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The Tunguska Mystery
  • Language: en
  • Pages: 322

The Tunguska Mystery

The purpose of the book is a dual one: to detail the nature and results of Tunguska investigations in the former USSR and present-day CIS, and to destroy two long-standing myths still held in the West. The first concerns alleged “final solutions” that have ostensibly been found in Russia or elsewhere. The second concerns the mistaken belief that there has been little or no progress in understanding the nature of the Tunguska phenomenon. All this is treated by the author in a scholarly and responsible manner. Although the book does present certain unusual findings of Russian and Ukrainian scholars, it is important to stress that this is not a sensational book; it is, rather, a serious exposition of the results of rational investigations into a difficult scientific problem. We are demonstrating the true complexity of the problem that is now entering its second century of existence. Simple meteoritic models cannot explain all the characteristics of this complicated event, and therefore certain so-called “unconventional hypotheses” about the nature of the Tunguska explosion are to be considered as well.

Contact Geometry and Nonlinear Differential Equations
  • Language: en
  • Pages: 472

Contact Geometry and Nonlinear Differential Equations

Shows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.

Quantum Groups
  • Language: en
  • Pages: 148

Quantum Groups

The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface puts the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.

The Snake
  • Language: en
  • Pages: 239

The Snake

The origins of the world, do we really know them? The rebellion of Satan, a theme that has given rise to a large number of legends, books and fables over the centuries. Preconceptions about how evil started and if anyone is running it are present in every self-respecting ancient story. How did the man appear? In addition to providing new insights in this regard, Project Magen, by the hand of this researcher, will focus its attention in this case on the figure of said shadowy character and the roots of knowledge about the appearance of man, both by reviewing the narratives that are have hovered around these aspects as in the information that we have been able to obtain and document, in order ...

The Tungus Event, Or, The Great Siberian Meteorite
  • Language: en
  • Pages: 178

The Tungus Event, Or, The Great Siberian Meteorite

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Recent Advances in Diffeologies and Their Applications
  • Language: en
  • Pages: 272

Recent Advances in Diffeologies and Their Applications

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.

Quantum Groups
  • Language: en
  • Pages: 352

Quantum Groups

The papers in this volume are based on the talks given at the conference on quantum groups dedicated to the memory of Joseph Donin, which was held at the Technion Institute, Haifa, Israel in July 2004. A survey of Donin's distinguished mathematical career is included. Several articles, which were directly influenced by the research of Donin and his colleagues, deal with invariant quantization, dynamical $R$-matrices, Poisson homogeneous spaces, and reflection equation algebras. The topics of other articles include Hecke symmetries, orbifolds, set-theoretic solutions to the pentagon equations, representations of quantum current algebras, unipotent crystals, the Springer resolution, the Fourier transform on Hopf algebras, and, as a change of pace, the combinatorics of smoothly knotted surfaces. The articles all contain important new contributions to their respective areas and will be of great interest to graduate students and research mathematicians interested in Hopf algebras, quantum groups, and applications. Information for our distributors: This book is copublished with Bar-Ilan University (Ramat-Gan, Israel).

UFOs and Government
  • Language: en
  • Pages: 594

UFOs and Government

Governments around the world have had to deal with the UFO phenomenon for a good part of a century. How and why they did so is the subject of UFOs and Government, a history that for the first time tells the story from the perspective of the governments themselves. It's a perspective that reveals a great deal about what we citizens have seen, and puzzled over, from the "outside" for so many years. The story, which is unmasked by the governments' own documents, explains much that is new, or at least not commonly known, about the seriousness with which the military and intelligence communities approached the UFO problem internally. Those approaches were not taken lightly. In fact, they were con...

Sakharov And Power: On The Other Side Of The Window
  • Language: en
  • Pages: 666

Sakharov And Power: On The Other Side Of The Window

This book is a testimony to the amazing life of Andrei Sakharov (1921-1989) — the great scientist and great man, the creator of the most terrible weapon in the history of mankind and at the same time the Nobel Peace Prize Winner. Sakharov's life is, one might say, an exciting detective story, a chain of incredible events, not accidental however, but dictated by the genius and fortitude of the protagonist. The theme of this book acquired new striking meanings after the 'Sakharov documents' of the KGB of the USSR and of the Politburo of the Soviet ruling Communist Party were declassified. 'I'm not on the top floor. I'm next to the top floor — on the other side of the window', Sakharov once...

Geometry in Partial Differential Equations
  • Language: en
  • Pages: 482

Geometry in Partial Differential Equations

This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.