Download or read book Test Configurations Stabilities and Canonical K hler Metrics written by Toshiki Mabuchi and published by Springer Nature. This book was released on 2021-03-25 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kähler cases. In this book, the unsolved cases of the conjecture will be discussed. It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds. Another important tool in our approach is the Chow norm introduced by Zhang. This is closely related to Ding’s functional, and plays a crucial role in our differential geometric study of stability. By discussing the Chow norm from various points of view, we shall make a systematic study of the existence problem of extremal Kähler metrics.

Download or read book An Introduction to Extremal Kahler Metrics written by Gábor Székelyhidi and published by American Mathematical Soc.. This book was released on 2014-06-19 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.

Download or read book Complex Monge Amp re Equations and Geodesics in the Space of K hler Metrics written by Vincent Guedj and published by Springer. This book was released on 2012-01-05 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.

Download or read book The Nuclear Many Body Problem written by Peter Ring and published by Springer Science & Business Media. This book was released on 2004-03-25 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Study Edition

Download or read book Explaining the Success of Nearest Neighbor Methods in Prediction written by George H. Chen and published by Foundations and Trends (R) in Machine Learning. This book was released on 2018-05-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the success of Nearest Neighbor Methods in Prediction, both in theory and in practice.

Download or read book Moduli of K stable Varieties written by Giulio Codogni and published by Springer. This book was released on 2019-06-27 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, Italy in 2017. The content focuses on the existence problem for canonical Kähler metrics and links to the algebro-geometric notion of K-stability. The book includes both surveys on this problem, notably in the case of Fano varieties, and original contributions addressing this and related problems. The papers in the latter group develop the theory of K-stability; explore canonical metrics in the Kähler and almost-Kähler settings; offer new insights into the geometric significance of K-stability; and develop tropical aspects of the moduli space of curves, the singularity theory necessary for higher dimensional moduli theory, and the existence of minimal models. Reflecting the advances made in the area in recent years, the survey articles provide an essential overview of many of the most important findings. The book is intended for all advanced graduate students and researchers who want to learn about recent developments in the theory of moduli space, K-stability and Kähler-Einstein metrics.

Download or read book Introduction to Embedded Systems Second Edition written by Edward Ashford Lee and published by MIT Press. This book was released on 2017-01-06 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the engineering principles of embedded systems, with a focus on modeling, design, and analysis of cyber-physical systems. The most visible use of computers and software is processing information for human consumption. The vast majority of computers in use, however, are much less visible. They run the engine, brakes, seatbelts, airbag, and audio system in your car. They digitally encode your voice and construct a radio signal to send it from your cell phone to a base station. They command robots on a factory floor, power generation in a power plant, processes in a chemical plant, and traffic lights in a city. These less visible computers are called embedded systems, and the software they run is called embedded software. The principal challenges in designing and analyzing embedded systems stem from their interaction with physical processes. This book takes a cyber-physical approach to embedded systems, introducing the engineering concepts underlying embedded systems as a technology and as a subject of study. The focus is on modeling, design, and analysis of cyber-physical systems, which integrate computation, networking, and physical processes. The second edition offers two new chapters, several new exercises, and other improvements. The book can be used as a textbook at the advanced undergraduate or introductory graduate level and as a professional reference for practicing engineers and computer scientists. Readers should have some familiarity with machine structures, computer programming, basic discrete mathematics and algorithms, and signals and systems.

Download or read book An Introduction to the K hler Ricci Flow written by Sebastien Boucksom and published by Springer. This book was released on 2013-10-02 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differential geometry, complex algebraic geometry and Riemannian geometry, and will hopefully foster further developments in this fascinating area of research. The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelman’s celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation). As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman’s ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman’s surgeries.

Download or read book Kahler Einstein Metrics and Integral Invariants written by Akito Futaki and published by . This book was released on 2014-09-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Macromolecular Protein Complexes III Structure and Function written by J. Robin Harris and published by Springer Nature. This book was released on 2020-11-30 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers important topics such as the dynamic structure and function of the 26S proteasome, the DNA replication machine: structure and dynamic function and the structural organization and protein–protein interactions in the human adenovirus capsid, to mention but a few. The 18 chapters included here, written by experts in their specific field, are at the forefront of scientific knowledge. The impressive integration of structural data from X-ray crystallography with that from cryo-electron microscopy is apparent throughout the book. In addition, functional aspects are also given a high priority. Chapter 1 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Download or read book Data Fusion Methodology and Applications written by Marina Cocchi and published by Elsevier. This book was released on 2019-05-11 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Fusion Methodology and Applications explores the data-driven discovery paradigm in science and the need to handle large amounts of diverse data. Drivers of this change include the increased availability and accessibility of hyphenated analytical platforms, imaging techniques, the explosion of omics data, and the development of information technology. As data-driven research deals with an inductive attitude that aims to extract information and build models capable of inferring the underlying phenomena from the data itself, this book explores the challenges and methodologies used to integrate data from multiple sources, analytical platforms, different modalities, and varying timescales. - Presents the first comprehensive textbook on data fusion, focusing on all aspects of data-driven discovery - Includes comprehensible, theoretical chapters written for large and diverse audiences - Provides a wealth of selected application to the topics included

Download or read book Beyond the Cognitive Map written by A. David Redish and published by MIT Press. This book was released on 1999 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are currently two major theories about the role of the hippocampus, a distinctive structure in the back of the temporal lobe. One says that it stores a cognitive map, the other that it is a key locus for the temporary storage of episodic memories. A. David Redish takes the approach that understanding the role of the hippocampus in space will make it possible to address its role in less easily quantifiable areas such as memory. Basing his investigation on the study of rodent navigation--one of the primary domains for understanding information processing in the brain--he places the hippocampus in its anatomical context as part of a greater functional system. Redish draws on the extensive experimental and theoretical work of the last 100 years to paint a coherent picture of rodent navigation. His presentation encompasses multiple levels of analysis, from single-unit recording results to behavioral tasks to computational modeling. From this foundation, he proposes a novel understanding of the role of the hippocampus in rodents that can shed light on the role of the hippocampus in primates, explaining data from primate studies and human neurology. The book will be of interest not only to neuroscientists and psychologists, but also to researchers in computer science, robotics, artificial intelligence, and artificial life.

Download or read book Quadratic Forms and Their Applications written by Eva Bayer-Fluckiger and published by American Mathematical Soc.. This book was released on 2000 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.

Download or read book The Content Analysis Guidebook written by Kimberly A. Neuendorf and published by SAGE. This book was released on 2017 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content analysis is a complex research methodology. This book provides an accessible text for upper level undergraduates and graduate students, comprising step-by-step instructions and practical advice.

Download or read book Finsler Geometry and Applications written by Aurel Bejancu and published by . This book was released on 1990 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Decision Making Under Uncertainty written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2015-07-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance. Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance. Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.

Download or read book The Topology of Torus Actions on Symplectic Manifolds written by Michèle Audin and published by Birkhäuser. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.