Format: Hardback, 663 pages, height x width: 235x155 mm, 37 Tables, color; 41 Illustrations,
color; 190 Illustrations, black and white; VIII, 663 p. 231 illus., 41 illus. in color.
Series: Springer Monographs in Mathematics
Pub. Date: 05-Oct-2022
ISBN-13: 9783031094958
This monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity.
The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, theyfve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, c 2020 and Structures of Domination in Graphs, c 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book.
1. Introduction.-
2. Historic background.-
3. Domination Fundamentals.-
4. Bounds in terms of order and size, and probability.-
5. Bounds in terms of degree.-
6. Bounds with girth and diameter conditions.-
7. Bounds in terms of forbidden subgraphs.-
8. Domination in graph families : Trees.-
9. Domination in graph families: Claw-free graphs.-
10. Domination in regular graphs including Cubic graphs.-
11. Domination in graph families: Planar graph.-
12. Domination in graph families: Chordal, bipartite, interval, etc.-
13. Domination in grid graphs and graph products.-
14. Progress on Vizing's Conjecture.-
15. Sums and Products (Nordhaus-Gaddum).-
16. Domination Games.-
17. Criticality.-
18. Complexity and Algorithms.-
19. The Upper Domination Number.-
20. Domatic Numbers (for lower and upper gamma) and other dominating partitions, including the newly introduced Upper Domatic Number.-
21. Concluding Remarks, Conjectures, and Open Problems.
Format: Hardback, 182 pages, height x width: 235x155 mm, 9 Tables, color; 6 Illustrations,
color; 14 Illustrations, black and white; VIII, 182 p. 20 illus., 6 illus. in color.,
Series: KIAS Springer Series in Mathematics 1
Pub. Date: 01-Oct-2022
ISBN-13: 9789811937071
This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction. Four of the chapters are expository in nature while one is based more directly on research. All deal with important areas of mathematics, however, such as algebraic geometry, topology, partial differential equations, Riemannian geometry, and harmonic analysis. This book is addressed to researchers who are interested in those subject areas.
Young-Hoon Kiem discusses classical enumerative geometry before string theory and improvements after string theory as well as some recent advances in quantum singularity theory, Donaldson?Thomas theory for Calabi?Yau 4-folds, and Vafa?Witten invariants.
Dongho Chae discusses the finite-time singularity problem for three-dimensional incompressible Euler equations. He presents Kato's classical local well-posedness results, Beale?Kato?Majda's blow-up criterion, and recent studies on the singularity problem for the 2D Boussinesq equations.
Simon Brendle discusses recent developments that have led to a complete classi cation of all the singularity models in a three-dimensional Riemannian manifold. He gives an alternative proof of the classi cation of noncollapsed steady gradient Ricci solitons in dimension 3.
Hyeonbae Kang reviews some of the developments in the Neumann?Poincare operator (NPO). His topics include visibility and invisibility via polarization tensors, the decay rate of eigenvalues and surface localization of plasmon, singular geometry and the essential spectrum, analysis of stress, and the structure of the elastic NPO.
Danny Calegari provides an explicit description of the shift locus as a complex of spaces over a contractible building. He describes the pieces in terms of dynamically extended laminations and of certain explicit gdiscriminant-likeh a ne algebraic varieties.
Young-Hoon Kiem: Enumerative Geometry, before and after String Theory.- Dongho Chae: On The Singularity Problem for the Euler Equations.- Simon Brendle: Singularity Models in the Three-Dimensional Ricci Flow.- Hyeonbae Kang: Spectral Geometry and Analysis of the Neumann-Poincare Operator, A Review.- Danny Calegari: Sausages and Butcher Paper.
Format: Paperback / softback, 193 pages, height x width: 235x155 mm,
5 Illustrations, black and white; X, 193 p. 5 illus.,
Series: Universitext
Pub. Date: 22-Sep-2022
ISBN-13: 9783031097997
Dieses Buch will dem Leser eine Einfuhrung in wichtige Techniken und Methoden der heutigen reellen Algebra und Geometrie vermitteln. An Voraussetzungen werden dabei nur Grundkenntnisse der Algebra erwartet, so dass das Buch fur Studenten mittlerer Semester geeignet ist.Das erste Kapitel enthalt zunachst grundlegende Fakten uber angeordnete Koerper und ihre reellen Abschlusse und behandelt dann verschiedene Methoden zur Bestimmung der Anzahl reeller Nullstellen von Polynomen. Das zweite Kapitel befasst sich mit reellen Stellen und gipfelt in Artins Loesung des 17. Hilbertschen Problems. Kapitel III schliesslich ist dem noch jungen Begriff des reellen Spektrums und seinen Anwendungen gewidmet."Neben dem 1987 erschienenen "Geometrie algebrique reelle" von J. Bochnak-M. Coste- M. Roy stellt die vorliegende Monographie das erste Lehrbuch auf diesem Gebiet dar... Damit liegt eine sehr empfehlenswerte Einfuhrung...vor..." (H. Mitsch, Monatshefte fur Mathematik 3/111, 1991)
1 Ordered fields and their real closures.- 2 Convex valuation rings and real places.- 3 The real spectrum.- 4 Recent developments.
Format: Hardback, 490 pages, height x width: 235x155 mm, 90 Illustrations,
color; 26 Illustrations, black and white; X, 490 p. 116 illus., 90 illus. in color
Series: Applied and Numerical Harmonic Analysis
Pub. Date: 18-Oct-2022
ISBN-13: 9783031097447
This contributed volume showcases the most significant results obtained from the DFG Priority Program on Compressed Sensing in Information Processing. Topics considered revolve around timely aspects of compressed sensing with a special focus on applications, including compressed sensing-like approaches to deep learning; bilinear compressed sensing - efficiency, structure, and robustness; structured compressive sensing via neural network learning; compressed sensing for massive MIMO; and security of future communication and compressive sensing.
Hierarchical compressed sensing (G. Wunder).- Proof Methods for Robust Low-Rank Matrix Recovery (T. Fuchs).- New Challenges in Covariance Estimation: Multiple Structures and Coarse Quantization (J. Maly).- Sparse Deterministic and Stochastic Channels: Identification of Spreading Functions and Covariances (Dae Gwan Lee).- Analysis of Sparse Recovery Algorithms via the Replica Method (A. Bereyhi).- Unbiasing in Iterative Reconstruction Algorithms for Discrete Compressed Sensing (F.H. Fischer).- Recovery under Side Constraints (M. Pesavento).- Compressive Sensing and Neural Networks from a Statistical Learning Perspective (E. Schnoor).- Angular Scattering Function Estimation Using Deep Neural Networks (Y. Song).- Fast Radio Propagation Prediction with Deep Learning (R. Levie).- Active Channel Sparsification: Realizing Frequency Division Duplexing Massive MIMO with Minimal Overhead (M. B. Khalilsarai).- Atmospheric Radar Imaging Improvements Using Compressed Sensing and MIMO (J. O. Aweda).- Over-the-Air Computation for Distributed Machine Learning and Consensus in Large Wireless Networks (M. Frey).- Information Theory and Recovery Algorithms for Data Fusion in Earth Observation (M. Fornasier).- Sparse Recovery of Sound Fields Using Measurements from Moving Microphones (A. Mertins).- Compressed Sensing in the Spherical Near-Field to Far-Field Transformation (C. Culotta-Lopez).
Format: Paperback / softback, 172 pages, height x width: 240x168 mm, VIII, 172 p.,
Series: Frontiers in Mathematics
Pub. Date: 21-Oct-2022
ISBN-13: 9783031120305
This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs.
Part I: Abstract Theory.- Gromov-Hausdorff distances.- Stability.- Continuity of Shift Operator.- Shadowing from Gromov-Hausdorff Viewpoint.- Part II: Applications to PDEs.- GH-Stability of Reaction Diffusion Equation.- Stability of Inertial Manifolds.- Stability of Chafee-Infante Equations.
Format: Hardback, 290 pages, height x width: 235x155 mm, 16 Tables, color; 12 Illustrations,
color; 12 Illustrations, black and white; X, 290 p. 24 illus., 12 illus. in color.,
Series: SISSA Springer Series 3
Pub. Date: 28-Oct-2022
ISBN-13: 9783031114984
This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research gbeginnersh in the field of enumerative geometry or related areas. This book can be read as an introduction to Hilbert schemes and Quot schemes on 3-folds but also as an introduction to localisation formulae in enumerative geometry. It is meant to be accessible without a strong background in algebraic geometry; however, three appendices (one on deformation theory, one on intersection theory, one on virtual fundamental classes) are meant to help the reader dive deeper into the main material of the book and to make the text itself as self-contained as possible.
1 Introduction.- 2 Counting in algebraic geometry.- 3 Background material.- 4 Informal introduction to Grassmannians.- 5 Relative Grassmannians, Quot, Hilb.- 6 The Hilbert scheme of points.- 7 Equivariant Cohomology.- 8 The Atiyah-Bott localisation formula.- 9 Applications of the localisation formula.- 10 The toy model for the virtual fundamental class and its localization.- 11 Degree 0 DT invariants of a local Calabi-Yau 3-fold.- 12 DT/PT correspondence and a glimpse of Gromov-Witten theory .- Appendix A: Deformation Theory.- Appendix B: Intersection Theory.- Appendix C: Perfect obstruction theories and virtual classes.
Format: Hardback, 224 pages, height x width: 235x155 mm, 1 Illustrations, black and white; XII, 224 p. 1 illus.,
Series: Mathematics of Data 1
Pub. Date: 24-Sep-2022
ISBN-13: 9783031066634
This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA). Covering a wide range of topics at levels of sophistication varying from elementary (matrix algebra) to esoteric (Grothendieck spectral sequence), it offers a mirror of data science aimed at a general mathematical audience.
The required algebraic background is developed in detail. The first third of the book reviews several core areas of mathematics, beginning with basic linear algebra and applications to data fitting and web search algorithms, followed by quick primers on algebra and topology. The middle third introduces algebraic topology, along with applications to sensor networks and voter ranking. The last third covers key contemporary tools in TDA: persistent and multiparameter persistent homology. Also included is a userfs guide to derived functors and spectral sequences (useful but somewhat technical tools which have recently found applications in TDA), and an appendix illustrating a number of software packages used in the field.
Based on a course given as part of a masters degree in statistics, the book is appropriate for graduate students.
Preface.-
1. Linear Algebra Tools for Data Analysis.-
2. Basics of Algebra: Groups, Rings, Modules.-
3. Basics of Topology: Spaces and Sheaves.-
4. Homology I: Simplicial Complexes to Sensor Networks.-
5. Homology II: Cohomology to Ranking Problems.-
6. Persistent Algebra: Modules over a PID.-
7. Persistent Homology.-
8. Multiparameter Persistent Homology.-
9. Derived Functors and Spectral Sequences.- Appendix A. Examples of Software Packages.- Bibliography.