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There have been remarkably few systematic expositions of the theory of derived categories since its inception in the work of Grothendieck and Verdier in the 1960s. This book is the first in-depth treatment of this important component of homological algebra. It carefully explains the foundations in detail before moving on to key applications in commutative and noncommutative algebra, many otherwise unavailable outside of research articles. These include commutative and noncommutative dualizing complexes, perfect DG modules, and tilting DG bimodules. Written with graduate students in mind, the emphasis here is on explicit constructions (with many examples and exercises) as opposed to axiomatics, with the goal of demystifying this difficult subject. Beyond serving as a thorough introduction for students, it will serve as an important reference for researchers in algebra, geometry and mathematical physics.
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This book collects papers from the 8th Conference on Non-Integer Order Calculus and Its Applications that have been held on September 20-21, 2016 in Zakopane, Poland. The preceding two conferences were held in Szczecin, Poland in 2015, and in Opole, Poland, in 2014. This conference provides a platform for academic exchange on the theory and application of fractional calculus between domestic and international universities, research institutes, corporate experts and scholars. The Proceedings of the 8th Conference on Non-Integer Order Calculus and Its Applications 2016 brings together rigorously reviewed contributions from leading international experts. The included papers cover novel various important aspects of mathematical foundations of fractional calculus, modeling and control of fractional systems as well as controllability, detectability, observability and stability problems for this systems.
Engineering. --- Complexity, Computational. --- Control engineering. --- Control. --- Complexity. --- Derived categories (Mathematics) --- Abelian categories --- Control and Systems Theory. --- Construction --- Industrial arts --- Technology --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers
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Ordered algebraic structures --- Triangularization (Mathematics) --- Comodules --- Koszul algebras --- Triangularisation (Mathématiques) --- Algèbres de Koszul --- Derived categories (Mathematics) --- Triangulated categories. --- Comodules. --- Koszul algebras. --- 51 <082.1> --- Mathematics--Series --- Triangularisation (Mathématiques) --- Algèbres de Koszul --- Triangulated categories --- Categories, Triangulated --- Abelian categories --- Associative algebras --- Modules (Algebra) --- Algèbre homologique. --- Algebra, Homological
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Algebraic topology --- Homology theory. --- Functions of bounded variation. --- Topological spaces. --- Homologie --- Fonctions à variation bornée --- Espaces topologiques --- 51 <082.1> --- Mathematics--Series --- Derived categories (Mathematics) --- Homology theory --- Fonctions à variation bornée --- Functions of bounded variation --- Topological spaces --- Spaces, Topological --- Cohomology theory --- Contrahomology theory --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables --- Abelian categories --- Functional analysis --- Analyse fonctionnelle --- Homologie. --- Groupes topologiques. --- Cohomologie. --- Topological groups --- Algèbre homologique. --- Algebra, Homological
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