This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler s Theorem for the plane, right up to the most recent results, such as Makar-Limanov s Theorem for locally nilpotent derivations of polynomial rings. Topics of special interest include: progress in the dimension three case, finiteness questions (Hilbert s 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. The reader will also find a wealth of pertinent examples and open problems and an up-to-date resource for research.
This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations.
The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves.
More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem.
A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
This is the second part of a 2-year course of abstract algebra for students beginning a professional study of higher mathematics.1 This textbook is based on courses given at the Independent University of Moscow and at the Faculty of Mathematics at the National Research University Higher School of Economics. In particular, it contains a large number of exercises that were discussed in class, some of which are provided with commentary and hints, as well as problems for independent solution that were assigned as homework.Working out the exercises is of crucial importance in understanding the subject matter of this book.
This book is the first volume of an intensive “Russian-style” two-year graduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them.
The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses.
This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.
Modal logics, both propositional and predicate, have been used in computer science since the late 1970s. One of the most important properties of modal logics of relevance to their applications in computer science is the complexity of their satisﬁability problem. The complexity of satisﬁability for modal logics is rather high: it ranges from NP-complete to undecidable for propositional logics and is undecidable for predicate logics. This has, for a long time, motivated research in drawing the borderline between tractable and intractable fragments of propositional modal logics as well as between decidable and undecidable fragments of predicate modal logics. In the present thesis, we investigate some very natural restrictions on the languages of propositional and predicate modal logics and show that placing those restrictions does not decrease complexity of satisﬁability. For propositional languages, we consider restricting the number of propositional variables allowed in the construction of formulas, while for predicate languages, we consider restricting the number of individual variables as well as the number and arity of predicate letters allowed in the construction of formulas. We develop original techniques, which build on and develop the techniques known from the literature, for proving that satisﬁability for a ﬁnite-variable fragment of a propositional modal logic is as computationally hard as satisﬁability for the logic in the full language and adapt those techniques to predicate modal logics and prove undecidability of fragments of such logics in the language with a ﬁnite number of unary predicate letters as well as restrictions on the number of individual variables. The thesis is based on four articles published or accepted for publication. They concern propositional dynamic logics, propositional branchingand alternating-time temporal logics, propositional logics of symmetric rela tions, and ﬁrst-order predicate modal and intuitionistic logics. In all cases, we identify the “minimal,” with regard to the criteria mentioned above, fragments whose satisﬁability is as computationally hard as satisﬁability for the entire logic.
Alienation After Derrida rearticulates the Hegelian-Marxist theory of alienation in the light of Derrida's deconstruction of the metaphysics of presence. Simon Skempton aims to demonstrate in what way Derridian deconstruction can itself be said to be a critique of alienation. In so doing, he argues that the acceptance of Derrida's deconstructive concepts does not necessarily entail the acceptance of his interpretations of Hegel and Marx. In this way the book proposes radical reinterpretations, not only of Hegel and Marx, but of Derridian deconstruction itself.
The critique of the notions of alienation and de-alienation is a key component of Derridian deconstruction that has been largely neglected by scholars to date. This important new study puts forward a unique and original argument that Derridian deconstruction can itself provide the basis for a rethinking of the concept of alienation, a concept that has received little serious philosophically engaged attention for several decades.
This report outlines a number of scenarios for the paths Asia may take in the next 20 years, and what the choice of each of these paths will mean for Russia and its role in Asian affairs. These scenarios do not attempt to make an accurate prediction for specifi c events based on linear projection of current events. Rather, they pursue three goals.
This overview report is based upon the scientific report for the Bering-Chukchi-Beaufort (BCB) region, which comprises parts of Canada, the United States and Russia. The scientific report describes current regional environmental conditions, global and regional drivers of change, and the human and ecological impacts of this change. It also emphasises is the diverse, inter-linked environmental, social and economic challenges that residents are already, or likely will be, experiencing from climate change and other regional and global-scale drivers. It considers the environmental and socio-economic changes to which inhabitants in the region are and will be adapting to. Finally, it provides a number of observations intended to help inform decision makers about how they might help their communities adapt to future changes.
In this new, fully revised edition of America’s Nonproﬁt Sector, renowned author Lester Salamon clariﬁes the scope, structure, ﬁnances, and operation of the nonproﬁt sector and examines how it has changed over time, both generally and in major ﬁelds like health care, education, arts, and religion.
New political, social and cultural reality in the first five years since the collapse of the Soviet Union.
This book constitutes the proceedings of the Third International Conference on Analysis of Images, Social Networks and Texts, AIST 2014, held in Yekaterinburg, Russia, in April 2014. The 11 full and 10 short papers were carefully reviewed and selected from 74 submissions. They are presented together with 3 short industrial papers, 4 invited papers and tutorials. The papers deal with topics such as analysis of images and videos; natural language processing and computational linguistics; social network analysis; machine learning and data mining; recommender systems and collaborative technologies; semantic web, ontologies and their applications; analysis of socio-economic data.
This book constitutes the proceedings of the Fourth International Conference on Analysis of Images, Social Networks and Texts, AIST 2015, held in Yekaterinburg, Russia, in April 2015. The 24 full and 8 short papers were carefully reviewed and selected from 140 submissions. The papers are organized in topical sections on analysis of images and videos; pattern recognition and machine learning; social network analysis; text mining and natural language processing.
This book constitutes the proceedings of the 5th International Conference on Analysis of Images, Social Networks and Texts, AIST 2016, held in Yekaterinburg, Russia, in April 2016. The 23 full papers, 7 short papers, and 3 industrial papers were carefully reviewed and selected from 142 submissions. The papers are organized in topical sections on machine learning and data analysis; social networks; natural language processing; analysis of images and video.
This volume contains the refereed proceedings of the 6th International Conference on Analysis of Images, Social Networks, and Texts (AIST 2017)1. The previous conferences during 2012–2016 attracted a significant number of students, researchers, academics, and engineers working on interdisciplinary data analysis of images, texts, and social networks. The broad scope of AIST made it an event where researchers from different domains, such as image and text processing, exploiting various data analysis techniques, can meet and exchange ideas. We strongly believe that this may lead to cross fertilisation of ideas between researchers relying on modern data analysis machinery. Therefore, AIST brought together all kinds of applications of data mining and machine learning techniques. The conference allowed specialists from different fields to meet each other, present their work, and discuss both theoretical and practical aspects of their data analysis problems. Another important aim of the conference was to stimulate scientists and people from industry to benefit from the knowledge exchange and identify possible grounds for fruitful collaboration. The conference was held during July 27–29, 2017. The conference was organised in Moscow, the capital of Russia, on the campus of Moscow Polytechnic University. This year, the key topics of AIST were grouped into six tracks: 1. General topics of data analysis chaired by Sergei Kuznetsov (Higher School of Economics, Russia) and Amedeo Napoli (LORIA, France) 2. Natural language processing chaired by Natalia Loukachevitch (Lomonosov Moscow State University, Russia) and Alexander Panchenko (University of Hamburg, Germany) 3. Social network analysis chaired by Stanley Wasserman (Indiana University, USA) 4. Analysis of images and video chaired by Victor Lempitsky (Skolkovo Institute of Science and Technology, Russia) and Andrey Savchenko (Higher School of Economics, Russia) 5. Optimisation problems on graphs and network structures chaired by Panos Pardalos (University of Florida, USA) and Michael Khachay (IMM UB RAS and Ural Federal University, Russia) 6. Analysis of dynamic behaviour through event data chaired by Wil van der Aalst (Eindhoven University of Technology, The Netherlands) and Irina Lomazova (Higher School of Economics, Russia) One of the novelties this year was the introduction of a new specialised track on process mining (Track 6).
This book constitutes the proceedings of the 6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017, held in Moscow, Russia, in July 2017.
The 29 full papers and 8 short papers were carefully reviewed and selected from 127 submissions. The papers are organized in topical sections on natural language processing; general topics of data analysis; analysis of images and video; optimization problems on graphs and network structures; analysis of dynamic behavior through event data; social network analysis.