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The Mathematics of Knots
The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.
Foundations of Knowledge Representation and Reasoning
The papers collected in this book cover a wide range of topics in asymptotic statistics. In particular up-to-date-information is presented in detection of systematic changes, in series of observation, in robust regression analysis, in numerical empirical processes and in related areas of actuarial sciences and mathematical programming. The emphasis is on theoretical contributions with impact on statistical methods employed in the analysis of experiments and observations by biometricians, econometricians and engineers.
Homotopy Theory of the Suspensions of the Projective Plane
Investigates the homotopy theory of the suspensions of the real projective plane. This book computes the homotopy groups up to certain range. It also studies the decompositions of the self smashes and the loop spaces with some applications to the Stiefel manifolds.
Singular Intersection Homology
The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.
Topology of Stratified Spaces
This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
$S$-Modules in the Category of Schemes
Gives a theory $S$-modules for Morel and Voevodsky's category of algebraic spectra over an arbitrary field $k$. This work also defines universe change functors, as well as other important constructions analogous to those in topology, such as the twisted half-smash product.
Topological Methods in Data Analysis and Visualization V
This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world’s leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.
$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type
The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
