Format: Hardback,
350 pages, height x width: 235x155 mm, XI, 350 p.
Pub. Date: 13-Jun-2022
ISBN-13: 9789811600166
This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds.
The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ?- -, hemi-slant ?- -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.
General Properties of Slant Submanifolds in Contact Metric Manifolds.- Curvature Inequalities for Slant Submanifolds in Pointwise Kenmotsu Space Forms.- Some Basic Inequalities on Slant submanifolds in Space forms.- Geometry of Warped Product Semi-Slant Submanifolds in Almost Contact Metric Manifolds.- Slant and Semi Slant Submanifolds of Almost Contact and Paracontact Metric Manifolds.- The Slant Submanifolds in the Setting of Metric f-manifolds.- Slant, Semi-Slant and Pointwise Slant Submanifolds of 3-Structure Manifolds.- Slant Submanifolds of Conformal Sasakian Space Forms.- Slant Curves and Magnetic Curves.- Contact Slant Geometry of Submersions and Pointwise Slant and Semi-Slant Warped Product Submanifolds.
Format: Hardback,
530 pages, height x width: 235x155 mm,
8 Tables, color; 17 Illustrations, black and white; X, 530 p. 17 illus
Pub. Date: 22-Jun-2022
ISBN-13: 9783030957599
This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariskifs equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom?Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more.
Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.
The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
1 Maria Aparecida Soares Ruas, Old and new results on density of stable mappings.- 2 David Mond and Juan Jose Nuno-Ballesteros, Singularities of mappings.- 3 Javier Fernandez de Bobadilla, Topological equisingularity: old problems from a new perspective (With an appendix by G. -M. Greuel and G. Pfister on Singular).- 4 Andras Nemethi, Surface singularities, Seiberg-Witten invariants of their links and lattice cohomology.- 5 Jean-Paul Brasselet, Characteristic classes.- 6 Paolo Aluffi, Segre classes and invariants of singular varieties.- 7 Roberto Callejas-Bedregal, Michelle F. Z. Morgado and Jose Seade, Milnor number and Chern classes for singular varieties: an Introduction.- 8 Tatsuo Suwa, Residues and hyperfunctions.- 9 Joseph Steenbrink, Mixed Hodge structures applied to singularities.- 10 Laurentiu G. Maxim and Joerg Schurmann, Constructible sheaf complexes in complex geometry and Applications.
Format: Hardback,
190 pages, height x width: 235x155 mm,
1 Illustrations, color; 44 Illustrations, black and white; XI, 190 p. 45 illus., 1 illus. in color
Series: Behaviormetrics: Quantitative Approaches to Human Behavior 14
Pub. Date: 22-May-2022
ISBN-13: 9789811909719
This book provides methods and applications of latent class analysis, and the following topics are taken up in the focus of discussion: basic latent structure models in a framework of generalized linear models, exploratory latent class analysis, latent class analysis with ordered latent classes, a latent class model approach for analyzing learning structures, the latent Markov analysis for longitudinal data, and path analysis with latent class models. The maximum likelihood estimation procedures for latent class models are constructed via the expectation?maximization (EM) algorithm, and along with it, latent profile and latent trait models are also treated. Entropy-based discussions for latent class models are given as advanced approaches, for example, comparison of latent classes in a latent class cluster model, assessing latent class models, path analysis, and so on. In observing human behaviors and responses to various stimuli and test items, it is valid to assume they are dominated by certain factors. This book plays a significant role in introducing latent structure analysis to not only young researchers and students studying behavioral sciences, but also to those investigating other fields of scientific research.
Overview of Basic Latent Structure Models.- Latent Class Cluster Analysis.- Latent Class Analysis with Ordered Latent Classes.- Latent Class Analysis with Latent Binary Variables: Application for Analyzing Learning Structures.- The Latent Markov Chain Model.- Mixed Latent Markov Chain Models.- Path Analysis in Latent Class Models.
Format: Hardback,
393 pages, height x width: 235x155 mm,
125 Illustrations, black and white; VI, 393 p. 125 illus.
Series: Trends in the History of Science
Pub. Date: 15-Jun-2022
Paper edition
ISBN-13: 9783030978358
This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models.
How to Grasp an Abstraction: Mathematical Models and Their Vicissitudes between 1830 and
1950. Introduction.- Knowing by Drawing: Geometric Material Models in 19th Century France.- Wilhelm Fiedler and his Models-the Polytechnic Side.- Models from the Nineteenth Century Used for Visualizing Optical Phenomena and Line Geometry.- Modeling Parallel Transport.- The great yogurt project: models and symmetry principles in early particle physics.- Interview with Myfanwy Evans: Entanglements on and Models of Periodic Minimal Surfaces.- The dialectics archetypes / types (universal categorical constructions / concrete models) in the work of Alexander Grothendieck.- 'Analogies,' 'Interpretations,' 'Images,' 'Systems' and 'Models': Some Remarks on the History of Abstract Representation in the Sciences since the Nineteenth Century.- Mappings, Models, Abstraction, and Imaging: Mathematical Contributions to Modern Thinking circa 1900.- Thinking with Notations: Epistemic Actions and Epistemic Activities in Mathematical Practice.- Matrices - Compensating the Loss of Anschauung .- Interview with Anja Sattelmacher: Between Viewing and Touching - Models and Their Materiality.- Interview with Ulf Hashagen: Exhibitions and Mathematical Models in the 19th and 20th Centuries.- Interview with Andreas Daniel Matt: Real-Time Mathematics.
Bibliog. data: 1st ed. 2022. 2022. x, 170 S. X, 170 p. 235 mm
Series: Springer Undergraduate Mathematics Series
ISBN-13: 9783030980245
An Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory.The subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently.With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study. Preface Introduction Chapter 1. First Steps Chapter 2. Polynomials, Subspaces, and Subrepresentations Chapter 3. Intertwining Maps, Complete Reducibility, and Invariant Inner Products Chapter 4. The Structure of the Symmetric Group Chapter 5. Sn Decomposition of Polynomial Spaces for n= 1,2,3. Chapter 6. The Group Algebra Chapter 7. The Irreducible Representations of Sn: Characters Chapter 8. The Irreducible Representations of Sn: Young Symmetrizers Chapter 9. Cosets, Restricted and Induced Representations Chapter 10. Direct Products of Groups, Young Subgroups and Permutation Modules Chapter 11. Specht Modules Chapter 12. Decomposition of Young Permutation Modules Chapter 13. Branching Relations> Bibliography Index R. Michael Howe spent 20 years in various roles in the music industry and earned a PhD in mathematics at the University of Iowa, becoming a professor at the University of Wisconsin-Eau Claire, where he is now Emeritus Professor. As a mathematics professor he has supervised research and independent study projects of scores of undergraduate students, at least a dozen of whom have gone on to earn a PhD in mathematics. He still enjoys playing music and his other hobbies include hiking, mountaineering, kayaking, biking and skiing.
Bibliog. data: 1st ed. 2022. 2022. xvii, 244 S. XVII, 244 p. 124 illus. 235 mm
Series: Mathematics in Mind
ISBN-13: 9783030964351
This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include:- The historical context of any topic that
involves how mathematical thinking emerged, focusing on archaeological and philological evidence. - Connection between math cognition and symbolism, annotation and other semiotic processes.- Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution.- Whether mathematics is an innate faculty or forged in cultural-historical context- What, if any, structures are shared between mathematics and language
Part I: Mathematics in Mind.- 1. The Origins of Mathematics in the Mind.- 2. Mathematics, the Human Mind, Verbal Language.- 3. Mathematics, Writing, and Notation.- 4. Mathematics, Deductive Logic, and Abstract Science.- 5. Computing and the Internet.- Part II: Spiral Patterns in Nature and Human Thought.- 6. The Mathematical Structure of Cyclic Phenomena.- 7. Spiral and Cyclic Structures in the Abiotic Inorganic Material World.- 8. Life is a Spiral and it is Cyclic.- 9. Spiral Thought Structures in History and Philosophy.- 10. The Spiral Structure of Marshall McLuhan"s Thinking.- 11. Spirals and the Arts.- Part III. Hyperlinking as Patterns of Connection.- 12. Pre-Digital Forms of Hypertext.- 13. Hypertext in the Digital Domain of Cyberspace.- 14. Hypermedia.- 15. Hyperlinking in the Spheres.- Epilogue.- References.