This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided.
We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contractible space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications.
After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc.
The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.
The present study generalizes the results of scientific research in the field of economic and mathematic simulation using elements of the theory of functions of complex variables (TFCV), which was conducted since 2004 under the author’s scientific supervision. Since the new results significantly extend the instrumental basis of scientific research in economics and possess their own theoretical base and logic, this section of economic and mathematic simulation was called “complex economics”. The study provides the fundamentals of this new scientific direction in economics and demonstrates how to use this theoretical base to build new economic and mathematic models that appear to be more adequate than models of real variables.
Most economists are absolutely unfamiliar or slightly familiar with the theory of functions complex variables. This is why, in this study, we would state briefly some provisions of this theory to get the reader acquainted with TFCV, and then formulate sequentially the principles of the theory of complex economy, its axiomatic core, basic conceptual positions of the theory, methods and models of the complex economics. Where necessary, theoretical provisions are verified by examples from the real economic practice.
The study is targeted at scientific workers, post-graduate students and doctors using economic and mathematic simulations in their activity.
Contributions in this volume focus on computationally efficient algorithms and rigorous mathematical theories for analyzing large-scale networks. Researchers and students in mathematics, economics, statistics, computer science and engineering will find this collection a valuable resource filled with the latest research in network analysis. Computational aspects and applications of large-scale networks in market models, neural networks, social networks, power transmission grids, maximum clique problem, telecommunication networks, and complexity graphs are included with new tools for efficient network analysis of large-scale networks.
This proceeding is a result of the 7th International Conference in Network Analysis, held at the Higher School of Economics, Nizhny Novgorod in June 2017. The conference brought together scientists, engineers, and researchers from academia, industry, and government.
It is more than 10 years ago that the first edition of this book has appeared. Since then, the field of computational invariant theory has been enjoying a lot of attention and activity, resulting in some important and, to us, exciting developments. This is why we think that it is time for a second enlarged and revised edition. Apart from correcting some mistakes and reorganizing the presentation here and there, we have added the following material: further results about separating invariants and their computation (Sects. 2.4 and 4.9.1), Symonds’ degree bound (Sect. 3.3.2), Hughes’ and Kemper’s extension of Molien’s formula (Sect. 3.4.2), King’s algorithm for computing fundamental invariants (Sect. 3.8.2), Broer’s criterion for the quasi- Gorenstein property (Sect. 3.9.11), Dufresne’s generalization of Serre’s result on polynomial invariant rings and her result with Jeffries (Sect. 3.12.2), Kamke’s algorithm for computing invariants of finite groups acting on algebras (Sect. 3.13), Kemper’s and Derksen’s algorithm for computing invariants of reductive groups in positive characteristic (Sect. 3.13), algorithms by Müller-Quade and Beth, Hubert and Kogan, and Kamke and Kemper for computing invariant fields and localizations of invariant rings (Sect. 4.10.1), and work by van den Essen, Freudenburg, Greuel and Pfister, Kemper, Sancho de Salas, and Tanimoto on invariants of the additive group and of connected solvable groups (Sect. 4.10.5).
Last but not least, this edition contains two new appendices, written by Vladimir Popov, on algorithms for deciding the containment of orbit closures and on a stratification of Hilbert’s nullcone. The second appendix has an addendum, authored by Norbert A’Campo and Vladimir Popov, containing the source code of a program for computing this stratification. We would like to thank Bram Broer, Emilie Dufresne, Vladimir Popov, Jim Shank, and Peter Symonds for valuable comments on a pre-circulated version of this edition, Vladimir Popov and Norbert A’Campo for their contributions to the book, and Ruth Allewelt at Springer-Verlag for managing the production process and for gently pushing us to finally finish our work and hand over the files. Ann Arbor,MI, USA Harm Derksen Munich, Germany Gregor Kemper July 2015
The book includes 71 papers submitted to the International conference in computer linguistics and intellectual technologies Dialogue 2017 and presents a broad spectrum of theoretical and applied research of natural language description, language simulation, and creation of applied computer technologies.
The book includes 64 papers submitted to the International conference in computer linguistics and intellectual technologies Dialogue 2019 and presents a broad spectrum of theoretical and applied research of natural language description, language simulation, and creation of applied computer technologies.
This book constitutes the proceedings of the 13th International Computer Science Symposium in Russia, CSR 2018, held in Moscow, Russia, in May 2018.
The 24 full papers presented together with 7 invited lectures were carefully reviewed and selected from 42 submissions. The papers cover a wide range of topics such as algorithms and data structures; combinatorial optimization; constraint solving; computational complexity; cryptography; combinatorics in computer science; formal languages and automata; algorithms for concurrent and distributed systems; networks; and proof theory and applications of logic to computer science.
Computer simulations are nowadays a rmly established third pillar of modern natural sciences, complementing experimentation and paper-and-pencil theoret- ical studies. Simulations, experiments in silico, prove indispensable in diverse areas of research in physics and other natural sciences. This volume collects papers based on presentations delivered at the Sec- ond International Conference on Computer Simulations in Physics and beyond (CSP2017), which took place October 9-12, 2017 in Moscow. The Conference, which continues a biannual tradition started by an innaugural conference in 2015, took place on campus of A.N. Tikhonov Moscow Institute of Electronics and Mathematics, was jointly organized by the National Research University Higher School of Economics, the Landau Insitute for Theoretical Physics and Science Center in Chernogolovka. As the name implies, the Conference is a multidisciplinary meeting, with a focus on computational physics and related subjects. Indeed, methods of computational physics prove useful in a broad spectrum of research in multiple branches of natural sciences, and this volume provides a sample. We hope that this volume will interest a wide range of readers, and we are already looking forward for the next conference in this biannual series.
The book is aimed at B1-B2 English language learners specifying in the fields of management and economics. It covers the aspect of ESP (English for specific purposes ) and is designed for developing the skills of reading and comprehending special texts from original sources. The material of the book fosters expanding and reinforcing professional vocabulary as well as perfecting communicating skills.
dance4life is a globally active organization within the fields of HIV, sexual and reproductive health and rights (SRHR) and the Millennium Development Goals, specifically aiming to establish a social youth movement consisting of 1 million agents4change by 2014. The central mission of dance4life is to power a movement that creates change at global and community level by taking action to improve young people’s SRHR, and in particular, improving access to sexuality education and youth-friendly services, and to challenge stigma and discrimination and break down taboos that surround sexuality, especially focusing on HIV and AIDS. KIT was invited to partner with dance4life on an impact assessment of dance4life’s work, with a focus on mixed methods and the involvement of the young people themselves. The assessment took place in two countries: Uganda and Russia. A pilot study was undertaken in the Netherlands to test the qualitative research instruments.
This is the first textbook on attribute exploration, its theory, its algorithms for applications, and some of its many possible generalizations. Attribute exploration is useful for acquiring structured knowledge through an interactive process, by asking queries to an expert. Generalizations that handle incomplete, faulty, or imprecise data are discussed, but the focus lies on knowledge extraction from a reliable information source.
The method is based on Formal Concept Analysis, a mathematical theory of concepts and concept hierarchies, and uses its expressive diagrams. The presentation is self-contained. It provides an introduction to Formal Concept Analysis with emphasis on its ability to derive algebraic structures from qualitative data, which can be represented in meaningful and precise graphics.
This book constitutes the proceedings of the 20th International Conference on Conceptual Structures, ICCS 2013, held in Mumbai, India, in January 2013. The 22 full papers presented were carefully reviewed and selected from 43 submissions for inclusion in the book. The volume also contains 3 invited talks. ICCS focuses on the useful representation and analysis of conceptual knowledge with research and business applications. It advances the theory and practice in connecting the user's conceptual approach to problem solving with the formal structures that computer applications need to bring their productivity to bear. Conceptual structures (CS) represent a family of approaches that builds on the successes of artificial intelligence, business intelligence, computational linguistics, conceptual modeling, information and Web technologies, user modeling, and knowledge management.
This book constitutes the refereed proceedings of the 17th International Conference on Conceptual Structures, ICCS 2009, which took place in Moscow, Russia, on July 26-31, 2009.
The 18 papers presented together with 5 invited contributions were carefully reviewed and selected from approximately 50 submissions. Originally centered around research on knowledge representation and reasoning with conceptual graphs, over the years ICCS has broadened its scope to include innovations from a wider range of theories and related practices, among them other forms of graph-based formalisms like RDF or existential graphs, formal concept analysis, semantic Web technologies, ontologies, concept mapping and more.
L’ouvrage est le fruit de deux programmes internationaux de recherche :«Confessiones et nationes. Traditions confessionnelles dans la formation des discours proto-nationaux et nationaux en Europe : fondements médiévaux, évolutions modernes et effets contemporains» , organisé par le Centre d’études ukrainiennes et biélorusses de l’Université Lomonossov de Moscou, aussi que de la journée d’étude « Nations et religions », organisée par l’Université Paris IV Sorbonne en 2009. Le projet global ambitionnait de trouver des éléments de réponse à trois grandes questions : Primo : comment les spécificités confessionnelles des christianismes « latin » et « grec » ont influées sur la construction des discours proto-nationaux, aux époques médiévale et moderne, dans les milieux orthodoxes, catholiques et protestants, en Europe ? Secundo : quelle fut, dans la perspective comparative de la longue durée, l’influence des discours identitaires médiévaux sur les représentations et les pratiques des discours nationaux et nationalistes des XIXe et XXe siècles ? Tertio : comment les spécificités confessionnelles des christianismes « latin » et « grec » ont-elles pesées sur la construction des discours supranationaux et a-nationaux, aux époques médiévale et moderne, et, éventuellement aux XIXe et XXe siècles ? Les études proposées dans ce volume apportent des éléments de reponse à ces grandes questions.