Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.
This book studies structural properties of Q-curvature from an extrinsic point of view by regarding it as a derived quantity of certain conformally covariant families of differential operators which are associated to hypersurfaces.
We study conformal symmetry breaking differential operators which map dif-ferential forms on Rn to differential forms on a codimension one subspace Rn−1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn−1. They correspond to homomorphisms of generalized Verma mod-ules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F -method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the re-lated branching problems restricting generalized Verma modules for so(n +1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, δ, d¯ and δ¯ and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover opera- tors of the Euclidean metrics on Rn and Rn−1 and the operators d, δ, d¯ and δ¯ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn−1, respectively.
Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.
Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.
Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.
We study conformal symmetry breaking differential operators which map dif-ferential forms on Rn to differential forms on a codimension one subspace Rn−1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn−1. They correspond to homomorphisms of generalized Verma mod-ules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F -method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the re-lated branching problems restricting generalized Verma modules for so(n +1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, δ, d¯ and δ¯ and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover opera- tors of the Euclidean metrics on Rn and Rn−1 and the operators d, δ, d¯ and δ¯ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn−1, respectively.
This book studies structural properties of Q-curvature from an extrinsic point of view by regarding it as a derived quantity of certain conformally covariant families of differential operators which are associated to hypersurfaces.
The second edition of this classic text book has been completely revised, updated, and extended to include chapters on biomimetic amination reactions, Wacker oxidation, and useful domino reactions. The first-class author team with long-standing experience in practical courses on organic chemistry covers a multitude of preparative procedures of reaction types and compound classes indispensable in modern organic synthesis. Throughout, the experiments are accompanied by the theoretical and mechanistic fundamentals, while the clearly structured sub-chapters provide concise background information, retrosynthetic analysis, information on isolation and purification, analytical data as well as current literature citations. Finally, in each case the synthesis is labeled with one of three levels of difficulty. An indispensable manual for students and lecturers in chemistry, organic chemists, as well as lab technicians and chemists in the pharmaceutical and agrochemical industries.
A Clear, Careful Textbook to Help Bible Students Interpret Scripture Pastors, thoughtful Christians, and students of Scripture must learn how to carefully read and understand the Bible, but it can be difficult to know where to start. In this clear, logical guide, Andreas J. Köstenberger and Gregory Goswell explain how to interpret Scripture from three effective viewpoints: canonical, thematic, and ethical. Biblical Theology is arranged book by book from the Old Testament (using the Hebrew order) through the New Testament. For each text, Köstenberger and Goswell analyze key biblical-theological themes, discussing the book's place in the overall storyline of Scripture. Next, they focus on the ethical component, showing how God seeks to transform the lives of his people through the inspired text. Following this technique, readers will better understand the theology of each book and its author. A Clearly Written Guide on Biblical Theology: Analyzes all 66 books of the Bible, with emphasis on the coherent, unified framework of Scripture Helps Readers Thoughtfully Interpret Scripture: Provides an essential foundation for a valid theological understanding of Scripture that informs Christian doctrine and ethics Ideal for Pastors, Academics, and Other Serious Students of Scripture: This clear, thoroughly researched guide can be used as a textbook in seminary classes studying biblical theology or the Old and New Testaments
Biometals in Autism Spectrum Disorders focuses on trace metals and autism. Compared to other references examining ASDs or metallomics, this book presents findings of abnormal metal homeostasis in ASD, providing an overview of current findings on trace metal biology, its role in ASD etiology, and how abnormal trace metal biology may be a common factor of several genetic and non-genetic causes of ASDs that were once considered unrelated. This comprehensive resource opens new vistas for the development of new therapies based on the targeted manipulation of trace metal homeostasis that will generate new awareness surrounding trace metal levels during pregnancy. Reviews the role of trace metals in brain development Summarizes research linking trace metals and autism Explores heterogenous phenotypes as a factor of genetic and non-genetic factors Includes animal and human stem research Contains many useful diagrams, tables and flow charts Proposes future therapies based on biometal homeostasis
Fasting: we’ve all heard of it. Countless celebrities and bestselling books have touted the benefits of fasting for weight loss, but what most of us don’t know is that the benefits of fasting extend far beyond that: the latest scientific findings show that fasting is the best and easiest way for us to fight disease and slow aging. In The Fasting Fix, Dr. Andreas Michalsen—one of the world’s leading experts on fasting—lays out the clear, indisputable science that fasting, when combined with a healthy diet, is the key to healing chronic illnesses and living longer. Dr. Michalsen draws from his decades of medical practice and original, cutting-edge scientific research, along with his deep knowledge about the human body and evolutionary history, to distill the simple truth about what and how we should eat in order to live healthier, longer lives. Learn which foods to eat and which we should avoid. And learn the specific fasting program—therapeutic fasting, intermittent fasting, or a combination of both—that will most benefit your specific lifestyle and health needs. With stories from patients he has successfully treated and detailed treatment programs for the most common chronic diseases—obesity, hypertension, diabetes, heart disease, kidney disease, arthrosis, rheumatism, irritable bowel syndrome, skin diseases, allergies and asthma, migraines, depression, neurological diseases, dementia and Alzheimer’s disease, and cancer—Dr. Michalsen shows us why other diets have failed, and how we can finally be healthy.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.