Yuriy Drozd's Books

Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems

By: Igor Burban,Yuriy Drozd

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Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems

By: Igor Burban,Yuriy Drozd

In this article the authors develop a new method to deal with maximal Cohen–Macaulay modules over non–isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen–Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen–Macaulay representation type. The authors' approach is illustrated on the case of k as well as several other rings. This study of maximal Cohen–Macaulay modules over non–isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.

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Page Count

134

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470425378

ISBN 13

9781470425371

Research Tendencies and Prospect Domains for AI Development and Implementation

By: Yuriy P. Kondratenko,Anatolii I. Shevchenko

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Research Tendencies and Prospect Domains for AI Development and Implementation

By: Yuriy P. Kondratenko,Anatolii I. Shevchenko

This River Rapid explores artificial intelligence (AI) implementation priorities, prospect domains, and new research tendencies and trends for AI development and implementation. Part 1 is devoted to the world’s priorities in AI implementation. Its main components are based on the analysis of the 50 National strategies for AI development, the world’s and NATO’s priorities in AI’s implementation, and methodological aspects for creating the Ukrainian AI conception and strategy, key priority areas for the introduction of AI in Ukraine, the conscience approach to AI systems design, and the discussion on the new generation computer system with embedded AI. Special attention is paid to perspectives of AI implementation in education and interrelation and inter-influence between AI and educational systems. Part 2 is devoted to some new tendencies in AI development and implementation. Many scientific results and discussions are directed to some new trends in contemporary AI research: AI systems and tools for shipping and shipbuilding; quantum computing and color optical fuzzy computing in applied AI’s R&D; AI for increasing the efficiency of the decision-making processes; neural networks for solving classification and recognition tasks. This book provides an overview of the recent developments in advanced AI systems including new theoretical findings and successful examples of practical implementation of the AI tools in different areas of human activities. The chapters are presented by invited high-caliber scientists from different countries (Ukraine, the United States of America, Poland, Norway, and the People’s Republic of China).

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Page Count

169

Publisher

CRC Press

Published Date

ISBN 10

8770046956

ISBN 13

9788770046954

Maximal Cohen-Macaulay Modules Over Non-isolated Surface Singularities and Matrix Problems

By: Igor Burban,Yurij A. Drozd

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Maximal Cohen-Macaulay Modules Over Non-isolated Surface Singularities and Matrix Problems

By: Igor Burban,Yurij A. Drozd

Chapter 11. Remarks on rings of discrete and tame CM-representation type -- 11.1. Non-reduced curve singularities -- 11.2. Maximal Cohen-Macaulay modules over the ring ̃ ((1,0)) -- 11.3. Other surface singularities of discrete and tame CM-representation type -- 11.4. On deformations of certain non-isolated surface singularities -- Chapter 12. Representations of decorated bunches of chains-II -- 12.1. Decorated conjugation problem -- 12.2. Some preparatory results from linear algebra -- 12.3. Reduction to the decorated chessboard problem -- 12.4. Reduction procedure for the decorated chessboard problem -- 12.5. Indecomposable representations of a decorated chessboard -- 12.6. Proof of the Classification Theorem -- References -- Back Cover

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134

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ISBN 10

147044058X

ISBN 13

9781470440589

Book's by Yuriy Drozd

Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems

Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems

Research Tendencies and Prospect Domains for AI Development and Implementation

Research Tendencies and Prospect Domains for AI Development and Implementation

Maximal Cohen-Macaulay Modules Over Non-isolated Surface Singularities and Matrix Problems

Maximal Cohen-Macaulay Modules Over Non-isolated Surface Singularities and Matrix Problems

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