An Invitation to Variational Methods in Differential Equations

This book provides a snapshot of privacy laws and practices from a varied set of jurisdictions in order to offer guidance on national and international contemporary issues regarding the processing of personal data and serves as an up-to-date resource on the applications and practice-relevant examples of data protection laws in different countries. Privacy violations emerging at an ever-increasing rate, due to evolving technology and new lifestyles linked to an intensified online presence of ever more individuals, required the design of a novel data protection and privacy regulation. The EU General Data Protection Regulation (GDPR) stands as an example of a regulatory response to these demands. The authors included in this book offer an in-depth analysis of the national data protection legislation of various countries across different continents, not only including country-specific details but also comparing the idiosyncratic characteristics of these national privacy laws to the GDPR. Valuable comparative information on data protection regulations around the world is thus provided in one concise volume. Due to the variety of jurisdictions covered and the practical examples focused on, both academics and legal practitioners will find this book especially useful, while for compliance practitioners it can serve as a guide regarding transnational data transfers. Elif Kiesow Cortez is Senior Lecturer at the International and European Law Program at The Hague University of Applied Sciences in The Netherlands.

Discover the practical power of advanced mathematics with "From Vectors to Tensors," available exclusively at Springer Shop. This essential textbook bridges the gap between abstract theory and real-world application, crafted by Professor Juan Ramon Ruiz-Tolosa and Professor Enrique Castillo. It transforms complex multilinear algebra into an accessible and powerful tool for solving practical problems. Forget esoteric language and dense theoretical treatises. This book is written from an applied perspective, maintaining rigorous mathematical standards while focusing on clear, numerical details. It is designed for graduate students, postgraduates, and professionals who need effective solutions. Whether you are a mathematician, physicist, engineer, or applied scientist, this guide provides the tensor tools necessary for your work. It assumes a foundational knowledge of linear algebra and serves as both a comprehensive course textbook and a vital consultation reference. Visit Springer Shop at https://link.springer.com to secure your copy. Elevate your analytical capabilities with a resource that prioritizes practical utility without sacrificing academic depth, empowering you to tackle complex challenges with confidence.

Discover advanced mathematical models and innovative techniques with "Pseudosolution of Linear Functional Equations," available now at Springer Shop. This essential text introduces robust methods for constructing pseudosolutions in both well-posed and ill-posed linear functional equations, addressing models for passive, active, and complex experimental designs. Explore detailed analysis of two primary functional equations: systems of linear algebraic equations and linear integral equations. The book develops sophisticated construction methods to handle passive right-hand side errors, considering various operator errors like passive measurements and active representation inaccuracies, along with their combinations. For deterministic and stochastic models in passive experiments, learn the method of least distances for building pseudosolutions. Active experiments are tackled using the maximum likelihood method, while combined models of regression, passive, and active experiments are addressed with integrated approaches. The text also presents regularized variants of these methods, specifically for systems of linear algebraic equations with degenerated matrices and for linear integral equations of the first kind. While pure mathematics often focuses on exact input data, applied mathematics frequently deals with the more complex challenge of perturbed data. This comprehensive volume is dedicated to the critical problem of pseudosolution construction, or parameter estimation, within fundamental areas of applied mathematics. It covers confluent models for passive and active experiments, as well as every possible mixed experimental scenario, providing invaluable insights for researchers and practitioners. Visit Springer Shop at https://link.springer.com to secure your copy and deepen your expertise in solving functional equations with real-world, imperfect data. Enhance your academic or professional library with this pivotal resource from a trusted leader in scientific publishing.

Discover the definitive geometric framework for understanding state spaces of operator algebras with "Geometry of State Spaces of Operator Algebras" from Springer Shop. This essential volume provides complete axiomatic characterizations for both associative and non-associative algebras, including C*-algebras, von Neumann algebras, JB-algebras, and JBW-algebras. It offers a thorough and updated presentation of key characterization theorems, making it an invaluable resource for researchers and advanced students in functional analysis and mathematical physics. Our book serves as a critical intermediate step, elucidating the state spaces of normed Jordan algebras to pave the way for characterizing their associative counterparts. For your convenience, we include a comprehensive appendix summarizing all necessary prerequisites on orientations of state spaces, C*-algebras, and von Neumann algebras. This ensures the text is self-contained, with clear references to foundational proofs for deeper study. At Springer Shop, we are committed to providing authoritative scientific content that advances academic research. Explore this and other specialized titles at https://link.springer.com to enhance your professional library with trusted publications. Secure your copy to gain a complete geometric description essential for cutting-edge work in operator theory and related disciplines.

Discover the groundbreaking insights of "Analysis on Lie Groups with Polynomial Growth," available exclusively at Springer Shop. This pioneering text is the first to systematically explore the profound and unexpected relationship between invariant differential operators and almost periodic operators on nilpotent Lie groups. It provides an essential framework for understanding second-order, right invariant, elliptic operators on the critical class of manifolds known as Lie groups with polynomial growth. Our book meticulously develops the necessary analytic and algebraic foundations, enabling a deep dive into this advanced area. A key achievement presented is the description of large time behavior for semigroups generated by complex second-order operators, utilizing innovative homogenization theory to deliver precise asymptotic expansions. This work uniquely transcends classical approaches by transforming intricate analytical challenges into more tractable algebraic problems. Ideal for graduate students and established researchers in analysis and Lie theory, this volume from Springer Shop represents a vital addition to your academic library. It assumes a foundational knowledge of semigroup and Lie group theory, guiding readers through sophisticated concepts with clarity. Visit link.springer.com to secure your copy of this seminal work and advance your research with authoritative, cutting-edge mathematical scholarship.

Discover a powerful approach to understanding complex differential equations with Solitons in Field Theory and Nonlinear Analysis, available now at Springer Shop. This essential text moves beyond the limitations of seeking closed-form solutions, which apply to only a narrow set of problems. Instead, it delves into the sophisticated second approach: investigating solutions through the lens of modern nonlinear analysis. Authored by a prominent and active researcher in the field, this book bridges the gap between advanced mathematics and theoretical physics. It provides invaluable insights for professionals and academics who are engaged with nonlinear systems. The content is meticulously crafted to be both rigorous and accessible, offering practical tools and deep theoretical understanding. Whether you are a mathematician exploring field theory or a physicist tackling nonlinear phenomena, this volume serves as a critical resource. It equips you with the analytical techniques needed to navigate and solve challenging problems. Explore this and other specialized titles at link.springer.com, your premier destination for authoritative scientific literature. Enhance your research and expand your analytical toolkit with this comprehensive guide from Springer Shop.

Discover the foundational research presented at the Intelligent Information Systems Symposium IIS'2002 with this essential proceedings volume from Springer Shop. This collection captures the cutting-edge discussions and papers from the eleventh symposium held in Sopot, Poland, a premier event organized by the Institute of Computer Science of the Polish Academy of Sciences. Since its inception in 1992, this symposium has grown from a small workshop into a major international conference, attracting leading scientists from universities across Europe, Asia, and North America. It serves as a critical forum for the latest advancements in Artificial Intelligence and its many applications. The 2002 symposium focused on pivotal intelligent information systems topics, including the development of decision trees and advanced classifier systems. It also featured significant research on neural networks and biologically inspired computational models, pushing the boundaries of machine learning. Key themes explored innovative clustering methods and sophisticated techniques for handling imprecision and uncertainty in data. The event further covered progress in deductive, distributed, and agent-based systems, highlighting the move towards more collaborative and applied research. This volume reflects the symposium's successful trend of increasing cooperative contributions and a growing diversity of practical applications derived from theoretical work. It is an invaluable resource for researchers, academics, and practitioners in computer science. For anyone studying the evolution of AI, machine learning, knowledge discovery, or soft computing, these proceedings offer direct access to the pioneering ideas presented. Secure your copy of this historical snapshot in AI development today at link.springer.com.

Discover the insightful analysis presented in "What Hampers Part-Time Work?" available now at Springer Shop. This essential volume, a refined version of the author's pivotal dissertation, delves into the complex dynamics of wages, hours restrictions, and employment. Conducted as part of the significant research project on working hour flexibility, this study is supported by the Centre for European Economic Research and the Fritz Thyssen Stiftung. Gain a deeper understanding of the economic and structural barriers affecting part-time employment across various sectors. The author extends sincere gratitude to advisors Prof. Wolfgang Franz and Prof. Daniel Hamermesh, whose expert guidance was instrumental in shaping this comprehensive work. Their valuable discussions and encouragement helped navigate the broader issues and technical challenges involved. This book is an invaluable resource for economists, policymakers, and students seeking to comprehend the factors limiting flexible work arrangements. Explore rigorous methodological analysis and model specifications that address key convergence problems in labor economics. Visit Springer Shop at https://link.springer.com to add this critical examination to your academic library and enhance your research with its profound insights.

Discover the next generation of quality management with "Dynamic Control of Quality in Production-Inventory Systems" from Springer Shop. This essential text moves beyond static models to present a sophisticated, coordinated approach for improving industrial performance. It addresses the real-world reality where quality control is never an isolated function, but deeply interconnected with your entire production and logistics workflow. The book's core methodology is built on robust Markov decision programming, providing a scientific framework for making superior operational decisions. Learn to conduct precise observations, tests, and inspections that directly enhance process efficiency and output. This dynamic perspective is crucial for modern operations seeking a competitive edge. Ideal for graduate-level courses in statistical process control, this volume also serves as an invaluable reference for professionals and researchers. Whether your field is mathematics, operations research, quality control, or production planning, you'll find actionable insights to optimize your systems. Visit Springer Shop at https://link.springer.com to explore this key resource. Elevate your expertise in operations management and logistics with a text that bridges advanced theory with practical application, helping you achieve significant savings and performance improvements in complex industrial environments.

Discover a more flexible approach to statistical challenges with "Soft Methods in Probability, Statistics and Data Analysis," available at Springer Shop. Real-world data analysis often involves vague information and imprecise requirements that classical theories struggle to handle. This essential text explores innovative frameworks designed to address these complexities, moving beyond traditional rigid models. The book presents a comprehensive collection of softening techniques that incorporate concepts from fuzzy sets, rough sets, and possibility theory. Expert contributors from diverse methodological backgrounds share their insights on belief functions and imprecise probabilities, offering practical solutions for modern data problems. These approaches provide the mathematical sophistication needed for today's ambiguous datasets while maintaining analytical rigor. Researchers and practitioners will find valuable methodologies for handling uncertainty in their statistical work. Each chapter demonstrates how soft methods can be applied to real analysis scenarios where conventional tools fall short. The content bridges theoretical advancements with practical applications, making complex concepts accessible and immediately useful. Visit Springer Shop at https://link.springer.com to explore this forward-thinking resource that redefines probability and statistics for contemporary challenges. Enhance your analytical toolkit with approaches that embrace uncertainty rather than avoid it, perfect for advanced students and professionals navigating imperfect data environments.

As e-commerce becomes the norm of business transactions and information be­ comes an essential commodity, it is vital that extensive efforts be made to examine and rectify the problems with the underlying architectures, processes, methods, that are involved in providing and and tools, as well as organizational structures, utilizing services relating to information technology. Such a holistic view of the relevant structures is required in order to identify all of the key aspects that can affect network security. Unfortunately, today's systems and practices, although they have proved to be useful and become widespread, contain significant unnecessary complexity. This complexity provides many loopholes that make systems and practices vulnerable to malicious attacks by hackers as well as by individual and organized criminals. FUrther, there are enormous risks due to malfunction of the systems. The holes in the network system cannot simply be plugged up by the use of cryptography and firewalls. While many changes need to be made in operating systems and system software with respect to security, this alone does not solve the problem. The problems cannot be solved by addressing only a single key aspect of network security. A holistic approach is required. Sumit Ghosh has provided in this book such a holistic view of the area of network security. Thus, it is a most welcome contribution.

There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group. The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993).

This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical properties. Wave equations are time dependent. However, use of the Fourier trans­ form reduces their study to that of harmonic systems: the harmonic Helmholtz equation, in the case of the acoustic equation, or the har­ monic Maxwell system. This book concentrates on the study of these harmonic problems, which are a first step toward the study of more general time-dependent problems. In each case, we give a mathematical setting that allows us to prove existence and uniqueness theorems. We have systematically chosen the use of variational formulations related to considerations of physical energy. We study the integral representations of the solutions. These representa­ tions yield several integral equations. We analyze their essential properties. We introduce variational formulations for these integral equations, which are the basis of most numerical approximations. Different parts of this book were taught for at least ten years by the author at the post-graduate level at Ecole Poly technique and the University of Paris 6, to students in applied mathematics. The actual presentation has been tested on them. I wish to thank them for their active and constructive participation, which has been extremely useful, and I apologize for forcing them to learn some geometry of surfaces.

This book is concerned with a number of theories that can be used for describ­ ing and analyzing systems of interacting components in case it is desirable or necessary to regard their time-dependent behavior. Society is becoming increasingly more dependent on complex computer­ based systems that are composed of several components that act concurrently and interact - to synchronize and communicate with each other. The com­ plexity of these systems arises to a great extent from the many ways in which their components can interact. The need that these components act and in­ teract on time as well adds considerably to the complexity. In developing such a system, it is important to be able to acquire a better understanding of the relevant issues at the conceptual level, to describe the system in a precise way at various levels of detail, and to analyze it on the basis of the descriptions. When the early algebraic theories about processes, such as ACP [16, 17, 20], CCS [49, 50] and CSP [27, 39], were developed for that purpose, the established opinion was still that timing is a concern that can more often than not be treated independently. It is therefore not surprising that timing is deliberately ignored in those theories. They have now all been extended to deal with timing.

"It is not the consciousness of men that defines their existence, but, on the contrary, their social existence determines their consciousness." Karl Marx In recent years, several researchers have argued that the design of multi-agent sys­ tems (MAS) in complex, open environments can benefit from social abstractions in order to cope with problems in coordination, cooperation and trust among agents, problems which are also present in human societies. The agent-mediated electronic institutions (e-institutions for short) is a new and promising field which focuses in the concepts of norms and institutions in order to pro­ vide normative frameworks to restrict or guide the behaviour of (software) agents. The main idea is that the interactions among a group of (software) agents are ruled by a set of explicit norms expressed in a computational language representation that agents can interpret. Such norms should not be considered as a negative constraining factor but as an aid that guides the agents' choices and reduces the complexity ofthe environment making the behaviour of other agents more predictable.

P.A. Blythe: Non-linear far-field theories in relaxing gas flows.- Meixner: Thermodynamics of deformable materials.- A.C. Pipkin: Non-linear phenomena in continua.- R.S. Rivlin: An introduction to non-linear continuum mechanics.- G.F. Smith: The generation of integrity bases.

The primary focus of this book is on explicating the direct method approach. Historically, direct methods have not been fully exploited in control problems. The key is constructing convergent minimizing families. Integration methods (for example the gradient method) and representation methods (such as the Ritz-Galerkin and Finite Element methods) are examined in this text in an abstract (with concrete examples) functional analytic way. The aim is to consider direct methods from a unified general point of view and to provide a stimulus for future research. Explicitly, implicitly and by example, potential areas of research interest are indicated. The book is a suitable reference for graduate students, researchers, applied mathematicians, and control engineers. Some of the material is of independent mathematical interest. The work may be used as a text for a graduate course or seminar on direct methods in control. A degree of mathematical sophistication and some knowledge of control theory is required.

This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.

This book treats ensembles of Young diagrams originating from group-theoretical contexts and investigates what statistical properties are observed there in a large-scale limit. The focus is mainly on analyzing the interesting phenomenon that specific curves appear in the appropriate scaling limit for the profiles of Young diagrams. This problem is regarded as an important origin of recent vital studies on harmonic analysis of huge symmetry structures. As mathematics, an asymptotic theory of representations is developed of the symmetric groups of degree n as n goes to infinity. The framework of rigorous limit theorems (especially the law of large numbers) in probability theory is employed as well as combinatorial analysis of group characters of symmetric groups and applications of Voiculescu's free probability. The central destination here is a clear description of the asymptotic behavior of rescaled profiles of Young diagrams in the Plancherel ensemble from both static and dynamic points of view.

This book gathers, in a beautifully structured way, recent findings on chain conditions in commutative algebra that were previously only available in papers. The majority of chapters are self-contained, and all include detailed proofs, a wealth of examples and solved exercises, and a complete reference list. The topics covered include S-Noetherian, S-Artinian, Nonnil-Noetherian, and Strongly Hopfian properties on commutative rings and their transfer to extensions such as polynomial and power series rings, and more. Though primarily intended for readers with a background in commutative rings, modules, polynomials and power series extension rings, the book can also be used as a reference guide to support graduate-level algebra courses, or as a starting point for further research.

This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.