Vicente P's Books

A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures

By: Vicente Cortés

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A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures

By: Vicente Cortés

Let $V = {\mathbb R}^{p,q}$ be the pseudo-Euclidean vector space of signature $(p,q)$, $p\ge 3$ and $W$ a module over the even Clifford algebra $C\! \ell^0 (V)$. A homogeneous quaternionic manifold $(M,Q)$ is constructed for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \wedge^2 W \rightarrow V$. If the skew symmetric vector valued bilinear form $\Pi$ is nondegenerate then $(M,Q)$ is endowed with a canonical pseudo-Riemannian metric $g$ such that $(M,Q,g)$ is a homogeneous quaternionic pseudo-Kahler manifold. If the metric $g$ is positive definite, i.e. a Riemannian metric, then the quaternionic Kahler manifold $(M,Q,g)$ is shown to admit a simply transitive solvable group of automorphisms. In this special case ($p=3$) we recover all the known homogeneous quaternionic Kahler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If $p>3$ then $M$ does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kahler manifolds. Then it is shown that for $q = 0$ the noncompact quaternionic manifold $(M,Q)$ can be endowed with a Riemannian metric $h$ such that $(M,Q,h)$ is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if $p>3$. The twistor bundle $Z \rightarrow M$ and the canonical ${\mathrm SO}(3)$-principal bundle $S \rightarrow M$ associated to the quaternionic manifold $(M,Q)$ are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution $\mathcal D$ of complex codimension one, which is a complex contact structure if and only if $\Pi$ is nondegenerate. Moreover, an equivariant open holomorphic immersion $Z \rightarrow \bar{Z}$ into a homogeneous complex manifold $\bar{Z}$ of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \vee^2 W \rightarrow V$ a homogeneous quaternionic supermanifold $(M,Q)$ is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold $(M,Q,g)$ if the symmetric vector valued bilinear form $\Pi$ is nondegenerate.

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American Mathematical Soc.

Published Date

ISBN 10

0821821113

ISBN 13

9780821821114

Functional Analysis and Infinite-Dimensional Geometry

By: Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

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Functional Analysis and Infinite-Dimensional Geometry

By: Marian Fabian,Petr Habala,Petr Hajek,Vicente Montesinos Santalucia,Jan Pelant,Vaclav Zizler

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

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455

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Springer Science & Business Media

Published Date

ISBN 10

1475734808

ISBN 13

9781475734805

Resolution of Curve and Surface Singularities in Characteristic Zero

By: K. Kiyek,J.L. Vicente

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Resolution of Curve and Surface Singularities in Characteristic Zero

By: K. Kiyek,J.L. Vicente

The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

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506

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Springer Science & Business Media

Published Date

ISBN 10

1402020295

ISBN 13

9781402020292

Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles

By: Oscar García-Prada,Peter Beier Gothen,Vicente Muñoz

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Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles

By: Oscar García-Prada,Peter Beier Gothen,Vicente Muñoz

Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. in this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and the authors carry out a careful analysis of them by studying their variation with this parameter. Thus the authors obtain in particular information about the topology of the moduli spaces of parabolic triples for the value of the parameter relevant to the study of parabolic Higgs bundles. The remaining critical submanifolds are also described: one of them is the moduli space of parabolic bundles, while the rem

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American Mathematical Soc.

Published Date

ISBN 10

0821839721

ISBN 13

9780821839720

Granular Gaseous Flows

A Kinetic Theory Approach to Granular Gaseous Flows

By: Vicente Garzó

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Granular Gaseous Flows

A Kinetic Theory Approach to Granular Gaseous Flows

By: Vicente Garzó

Back Cover Text: This book addresses the study of the gaseous state of granular matter in the conditions of rapid flow caused by a violent and sustained excitation. In this regime, grains only touch each other during collisions and hence, kinetic theory is a very useful tool to study granular flows. The main difference with respect to ordinary or molecular fluids is that grains are macroscopic and so, their collisions are inelastic. Given the interest in the effects of collisional dissipation on granular media under rapid flow conditions, the emphasis of this book is on an idealized model (smooth inelastic hard spheres) that isolates this effect from other important properties of granular systems. In this simple model, the inelasticity of collisions is only accounted for by a (positive) constant coefficient of normal restitution. The author of this monograph uses a kinetic theory description (which can be considered as a mesoscopic description between statistical mechanics and hydrodynamics) to study granular flows from a microscopic point of view. In particular, the inelastic version of the Boltzmann and Enskog kinetic equations is the starting point of the analysis. Conventional methods such as Chapman-Enskog expansion, Grad’s moment method and/or kinetic models are generalized to dissipative systems to get the forms of the transport coefficients and hydrodynamics. The knowledge of granular hydrodynamics opens up the possibility of understanding interesting problems such as the spontaneous formation of density clusters and velocity vortices in freely cooling flows and/or the lack of energy equipartition in granular mixtures. Some of the topics covered in this monograph include: Navier-Stokes transport coefficients for granular gases at moderate densities Long-wavelength instability in freely cooling flows Non-Newtonian transport properties in granular shear flows Energy nonequipartition in freely cooling granular mixtures Diffusion in strongly sheared granular mixtures Exact solutions to the Boltzmann equation for inelastic Maxwell models

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419

Publisher

Springer

Published Date

ISBN 10

3030044440

ISBN 13

9783030044442

Banach Space Theory

The Basis for Linear and Nonlinear Analysis

By: Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler

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Banach Space Theory

The Basis for Linear and Nonlinear Analysis

By: Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

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820

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441975152

ISBN 13

9781441975157

An Introduction to Modern Analysis

By: Vicente Montesinos,Peter Zizler,Václav Zizler

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An Introduction to Modern Analysis

By: Vicente Montesinos,Peter Zizler,Václav Zizler

Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.

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884

Publisher

Springer

Published Date

ISBN 10

3319124811

ISBN 13

9783319124810

Biorthogonal Systems in Banach Spaces

By: Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler

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Biorthogonal Systems in Banach Spaces

By: Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

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352

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Springer Science & Business Media

Published Date

ISBN 10

038768915X

ISBN 13

9780387689159

Geometry and Topology of Manifolds: Surfaces and Beyond

By: Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo

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Geometry and Topology of Manifolds: Surfaces and Beyond

By: Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo

This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.

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408

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470461323

ISBN 13

9781470461324

Antedependence Models for Longitudinal Data

By: Dale L. Zimmerman,Vicente A. Núñez-Antón

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Antedependence Models for Longitudinal Data

By: Dale L. Zimmerman,Vicente A. Núñez-Antón

The First Book Dedicated to This Class of Longitudinal Models Although antedependence models are particularly useful for modeling longitudinal data that exhibit serial correlation, few books adequately cover these models. By gathering results scattered throughout the literature, Antedependence Models for Longitudinal Data offers a convenient, systematic way to learn about antedependence models. Illustrated with numerous examples, the book also covers some important statistical inference procedures associated with these models. After describing unstructured and structured antedependence models and their properties, the authors discuss informal model identification via simple summary statistics and graphical methods. They then present formal likelihood-based procedures for normal antedependence models, including maximum likelihood and residual maximum likelihood estimation of parameters as well as likelihood ratio tests and penalized likelihood model selection criteria for the model’s covariance structure and mean structure. The authors also compare the performance of antedependence models to other models commonly used for longitudinal data. With this book, readers no longer have to search across widely scattered journal articles on the subject. The book provides a thorough treatment of the properties and statistical inference procedures of various antedependence models.

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288

Publisher

CRC Press

Published Date

ISBN 10

1420064274

ISBN 13

9781420064278

Global Riemannian Geometry: Curvature and Topology

By: Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer

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Global Riemannian Geometry: Curvature and Topology

By: Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.

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121

Publisher

Springer Nature

Published Date

ISBN 10

3030552934

ISBN 13

9783030552930

Handbook of Pseudo-Riemannian Geometry and Supersymmetry

By: Vicente Cortés

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Handbook of Pseudo-Riemannian Geometry and Supersymmetry

By: Vicente Cortés

The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.

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972

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190795

ISBN 13

9783037190791

Renormings in Banach Spaces

A Toolbox

By: Antonio José Guirao,Vicente Montesinos,Václav Zizler

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Renormings in Banach Spaces

A Toolbox

By: Antonio José Guirao,Vicente Montesinos,Václav Zizler

This monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections. The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists and detailed indices that may lead to expected or unexpected information. Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research.

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621

Publisher

Springer Nature

Published Date

ISBN 10

3031086554

ISBN 13

9783031086557

Layered Double Hydroxides

Present and Future

By: Vicente Rives

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Layered Double Hydroxides

Present and Future

By: Vicente Rives

Layered double hydroxides are one of the variety of names given to a family of layered materials first discovered in Sweden in 1842. These materials are interesting because their layer cations can be changed among a wide selection, and the interlayer anion can also be (nearly) freely chosen. Like cationic clays, they can be pillared and can exchange interlayer species -- thus increasing applications and making new routes to derivatives. The principle areas of application include catalyst support, anion scavengers, polymer stabilisers, and antacids. In the last several years, reviews and studies of LDHs have dealt with these uses. This book aims to update the current body of LDH knowledge from a wide array of views. The first section addresses the synthesis and physiochemical characterisation of these materials, and section two focuses on the applications of LDHs.

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Page Count

518

Publisher

Nova Publishers

Published Date

ISBN 10

1590330609

ISBN 13

9781590330609

Book's by Vicente P

A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures

A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures

Functional Analysis and Infinite-Dimensional Geometry

Functional Analysis and Infinite-Dimensional Geometry

Resolution of Curve and Surface Singularities in Characteristic Zero

Resolution of Curve and Surface Singularities in Characteristic Zero

Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles

Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles

Granular Gaseous Flows

Granular Gaseous Flows

Banach Space Theory

Banach Space Theory

An Introduction to Modern Analysis

An Introduction to Modern Analysis

Biorthogonal Systems in Banach Spaces

Biorthogonal Systems in Banach Spaces

Geometry and Topology of Manifolds: Surfaces and Beyond

Geometry and Topology of Manifolds: Surfaces and Beyond

Antedependence Models for Longitudinal Data

Antedependence Models for Longitudinal Data

Global Riemannian Geometry: Curvature and Topology

Global Riemannian Geometry: Curvature and Topology

Handbook of Pseudo-Riemannian Geometry and Supersymmetry

Handbook of Pseudo-Riemannian Geometry and Supersymmetry

Renormings in Banach Spaces

Renormings in Banach Spaces

Layered Double Hydroxides

Layered Double Hydroxides

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