This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.
The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.
This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.
Embark on an epic journey that defies genre, seamlessly blending elements of dystopian and historical fiction while traversing time, from Eden’s ancient gardens to the enduring enclaves of the USSR, and even further, to celestial chambers scattered among the stars. The Judas Kiss offers you a spellbinding odyssey that navigates through epochs and landscapes, unified by the presence of a mysterious child. Could he be an Armenian boy orphaned by the Spitak earthquake, a Yazidi warrior lost in a maze of time, or even an angel on a divine mission? Witness the biblical wanderings of Moses and the poignant tribulations of a Soviet émigré. Explore clandestine labs and remote Central Asian villages suspended in the mountains. Meet a cast of eccentric scientists and cryptic sorcerers, each wielding enigmatic powers. As the narrative unfolds, humanity faces existential threats: a virulent virus and cosmic rifts that could annihilate the world. Set against a backdrop that is both hauntingly recognizable and captivatingly otherworldly, The Judas Kiss invites you to confront the boundaries of loyalty and betrayal in a cosmos as awe-inspiring as it is perilous.
This book describes the life and achievements of the great french mathematician, Élie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential geometry, as well as later developments stemming from his ideas. The volume includes a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.
Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research. The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering.
This book examines the staggering popularity of early-twentieth-century Russian detective serials. Traditionally maligned as “Pinkertonovshchina,” these appropriations of American and British detective stories featuring Nat Pinkerton, Nick Carter, Sherlock Holmes, Ethel King, and scores of other sleuths swept the Russian reading market in successive waves between 1907 and 1917, and famously experienced a “red” resurgence in the 1920s under the aegis of Nikolai Bukharin. The book presents the first holistic view of “Pinkertonovshchina” as a phenomenon, and produces a working model of cross-cultural appropriation and reception. The “red Pinkerton” emerges as a vital “missing link” between pre- and post-Revolutionary popular literature, and marks the fitful start of a decades-long negotiation between the regime, the author, and the reading masses.
The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.
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