to make flying safer.

Author: Ehsan Zarei
Publisher: N.A
ISBN: 9781291722000
Page: 178
View: 8814

• Science

## Physics of Quantum Rings

Publisher: Springer Science & Business Media
ISBN: 3642391974
Category: Science
Page: 487
View: 7490
This book deals with a new class of materials, quantum rings. Innovative recent advances in experimental and theoretical physics of quantum rings are based on the most advanced state-of-the-art fabrication and characterization techniques as well as theoretical methods. The experimental efforts allow to obtain a new class of semiconductor quantum rings formed by capping self-organized quantum dots grown by molecular beam epitaxy. Novel optical and magnetic properties of quantum rings are associated with non-trivial topologies at the nanoscale. An adequate characterization of quantum rings is possible on the basis of modern characterization methods of nanostructures, such as Scanning Tunneling Microscopy. A high level of complexity is demonstrated to be needed for a dedicated theoretical model to adequately represent the specific features of quantum rings. The findings presented in this book contribute to develop low-cost high-performance electronic, spintronic, optoelectronic and information processing devices based on quantum rings.

• Science

## Atomistic Simulation of Quantum Transport in Nanoelectronic Devices

(With CD-ROM)
Author: Yu Zhu,Lei Liu
Publisher: World Scientific
ISBN: 9813141441
Category: Science
Page: 436
View: 6811
Computational nanoelectronics is an emerging multi-disciplinary field covering condensed matter physics, applied mathematics, computer science, and electronic engineering. In recent decades, a few state-of-the-art software packages have been developed to carry out first-principle atomistic device simulations. Nevertheless those packages are either black boxes (commercial codes) or accessible only to very limited users (private research codes). The purpose of this book is to open one of the commercial black boxes, and to demonstrate the complete procedure from theoretical derivation, to numerical implementation, all the way to device simulation. Meanwhile the affiliated source code constitutes an open platform for new researchers. This is the first book of its kind. We hope the book will make a modest contribution to the field of computational nanoelectronics. Contents:IntroductionThe NECPA TheoryThe NECPA-LMTO MethodNanoDsim: The Package DesignNanoDsim: Bulk SystemsNanoDsim: Two-Probe SystemsNanoDsim: Optimization and ParallelizationKaleidoscope of the Physics in Disordered SystemsAppendix Readership: Post-graduate students or professional researchers who are interested in computational physics, device physics, quantum transport, disorder systems, and overlap of the above.

## Handbook on the Economics of Ecosystem Services and Biodiversity

Author: Paulo A L D Nunes,Pushpam Kumar,Tom Dedeurwaerdere
Publisher: Edward Elgar Publishing
ISBN: 1781951519
Page: 6008
View: 9211
In recent years, there has been a marked proliferation in the literature on economic approaches to ecosystem management, which has created a subsequent need for real understanding of the scope and the limits of the economic approaches to ecosystems and

• Science

## Ecosystem Services for Well-Being in Deltas

Integrated Assessment for Policy Analysis
Author: Robert J. Nicholls,Craig W. Hutton,W. Neil Adger,Susan E. Hanson,Md. Munsur Rahman,Mashfiqus Salehin
Publisher: Springer
ISBN: 3319710931
Category: Science
Page: 593
View: 3527