Format: Hardback, 612 pages, height x width: 235x155 mm, weight: 1105 g, 1 Illustrations, black and white; XX, 612 p. 1 illus.,
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 75
Pub. Date: 03-Aug-2022
ISBN-13: 9783031104466
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories.
Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences.
Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.
Part I The Elementary Theory of Simplicial and Dendroidal Sets.- 1 Operads.- 2 Simplicial Sets.- 3 Dendroidal Sets.- 4 Tensor Products of Dendroidal Sets.- 5 Kan Conditions for Simplicial Sets.- 6 Kan Conditions for Dendroidal Sets.- Part II The Homotopy Theory of Simplicial and Dendroidal Sets.- 7 Model Categories.- 8 Model Structures on the Category of Simplicial Sets.- 9 Three Model Structures on the Category of Dendroidal Sets.- Part III The Homotopy Theory of Simplicial and Dendroidal Spaces.- 10 Reedy Categories and Diagrams of Spaces.- 11 Mapping Spaces and Bousfield Localizations.- 12 Dendroidal Spaces and -Operads.- 13 Left Fibrations and the Covariant Model Structure.- 14 Simplicial Operads and -Operads.- Epilogue.- References.- Index.
Format: Paperback / softback, 232 pages, height x width: 235x155 mm, 25 Illustrations,
color; 12 Illustrations, black and white; VIII, 232 p. 37 illus., 25 illus. in color
Series: SpringerBriefs in Mathematics
Pub. Date: 09-Oct-2022
ISBN-13: 9783031116971
This book focuses on linear time eigenvalue location algorithms for graphs. This subject relates to spectral graph theory, a field that combines tools and concepts of linear algebra and combinatorics, with applications ranging from image processing and data analysis to molecular descriptors and random walks. It has attracted a lot of attention and has since emerged as an area on its own.
Studies in spectral graph theory seek to determine properties of a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors have surprisingly many connections with the structure of a graph. This book approaches this subject under the perspective of eigenvalue location algorithms. These are algorithms that, given a symmetric graph matrix M and a real interval I, return the number of eigenvalues of M that lie in I. Since the algorithms described here are typically very fast, they allow one to quickly approximate the value of any eigenvalue, which is a basic step in most applications of spectral graph theory. Moreover, these algorithms are convenient theoretical tools for proving bounds on eigenvalues and their multiplicities, which was quite useful to solve longstanding open problems in the area. This book brings these algorithms together, revealing how similar they are in spirit, and presents some of their main applications.
This work can be of special interest to graduate students and researchers in spectral graph theory, and to any mathematician who wishes to know more about eigenvalues associated with graphs. It can also serve as a compact textbook for short courses on the topic.
Preface.- Introduction.- Preliminaries.- Locating Eigenvalues in Trees.- Graph Representations.- Locating Eigenvalues in Threshold Graphs and Cographs.- Locating Eigenvalues in Arbitrary Graphs.- Locating Eigenvalues in Distance Hereditary Graphs.- Some Other Algorithms.- References.
Format: Hardback, 298 pages, height x width: 235x155 mm, 1 Illustrations, color;
36 Illustrations, black and white; XII, 298 p. 37 illus., 1 illus. in color
Series: Trends in Logic 60
Pub. Date: 07-Oct-2022
ISBN-13: 9783031097058
This open access book makes a case for extending logic beyond its traditional boundaries, to encompass not only statements but also also questions. The motivations for this extension are examined in detail. It is shown that important notions, including logical answerhood and dependency, emerge as facets of the fundamental notion of entailment once logic is extended to questions, and can therefore be treated with the logicianfs toolkit, including model-theoretic constructions and proof systems.
After motivating the enterprise, the book describes how classical propositional and predicate logic can be made inquisitive?i.e., extended conservatively with questions?and what the resulting logics look like in terms of meta-theoretic properties and proof systems. Finally, the book discusses the tight connections between inquisitive logic and dependence logic.
1. Introduction.-
2. On the role of questions in logic.-
3. Questions in propositional logic.-
4. Reasoning with questions.-
5. Questions in first-order logic.-
6. Questions in modal logic.-
7. Connections with intuitionistic logic.-
8. Connections with dependence logic.-
9. Conclusion.
Format: Hardback, 197 pages, height x width: 235x155 mm, 57 Tables, color; 59 Illustrations,
color; 11 Illustrations, black and white; IX, 197 p. 70 illus., 59 illus. in color.
Series: Applied Mathematical Sciences 210
Pub. Date: 18-Oct-2022
ISBN-13: 9783031086588
This monograph is devoted to Eulerian models for fluid-structure interaction by applying the original point of view of level set methods.
In the last 15 years, Eulerian models have become popular tools for studying fluid-structure interaction problems. One major advantage compared to more conventional methods such as ALE methods is that they allow the use of a single grid and a single discretization method for the different media. Level set methods in addition provide a general framework to follow the fluid-solid interfaces, to represent the elastic stresses of solids, and to model the contact forces between solids.
This book offers a combination of mathematical modeling, aspects of numerical analysis, elementary codes and numerical illustrations, providing the reader with insights into ??the applications and performance of these models.
Assuming background at the level of a Masterfs degree, Level Set Methods for Fluid-Structure Interaction provides researchers in the fields of numerical analysis of PDEs, theoretical and computational mechanics with a basic reference on the topic. Its pedagogical style and organization make it particularly suitable for graduate students and young researchers.
1. Level Set methods and Lagrangian interfaces.-
2. Mathematical tools for continuum mechanics.-
3. Interaction of an incompressible fluid with an elastic membrane.-
4. Immersed bodies : the case of elastic bodies.-
5. Immersed bodies : the case of rigid bodies.-
6. Interaction between bodies by the Level Set method.-
7. Appendix.-
8. References.
Format: Hardback, 507 pages, height x width: 235x155 mm, 13 Tables, color; 13 Illustrations, color; X, 507 p. 13 illus. in color
Series: Springer Monographs in Mathematics
Pub. Date: 09-Nov-2022
ISBN-13: 9783031108846
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein?Vishik?Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the readerfs convenience).
Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling.
The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac?Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction.
Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.
Format: Hardback, 187 pages, height x width: 235x155 mm, 50 Tables, color; 50 Tables, black and white;
5 Illustrations, color; 17 Illustrations, black and white; XII, 187 p. 22 illus., 5 illus. in color.
Series: Springer Texts in Statistics
Pub. Date: 14-Oct-2022
ISBN-13: 9783031098383
Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability?keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics:
Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.
Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.
Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.
Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information?scientific evidence?ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.
This book would be relevant to students, practitioners, and applied statisticians interested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes.
Format: Hardback, 390 pages, height x width: 235x155 mm, 46 Illustrations, color;
3 Illustrations, black and white; VI, 390 p. 49 illus., 46 illus. in color
Series: Trends in Mathematics
Pub. Date: 09-Oct-2022
ISBN-13: 9783031119378
This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.
M. C. Brambilla, O. Dumitrescu, E. Postinghel, "Weyl cycles on the blow-up of $P^4$ at eight points".- A. Brigaglia, "Simson's reconstruction of Apollonius' Loci Plani. Modern ideas in classical language".- F. Catanese, "Kummer quartic surfaces, strict self-duality, and more".- L. Chiantini e Giorgio Ottaviani, "A footnote to a footnote to a paper of B. Segre".- T. Dedieu and E. Sernesi, "Deformations and extensions of Gorenstein weighted projective spaces".- V. Di Gennaro and Davide Franco, "Intersection cohomology and Severi Varieties".- O. Dumitrescu and R. Miranda, "Cremona Orbits in $\mathbb P^4$ and Applications".- F. Flamini and P. Supino, "On some components of Hilbert schemes of curves".- Gerard van der Geer, "Siegel modular forms of degree two and three and invariant theory".- A. Laface and L. Ugaglia, "On intrinsic negative curves".- Angelo F. Lopez, with an appendix by Thomas Dedieu, "On the extendibility of projective varieties: a survey".- M. Mella, "The minimal Cremona degree of quartic surfaces".- M. Mendes Lopes and R. Pardini, "On the degree of the canonical map of a surface of general type".- C. Pedrini, "Hyperkaehler varieties with a motive of abelian type".- F. Polizzi and P. Sabatino, "Finite quotients of surface braid groups and double Kodaira fibrations".- Y. Prokhorov and M. Zaidenberg, "Affine cones over Fano-Mukai fourfolds of genus 10 are flexible".- J. Roe, "Enriques diagrams under pullback by a double cover".- E. Rogora, "The "projective spirit" in Segre's lectures on differential equations".