Author: Jean-Louis Loday

Publisher: Springer Science & Business Media

ISBN: 3662217392

Pages: 454

Year: 2013-06-29

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This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Author: Jacob Lurie

Publisher: Princeton University Press

ISBN: 1400830559

Pages: 944

Year: 2009-07-06

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Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.

Author: Tom Leinster

Publisher: Cambridge University Press

ISBN: 0521532159

Pages: 433

Year: 2004-07-22

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Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. The heart of this book is the language of generalized operads. This is as natural and transparent a language for higher category theory as the language of sheaves is for algebraic geometry, or vector spaces for linear algebra. It is introduced carefully, then used to give simple descriptions of a variety of higher categorical structures. In particular, one possible definition of n-category is discussed in detail, and some common aspects of other possible definitions are established. This is the first book on the subject and lays its foundations. It will appeal to both graduate students and established researchers who wish to become acquainted with this modern branch of mathematics.

Author: A.M. Mathai, Ram Kishore Saxena, Hans J. Haubold

Publisher: Springer Science & Business Media

ISBN: 1441909168

Pages: 268

Year: 2009-10-10

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TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.

Author: Dave Benson

Publisher: Cambridge University Press

ISBN: 0521853877

Pages: 411

Year: 2007

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Explores interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.

Author: Martin Olsson

Publisher: American Mathematical Soc.

ISBN: 1470427982

Pages: 298

Year: 2016-05-13

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This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.

Author: Matthew Fuller

Publisher: MIT Press

ISBN: 0262062747

Pages: 334

Year: 2008

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A cultural field guide to software: artists, computer scientists, designers, cultural theorists, programmers, and others define a new field of study and practice.

Author: David Diez, Christopher Barr, Mine Çetinkaya-Rundel

Publisher:

ISBN: 1943450048

Pages:

Year: 2015-07-02

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The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources.

Author: Melissa Leach, Ian Scoones, Andy Stirling

Publisher: Routledge

ISBN: 1849710937

Pages: 212

Year: 2010

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Introducing a new pathways approach for understanding and responding to sustainability challenges, this title explores practical ways forward for building pathways to sustainability.

Author: David H. Bailey, Jonathan Borwein, Neil Calkin, Russell Luke, Roland Girgensohn, Victor Moll

Publisher: CRC Press

ISBN: 1439864330

Pages: 337

Year: 2007-05-31

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With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doing to highlight some of the key algorithms and to teach some of the key experimental approaches.

Author: Frédéric Barbaresco, Frank Nielsen

Publisher: MDPI

ISBN: 3038424242

Pages: 472

Year: 2018-04-06

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This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy

Author: Committee on Physical Activity and Physical Education in the School Environment, Food and Nutrition Board, Institute of Medicine

Publisher: National Academies Press

ISBN: 0309283140

Pages: 475

Year: 2013-11-13

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Physical inactivity is a key determinant of health across the lifespan. A lack of activity increases the risk of heart disease, colon and breast cancer, diabetes mellitus, hypertension, osteoporosis, anxiety and depression and others diseases. Emerging literature has suggested that in terms of mortality, the global population health burden of physical inactivity approaches that of cigarette smoking. The prevalence and substantial disease risk associated with physical inactivity has been described as a pandemic. The prevalence, health impact, and evidence of changeability all have resulted in calls for action to increase physical activity across the lifespan. In response to the need to find ways to make physical activity a health priority for youth, the Institute of Medicine's Committee on Physical Activity and Physical Education in the School Environment was formed. Its purpose was to review the current status of physical activity and physical education in the school environment, including before, during, and after school, and examine the influences of physical activity and physical education on the short and long term physical, cognitive and brain, and psychosocial health and development of children and adolescents. Educating the Student Body makes recommendations about approaches for strengthening and improving programs and policies for physical activity and physical education in the school environment. This report lays out a set of guiding principles to guide its work on these tasks. These included: recognizing the benefits of instilling life-long physical activity habits in children; the value of using systems thinking in improving physical activity and physical education in the school environment; the recognition of current disparities in opportunities and the need to achieve equity in physical activity and physical education; the importance of considering all types of school environments; the need to take into consideration the diversity of students as recommendations are developed. This report will be of interest to local and national policymakers, school officials, teachers, and the education community, researchers, professional organizations, and parents interested in physical activity, physical education, and health for school-aged children and adolescents.

Author: Kai Behrend

Publisher: American Mathematical Soc.

ISBN: 0821829297

Pages: 93

Year: 2003

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This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.

Author: Douglas Altman, David Machin, Trevor Bryant, Martin Gardner

Publisher: John Wiley & Sons

ISBN: 1118702506

Pages: 256

Year: 2013-06-03

View: 522

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This highly popular introduction to confidence intervals has been thoroughly updated and expanded. It includes methods for using confidence intervals, with illustrative worked examples and extensive guidelines and checklists to help the novice.

Author: National Defense University (US)

Publisher: Createspace Independent Publishing Platform

ISBN: 1975720423

Pages: 402

Year: 2017-08-24

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The world order built upon the Peace of Westphalia is faltering. State fragility or failure are endemic, with no fewer than one-third of the states in the United Nations earning a "high warning"-or worse-in the Fragile States Index, and an equal number suffering a decline in sustainability over the past decade.1 State weakness invites a range of illicit actors, including international terrorists, globally networked insurgents, and transnational criminal organizations (TCOs). The presence and operations of these entities keep states weak and incapable of effective governance, and limit the possibility of fruitful partnerships with the United States and its allies. Illicit organizations and their networks fuel corruption, eroding state legitimacy among the governed, and sowing doubt that the state is a genuine guardian of the public interest. These networks can penetrate the state, leading to state capture, and even criminal sovereignty.2 A growing number of weak and corrupt states is creating gaping holes in the global rule-based system of states that we depend on for our security and prosperity. Indeed, the chapters of this book suggest the emergence of a highly adaptive and parasitic alternative ecosystem, based on criminal commerce and extreme violence, with little regard for what we commonly conceive of as the public interest or the public good. The last 10 years have seen unprecedented growth in interactivity between and among a wide range of illicit networks, as well as the emergence of hybrid organizations that use methods characteristic of both terrorist and criminal groups. In a convergence of interests, terrorist organizations collaborate with cartels, and trafficking organizations collude with insurgents. International terrorist organizations, such as al-Qaeda and Hezbollah, engage energetically in transnational crime to raise funds for their operations. Prominent criminal organizations like Los Zetas in Mexico and D-Company in Pakistan have adopted the symbolic violence of terrorists-the propaganda of the deed-to secure their "turf." And networked insurgents, such as the Islamic State of Iraq and the Levant (ISIL), the Revolutionary Armed Forces of Colombia (FARC), and the Liberation Tigers of Tamil Eelam (LTTE), have adopted the techniques of both crime and terror.