Marcelo Aguiar's Books

Coxeter Bialgebras

By: Marcelo Aguiar,Swapneel Mahajan

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The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.

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Page Count

897

Publisher

Cambridge University Press

Published Date

ISBN 10

100924373X

ISBN 13

9781009243735

Bimonoids for Hyperplane Arrangements

By: Marcelo Aguiar,Swapneel Mahajan

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Bimonoids for Hyperplane Arrangements

By: Marcelo Aguiar,Swapneel Mahajan

The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel-Hopf, Poincar -Birkhoff-Witt, and Cartier-Milnor-Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.

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Page Count

853

Publisher

Cambridge University Press

Published Date

ISBN 10

110849580X

ISBN 13

9781108495806

Hopf Monoids and Generalized Permutahedra

By: Marcelo Aguiar,Federico Ardila

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Hopf Monoids and Generalized Permutahedra

By: Marcelo Aguiar,Federico Ardila

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124

Publisher

American Mathematical Society

Published Date

ISBN 10

1470467089

ISBN 13

9781470467081

Coxeter Groups and Hopf Algebras

By: Marcelo Aguiar

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Coxeter Groups and Hopf Algebras

By: Marcelo Aguiar

An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject.

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Page Count

201

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853546

ISBN 13

9780821853542

Communication Systems

By: Marcelo S. Alencar,Valdemar C. da Rocha

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Communication Systems

By: Marcelo S. Alencar,Valdemar C. da Rocha

Presents main concepts of mobile communication systems, both analog and digital Introduces concepts of probability, random variables and stochastic processes and their applications to the analysis of linear systems Includes five appendices covering Fourier series and transforms, GSM cellular systems and more

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Page Count

421

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387270973

ISBN 13

9780387270975

Chains of Gold

Portuguese Migration to Argentina in Transatlantic Perspective

By: Marcelo Borges

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Chains of Gold

Portuguese Migration to Argentina in Transatlantic Perspective

By: Marcelo Borges

Why did migrants from southern Portugal choose Argentina instead of following the traditional path to Brazil? Starting with this question, this book explores how, at the turn of the twentieth century, rural Europeans developed distinctive circuits of transatlantic labor migration linked to diverse immigrant communities in the Americas. It looks at transoceanic moves in the larger context of migration systems, examining their connections and the crucial role of social networks in migrants’ geographic mobility and adaptation. Combining regional and local perspectives on both sides of the Atlantic, Chains of Gold provides a vivid account of the trajectories of migrant men and women as they moved from rural Portugal to contrasting places of settlement in the Argentine pampas and Patagonia.

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Page Count

369

Publisher

BRILL

Published Date

ISBN 10

9047429923

ISBN 13

9789047429920

Cellular Network Planning

By: Marcelo Sampaio de Alencar,Djalma de Melo Carvalho Filho

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Cellular Network Planning

By: Marcelo Sampaio de Alencar,Djalma de Melo Carvalho Filho

Over the recent years, few books have been published covering all the subjects needed to understand the very fundamental concepts of cell planning. Most books which deal with this topic are destined to very specific audiences, and the vast majority introduce the subject at a very basic, or technical, level, or are destined to an academic audience. Cellular Network Planning begins with an introduction to the subject, covering conventional and contemporary wireless systems. Spectral allocation and the frequency plan are discussed, along with the essential characteristics of wireless systems. The design of mobile cellular systems includes cell planning, traffic and channel problems. The book presents a review of existing models, considering both green field dimensioning and network expansion strategies, and discusses multi-objective optimization and base station deployment based on artificial immune systems. It also discusses a cost-effective base station deployment approach based on artificial immune systems, and introduces the modified MO-AIS algorithm.

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Page Count

199

Publisher

CRC Press

Published Date

ISBN 10

1000799328

ISBN 13

9781000799323

The Unintended Consequences of Peace

Peaceful Borders and Illicit Transnational Flows

By: Arie Marcelo Kacowicz,Exequiel Lacovsky,Keren Sasson,Daniel F. Wajner

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The Unintended Consequences of Peace

Peaceful Borders and Illicit Transnational Flows

By: Arie Marcelo Kacowicz,Exequiel Lacovsky,Keren Sasson,Daniel F. Wajner

Scholars of international relations generally consider that under conditions of violent conflict and war, smuggling and trans-border crime are likely to thrive. In contrast, this book argues that in fact it is globalisation and peaceful borders that have enabled transnational illicit flows conducted by violent non-state actors, including transnational criminal organizations, drug trafficking organizations, and terrorist cells, who exploit the looseness and demilitarization of borderlands. Empirically, the book draws on case studies from the Americas, compared with other regions of the world experiencing similar phenomena, including the European Union and Southeast Europe (the Western Balkans), Southern Africa, and Southeast Asia. To explain the phenomenon in itself, the authors examine the type of peaceful borders and regimes involved in each case; how strong each country is in the governance of their borderlands; their political willingness to control their peaceful borders; and the prevailing socio-economic conditions across the borderlands.

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Page Count

313

Publisher

Cambridge University Press

Published Date

ISBN 10

1009007742

ISBN 13

9781009007740

The Mitigation Doctrine

A Proposal for its Regulation in Brazil

By: Marcelo Lapolla PhD

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The Mitigation Doctrine

A Proposal for its Regulation in Brazil

By: Marcelo Lapolla PhD

The “duty to mitigate loss” doctrine has been the object of study in many jurisdictions, which have interpreted and applied it in a wide range of situations and in different ways. In Brazil, however, only recent discussions have brought light to this subject. Worldwide, researchers have debated its nature – whether a duty or a principle – and the most proper way to address it (e.g.: if duty to mitigate loss or damages; duty to rescue; avoidable consequences doctrine). Studies have also detailed its application in different situations, such as in contracts and torts, among suppliers, consumers and national and international commerce, for instance. Ultimately, responding to the shift for globalized relations involving parties from different jurisdictions, the development of the doctrine and its standardization by Common Law courts, Civil Law codifications and international rules have allowed emerging countries to take advantage of the lessons learnt in more experienced systems and helped them regulate their own in the most suitable form. The purpose of this book is to provide an in-depth study of the “duty to mitigate loss” – from its origin to its current application in selected jurisdictions – so as to comprehensively come up with a proposition that is sufficiently adequate to fill the Brazilian legal framework gap diagnosed with respect to its effective regulation.

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Page Count

166

Publisher

iUniverse

Published Date

ISBN 10

1663261385

ISBN 13

9781663261380

Where does religion end?

By: Marcelo da Luz

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Where does religion end?

By: Marcelo da Luz

The author's decision to leave religion, after experiencing a profound growth crisis, founded itself in the free action of one, who after walking tenaciously, has extinguished an existential possibility and reached a new realm of understanding about the realities of the consciousness and the universe. The inner freedom encountered to make this kind of decision was the result of a gradual self-confrontation. This author perceived the necessity to dispel the fear associated with questioning his habitual suppositions and to look beyond the limits of the indoctrination he had received. For a long time, while still religious, he named this fearlessness "a quest for wisdom" or "the spirituality of an unsettled heart". Nowadays, in light of the experiences had, he prefers to emphasize the courage to evolve, which requires, five years after the abjuration, the assumption of speaking publicly about the dissidence that was effected. When dissidents of ideologies or institutions start talking or writing about their experiences, it is necessary to observe the kind of motivation and intention implicit in the decision made. The former militant, the former integrant, the former partisan, the former something, in spite of the effort to affirm that they are no longer part of the institution to which they once belonged, may continue to define themselves based on the institution. In this case the person is still a "former" in relation to what they intend to deny. Perhaps, in their eagerness to critically speak out about the reasons underlying their abandonment of a certain idea or organization, they still flaunt the previous condition as a trophy, unfurling the pride of being a "former". The ambiguity in question lies in the fact that the person's point of reference continues to be in the no longer desired way of living or thinking.

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Page Count

465

Publisher

Associação Internacional Editares

Published Date

ISBN 10

8584770909

ISBN 13

9788584770908

Introduction to General Relativistic and Scalar-tensor Cosmologies

By: Marcelo Samuel Berman

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Introduction to General Relativistic and Scalar-tensor Cosmologies

By: Marcelo Samuel Berman

This book offers an introduction to General Relativity and its mathematical tools, together with an introduction to relativistic and scalar-tensor cosmologies. Part I deals with Tensor Calculus. Part II introduces General Relativity Theory, while Part III deals with Relativistic Cosmology. In Part IV we work Scalar-Tensor theories, concentrating in Cosmological Models. In the last chapters, the cosmological models presented, become more and more sophisticated, including some new cases, never published elsewhere, in which all fundamental "constants" are made to vary, with the age of the Universe, namely, the gravitational, the cosmological, the coupling Brans-Dicke "constants", the speed of light, Planck's "fine -structure "constant" alpha" etc. This is a mathematical cosmology textbook that may lead undergraduates, and graduate students, to one of the frontiers of research, while keeping the prerequisites to a minimum, because most of the theory in the book requires only prior knowledge of Calculus and a University Physics course.

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284

Publisher

Nova Publishers

Published Date

ISBN 10

1600210139

ISBN 13

9781600210136

Introduction to General Relativity and the Cosmological Constant Problem

By: Marcelo Samuel Berman

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Introduction to General Relativity and the Cosmological Constant Problem

By: Marcelo Samuel Berman

This book is an introductory text in General Relativity, while also focusing some solutions to the cosmological constant problem, which consists in an amazing 100 orders of magnitude discrepancy between the value of this constant in the present Universe, and its estimated value in the very early epoch. The author suggests that the constant is in fact, a time-varying function of the age of the Universe. The book offers a wealth of cosmological models, treats up to date findings, like the verification of the Lense-Thirring effect in the year 2004, and the recently published research by Cooperstock and Tieu (2005) suggesting that "dark" matter is not a necessary concept in order to explain the rotational velocities of stars around galaxies' nuclei. This is a mathematical cosmology textbook that may lead undergraduates, and graduate students to one of the frontiers of research, while keeping the prerequisites to a minimum, because most of the theory in the book requires only prior knowledge of Calculus and a University Physics course.

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Page Count

232

Publisher

Nova Publishers

Published Date

ISBN 10

1594547173

ISBN 13

9781594547171

Bimonoids for Hyperplane Arrangements

By: Marcelo Aguiar,Swapneel Mahajan

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Bimonoids for Hyperplane Arrangements

By: Marcelo Aguiar,Swapneel Mahajan

The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel–Hopf, Poincaré–Birkhoff–Witt, and Cartier–Milnor–Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.

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Page Count

854

Publisher

Cambridge University Press

Published Date

ISBN 10

1108852785

ISBN 13

9781108852784

Coxeter Bialgebras

By: Marcelo Aguiar,Swapneel Mahajan

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Coxeter Bialgebras

By: Marcelo Aguiar,Swapneel Mahajan

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Page Count

897

Publisher

Cambridge University Press

Published Date

ISBN 10

100924373X

ISBN 13

9781009243735

Topics in Hyperplane Arrangements

By: Marcelo Aguiar,Swapneel Mahajan

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Topics in Hyperplane Arrangements

By: Marcelo Aguiar,Swapneel Mahajan

This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Möbius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.

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Page Count

639

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470437112

ISBN 13

9781470437114

Hopf Monoids and Generalized Permutahedra

By: Marcelo Aguiar,Federico Ardila

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Hopf Monoids and Generalized Permutahedra

By: Marcelo Aguiar,Federico Ardila

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124

Publisher

American Mathematical Society

Published Date

ISBN 10

1470467089

ISBN 13

9781470467081

Book's by Marcelo Aguiar

Coxeter Bialgebras

Coxeter Bialgebras

Bimonoids for Hyperplane Arrangements

Bimonoids for Hyperplane Arrangements

Hopf Monoids and Generalized Permutahedra

Hopf Monoids and Generalized Permutahedra

Coxeter Groups and Hopf Algebras

Coxeter Groups and Hopf Algebras

Communication Systems

Communication Systems

Chains of Gold

Chains of Gold

Cellular Network Planning

Cellular Network Planning

The Unintended Consequences of Peace

The Unintended Consequences of Peace

The Mitigation Doctrine

The Mitigation Doctrine

Where does religion end?

Where does religion end?

Introduction to General Relativistic and Scalar-tensor Cosmologies

Introduction to General Relativistic and Scalar-tensor Cosmologies

Introduction to General Relativity and the Cosmological Constant Problem

Introduction to General Relativity and the Cosmological Constant Problem

Bimonoids for Hyperplane Arrangements

Bimonoids for Hyperplane Arrangements

Coxeter Bialgebras

Coxeter Bialgebras

Topics in Hyperplane Arrangements

Topics in Hyperplane Arrangements

Hopf Monoids and Generalized Permutahedra

Hopf Monoids and Generalized Permutahedra

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