Format: Paperback 668 pages, height x width: 235x155 mm, 129 Illustrations, color; 76 Illustrations, black and white; XI, 668 p. 205 illus., 129 illus. in color.,
Series: Research Perspectives CRM Barcelona 16
Pub. Date: 13-Aug-2024
ISBN-13: 9783031559419
This book includes contributions from the conference held in Barcelona in 2022. It brings together researchers interested in the Anthropological Theory of the Didactic (ATD) and aims at the following objectives: Establishing an updated overview of the results and progress in the ATD, concerning both basic research and the development of education systems, including teacher education; Developing a research programme around the most relevant open problems, either related to difficulties affecting education systems or the development of didactics as a scientific discipline; Identifying and studying the specific problems raised by the extension of the ATDfs conceptual and methodological tools to other fields. The conference is structured around the following thematic axis: Axis 1: Development of the foundations, tools and aims of research in the framework of the ATD ? Axis 2: The Curriculum Problem and the paradigm of questioning the world ? Axis 3: ATD and the professionalization of the teaching profession.
What is Questioning the World? Towards an Epistemological and Curricular Break.- Problematic Issues Regarding Didactic Paradigms.- The Paradidactic: A (would-be) Fundamental Theory of Noospheres.- About a Didactic Model of Reference for the Teacher Position.- Study vs Learning: Mesogenesis and the Denial of the Didactic.- Is it the Same Twelfth? Questioning an Unquestioned Principle.- About the Mapping of Personal Practice Paths in the ATD.
Format: Paperback , 292 pages, height x width: 235x155 mm, X, 292 p.,
Series: Universitext
Pub. Date: 30-Oct-2024
ISBN-13: 9783662697207
This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity.
Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the PoincareHopf and ChernGaussBonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material.
The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.
1 Manifolds.- 2 Vector Bundles and Tensors.- 3 Riemannian Manifolds.- 4
The PoincareHopf Theorem and the ChernGausBonnet Theorem.- 5 Geodesics.- 6
Homogeneous Spaces.- 7 Symmetric Spaces.- 8 General Relativity.- A Solutions
to Selected Exercises.
Format: Paperback 80 pages, height x width: 235x155 mm, 1 Illustrations, color; 4 Illustrations, black and white; VII, 80 p. 5 illus., 1 illus. in color.,
Series: SpringerBriefs in Computer Science
Pub. Date: 17-Oct-2024
ISBN-13: 9783031705878
Are you a technologist or innovator looking to stay ahead in the rapidly evolving world of haptic technology? "Advances, Applications and the Future of Haptic Technology" is your essential guide to understanding and predicting trends that can shape how you use haptics in your products and strategies.
This book begins by defining haptic technology and its classifications. It then traces the evolution of haptic feedback systems and explores their historical significance. Through real-world case studies, the book demonstrates how haptic feedback is reshaping industries like healthcare and gaming, enhancing medical training, and creating immersive gaming experiences.
For innovators, the book addresses the challenges of implementing haptic technology across various domains, highlighting technical complexities and ergonomic considerations. For technologists, this book provides insights into the trade-offs of adopting haptics, examining the evolution of these systems with a focus on personal communication devices and the automotive industry. It also analyzes the factors influencing impact and features foresight frameworks to provide you with strategies for the future of haptic innovation. Additionally, the book explores intellectual property trends in the health, gaming, and automotive sectors to highlight key haptic innovations.
Introduction.- Exploring the role of haptic technology in healthcare.-
Exploring haptic technologys role in gaming and entertainment.- Challenges
of designing haptic experiences.- Haptic technology adoption and future
trends.- Conclusions and final remarks.
Format: Hardback, 348 pages, height x width: 235x155 mm, X, 300 p.,
Series: Operator Theory: Advances and Applications 304
Pub. Date: 24-Dec-2024
ISBN-13: 9783031734298
The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications.
The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization.
Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented.
- Part I Quaternionic functional analysis and related topics.- Functions of a Quaternionic Variable.- Quaternionic Banach and Hilbert Spaces.- Quaternionic Linear Operators on a Hilbert Space.- Reproducing Kernel Hilbert Spaces.- Part II Spaces of Slice Hyperholomorphic Functions.- Slice Hyperholomorphic Hardy Spaces.- de Branges Spaces.- Slice Hyperholomorphic Bergman Spaces.- Slice Hyperholomorphic Bloch, Besov and Dirichlet Spaces.- Slice Hyperholomorphic Fock Space.- Wiener Algebras.- Part III Various Extensions.- Slice Polyanalytic Functions.- Several Quaternionic Variables.- Function Spaces and Spectral Theories.
Format: Paperback 158 pages, height x width: 235x155 mm, 58 Illustrations, black and white; VIII, 158 p. 58 illus.,
Series: Lecture Notes in Mathematics 2361
Pub. Date: 02-Nov-2024
ISBN-13: 9783031716157
This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds. It contains a complete proof of the Twisted Morse Homology Theorem, which says that on a closed finite-dimensional smooth manifold the homology of the MorseSmaleWitten chain complex with coefficients in a bundle of abelian groups G is isomorphic to the singular homology of the manifold with coefficients in G. It also includes proofs of twisted Morse-theoretic versions of well-known theorems such as Eilenberg's Theorem, the Poincare Lemma, and the de Rham Theorem. The effectiveness of twisted Morse complexes is demonstrated by computing the Lichnerowicz cohomology of surfaces, giving obstructions to spaces being associative H-spaces, and computing Novikov numbers. Suitable for a graduate level course, the book may also be used as a reference for graduate students and working mathematicians or physicists.
1. Introduction.- 2. The Morse Complex with Local Coefficients.-
3. The Homology Determined by the Isomorphism Class of G.- 4. Singular and
CW-Homology with Local Coefficients.- 5. Twisted Morse Cohomology and
Lichnerowicz Cohomology.- 6. Applications and Computations.
Format: Paperback 216 pages, height x width: 235x155 mm, 7 Illustrations, color; 7 Illustrations, black and white; X, 190 p. 13 illus., 7 illus. in color.,
Series: Lecture Notes in Mathematics 2358
Pub. Date: 03-Dec-2024
ISBN-13: 9783031740343
This up-to-date overview of Bayesian nonparametric statistics provides both an introduction to the field and coverage of recent research topics, including deep neural networks, high-dimensional models and multiple testing, Bernstein-von Mises theorems and variational Bayes approximations, many of which have previously only been accessible through research articles. Although Bayesian posterior distributions are widely applied in astrophysics, inverse problems, genomics, machine learning and elsewhere, their theory is still only partially understood, especially in complex settings such as nonparametric or semiparametric models. Here, the available theory on the frequentist analysis of posterior distributions is outlined in terms of convergence rates, limiting shape results and uncertainty quantification. Based on lecture notes for a course given at the St-Flour summer school in 2023, the book is aimed at researchers and graduate students in statistics and probability.
1. Introduction, rates I.-2. Rates II and first examples.-3. Adaptation I: smoothness.-4. Adaptation II: high-dimensions and deep neural networks.-
5. Bernstein-von Mises I: functionals.-
6. Bernstein-von Mises II: multiscale and applications.-
7. classification and multiple testing.-
8. Variational approximations.
Format: Hardback, 519 pages, height x width: 235x155 mm, 60 Illustrations, color; 143 Illustrations, black and white; X, 250 p. 100 illus., 40 illus. in color.
Pub. Date: 19-Jan-2025
ISBN-13: 9789819782680
This book integrates the fundamentals of asymmetric multidimensional scaling, spectral graph theory, graph embedding theory, and various dynamical systems theories, that deal with the static and dynamic aspects of asymmetric phenomena. In this way, it provides a comprehensive introduction to theories and methods for analyzing phenomena observed universally in social, behavioral, economical, geographical, biological, neural, chemical reaction and other networks. The topics addressed in here include the notions of asymmetric similarity matrices, graph spectra, dimension reduction, and difference and differential equations to describe the dynamics of networks, bifurcation of vector fields, Mandelbrot sets, fractals and chaos, and Hilbert spaces. Illustrated by carefully chosen examples and supported by extensive simulation studies, the book is highly recommended to readers who seek to discover static asymmetric structures among members or nodes. It also appeals to those who want to understand the kinds of dynamics that are theoretically possible in their research domains.
Birds-eye view of asymmetric interactions among elements.- Chinos
ASYMSCAL.- GIPSCAL.- HFM.- How to use HFM for asymmetric MDS.