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Die Arbeit geht der Frage nach, inwieweit ein motivierter Zusammenhang zwischen der expliziten Derivation und der Kategorie Genus, definiert als Dimension nominaler Quantifikation, festzustellen ist. Dazu werden sprachtheoretische Grundlagen und Erkenntnisse aus der Sprachtypologie auf die Diachronie der Suffigierung und verwandter Phänomene (etwa der Zirkumfigierung) des Deutschen angewendet. Da die wortbildenden Suffixe - im Gegensatz zum Gegenwartsdeutschen - in früheren Sprachstufen oft Substantive mit mehreren Genera bildeten, wird die Frage erörtert, inwieweit die Suffixe zunehmend paradigmatischer wurden, d.h. Entwicklungen zeigen, die typisch für einen Aufbau von grammatischer Komplexität sind, bzw. wie sich der Aufbau von Komplexität vollzog. In diesem Zusammenhang lässt sich diachron eine Spezialisierung von Suffixen auf ein bestimmtes Genus feststellen. Das bedeutet, dass eine Korrelation zwischen der expliziten Derivation bzw. entsprechender Suffixe und der Kategorie Genus in früheren Sprachepochen nicht bzw. nicht im selben Maße bestanden hat. Somit lässt sich ein Sprachwandelprozess im Sinne einer Grammatikalisierung von Quantifikation durch Genussuffixe feststellen.

German language --- Gender. --- Countability. --- Grammaticalization. --- Quantification. --- Suffixing.

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Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.

Predicate calculus. --- Calculus, Predicate --- Quantification theory --- Logic, Symbolic and mathematical

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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

preclinical imaging --- PET --- SPECT --- MRI --- ultrasound --- microscopy --- quantification

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This graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional. The quantization of gravity is the main missing piece of theoretical physics, but in two dimensions it can be done explicitly with elementary mathematical tools, but it still has most of the conceptional riddles present in higher dimensional (not yet known) quantum gravity. It provides an introduction to a very interdisciplinary field, uniting physics (quantum geometry) and mathematics (combinatorics) in a non-technical way, requiring no prior knowledge of quantum field theory or general relativity. Using the path integral, the chapters provide self-contained descriptions of random walks, random trees and random surfaces as statistical systems where the free relativistic particle, the relativistic bosonic string and two-dimensional quantum gravity are obtained as scaling limits at phase transition points of these statistical systems. The geometric nature of the theories allows one to perform the path integral by counting geometries. In this way the quantization of geometry becomes closely linked to the mathematical fields of combinatorics and probability theory. By counting the geometries, it is shown that the two-dimensional quantum world is fractal at all scales unless one imposes restrictions on the geometries. It is also discussed in simple terms how quantum geometry and quantum matter can interact strongly and change the properties both of the geometries and of the matter systems. It requires only basic undergraduate knowledge of classical mechanics, statistical mechanics and quantum mechanics, as well as some basic knowledge of mathematics at undergraduate level. It will be an ideal textbook for graduate students in theoretical and statistical physics and mathematics studying quantum gravity and quantum geometry. Key features: Presents the first elementary introduction to quantum geometry Explores how to understand quantum geometry without prior knowledge beyond bachelor level physics and mathematics. Contains exercises, problems and solutions to supplement and enhance learning.

Geometric quantization. --- Quantum gravity. --- Quantification géométrique. --- Gravité quantique.

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Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These 'Berry phases' describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.

Electronic structure. --- Geometric quantum phases. --- Quantum electronics. --- Electronics. --- Structure électronique. --- Quantification géométrique. --- Électronique quantique. --- Électronique. --- Structure électronique. --- Quantification géométrique. --- Électronique quantique. --- Électronique.