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"This book tells engaging stories about the science of dendrochronology, the study of tree growth rings. From studying tree rings, scientists can learn about the past climate on earth, and sometimes tree-ring data provide evidence of natural events that affected human history. Connecting natural history (as read through tree rings) to human history is at the heart of this book"--

Archeology --- World history --- Dendrochronology. --- Tree-rings.

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The distinguished private collection, known as the Griffin Collection, comprises in its entirety examples of every category of ring ? signet, devotional, memorial, decorative ? dating from antiquity to modern times. This catalogue, focusing on about 150 rings in the collection, is concerned with perhaps the most personal rings of all, those associated with love and marriage. Some can be recognised by the figure of Cupid armed with his quiver of golden arrows, others by the symbols of heart and clasped hands. However, the majority are gold bands, sometimes plain and occasionally decorated, that are inscribed with mottoes in English expressing the admiration, affection, and pledges of fidelity which bind humankind together.00Known as posies or little poems because they often rhyme, these mottoes were current on rings from the late Middle Ages until the middle of the 19th century. Through these rings, Ms. Scarisbrick engagingly tells the long story of the relations between the sexes from the fifteenth century, when the cult of courtly love was superseded by an idealization of monogamous marriage, to an end in the twentieth century as a result of a different moral outlook.

Rings --- Courtship --- Inscriptions --- Private collections --- History

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This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over skew PBW extensions from a matrix point of view. To make this theory constructive, the theory of Gröbner bases of left (right) ideals and modules for bijective skew PBW extensions is developed. For example, syzygies and the Ext and Tor modules over these rings are computed. Finally, applications to some key topics in the noncommutative algebraic geometry of quantum algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded Artin–Schelter regular algebras, and the noncommutative Zariski cancellation problem. The book is addressed to researchers in noncommutative algebra and algebraic geometry as well as to graduate students and advanced undergraduate students.

Associative rings. --- Rings (Algebra). --- Category theory (Mathematics). --- Homological algebra. --- Algorithms. --- Associative Rings and Algebras. --- Category Theory, Homological Algebra. --- Algorism --- Algebra --- Arithmetic --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Foundations --- Ring extensions (Algebra) --- Noncommutative rings. --- Categories (Mathematics) --- Non-commutative rings --- Associative rings --- Extensions of rings (Algebra) --- Associative algebras. --- Algebra, Homological. --- Algebras, Associative

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The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.

K-theory. --- Nonassociative rings. --- Rings (Algebra). --- Group theory. --- Commutative algebra. --- Commutative rings. --- Category theory (Mathematics). --- Homological algebra. --- K-Theory. --- Non-associative Rings and Algebras. --- Group Theory and Generalizations. --- Commutative Rings and Algebras. --- Category Theory, Homological Algebra. --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Rings (Algebra) --- Algebra --- Groups, Theory of --- Substitutions (Mathematics) --- Algebraic rings --- Ring theory --- Algebraic fields --- Algebraic topology --- K-theory

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This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

Operator theory. --- Mathematical physics. --- Associative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Operator Theory. --- Mathematical Physics. --- Associative Rings and Algebras. --- Topological Groups, Lie Groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Physical mathematics --- Physics --- Functional analysis --- Mathematics --- Hilbert algebras. --- Hilbert space. --- Operator algebras. --- Science --- Mathematics.