2 dimensional categories, Johnson, Niles (associate Professor, Associate Professor, Ohio State University) Yau, Donald (professor, Professor, Ohio State University)
Автор: Johnson, Niles (associate Professor, Associate Professor, Ohio State University) Yau, Donald (professor, Professor, Ohio State University) Название: 2 dimensional categories ISBN: 0198871384 ISBN-13(EAN): 9780198871385 Издательство: Oxford Academ Рейтинг: Цена: 58080.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory.
Название: Lectures on Tensor Categories and Modular Functors, Bojko Bakalov and Alexander Kirillov, Jr. ISBN: 0821826867 ISBN-13(EAN): 9780821826867 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 30090.00 T Наличие на складе: Невозможна поставка. Описание: Gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory).
Автор: Matthew Ballard; Charles Doran; David Favero; Eric Название: Superschool on Derived Categories and D-branes ISBN: 3030062708 ISBN-13(EAN): 9783030062705 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math.Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.
Автор: Simona Paoli Название: Simplicial Methods for Higher Categories ISBN: 3030056732 ISBN-13(EAN): 9783030056735 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic.While strict n-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular n-fold categories, is one of the simplest known algebraic structures yielding a model of weak n-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory.As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the interconnections between the main ideas and results.
Автор: Ballard Название: Superschool on Derived Categories and D-branes ISBN: 3319916254 ISBN-13(EAN): 9783319916255 Издательство: Springer Рейтинг: Цена: 167700.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Abelian and Triangulated Categories (C. Hanratty).- Derived Categories and Derived Functors (N.K. Chidambaram).- Introduction to Quivers (M. Chinen).- Semi-orthogonal Decompositions of Derived Categories (Y. Liu).- Introduction to Bridgeland Stability Conditions (R. Tramel).- A Brief Introduction to Geometric Invariant Theory (N. Grieve).- Birational Geometry and Derived Categories (C. Diemer).- Introduction to Mirror Symmetry (R. Hughes).- Batyrev Mirror Symmetry (M. Talpo).- Differential Graded Categories (A.A. Takeda).- Introduction to Symplectic Geometry and Fukaya Category (A.Z. Zhang).- Homological Mirror Symmetry (A. Harder).- The Syz Conjecture Via Homological Mirror Symmetry (D. Bejleri).- The Derived Category of Coherent Sheaves and B-model Topological String Theory (S. Pietromonaco).- Introduction to Topological String Theories (K. Osuga).- An Overview of B-branes in Gauged Linear Sigma Models (N. Ishtiaque).
Автор: Heunen Chris Название: Categories for Quantum Theory ISBN: 0198739613 ISBN-13(EAN): 9780198739616 Издательство: Oxford Academ Рейтинг: Цена: 54910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Categories for Quantum Theory: An Introduction lays foundations for an approach to quantum theory that uses category theory, a branch of pure mathematics. Prior knowledge of quantum information theory or category theory helps, but is not assumed, and basic linear algebra and group theory suffices.
Автор: Denis-Charles Cisinski; Fr?d?ric D?glise Название: Triangulated Categories of Mixed Motives ISBN: 3030332411 ISBN-13(EAN): 9783030332419 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The primary aim of this monograph is to achieve part of Beilinson`s program on mixed motives using Voevodsky`s theories of A1-homotopy and motivic complexes.
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.
The topics presented in this volume are:
dynamics of stochastic reaction-diffusion equations;
stochastic It -Volterra backward equations in Banach spaces;
stochastic equations of Schr dinger type;
optimal control of stochastic Navier-Stokes equations;
quantum Hamilton equations from stochastic optimal control theory.
This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Автор: Shuichi Shinmura Название: High-dimensional Microarray Data Analysis ISBN: 9811359970 ISBN-13(EAN): 9789811359972 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book shows how to decompose high-dimensional microarrays into small subspaces (Small Matryoshkas, SMs), statistically analyze them, and perform cancer gene diagnosis. The information is useful for genetic experts, anyone who analyzes genetic data, and students to use as practical textbooks.Discriminant analysis is the best approach for microarray consisting of normal and cancer classes. Microarrays are linearly separable data (LSD, Fact 3). However, because most linear discriminant function (LDF) cannot discriminate LSD theoretically and error rates are high, no one had discovered Fact 3 until now. Hard-margin SVM (H-SVM) and Revised IP-OLDF (RIP) can find Fact3 easily. LSD has the Matryoshka structure and is easily decomposed into many SMs (Fact 4). Because all SMs are small samples and LSD, statistical methods analyze SMs easily. However, useful results cannot be obtained. On the other hand, H-SVM and RIP can discriminate two classes in SM entirely. RatioSV is the ratio of SV distance and discriminant range. The maximum RatioSVs of six microarrays is over 11.67%. This fact shows that SV separates two classes by window width (11.67%). Such easy discrimination has been unresolved since 1970. The reason is revealed by facts presented here, so this book can be read and enjoyed like a mystery novel.Many studies point out that it is difficult to separate signal and noise in a high-dimensional gene space. However, the definition of the signal is not clear. Convincing evidence is presented that LSD is a signal. Statistical analysis of the genes contained in the SM cannot provide useful information, but it shows that the discriminant score (DS) discriminated by RIP or H-SVM is easily LSD. For example, the Alon microarray has 2,000 genes which can be divided into 66 SMs. If 66 DSs are used as variables, the result is a 66-dimensional data. These signal data can be analyzed to find malignancy indicators by principal component analysis and cluster analysis.
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems illuminates the underlying mathematics of semi-tensor product (STP), a generalized matrix product that extends the conventional matrix product to two matrices of arbitrary dimensions. Dimension-varying systems feature prominently across many disciplines, and through innovative applications its newly developed theory can revolutionize large data systems such as genomics and biosystems, deep learning, IT, and information-based engineering applications.
Provides, for the first time, cross-dimensional system theory that is useful for modeling dimension-varying systems.
Offers potential applications to the analysis and control of new dimension-varying systems.
Investigates the underlying mathematics of semi-tensor product, including the equivalence and lattice structure of matrices and monoid of matrices with arbitrary dimensions.
Автор: Zhuangqi Cao; Cheng Yin Название: Advances in One-Dimensional Wave Mechanics ISBN: 3662513331 ISBN-13(EAN): 9783662513330 Издательство: Springer Рейтинг: Цена: 87060.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book examines the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Covers scattered sub-waves and new results using the Analytical Transfer Matrix method.
Автор: A.F.G. Wyatt; H.J. Lauter Название: Excitations in Two-Dimensional and Three-Dimensional Quantum Fluids ISBN: 1468459392 ISBN-13(EAN): 9781468459395 Издательство: Springer Рейтинг: Цена: 104480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Proceedings of a NATO ARW held in Exeter, UK, August 10--15, 1990
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