Russia first encountered Alaska in 1741 as part of the most ambitious and expensive expedition of the entire eighteenth century. For centuries since, cartographers have struggled to define and develop the enormous region comprising northeastern Asia, the North Pacific, and Alaska. The forces of nature and the follies of human error conspired to make the area incredibly difficult to map. Exploring and Mapping Alaska focuses on this foundational period in Arctic cartography. Russia spurred a golden era of cartographic exploration, while shrouding their efforts in a veil of secrecy. They drew both on old systems developed by early fur traders and new methodologies created in Europe. With Great Britain, France, and Spain following close behind, their expeditions led to an astounding increase in the world’s knowledge of North America. Through engrossing descriptions of the explorations and expert navigators, aided by informative illustrations, readers can clearly trace the evolution of the maps of the era, watching as a once-mysterious region came into sharper focus. The result of years of cross-continental research, Exploring and Mapping Alaska is a fascinating study of the trials and triumphs of one of the last great eras of historic mapmaking.
This extraordinary book charts the development of Russia’s relations with the Middle East from the 1950s to the present. It covers both high and low points – the closeness to Nasser’s Egypt, followed by reversal; the successful invasion of Afghanistan which later turned into a disaster; the changing relationship with Israel which was at some time surprisingly close; the relationship with Syria, which continues to be of huge significance; and much more. Written by one of Russia’s leading Arabists who was himself involved in the formation and implementation of policy, the book is engagingly written, extremely insightful, telling us things which only the author is in a position to tell us, and remarkably frank, not sparing senior Soviet and Russian figures from criticism. The book includes material based on the author’s conversations with other leading participants.
This book is a translation from Russian of Part III of the book Mathematics via Problems: From Olympiads and Math Circles to Profession. Part I, Algebra, and Part II, Geometry, have been published in the same series. The main goal of this book is to develop important parts of mathematics through problems. The authors tried to put together sequences of problems that allow high school students (and some undergraduates) with strong interest in mathematics to discover such topics in combinatorics as counting, graphs, constructions and invariants in combinatorics, games and algorithms, probabilistic aspects of combinatorics, and combinatorial geometry. Definitions and/or references for material that is not standard in the school curriculum are included. To help students that might be unfamiliar with new material, problems are carefully arranged to provide gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions. The book is based on classes taught by the authors at different times at the Independent University of Moscow, at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school students and undergraduates, their teachers, and organizers of summer camps and math circles. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, SLMath (formerly MSRI) and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Assisted by Scott Olsen (Central Florida Community College, USA) This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the “Mathematics of Harmony,” a new interdisciplinary direction of modern science. This direction has its origins in “The Elements” of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the “golden” algebraic equations, the generalized Binet formulas, Fibonacci and “golden” matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and “golden” matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science.
Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Russian influence in Central Asia is waning. Since attaining independence, Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan have forged their own paths—building relationships with outside powers and throwing off the last vestiges of Soviet domination. But in many ways, Moscow still sees Central Asia through the lens of the Soviet Union, and it struggles to redefine Russian relations with the region. In The Fight for Influence, Alexey Malashenko offers a comprehensive analysis of Russian policies and prospects in Central Asia. It is clear that Russian policy in the formerly Soviet-controlled region is entering uncharted territory. But does Moscow understand the fundamental shifts under way? Malashenko argues that it is time for Russia to rethink its approach to Central Asia. Contents 1. Wasted Opportunities 2. Regional Instruments of Influence 3. Russia and Islam in Central Asia: Problems of Migration 4. Kazakhstan and Its Neighborhood 5. Kyrgyzstan—The Exception 6. Tajikistan: Authoritarian, Fragile, and Facing Difficult Challenges 7. Turkmenistan: No Longer Exotic, But Still Authoritarian 8. Uzbekistan: Is There a Potential for Change? Conclusion Who Challenges Russia in Central Asia?
This book develops an integrative view of individuality that relies on a polysystemic approach. It considers and combines two systems, namely, individuality and intelligence with creativity in a theoretical and empirical way. It focuses on cross-theoretical and empirical integrations, unifying the theory of integral individuality of V. S. Merlin with the structural-dynamic theory of intelligence of D. V. Ushakov and the theory of divergent (creative) thinking of J. Guilford. As the book shows, these theories hold together, describing and revealing a new fragment of the integral individuality at the expense of intelligence and creativity.
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Only the very best dared to play for a win against Tigran Petrosian. The 9th World Champion was extremely difficult to beat because his defensive techniques were virtually unmatched. In the rare case that someone managed to bring him into difficulties they ran a serious risk of having to face a vicious counterattack. Former Russian Champion Alexei Bezgodov explains to a wide range of players how they can employ the skills of ‘the Tiger'. How to deal with pressure, how to anticipate threats or march you King out of danger even if it feels you are entering a minefield. That you should not hesitate to give up an exchange or spoil your own pawn structure if the position calls for it. How to find unlikely decoys and start a counterattack. This book aims to help amateur players improve the standard of their defensive play. In many training programs a serious analysis of the art of defense is lacking. That explains why most club players are much better at attacking than at coping with adversity and difficult positions. ‘Defend Like Petrosian' points the way to creative solutions and will help you save lots of points.
This extraordinary book charts the development of Russia’s relations with the Middle East from the 1950s to the present. It covers both high and low points – the closeness to Nasser’s Egypt, followed by reversal; the successful invasion of Afghanistan which later turned into a disaster; the changing relationship with Israel which was at some time surprisingly close; the relationship with Syria, which continues to be of huge significance; and much more. Written by one of Russia’s leading Arabists who was himself involved in the formation and implementation of policy, the book is engagingly written, extremely insightful, telling us things which only the author is in a position to tell us, and remarkably frank, not sparing senior Soviet and Russian figures from criticism. The book includes material based on the author’s conversations with other leading participants.
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