This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators
This volume collects for the first time in English the most representative and enlightening of Prokofiev's letters, including some previously suppressed missives that have never before been published. Expertly translated and annotated by Harlow Robinson, the correspondence presented here covers Prokofiev's earliest years at St. Petersburg Conservatory, his extensive worldwide travels, and his return to Moscow. Among the correspondents are childhood friend Vera Alpers, harpist Eleonora Damskaya, ballet impresario Sergei Diaghilev, theatrical director Vsevolod Meyerhold, Soviet critic Boris Asafiev, composers Vernon Duke and Nikolai Miaskovsky, soprano Nina Koshetz, musicologist Nicolas Slonimsky, violinist Jascha Heifetz, conductor Serge Koussevitsky, and film director Sergei Eisenstein. Prokofiev vividly describes, often with dramatic flair and a quirky sense of humor, concerts, performances, his compositions, political events, and meetings with other musicians and composers. His observations are peppered with musical gossip as well as eccentric, original, and disarmingly apolitical insights.
Investigating the relationship between the magnetic properties and structure of molecules, molecular magnetochemistry, is an area of growing interest to scientists in a variety of fields, including physical, organic and inorganic chemistry, molecular physics, and biophysics. For the first time, systematic results on magnetic properties of molecules such as mean magnetic susceptibility, their anisotropies and principal magnetic axes are presented. Molecular Magnetochemistry is a comprehensive and up-to-date view on experimental methods not covered in previous volumes, including the Zeeman effect in vapor phase and magnetic birefringence of diamagnetic systems (Cotton-Mouton Effect). The relationship between magnetic and related electrical phenomena is also described, summing up experimental data on magnetic and electrical anisotropies and components of molecular quadrupole moments.
Power Electronics Basics: Operating Principles, Design, Formulas, and Applications provides fundamental knowledge for the analysis and design of modern power electronic devices. This concise and user-friendly resource:Explains the basic concepts and most important terms of power electronicsDescribes the power assemblies, control, and passive compon
Breaking free, Felix gets the support of his longtime friend. The fugitives are divided into three groups and go in different directions. Sometimes dangerous and sometimes funny stories happen to them. Meanwhile, Felix and Gleb are hiding on the island of Bali. Buying weapons for self-defense, they fall into the hands of modern pirates. They manage to free themselves only thanks to the experience of Gleb. But even in the Javanese jungle, the Owner's people are trying to get them. The main characters have to fight local wars with the use of all modern weapons. And here, finally, the reader will discover the name of the "gray cardinal", a man of intelligence, cynicism and cruelty. It turns out that the soulless Mistress is just a puppet in his hands. Having missed Felix, she herself becomes a victim of a manipulator and is forced to go on the run.
This book provides an accessible yet comprehensive description of the application methods of group analysis to integro-differential equations. It offers both fundamental theoretical and algorithmic aspects of these methods and includes instructive examples.
A New Imperial History of Northern Eurasia, 600-1700 proposes a new language for studying and conceptualizing the spaces, societies, and institutions that existed on the territory of today's Northern Eurasia. This is not the story of a certain present-day state or people evolving through consecutive historical stages. Rather, the book is a modern analytical approach to the problem of human diversity as a fundamental social condition. Through cooperation and confrontation, various attempts to manage diversity fostered processes of societal self-organization, as new ideas, practices, and institutions were developed virtually from scratch or radically altered. Essentially, this is the story of individuals and societies creatively responding to their natural and social environments in unique historical circumstances. This volume explores how the mutual interactions of several local socio-political arrangements, and attempts to integrate with one of the universal cultures of the time, caused a string of unintended consequences. As a result, the enormous landmass from the Carpathian Mountains in the west to the Pacific Ocean in the east, from the Polar Circle in the north to the steppe belt in the south was divided among several regional powers. Ultimately unable to overtake each other by military force, they were locked in a zero-sum game until the uneven development of modern state institutions tilted the balance in favor of one of them Russia.
The Eurasianist movement was launched in the 1920s by a group of young Russian émigrés who had recently emerged from years of fighting and destruction. Drawing on the cultural fermentation of Russian modernism in the arts and literature, as well as in politics and scholarship, the movement sought to reimagine the former imperial space in the wake of Europe's Great War. The Eurasianists argued that as an heir to the nomadic empires of the steppes, Russia should follow a non-European path of development. In the context of rising Nazi and Soviet powers, the Eurasianists rejected liberal democracy and sought alternatives to Communism and capitalism. Deeply connected to the Russian cultural and scholarly milieus, Eurasianism played a role in the articulation of the structuralist paradigm in interwar Europe. However, the movement was not as homogenous as its name may suggest. Its founders disagreed on a range of issues and argued bitterly about what weight should be accorded to one or another idea in their overall conception of Eurasia. In this first English language history of the Eurasianist movement based on extensive archival research, Sergey Glebov offers a historically grounded critique of the concept of Eurasia by interrogating the context in which it was first used to describe the former Russian Empire. This definitive study will appeal to students and scholars of Russian and European history and culture.
This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations.
This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators
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