We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in thermodynamics. We consider semiclassical methods for tunnel quantization in thermodynamics as well as those for second and ultrasecond quantization (the creation and annihilation operators for pairs of particles). Each noble gas is associated with a new critical point of the limit negative pressure. The negative pressure is equivalent to covering the (P,Z) diagram by the second sheet.
Higher School of Economics (HSE) and supported by the Information Retrieval Specialist Group at the British Computer Society (BCS–IRSG). The conference was held during March 24–27, 2013, in Moscow, Russia – the easternmost location in the history of the ECIR series. ECIR 2013 received a total of 287 submissions in three categories: 191 full papers, 78 posters, and 18 demonstrations. The geographical distribution of the submissions is as follows: 70% were from Europe (including 9% from Russia), 17% from Asia, 12% from North and South America, and 3% from the rest of the world. All submissions were reviewed by at least three members of an international two-tier Program Committee. Of the papers submitted to the main research track, 30 were selected for oral presentation and 25 for poster/short presentation (16% and 13%, respectively, hence a 29% acceptance rate). In addition, 38 posters (49%) and 10 demonstrations (56%) were accepted. The accepted contributions represent the state of the art in information retrieval, cover a diverse range of topics, propose novel applications, and indicate promising directions for future research. Out of accepted contributions, 66% have a student as the primary author. We gratefully thank all Program Committee members for their time and efforts ensuring a high-quality level of the ECIR 2013 program. Additionally, ECIR 2013 hosted four tutorials and two workshops covering various IR-related topics. We express our gratitude to the Workshop Chair, Evgeniy Gabrilovich, and the Tutorial Chair, Djoerd Hiemstra, and the members of their committees.
– Searching the Web of Data
– Practical Online Retrieval Evaluation
– Cross-Lingual Probabilistic Topic Modeling and Its Applications in Information
– Distributed Information Retrieval and Applications
– From Republicans to Teenagers: Group Membership and Search (GRUMPS)
– Integrating IR Technologies for Professional Search
The conference included a Mentoring Program and Doctoral Consortium.
We thank Mikhail Ageev and Hideo Joho and Dmitriy Ignatov, respectively, for coordinating these activities.
We would like to thank our invited speakers – Mor Naaman (Rutgers University, Social Media Information Lab) and the winner of the Karen Sparck Jones award. The Industry Day took place on the final day of the conference and featured a bright assortment of talks given by prominent researchers and practitioners: Paul Ogilvie (LinkedIn), Hilary Mason (bitly), Antonio Gulli (Bing), Andrey Kalinin (Mail.Ru), Jimmy Lin (Twitter/University of Maryland), Marc Najork (Microsoft Research), and Andrey Styskin (Yandex), to whom we express our gratitude. We appreciate generous financial support from Yandex and HSE, as well as from our sponsorsMail.Ru and Russian Foundation for Basic Research (platinum level), Google and ABBYY
Logic deals with the fundamental notions of truth and falsity. Modal logic arose from the philosophical study of “modes of truth” with the two most common modes being “necessarily true” and “possibly true”. Research in modal logic now spans the spectrum from philosophy, computer science and mathematics using techniques from relational structures, universal algebra, topology, and proof theory. These proceedings record the papers presented at the 2016 conference on Advances in Modal Logic, a biennial conference series with an aim to report on important new developments in pure and applied modal logic. As indicated above, there are new developments in using modal logic to reason about obligations, about programs, about time, about combinations of modal logics and even about negation itself.
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well.
The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces.
The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion.
Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework.
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 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.
The main research subject of this book is the phenomenon of the "positive deviation" in Sabaic epigraphy, i.e. the use of the plural in the places where one would expect the singular or dual. The quantitative analysis of this phenomenon undertaken in this book leads me to the supposition that its main causes are social and not purely linguistic, though the linguistic trend towards the supplanting of the dual by the plural observed in Middle Sabaic epigraphy can partly (but only partly) explain the positive deviation from the dual. Hence, the study of this phenomenon leads me to the following suppositions with respect to the social history of ancient Yemen: (1.) Clan organization seems to have played an important role in the social life of Middle Sabaean society (= the Middle Sabaean cultural-political area = the Northern part of the area of the Middle Sabaic epigraphy, the 1st century BC - the 4th century AD): (1.a.) All the main types of immovable property (fields, vineyards, houses, irrigation structures, wells &c) were considered as a rule almost without exceptions to be the property of clan groups, but not of the individuals. (1.b.) Clan groups (not individuals) were considered to be chiefs of the tribes.
1.c. Clan groups were often considered to be both objects of the client dependence, and the patrons of the clients ('dm).
1.d. Tribes were often considered to consist of clan groups (not of individuals).
2. In the Ancient Sabaean cultural-political area (the 1st millennium BC) the role of the clan organization was remarkably less important.
2.a. It is impossible to say that almost all kinds of immovable property were considered here to be in the possession of clans. In the majority of the cases individual (not clan) possessions are mentioned in the Ancient Sabaean inscriptions. Though private ownership might not have become completely universal in the Ancient Period, it is quite evident that the process of the formation and proliferation of this form of ownership went quite far in this Period.
2.b. In the Ancient Period the individual forms of cliental dependence seem to have played a much more important role than the clan ones. In the majority of the cases individual persons (not clients) were considered to be both "patrons" and "clients".
2.c. Individual persons (not clans) were usually considered to be leaders of tribes and communities in the Ancient Period.
2.d. Tribes were always considered to consist of individuals (not clans) in this period.
3. One may suppose that the process of the formation of the state and civilization in the Lowlands went far enough in the Ancient Period to cause a considerable decline of the clan organization and the ejecting of it to the periphery (both in the spatial and social senses of this word) of the social system.
4. Hence, it is possible to suppose that with the transition from the Ancient to Middle Period the clan organisation in the "North" significantly consolidated, its social importance considerably grew.
5. The "archaization" of the social life in the Southern (Himyarite-Radmanite) part of the area of the Middle Sabaic epigraphy (most of which was a part of the Qatabanian cultural-political area in the Ancient Period) was less strong than in the Northern ("Sabaean") part. The Ancient "individualized" tradition survived in the South to some extent, and the positions of the clan organization were not so solid here as they were in the North.
6.The above-mentioned social changes fit quite well in the general picture of the Pre-Islamic Yemeni history.
6.a. Several factors described in Chapter 4 caused a significant decline of the Sabaean state and civilization by the end of the 1st millennium BC. The weakening state organization seems to have become incapable of providing guarantees of life and property to individuals, and it was the clan organization that took on these functions to a considerable extent. As a result we can see by the Middle Period the consolidation of the clan organization which acted as a partial substitute for the weak state. This process can be also considered as quite an adequate social adaptation to the new situation which appeared in the Sabaean cultural-political area by the end of the 1st millennium BC with the relative decline of the Sabaean Lowlands (caused by the above-mentioned factors) and the rise of the importance of the "Sabaean" Highlands. Indeed, the Middle "Sabaean" political system, which was much less like a regular state than the Ancient one which included strong clan and tribal structures as its integral elements, turned out to be a really effective form of socio-political organization for a complex society in the Northern Highlands. Most political entities which appeared in this region from that time till the present have showen evident similarities to the Middle "Sabaean" socio-political organization.
6.b. The Middle Sabaean political system may be also characterized as consisting of a weak state in its centre and strong chiefdoms on its periphery. However, there is no doubt that this was a real system, i.e. it had some integrative properties which could not be reduced to the characteristics of its elements. It should be also taken into consideration that the state and chiefdoms were not the only elements of this political system. It included as well e.g. a sub-system of temple centres and the civil community of M_rib, as well as some true tribes (not chiefdoms) in the area of the Sabaean Lowlands, primarily the tribes of the Amirite confederation. With the transition from the Ancient to Middle Period the Sabaean political system was essentially transformed, becoming as a whole very different from the "state", but remaining, however, on basically the same level of political complexity. Without losing any political complexity and sophistication, the Middle "Sabaeans" managed to solve in quite different ways the problems which in complex societies are normally solved by states, such as the mobilization of resources for the functioning of the governing sub-system, the territorial organization of a vast space and the provision of guarantees of life and property. The Middle "Sabaean" experience seems to demonstrate that a large, complex, highly developed (in comparison with for example an average chiefdom) and integrated territorial entity need not necessarily be organized politically as a state. This appears to show that for the "early state" the transition to the "mature state" or complete "degeneration" into "tribes" and "chiefdoms" were not the only ways of possible evolution. One of the possible alternatives was its transformation into a "political system of the Middle Sabaean type". The real processes of political evolution seem to have been actually much less "unilinear" than is sometimes supposed. A significant transformation appears to have occurred in the area in the Early Islamic Period, and by the late Middle Ages the political system of the former "Sabaean" region seems to have consisted mainly of a stronger state in its centre and true tribes (not chiefdoms) on its periphery, whereas regular state structures persisted in the Southern (former Himyarite) cultural-political area.
6.c. The decline of the Ancient Qatabanian state took place significantly later than that of the Ancient Sabaean one. As a result the social continuity between the Ancient and the Middle Period in the Qatabanian cultural-political area was stronger, and the social transformation in the "South" turned out to be less dramatic. As a result in the Middle Period the state organization in the "South" appears considerably stronger than in the "North"; whereas the clan organization seems to have been much weaker. Quite an impressive feature of Yemeni history is that we find a more or less similar picture in 20th century Yemen: very strong clan-tribal structures and very weak state ones in the Yemeni Uplands to the north of Naq_l Yili (in the "Sabaean Highlands") and relatively weak clan-tribal structures and relatively strong state ones to the south of it, in the "Himyarite Highlands". Thus the above described picture appears as almost invariable in Yemeni history since the first centuries AD. This fact leads one to the supposition that there must be some fundamental basis for such a stable difference between the "North" and the "South". Its main objective factor is evident: the significant difference in the geographical conditions. It is really remarkable to find that the Highland territories of the two Middle Period cultural-political areas are practically identical with two main ecological zones of the Yemeni uplands.
7. The clan organization was not universal, even in the Middle Sabaean cultural-political area. The dense network of the clan relations was considerably weaker near the king and, perhaps, the most important temple centres, as they stood outside the clan organization and above it. In spatial dimensions, the zone of the weaker clan relations could be localized in the area of Marib and, perhaps, Nashq, Nashshan and San'a'.
Том содержит труды 13й конференции AGCT и конференции Geocrypt. Темы конференций - различные аспекты арифметической и алгебраической геометрии, теории чисел, теории кодирования, криптографии. Основные направления, обсуждавшиеся на конференциях, включают в себя теорию кривых над конечными полями, теорию абелевых многообразий над глобальными и конечными полями, теорию дзета и L-функций, асимптотические проблемы в теории чисел и алгебраической геометрии, алгоритмические вопросы теории кривых и абелевых многообразий, теорию кодов, исправляющих ошибки, в особенности, теорию алгебро-геометрических кодов, криптографические вопросы, связанные с кривыми и абелевыми многообразиями.
The text introduces all main subjects of "naive" (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.