This collection of papers by leading researchers gives a broad picture of current research directions in geometric aspects of partial differential equations. Based on lectures presented at a Minisymposium on Spectral Invariants - Heat Equation Approach, held in September 1998 at Roskilde University in Denmark, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are new index theorems as well as new calculations of the eta-invariant, of the spectral flow, of the Maslov index, of Seiberg-Witten monopoles, heat kernels, determinants, non-commutative residues, and of the Ray-Singer torsion. New types of boundary value problems for operators of Dirac type and generalizations to manifolds with cuspidal ends, to non-compact and to infinite-dimensional manifolds are also discussed. Throughout the book, the use of advanced analysis methods for gaining geometric insight emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on geometric aspects of partial differential equations and spectral invariants.
In July 2007 a conference entitled «Ethical Liberalism in Contemporary Societies» was hosted by the Collegium Polonicum in Słubice, Poland. The conference was organised through collaboration between the Interdisciplinary Centre for Ethics at the European University Viadrina Frankfurt (Oder) and the Collegium Polonicum, a joint institution of the European University Viadrina Frankfurt (Oder) and the Adam Mickiewicz University Poznań. This volume collects the contributions to this conference. The problematics of liberalism affects ethicists and philosophers not only in Europe but also in Latin America and the Middle East. Scholars from these three regions met to discuss the role that the ethical aspect of liberal thought can play in the contemporary world. They also approached ethical liberalism from a historical perspective. Focusing on ethical liberalism's interconnectedness with politics, globalisation and culture, the conference participants not only elaborated on theoretical approaches, but also turned their attention to empirical case studies. This volume presents their thoughts and contributions which, although naturally fragmentary, are symptomatic of the present day and age.
Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.
Proceedings of the Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, Roskilde University, Roskilde, Denmark, August 6-9, 2003
Proceedings of the Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, Roskilde University, Roskilde, Denmark, August 6-9, 2003
In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
Legacy of the White Eagle is the true story of author Julian E. Kulski's childhood resistance to Germany's occupation of his native Poland in World War II. When the Nazi invasion in 1939 shattered Poland's democratic government and Kulski's Christian family, Kulski swore an oath of secrecy and became a freedom fighter at the age of 12. He struggled against the occupation and survived as a prisoner of war until American soldiers rescued him from a German prison camp at age 16. A handful of maps and black-and-white illustrations enhance Legacy of the White Eagle, as does an accompanying DVD with videotaped interviews with Kulski and surviving freedom fighters in Warsaw, and also a teacher's guide recommending topics for students' research.
Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski''s work in the theory of elliptic operators. Sample Chapter(s). Contents (42 KB). Contents: On the Mathematical Work of Krzysztof P Wojciechowski: Selected Aspects of the Mathematical Work of Krzysztof P Wojciechowski (M Lesch); Gluing Formulae of Spectral Invariants and Cauchy Data Spaces (J Park); Topological Theories: The Behavior of the Analytic Index under Nontrivial Embedding (D Bleecker); Critical Points of Polynomials in Three Complex Variables (L I Nicolaescu); Chern-Weil Forms Associated with Superconnections (S Paycha & S Scott); Heat Kernel Calculations and Surgery: Non-Laplace Type Operators on Manifolds with Boundary (I G Avramidi); Eta Invariants for Manifold with Boundary (X Dai); Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups (K Furutani); Remarks on Nonlocal Trace Expansion Coefficients (G Grubb); An Anomaly Formula for L 2- Analytic Torsions on Manifolds with Boundary (X Ma & W Zhang); Conformal Anomalies via Canonical Traces (S Paycha & S Rosenberg); Noncommutative Geometry: An Analytic Approach to Spectral Flow in von Neumann Algebras (M-T Benameur et al.); Elliptic Operators on Infinite Graphs (J Dodziuk); A New Kind of Index Theorem (R G Douglas); A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk (S Klimek); Star Products and Central Extensions (J Mickelsson); An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators (T Wurzbacher); Theoretical Particle, String and Membrane Physics, and Hamiltonian Dynamics: T-Duality for Non-Free Circle Actions (U Bunke & T Schick); A New Spectral Cancellation in Quantum Gravity (G Esposito et al.); A Generalized Morse Index Theorem (C Zhu). Readership: Researchers in modern global analysis and particle physics.
Proceedings of the Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, Roskilde University, Roskilde, Denmark, August 6-9, 2003
Proceedings of the Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, Roskilde University, Roskilde, Denmark, August 6-9, 2003
In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.
Finite element analysis is an engineering method for the numerical analysis of complex structures. This book provides a bird's eye view on this very broad matter through 27 original and innovative research studies exhibiting various investigation directions. Through its chapters the reader will have access to works related to Biomedical Engineering, Materials Engineering, Process Analysis and Civil Engineering. The text is addressed not only to researchers, but also to professional engineers, engineering lecturers and students seeking to gain a better understanding of where Finite Element Analysis stands today.
This revised and extended second edition covers problems concerning the design and realization of digital control algorithms for power electronics circuits using digital signal processing (DSP) methods. This book discusses signal processing, starting from analog signal acquisition, through conversion to digital form, methods of filtration and separation, and ending with pulse control of output power transistors. The book is focused on two applications for the considered methods of digital signal processing, a three-phase shunt active power filter and a digital class-D audio power amplifier. The book bridges the gap between power electronics and digital signal processing. Many control algorithms and circuits for power electronics in the current literature are described using analog transmittances. This may not always be acceptable, especially if half of the sampling frequencies and half of the power transistor switching frequencies are close to the band of interest. Therefore in this book, a digital circuit is treated as a digital circuit with its own peculiar characteristics, rather than an analog circuit. This helps to avoid errors and instability. This edition includes a new chapter dealing with selected problems of simulation of power electronics systems together with digital control circuits. The book includes numerous examples using MATLAB and PSIM programs.
Elliptic boundary problems have enjoyed interest recently, espe cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.
Judges and lawyers have to shape their moral competences in order to maintain their professional ethics at a high standard if they want to effectively meet the challenges that modern society will throw at them. This requirement is due to the growing expectation that they will be socially and morally responsible for the law. Thus, the need to place ethics at the heart of legal education, and to make ethical reflection pervasive in academic courses, becomes more obvious every day. Using the concept and examples of moral dilemmas is a way of facilitating this task. The main purpose of this book is to analyse the concept of moral dilemma in context of judicial and legal ethics, and to provide material for legal education. The structure of this book is designed with this double aim in mind. The theoretical part presents the concept of dilemmas on grounds of metaethics and the perspectives for its application in a professional legal context. The former encompasses situations of conflict of duties or obligations, in which the choice of one conduct necessarily prevents a different conduct, and therefore leads to an unacceptable outcome. Hence, the situation of dilemma always involves an issue of moral responsibility and the problem of “dirty hands”. How such situations are present in legal practice and how to deal with them is the main concern of this part. The considerations are divided into three levels of reflection – deontological, axiological, and moral responsibility. The practical part of the book contains an overview of 150 dilemmas that can be useful in legal ethics or other legal courses. The dilemmas are divided into chapters covering the following branches of law: criminal law, civil and commercial law, family and custody law, labour and social security law, and constitutional law. Every dilemma presents a description of the facts, a reconstruction of dilemma, its standard solution and some critical remarks from a meta-ethical perspective. The dilemmas cover situations regularly met in everyday practice, as well as examples of more exceptional challenges in connection with constitutional crises that have occurred in Poland in recent years.
There is no doubt that Jerusalem in the Bible is a city of great historical and theological significance. However, many modern readers are unaware that authors writing in Greek used its two names, Ierousalem and Heriosolyma. Among the few who used both names simultaneously is Luke the Evangelist. Commentators of this onomastic phenomenon have tried to explain this fact in various ways, referring to Luke's literary and theological choices or denying its meaning altogether. Krzysztof Mielcarek's monograph proposes a new view and explanation of this phenomenon in a theological-historical key. In his opinion, Luke's choices may be underpinned by his deep immersion in the world and terminological richness of the Septuagint, as well as important historical events that influenced the perception of the Holy City by the Hellenistic Jewish community and later also by the early Christians.
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