Format: Paperback / softback, 218 pages, height x width: 235x155 mm, weight: 361 g, 1 Illustrations, black and white; XII, 218 p. 1 illus.
Pub. Date: 14-Jan-2023
ISBN-13: 9783031239250
Although women participated in shaping scientific thinking from the outset, they very rarely became visible. This imbalance continues today, although there are currently more female scientists than ever before. Lars Jaeger spans an arc from antiquity to the present day and portrays the lives and work of the most important female scientists and mathematicians in essay-like introductions. From Hypatia of Alexandria to Emmy Noether and Lisa Randall, they have all achieved great things, decisively advanced science and yet often could not step out of the shadow of their male colleagues. In addition to the exciting portraits of the individual women scientists, the book also sheds light on gender relations in science and their agonisingly slow evolution in favour of women.
1. Hypatia of Alexandria.-
2. Hildegard von Bingen.-
3. Emilie du Chatelet.-
4. Laura Bassi.-
5. Sophie Germain.-
6. Caroline Herschel.-
7. Ada Lovelace.-
8. Sofja Kowalevskaja.-
9. Marie Curie.-
10. Lise Meitner.-
11. Emmy Noether.-
12. Grete Hermann.-
13. Chien-Shiung Wu.-
14. Rosalind Franklin.-15. Jane Goodall.-
16. Jocelyn Bell Burnell.-
17. Lisa Randall.-
18. Maryam Mirzakhani.
Format: Hardback, 172 pages, height x width: 235x155 mm, 35 Illustrations, black and white; X, 172 p. 35 illus.
Series: Mathematics in Mind
Pub. Date: 01-Apr-2023
ISBN-13: 9783031232442
This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce's mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce's idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce's conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician.
1. Introduction.-
2. Meritocratism, Errors, and the Community of Inquiry.-
3. Logic and Mathematics.-
4. Peirce's Transcendental Deduction.-
5. Sign Relation. - 6 One, Two, Three.-
7. Iconicity and Novelty.-
8. The General and the Particular.-
9. Diagrams Between Images and Schema.-
10. Existential Graphs.-
11. Iconicity, Similarity, and Habitual Action.-
12. Mapping Philosophy.-
13. L'Image-Mouvement, Mathematically Sublime, and the Perception of Totality.-
14. The Metaphysics of Continuity.-
15. Conclusion.
Format: Paperback / softback, 384 pages, height x width: 235x155 mm, 6 Illustrations, black and white; X, 384 p. 6 illus.
Series: Grundlehren Text Editions
Pub. Date: 13-Apr-2023
Publisher: Springer International Publishing AG
ISBN-13: 9783031255694
This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles. The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier-Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained. This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.
1. Line Bundles on Complex Tori.- 2 Abelian Varieties.- 3 Moduli Spaces.- 4 Jacobian Varieties.- 5 Main Examples of Abelian Varieties.- 6 The Fourier Transform for Sheaves and Cycles.- 7 Introduction to the Hodge Conjecture for Abelian Varieties.
Format: Paperback / softback, 115 pages, height x width: 235x155 mm, 22 Tables, color; 1 Illustrations, color; 2 Illustrations, black and white; X, 115 p. 3 illus., 1 illus. in color
Series: SpringerBriefs on PDEs and Data Science
Pub. Date: 03-Apr-2023
ISBN-13: 9789811987991
This book is the first organized collection of some results that have been obtained by the authors, their collaborators, and other researchers in the variational approach to structured deformations. It sets the basis and makes more accessible the theoretical apparatus for assigning an energy to a structured deformation, thereby providing motivation to researchers in applied mathematics, continuum mechanics, engineering, and materials science to study the deformation of a solid body without committing at the outset to a specific mechanical theory. Researchers will benefit from an approach in which elastic, plastic, and fracture phenomena can be treated in a unified way. The book is intended for an audience acquainted with measure theory, the theory of functions of bounded variation, and continuum mechanics. Any students in their last years of undergraduate studies, graduate students, and researchers with a background in applied mathematics, the calculus of variations, and continuum mechanics will have the prerequisite to read this book.
1. Introduction.-
2. Mathematical preliminaries.-
3. Energetic relaxation to first-order structured deformations.-
4. Energetic relaxation to second-order structured deformations.-
5. Outlook for future research.
Format: Paperback / softback, 519 pages, height x width: 235x155 mm, VIII, 519 p.; VIII, 519 p.
Series: International Series of Numerical Mathematics 172
Pub. Date: 05-Mar-2023
ISBN-13: 9783030793951
Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.
S. Bartels, S. Hertzog, Error Bounds for Discretized Optimal Transport and its Reliable Efficient Numerical Solution.- H. G. Bock, E. Kostina, M. Sauter, J. P. Schloeder, M. Schloeder, Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems.- S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.- S. Dempe, F. Harder, P. Mehlitz, G. Wachsmuth, Analysis and Solution Methods for Bilevel Optimal Control Problems.- M. Herrmann, R. Herzog, S. Schmidt, J. Vidal-Nunez, A Calculus for Non-Smooth Shape Optimization with Applications to Geometric Inverse Problems.- R. Herzog, D. Knees, C. Meyer, M. Sievers, A. Stoetzner, S. Thomas, Rate-Independent Systems and Their Viscous Regularizations: Analysis, Simulation, and Optimal Control.- D. Ganhururu, M. Hintermuller, S.-M. Stengl, T. M. Surowiec, Generalized Nash Equilibrium Problems with Partial Differential Operators: Theory, Algorithms, and Risk Aversion.- A. Alphonse, M. Hintermuller, C. N. Rautenberg, Stability and Sensitivity Analysis for Quasi-Variational Inequalities.- C. Grassle, M. Hintermuller, M.Hinze, T. Keil, Simulation and Control of a Nonsmooth Cahn-Hilliard Navier-Stokes System with Variable Fluid Densities.- C. Kanzow, V. Karl, D.Steck, D. Wachsmuth, Safeguarded Augmented Lagrangian Methods in Banach Spaces.- M. Hahn, C. Kirches, P. Manns, S. Sager, C. Zeile, Decomposition and Approximation for PDE-Constrained Mixed-Integer Optimal Control.- C. Christof, C. Meyer, B. Schweizer, S. Turek, Strong Stationarity for Optimal Control of Variational Inequalities of the Second Kind.- A. Hehl, M. Mohammadi, I. Neitzel, W. Wollner, Optimizing Fracture Propagation Using a Phase-Field Approach.- A. Schiela, M. Stoecklein, Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain.- O. Weiss, A. Walther, S.Schmidt, Algorithms based on Abs-Linearization for Nonsmooth Optimization with PDE Constraints.- V. Schulz, K.Welker, Shape Optimization for Variational Inequalities of Obstacle Type: Regularized and Unregularized Computational Approaches.- J. Becker, A.Schwartz, S.Steffensen, A. Thunen, Extensions of Nash Games in Finite and Infinite Dimensions with Applications.