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Triesch E: Diskrete Mathematik

Diskrete Mathematik

Theorie und Werkzeuge zur Lösung von Abzähl- und Existenzproblemen

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fields This book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

This book is useful not only for young but also for mature scientists who are preparing methods for studying natural environmental phenomena and their alteration by human activity.As spatio-temporal scales of natural environmental phenomena become larger, the variance of their fluctuations increases or decreases over wide ranges. Such signals appear not only in environmental dynamics but everywhere, even in seemingly unrelated fields. When one looks at these signals more closely, one finds that they are governed by specific, measurable scaling laws, that is, a statistical relationship between big and small, between fast and slow.In this book, the authors describe and explain processes that have puzzled environmental science for decades, such as the climate crisis, clouds, turbulence, earthquakes, cosmic rays, sea wind waves, hurricanes, floods, radiation field in the climate system, ozone hole, greenhouse effect, air pollution, El Nino / La Nina, nowcasting models.

The Stochastic Nature of Environmental Phenomena and Processes

Cambridge Studies in Advanced Mathematics

Intended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.

Equivariant Cohomology in Algebraic Geometry

An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields Exponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck’s creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving the Riemann hypothesis part of the Weil conjectures, established the importance of the monodromy groups of these local systems. Deligne’s theorem shows that the monodromy group of the local system incarnating a given family of exponential sums determines key statistical properties of the family of exponential sums in question. Despite the apparent simplicity of this relation of monodromy groups to statistical properties, the actual determination of the monodromy group in any particular situation is highly nontrivial and leads to many interesting questions. This book is devoted to the determination of the monodromy groups attached to various explicit families of exponential sums, especially those attached to hypergeometric sheaves, arguably the simplest local systems on G_m, and to some simple (in the sense of simple to write down) one-parameter families of one-variable sums. These last families turn out to have surprising connections to hypergeometric sheaves. One of the main technical advances of this book is to bring to bear a group-theoretic condition (S+), which, when it applies, implies very strong structural constraints on the monodromy group, and to show that (S+) does indeed apply to the monodromy groups of most hypergeometric sheaves.

Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

Quantum Communication and Cryptography introduces readers to the theory of quantum cryptography, with a focus will on quantum key distribution (QKD) and more advanced quantum cryptographic protocols beyond QKD. It contains a brief introduction to the field of modern cryptography that is needed to fully appreciate and understand how quantum cryptographic systems are proven secure, and how they can be safely used in combination with current day classical systems. Readers are then introduced to quantum key distribution (QKD) - perhaps the most celebrated, and currently the most practical, of quantum cryptographic techniques. Basic protocols are described, and security proofs are given, providing readers with the knowledge needed to understand how QKD protocols are proven secure using modern, state- of-the-art definitions of security. Following this, more advanced QKD protocols are discussed, along with alternative quantum and classical methods to improve QKD performance. Finally, alternative quantum cryptographic protocols are covered, along with a discussion on some of the practical considerations of quantum secure communication technology. Throughout, protocols are described in a clear and consistent manner that still provides comprehensive, theoretical proofs and methods.

Quantum Communication and Cryptography

Springer Handbooks

Springer Handbook of Reliability

Agent-Based Models with MATLAB introduces Agent-Based Modeling (ABM), one of the most important methodologies for complex systems modeling. The book explores computational implementations and accompanying MATLAB software code as a means of inspiring readers to apply agent-based models to solve a diverse range of problems. It comes with a large amount of software code that accompanies the main text, and the modeling systems described in the book are implemented using MATLAB as the programming language. Despite the heavy mathematical components of Agent-Based Models and complex systems, it is possible to utilize these models without in-depth understanding of their mathematical fundamentals. This book enables computer scientists, mathematicians, researchers, and engineers to apply ABM in a wide range of research and engineering applications. It gradually advances from basic to more advanced methods while reinforcing complex systems through practical, hands-on applications of various computational models.

Agent-Based Models with MATLAB

The study of one-shot devices such as automobile airbags, fire extinguishers, or antigen tests, is rapidly becoming an important problem in the area of reliability engineering. These devices, which are destroyed or must be rebuilt after use, are a particular case of extreme censoring, which makes the problem of estimating their reliability and lifetime challenging. However, classical statistical and inferential methods do not consider the issue of robustness. Statistical Modeling and Robust Interference for One-shot Devices offers a comprehensive investigation of robust techniques of one-shot devices under accelerated-life tests. With numerous examples and case studies in which the proposed methods are applied, this book includes detailed R codes in selected chapters to help readers implement their own codes and use them in the proposed examples and in their own research on one-shot devicetesting data. Researchers, mathematicians, engineers, and students working on acceleratedlife testing data analysis and robust methodologies will find this to be a welcome resource.

Statistical Modeling and Robust Inference for One-shot Devices

Chapman & Hall/CRC Studies in Informatics Series

Presenting first-order and propositional methods as well as implementation issues, this book provides a state-of-the-art introduction to the automation of logic. It focuses on superposition calculus and related rewriting techniques. It also covers decision procedures for certain theories and includes real-world applications. Along with the relevant theory, each chapter contains implementation methods, historical background, suggestions for further reading, and software. Supplemental materials and resources are provided on the book's website and a solutions manual is available for qualifying instructors.

Automation of Logic

SpringerBriefs in Materials

This book delves into the foundational principles governing the treatment of molecular networks and "chemical space"-the comprehensive domain encompassing all physically achievable molecules-from the perspectives of vector space, graph theory, and data science. It explores similarity kernels, network measures, spectral graph theory, and random matrix theory, weaving intriguing connections between these diverse subjects. Notably, it emphasizes the visualization of molecular networks. The exploration continues by delving into contemporary generative deep learning models, increasingly pivotal in the pursuit of new materials possessing specific properties, showcasing some of the most compelling advancements in this field. Concluding with a discussion on the meanings of discovery, creativity, and the role of artificial intelligence (AI) therein.
Its primary audience comprises senior undergraduate and graduate students specializing in physics, chemistry, and materials science. Additionally, it caters to those interested in the potential transformation of material discovery through computational, network, AI, and machine learning (ML) methodologies.

Navigating Molecular Networks

De Gruyter Series in Probability and Stochastics

Stochastic Hierarchical Complex Dynamic Network-centric Models

Epidemiological Processes in the Biological and Social Sciences

Frontiers in Mathematics

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Readers will better understand how the methods of Euler systems and Kolyvagin systems can be adapted to Heegner points and CM points. Also offered is a comprehensive overview of the most important classical and recent results on these objects. Shafarevich-Tate Groups will be a valuable resource to those interested in this active area of research.

Shafarevich-Tate Groups

Diskrete Mathematik

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